Answers
Answer:
(i) x ≤ 1
(ii) ℝ except 0, -1
(iii) x > -1
(iv) ℝ except π/2 + nπ, n ∈ ℤ
Step-by-step explanation:
(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:
[tex]1-x \ge 0[/tex]
[tex]1 \ge x[/tex]
[tex]\boxed{x \le 1}[/tex]
(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.
[tex]0 = x^2+x[/tex]
[tex]0 = x(x + 1)[/tex]
[tex]x = 0[/tex] OR [tex]x = -1[/tex]
So, the domain of the function is:
[tex]R \text{ except } 0, -1[/tex]
(ℝ stands for "all real numbers")
(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:
[tex]x+ 1 > 0[/tex]
[tex]\boxed{x > -1}[/tex]
(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.
[tex]\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z[/tex]
(ℤ stands for "all integers")
Answer:
(i) x ≤ 1
(ii) All real numbers except x = 0 and x = -1.
(iii) x > -1
(iv) All real numbers except x = π/2 + πn, where n is an integer.
Step-by-step explanation:
What is the domain?The domain of a function is the set of all possible input values (x-values).
[tex]\hrulefill[/tex]
[tex]\textsf{(i)} \quad f(x)=\sqrt{1-x}[/tex]
For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.
Solve the inequality:
[tex]\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}[/tex]
(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).
Hence, the domain of f(x) is all real numbers less than or equal to -1.
[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}[/tex]
[tex]\hrulefill[/tex]
[tex]\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}[/tex]
To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.
Set the denominator to zero and solve for x:
[tex]\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}[/tex]
Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.
[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}[/tex]
[tex]\hrulefill[/tex]
[tex]\textsf{(iii)}\quad h(x) = \log_7(x + 1)[/tex]
For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.
Therefore, for function h(x), x + 1 > 0.
Solve the inequality:
[tex]\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}[/tex]
Therefore, the domain of h(x) is all real numbers greater than -1.
[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}[/tex]
[tex]\hrulefill[/tex]
[tex]\textsf{(iv)} \quad k(x) = \tan x[/tex]
The tangent function can also be expressed as the ratio of the sine and cosine functions:
[tex]\tan x = \dfrac{\sin x}{\cos x}[/tex]
Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.
From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.
The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.
Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.
[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}[/tex]
Related Questions
“y varies jointly as x and z”. Write the appropriate joint-variation equation, and then find “y” for the given value of “x” and “z”.
y = 12 when x = 4 and z = 5, find “y” when x = 6 and z = 3.
Answers
Answer:
y = kxz. y = 10.8
Step-by-step explanation:
y = kxz, where k is a constant.
12 = k(4)(5) = 20k
k = 12/20 = 0.6.
y = kxz
= (0.6) (6) (3)
= 10.8
en una oficina trabajan 8 profesionales
Answers
The number of professionals in the office, given that 8 professionals is 20 % would be 40 professionals.
How to find the number of professionals ?To calculate the total number of staff in the office, use the following formula :
Total staff = ( Professionals / Percentage ) x 100
Professionals = 8 professionals
Percentage = 20 %
Plugging in the values, we get :
Total staff = ( 8 / 20 ) x 100
Total staff = 0. 40 x 100
Total staff = 40 professionals
In conclusion, the office would have a total of 40 professionals if 8 professionals are 20 % of staff.
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Full question is:
en una oficina trabajan 8 profesionales haciendo un porcentaje de 20%. calcular el numero del personal de tal oficina
Translated is:
8 professionals work in an office making a percentage of 20%. Calculate the number of staff in such an office.
The function g(x) is a translation 2 units right and 5 units up of fx)-√√x. Which of
the following represents g(x)?
8(x)=√√x-2+5
8(x) = 2√√x+5
8(x) = √√x+5+2
8(x)=√x+2-5
Answers
The correct representation of the function g(x) as a translation 2 units right and 5 units up of f(x) = -√√x is:
g(x) = -√√(x - 2) + 5.
To perform a translation 2 units right, the x-coordinate needs to be replaced with (x - 2). This shift moves the entire graph horizontally to the right by 2 units.
Additionally, to shift the graph 5 units up, we add 5 to the function. Thus, the function g(x) is obtained by taking the negative square root of the square root of (x - 2) and then adding 5 to the result.
Among the given options, g(x) = -√√(x - 2) + 5 accurately represents the translation described, while the other options either have incorrect sign placement, incorrect order of operations, or an incorrect translation direction.
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Need the answer for this please!!
Answers
In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (5x - 30)°. We need to solve for the value of x.
According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:
(3x + 10) + (5x - 30) + 90 = 180
Let's simplify the equation:
3x + 10 + 5x - 30 + 90 = 180
8x + 70 = 180
Next, we'll isolate the variable term by subtracting 70 from both sides of the equation:
8x = 180 - 70
8x = 110
To solve for x, we'll divide both sides of the equation by 8:
x = 110 / 8
Now, let's calculate the value of x:
x ≈ 13.75
Therefore, the value of x is approximately 13.75.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.
there are 148 legs in a farmyard full of goats and chickens. there are 62 total animals, how many of each are there
Answers
Answer:
Let’s use x to represent the number of goats and y to represent the number of chickens. We know that there are 62 animals in total, so x + y = 62. We also know that there are 148 legs in total, so 4x + 2y = 148 (since goats have four legs and chickens have two).
We can solve for x and y by using substitution or elimination method. Let’s use substitution method here. From x + y = 62, we can get x = 62 - y. Substituting this into 4x + 2y = 148 gives us:
4(62 - y) + 2y = 148 248 - 4y + 2y = 148 248 - 2y = 148 100 = 2y y = 50
So there are 50 chickens on the farmyard. Substituting this into x + y = 62 gives us:
x + 50 = 62 x = 12
So there are 12 goats in the farmyard.
Therefore, there are 12 goats and 50 chickens on the farmyard.
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Lindsey is debt-free, has a fully funded emergency fund, and is ready to start saving for a house! She makes $4,000 per month in take-home pay and is looking to purchase a home worth $140,000. She’s trying to figure out how much to save for a down payment on her new home.
Answers
The Lindsey should save around $28,000 for the down payment. If she wants to expedite her savings, she can look into cutting down expenses or increasing her income.
Congratulations to Lindsey for being debt-free and having a fully funded emergency fund! As for her question, the down payment for a house usually ranges from 3% to 20% of the home's purchase price.
Based on Lindsey's desired home worth $140,000, the down payment can range from $4,200 (3%) to $28,000 (20%).
However, it's recommended to aim for a 20% down payment to avoid private mortgage insurance (PMI) and to lower monthly payments. Best of luck to Lindsey on her journey towards homeownership
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answer from the 4 options.
ASAP
Answers
Answer :
From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.
Opposite sides of Parallelogram are equal.XY = WZ
3a - 4 = a + 2
3a - a = 2 + 4
2a = 6
a = 6/2
a = 3
Now put the value of a in XY
XY = 3a - 4
XY = 3(3) - 4
XY = 9 - 4
XY = 5Similarly,
XW = YZ
2b = b + 1
2b - b = 1
1b = 1
b = 1
Now put the value of b in YZ
YZ = 2b
YZ = 2 × 1
YZ = 2XY = 5 and YZ = 2Answer :
D. XY = 5 , YZ = 2Step-by-step explanation :
As We Know that Opposite sides of the Parallelogram are equal.
SO,
(i) YZ = XW (opposite sides)
YZ = 2bXW = b + 1→ 2b = b + 1
→ 2b - b = 1
→ b = 1
Since, YZ = 2b
→ YZ = 2 × 1
→ YZ = 2.
Also,
(ii) XY = WZ (opposite sides)
XY = 3a - 4WZ = a + 2→ 3a - 4 = a + 2
→ 3a - a = 2 + 4
→ 2a = 6
→ a = 6/2
→ a = 3 .
Since, XY = 3a - 4
putting the value of a = 3.
=> 3(3) - 4
→ 9 - 4
→ 5
XY = 5.
Therefore, Option D is the required answer.
Which of the following functions have the following attributes?
-2 is a zero with multiplicity 2
5 is a zero with multiplicity 1
The graph is tangent to x-axis at x = 1
Answers
The function f(x) = (x+2)²(x-1)(x-5)² has-2 is a zero with multiplicity 2
5 is a zero with multiplicity 1 and the graph is tangent to x-axis at x = 1
For the function f(x) = (x+2)²(x-1)(x-5)²
-2 is a zero with multiplicity 2
This is represented by the factor (x+2)², indicating that -2 is a zero that appears twice in the function.
5 is a zero with multiplicity 1
This is represented by the factor (x-5), indicating that 5 is a zero that appears once in the function.
The graph is tangent to the x-axis at x = 1:
This is represented by the factor (x-1), indicating that the graph touches the x-axis at x = 1.
Therefore, the function f(x) = (x+2)²(x-1)(x-5)² has all the specified attributes.
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Line contains points (−4,0)
and (0,−2). Find the distance between line and the point P(4,1). Round your answer to the nearest hundredth, if necessary.
Answers
The distance between line and the point P(4,1) is,
⇒ d = 4.47
We have to given that;
Line contains points (- 4,0) and (0, - 2).
Since, The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Hence, The equation of line is,
⇒ y - 0 = (- 2 - 0) / (0 - (- 4)) (x - (- 4))
⇒ y = - 2/4 (x + 4)
⇒ y = - 1/2 (x + 4)
⇒ y = - 1/2x - 2
⇒ 2y = - x - 4
⇒ 2y + x + 4 = 0
So, The distance between the line 2y + x + 4 = 0 and the point P(4, 1) is:
⇒ d = (2 × 1 + 4 + 4) / √(2² + 1)
⇒ d = 10 / √5
⇒ d = 2√5
⇒ d = 2 x 2.23
⇒ d = 4.47
Thus, The distance between line and the point P(4,1) is,
⇒ d = 4.47
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(question 7) calculus
Answers
Answer:
A. -0.693147
Step-by-step explanation:
Replace f(x) with y in the given function:
[tex]y=\left(\dfrac{1}{2}\right)^x[/tex]
Take natural logs of both sides of the equation:
[tex]\ln y=\ln \left(\dfrac{1}{2}\right)^x[/tex]
[tex]\textsf{Apply the log power law:} \quad \ln a^n=n \ln a[/tex]
[tex]\ln y=x\ln \left(\dfrac{1}{2}\right)[/tex]
Differentiate using implicit differentiation.
Place d/dx in front of each term of the equation:
[tex]\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln \left(\dfrac{1}{2}\right)[/tex]
Differentiate with respect to x:
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln \left(\dfrac{1}{2}\right)[/tex]
[tex]\textsf{Apply the log quotient law:} \quad \ln \left(\dfrac{a}{b}\right) = \ln a - \ln b[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=\ln(1)-\ln(2)[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=0-\ln(2)[/tex]
[tex]\dfrac{1}{y} \dfrac{\text{d}y}{\text{d}x}=-\ln(2)[/tex]
Multiply both sides by y:
[tex]\dfrac{\text{d}y}{\text{d}x}=-y\ln (2)[/tex]
Substitute back in the expression for y:
[tex]\dfrac{\text{d}y}{\text{d}x}=-\left(\dfrac{1}{2}\right)^x\ln (2)[/tex]
Therefore, the differentiated function is:
[tex]f'(x)=-\ln(2)\left(\dfrac{1}{2}\right)^x[/tex]
To find f'(0), substitute x = 0 into the differentiated function:
[tex]\begin{aligned}x=0 \implies f'(0)&=-\ln(2) \left(\dfrac{1}{2}\right)^0\\&=-\ln(2) \cdot 1\\&=-\ln(2) \\&=-0.693147\; \sf (6\;d.p.)\end{aligned}[/tex]
The 2008 attendance at the Ohio State Fair was at least 16,700 less than the attendance in 2009. If the attendance in 2008 was 809,300, write and solve an inequality to find the 2009 attendance
Answers
The solution to the inequality indicates that the attendance in 2009 must be 826,000 or more.
Let's assume the attendance in 2009 is represented by the variable A. According to the given information, the attendance in 2008 was at least 16,700 less than the attendance in 2009.
Mathematically, we can express this as:
A - 16,700 ≥ 809,300
To find the attendance in 2009, we need to solve this inequality.
First, we add 16,700 to both sides of the inequality:
A - 16,700 + 16,700 ≥ 809,300 + 16,700
Simplifying, we have:
A ≥ 826,000
Therefore, the attendance in 2009 is greater than or equal to 826,000.
In this case, the inequality A ≥ 826,000 indicates that the attendance in 2009 must be equal to or greater than 826,000 for the statement to hold true.
If the attendance in 2009 is less than 826,000, it would not satisfy the given condition that the attendance in 2008 was at least 16,700 less than the attendance in 2009.
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Question 2 of 9
17 - (9 - 10) = (17- 9) - 10
O A. True
3
B. False
Answers
A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time.
After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments.
Which statements about this study are true?
This study uses blocking.
This study uses a repeated measures design.
This study uses blinding.
This study uses random sampling.
This study uses a control group.
Answers
This study uses a repeated measures design, random sampling, and a control group.
What is Repeated Measures Design?Repeated measures design is used because each child experiences all treatments over time. Random sampling is present as children were randomly selected.
The control group is the group with no screen time. Blocking isn't used as participants aren't grouped based on shared characteristics affecting the response. Blinding isn't used as it's not mentioned that participants or researchers are unaware of the treatment given, which would prevent bias.
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pls help will mrak brainleist
Answers
Answer:
x = 18°Step-by-step explanation:
We know that,
sum of three side of triangle is 180°
So,
x + 72° + 90° = 180°
x + 162° = 180°
x = 180° - 162°
x = 18°
[tex]\underline{\rule{190pt}{4pt}}[/tex]
The value of x in the triangle is 18 degrees.
The given triangle is a right angled triangle.
We have to find the value of x.
As the triangle is a right angle one angle is 90 degrees.
And the other angle is 72 degrees.
The missing angle is x which we have to find.
By angle sum property we know that the sum of three angles is 180 degrees in a triangle.
72+90+x=180
Combine the like terms:
162+x=180
Subtract 162 from both sides:
x=180-162
When one hundred sixty two is subtracted from one hundred eighty, we get 18.
x=18 degrees
Hence, 18 degrees is the value of x in the triangle.
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Suppose you own 125 shares of a stock that pays a dividend of $0.29 per
share per year. How much will you receive in dividends over 6 years,
assuming the dividends stay the same and you buy no more stock?
OA. $161.25
OB. $217.50
C. $174.00
D. $36.25
PREVIOUS
Answers
Hello !
125 * $0.29 * 6 = $217.50
I WILL GIVE THE BRAINIEST
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Answers
An equation can be written to determine the number of students that went on this trip is: C. [tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]
How to write an equation to determine the number of students that went on this trip?In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;
Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;
[tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]
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Complete Question:
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.
Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
Which graph represents the function g(x) = 7cosx after a shift of StartFraction 5 pi Over 3 EndFraction units to the right?
Answers
The graph of the function g(x) = 7cosx after the shift of 5/3 is shown by the second graph.
What are trigonometric functions?A right-angled triangle's relationship between its angle and sides is represented by a series of functions known as trigonometric functions.
What is Cosine (Cos) Function?
The ratio of the neighbouring side to the hypotenuse is known as the cos function (cosine function) in a triangle.
The range of cosine function lies between -1 to 1.
Calculation for the range of given function:
The given function is, g(x) = 7cosx
Consider x = 0, put in the function.
g(x) = 7cos0
g(x) = 7×1
g(x) = 7
As, for the domain of x = 0 range is 7. the graph will shift upward with 7 units from origin.
Now, according to question, there is a shift of 5/3 of the graph, which means this 7 shift upward will move to 5/3 .
This condition is satisfied by the second graph.
Therefore, the shift for the function g(x) = 7cosx is shown correctly by the second graph.
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Answer:
B
Step-by-step explanation:
I took the test and graph B was the correct one
if y=- 5x {}^{2} determine the value of..
y if x=0
Answers
Answer:
Step-by-step explanation:
y = -5x^2
if x = 0 , then
y = -5(0)
y = 0
A box contains 19 large marbles and 11 small marbles. Each marble is either green or white. 3 of the large marbles are green, and 4 of
the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your
answer as a fraction or a decimal number rounded to four decimal places.
Answers
The probability of selecting a large or green marble is 0.7333.
The probability of selecting a large marble is 19/30 (19 large marbles out of 30 total marbles). The probability of selecting a green marble is 3/30 (3 green marbles out of 30 total marbles).
To find the probability of selecting a large or green marble, you need to find the probability of selecting a marble that is either large or green. This is known as the union of two events. The union of two events is found by adding the individual probabilities of each event together.
The probability of selecting a large or green marble is 19/30 + 3/30 = 22/30 = 0.7333.
Therefore, the probability of selecting a large or green marble is 0.7333.
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DATE 02 June 04 June TRANSACTION DESCRIPTION Opening Balance ATM Cash Debit card Payment Clothing Debit card POS Purchase Debit card POS Purchase #Monthly account fee 12 June 17 June 29 June 29 June #Service fees Zorro MTN Molino AMOUNT 100,00 A 1004.00 2840.00 12.50 5.25 CREDIT CHARGES 5154.69 5154 69 5034,69 4030 69 1190.69 B 1172.94 5.25 3.2.1 What is the opening balance? 3.2.2 The opening balance is on the credit side. Explain the implications on the bank statement 3.2.3 If Gloria decides to withdraw money at Capital bank ATM, how is this going to aff her finances? 3.2.4 Calculate the value of B
Answers
The opening balance is 100.00 A. Its placement on the credit side implies funds deposited before the statement period. The specific impact on Gloria's finances and the value of B are not provided.
Based on the provided information, let's address each question:
3.2.1 The opening balance is 100.00 A (currency is not specified). This amount represents the initial balance in the bank account before any transactions occur.
3.2.2 When the opening balance is on the credit side of the bank statement, it indicates that there were funds deposited or credited to the account before the statement period. In this case, the opening balance of 100.00 A suggests that there were funds deposited or credited into the account before the statement period began.
3.2.3 If Gloria decides to withdraw money at Capital Bank ATM, her account balance will decrease by the amount of the withdrawal. The specific amount of the withdrawal is not mentioned in the provided information, so we cannot determine the exact impact on her finances. However, it's important to note that ATM withdrawals may also incur transaction fees, which could further reduce her account balance.
3.2.4 Based on the information given, the value of B is not explicitly provided. It seems to be missing or not specified in the provided data. Without knowing the value of B, it is not possible to calculate it.
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help me please so hard
Answers
Gradient is another word for slope.
Slope = rise/run = (y2-y1)/(x2-x1)
So pick 2 points.
Let's do line A first.
(1,1) and (2,4)
slope = (1-4)/(1-2)
= -3/-1 = 3
The slope (aka gradient) of line A = 3.
Line B.
(0,5) and (1,1)
slope = (5-1)/(0-1)
= 4/-1
= -4
The slope (aka gradient) of line B = -4.
Buying vs Leasing Given the below lease terms at a local car dealership, what is the total cash paid by the end of the lease when at signing the dealership required a down payment, security deposit, acquisition fee at signing and all the monthly payments paid? Length of lease 48 = months MSRP of the car = $29,750 Purchase value of the car after lease = $19,900 Down payment =$2,800 Monthly payment =$595 Security deposit =$575 Acquisition fee =$400
Answers
Down payment = $2,800
Security deposit = $575
Acquisition fee = $400
Total initial payment = Down payment + Security deposit + Acquisition fee
Total initial payment = $2,800 + $575 + $400 = $3,775
Total monthly payments = Monthly payment x Length of lease
Total monthly payments = $595 x 48 = $28,560
Total cash paid by the end of the lease = Total initial payment + Total monthly payments - Residual value
Residual value = Purchase value of the car after lease = $19,900
Total cash paid by the end of the lease = $3,775 + $28,560 - $19,900
Total cash paid by the end of the lease = $12,435
Therefore, the total cash paid by the end of the lease, including the down payment, security deposit, acquisition fee, and all the monthly payments, is $12,435.
Solve for c.
(5c-3) ÷ 4 = 8
c = [?]
Answers
Simplify 5c-3/4
(5c-3)/4-8=0
You rewrite the whole as a fraction using 4 as the denominator:
8=8/1=8*4/4
(5c-3)-(8*4)/4= 5c-35/4
Pull out like factors:
5*(c-7)/4=0
To get rid of the denominator:
5*(c-7)/4*4=0*4
So now it’s,
5*(c-7)=0
Solve 5=0 which has no solution.
Solve c-7=0 adding 7 to both sides. C=7 :)
good people please help me!!!!!!
2.1show a=2,b=-2,c=-10 and d=-6
2.2 calculate the co-ordinate of turning point B
Answers
The coordinates of the point of intersection of the tangent and the secant are;
T(a, b) = (9/5, -14/5)
C = (0, -1)
What is a tangent to a circle?A tangent is a line or segment that touches a circle only once.
The equation of the line AN is; y - 2 = ((-2 - 2)/(2 - 3)) × (x - 3)
y = 4·x - 12 + 2 = 4·x - 10
y = 4·x - 10
The coordinates of the center of the circle is; ((-5 + 3)/2, (4 + 2)/2) = (-1, 3)
The radius of the circle is; √((3 - (-1))² + (2 - 3)²) = √(17)
The equation of the circle is; (x + 1)² + (y - 3)² = 17
The point C indicates;
(0 + 1)² + (y - 3)² = 17
(y - 3)² = 17 - 1 = 16
y - 3 = √(16) = ±4
y = 4 + 3 = 7, and y = -4 + 3 = -1
The coordinates of the point C is; (0, -1)
The slope of AC = (2 - (-1))/(3 - 0) = 1
AC is perpendicular to BC
The slope of BC = -1
The equation of BC is therefore; y - 4 = -(x - (-5)) = -x - 5
y = -x - 1
The equation of the segment AN is; y - 2 = ((2 - (-2))/(3 - 2))×(x - 3)
y - 2 = 4·(x - 3)
y = 4·x - 12 + 2 = 4·x - 10
-x - 1 = 4·x - 10
x-coordinate of T = 9/5
The y-coordinate of T = -9/5 - 1 = -14/5
Therefore, at the point T, we get; (9/5, -14/5)
a = 9/5, b = -14/5, C = (0, -1)
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Each member of a sports club plays at least one of soccer, rugby, or tennis. The following information is known: 43 members play tennis, 11 play tennis and rugby, 7 play tennis and soccer, 6 play soccer and rugby, 84 play rugby or tennis, 68 play soccer or rugby, and 4 play all three sports.
1. Display the information in a Venn diagram.
2. How many members play soccer only?
3. How many members play tennis or soccer, but not rugby?
4. How many members play exactly two sports?
5. How many members play at least one sport?
6. If 60 members play soccer, how many members play tennis?
Answers
1. The number of members who play soccer only is 59.
2. The number of members who play tennis or soccer, but not rugby, is 37.
3. The number of members who play exactly two sports is 20.
4. The number of members who play at least one sport is 195.
5. If 60 members play soccer, then 7 members play tennis.
1. To find the number of members who play soccer only, we need to subtract the members who play soccer and other sports from the total number of soccer players.
Soccer only = Total soccer players - (Soccer and Rugby) - (Soccer and Tennis) + (All three sports)
Soccer only = 68 - 6 - 7 + 4
Soccer only = 59
Therefore, 59 members play soccer only.
2. To find the number of members who play tennis or soccer but not rugby, we need to subtract the members who play all three sports from the total number of tennis and soccer players.
Tennis or Soccer (not rugby) = (Tennis + Soccer) - (All three sports)
Tennis or Soccer (not rugby) = 43 + 68 - 4
Tennis or Soccer (not rugby) = 107
Therefore, 107 members play tennis or soccer but not rugby.
3. To find the number of members who play exactly two sports, we need to add the members who play tennis and soccer (TS), tennis and rugby (TR), and soccer and rugby (RS).
Exactly two sports = TS + TR + RS
Exactly two sports = 7 + 11 + 6
Exactly two sports = 24
Therefore, 24 members play exactly two sports.
4. To find the number of members who play at least one sport, we can add the number of members who play each sport individually (Tennis, Rugby, Soccer) and then subtract the number of members who play none of the sports.
At least one sport = Tennis + Rugby + Soccer - None
At least one sport = 43 + 84 + 68 - 0
At least one sport = 195
Therefore, 195 members play at least one sport.
5. If 60 members play soccer, we can calculate the number of members who play tennis by subtracting the members who play both sports (TS) and the members who play soccer only from the total number of soccer players.
Tennis = Total soccer players - (Soccer only) - (TS)
Tennis = 60 - 59 - 7
Tennis = -6
It is not possible to have a negative number of members playing tennis. Please double-check the provided information or calculations.
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Which side lengths form a right triangle?
Choose all answers that apply:
A 5,√8,33
B 8, 15, 17
√2, √2,2
Answers
Answer:
B and C
Step-by-step explanation:
We can determine which three sides will form a right triangle using the Pythagorean theorem, which is
a^2 + b^2 = c^2, where
a and b are the legs,and c is the hypotenuse and the longest sidesThus, a three side lengths can only form a right triangle if the sum of the squares of the shorter sides equal the square of the longest side (the hypotenuse)We can simply check A, B, and C to see which side lengths form a right triangle:A:
5 and √8 (approximately 2.236) are the shorter sides, so we plug these in for a and b in the Pythagorean theorem; 33 is the longest side, so we plug it in for c:5^2 + (√8)^2 = 33^2
25 + 8 = 1089
33 ≠ 1089
Because 33 is not equal to 1089, these three lengths do not form a right triangle.
B:
8 and 15 are the shorter sides, so we plug these in for a and b in the Pythagorean theorem;17 is the longest side, so we plug it in for c:8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Thus, these three side lengths form a right triangle.
C:
The two √2 (approximately 1.414) are the shorter sides, we plug these in for a and b in the Pythagorean theorem;2 is the longest side, so we plug it in for c:(√2)^2 + (√2)^2 = 2^2
2 + 2 = 4
4 = 4
Thus, these three side lengths also form a right triangle.
x − y = y − x proposition or not?
Answers
The proposition x − y = y − x is true.
We are given that;
The equation x − y = y − x
Now,
X − y = -(y - X)
-(y - X) + 2X - 2X = y - X + X - y = y - x.
Similarly, y - x = -(x - y)
-(x - y) + 2y - 2y = x - y + y - x = X - y.
Both sides of the equation are equal.
Therefore, by the given function answer will be true.
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How can I simplify this
The result should be three
Answers
The image you provided is a mathematical expression written in a non-standard format. To simplify it and obtain the result of 3, we can break it down step by step.
The expression can be written as follows:
(8c8) * (8x83)
Let's simplify each part separately:
(8c8):
The term "8c8" represents the combination or binomial coefficient. In general, the combination "nCr" is calculated as n! / (r! * (n-r)!), where "!" denotes factorial. When r = n (as is the case here with 8c8), the combination simplifies to 1. Therefore, 8c8 equals 1.
(8x83):
The term "8x83" represents multiplication between the numbers 8 and 83, which equals 664.
Now, let's put it all together:
(8c8) * (8x83) = 1 * 664 = 664
According to the given expression, the simplified result is 664, not 3. Please double-check the expression or provide further clarification if needed.
After a 95% reduction, you purchase a new television on sale for $181. What was the original price of the television? Round your solution to the nearest cent.
Answers
Answer:
The original price of the television was $3620.00.
Answer:
$3620.00
Step-by-step explanation:
5% = 181
1% = 36.2
100% = 3620
What equation is equivalent to 8.8 x 10^9 divided by 2.2 x 10^-3?