With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
What do we mean by Quotient?In this example, the number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4. The quotient and divisor are always less than their dividend, as you can see.So, h(t) = 24:
= 50Then, calculate as follows:
h(t) = - 1624 = 50 - 1616 = 50 - 2416 = 26 = 26/16t = √26/16t = 1.3secTherefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
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Graph using slope-intercept form.
3x-2y<10
Answer:
3x-2y=10
2y=3x-10
Y=(3/2)x-5
Slope m=3/2
Answer:
See attachment.
Step-by-step explanation:
Slope-intercept form:
[tex]\boxed{y=mx+b}[/tex]
where:
m = slopeb = y-intercept-----------------------------------------------------------------------------------
Given inequality:
[tex]3x-2y < 10[/tex]
Rearrange the given inequality to make y the subject:
[tex]\implies 3x-2y+2y < 10+2y[/tex]
[tex]\implies 3x < 10+2y[/tex]
[tex]\implies 3x-10 < 10+2y-10[/tex]
[tex]\implies 3x-10 < 2y[/tex]
[tex]\implies 2y > 3x-10[/tex]
[tex]\implies \dfrac{2y}{2} > \dfrac{3}{2}x-\dfrac{10}{2}[/tex]
[tex]\implies y > \dfrac{3}{2}x-5[/tex]
Compare this with the slope-intercept form.
Therefore:
slope = ³/₂y-intercept = (0, -5)When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.To graph the given inequality using its slope and y-intercept:
Plot the y-intercept → point (0, -5). As the slope is ³/₂, plot another point 3 units up and 2 units right from (0, -5) → point (2, -2). Draw a dashed straight line through the two points.Shade above the line.Learn more about graphing inequalities here:
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Which of the ten basic functions in
our toolkit have graphs that look the
same when reflected of the y-axis
and then reflected over the x-axis?
Answer:
a) x³, 1/x, x, sin(x)
Step-by-step explanation:
You want to know which list of functions has the same graph when reflected across both the y- and x-axes.
Odd functionReflection across the y-axis transforms the function to ...
f(x) ⇒ f(-x)
Reflection across the x-axis transforms the function to ...
f(x) ⇒ -f(x)
Hence, reflection across both axes transforms the function to ...
f(x) ⇒ -f(-x)
A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:
x³ = -(-x)³ . . . . true
1/x = -(1/-x) . . . . true
x = -(-x) . . . . true
sin(x) = -sin(-x) . . . . true
cos(x) = -cos(-x) . . . . false
e^x = -e^-x . . . . false
|x| = -|-x| . . . . false
The basic functions that are odd are ...
x³, 1/x, x, sin(x)
Jaya's monthly bank statement showed the following deposits and withdrawals:
$31.87, -−$34.19, -−$58.47, $48.57, -−$13.16
If Jaya's balance in the account was $94.42 at the beginning of the month, what was the account balance at the end of the month?
If Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04 .
In the question ,
it is given that Jaya's account balance at beginning of month was $94.42 ,
first transaction +$31.87 ,
means Jaya deposited $31.87
So Account balance = $94.42+$31.87 = $126.29
Second transaction -$34.19 ,
means Jaya withdraw $34.19
So Account balance = $126.29-$34.19 = $92.10
third transaction -$58.47 ,
means Jaya withdraw $58.47
So Account balance = $92.10-$58.47 = $33.63
fourth transaction +$48.57,
means Jaya deposited $48.57
So Account balance = $33.63+$48.57 = $82.20
fifth transaction -$13.16 ,
means Jaya withdraw $13.16
So Account balance = $82.20-$13.16 = $69.04
Therefore , if Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04 .
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what is the domain of the relation shown below?
The correct option C { -3, 1, 2, 6} is the domain of the relation given.
What is described as the domain?A function's domain is the set of the all the values within which the function is defined, and its range is the set of all values which f takes.The domain of such a function is indeed the set of values that can be plugged into it. This set contains the x values together in function like f(x). A function's range is the set of values which the function can take. This is the set of values that function returns after we enter an x value.For the given relation in the question;
The values which are input in the function is called domain.
In put values are - { -3, 1, 2, 6}
Thus, domain of the given relation is { -3, 1, 2, 6}.
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2a + 3b = 8 and 4x + 10y = 50
(i) What is the value of 6a + 9b?
(ii) What is the value of 2x + 5y?
a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.
b. The value of 2x + 5y is 25.
How to illustrate the information?a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:
6a + 9b = 3(2a + 3b)
This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24
(ii) What is the value of 2x + 5y?
4x + 10y = 50
It should be noted that this can be divided through by 2. This will be;
(4x + 10y = 50) / 2
2x + 5y = 25
The value is 25.
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on a coordinate plane, point a is located (-2,2) and point b is located at (6,-1). determine the coordinates of the point that is 7/8 of the distance from a to b
The coordinates of the point between points a to b are (5, -5/8)
How to determine the coordinate of the point on the line segment?We have the following endpoints on the segment
A = (-2, 2)
B = (6, -1)
The line ratio is given as the following fraction
Ratio, m : n = 7/8
Express the fraction as a ratio
So, we have
m : n = 7 : 8 - 7
Evaluate the difference
So, we have
m : n = 7 : 1
The coordinate of the point is then calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
Substitute the known values in the above equation
Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)
Evaluate the products in the above equation
So, we have
Point = 1/8 * (42 -2, -7 + 2)
Evaluate the sum and the difference
So, we have
Point = 1/8 * (40, -5)
Evaluate the products
So, we have
Point = (5, -5/8)
Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)
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Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.
How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?
Step-by-step explanation:
Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.
How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?
..
please post full questions
please followIf m angle ABD=100^ , what is the relationship between AD and CD? OAD AD + DC < AC; CD = AD; CD > AD; CD < AD
Answer: CD<AD
Step-by-step explanation:
Just got it right on the test.
Answer: CD<AD
Step-by-step explanation:
Took the test!
Solve the equation 4 > lxl + 1
Answer:A) 3
Step-by-step explanation:
A function and its graph are given. Find the domain. (Enter your answer using interval notation.)
f(x) =
x − 3
x − 8
The domain for the rational function is the set of all real numbers except for 8, this is written as:
{x | x ∈ R, x≠8}
How to find the domain of the given function?
For any function f(x), the domain is the set of the possible inputs.
In this case, we have the rational function:
f(x) = (x - 3)/(x - 8)
Now, we start by assuming that the domain is the set of all real numbers, and then we remove all the problematic values.
Now, we can't divide by zero, so the value of x that makes the denominator zero needs to be removed, that is such:
x - 8 = 0
x = 8
So the domain is the set of all real numbers except for 8, this is written as:
{x | x ∈ R, x≠8}
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You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven. Explain the meaning of each statement.
a. f(0)=67
b. f(3.75)=165
c. f(3)=f(4)
d. f(3.75)>f(4)
You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.
a) At t = 0
temperature of turkey is 67 degree Fahrenheit
b) At t = 3.75
temperature of turkey is 165 degree Fahrenheit
c) t = 3
temperature of turkey is 4 degree Fahrenheit
d) at t = 3.75
temperature of turkey is 169 degree Fahrenheit
What is basic algebra ?Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done.
Given that : You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.
a) At t = 0
temperature of turkey is 67 degree Fahrenheit
b) At t = 3.75
temperature of turkey is 165 degree Fahrenheit
c) t = 3
temperature of turkey is 4 degree Fahrenheit
d) at t = 3.75
temperature of turkey is 169 degree Fahrenheit
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Similarities and differences between AAS and ASA Congruence Postulates
Answer:
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
Step-by-step explanation:
ASA: Angle, Side, Angle
AAS: Angle, Angle, Side
Similarity: Both are geometry terms, used in proofs.
Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.
I am going to use the drawer to show the differences:
How far can a woman drive into the tiwnif she drives out at 40 miles per hour,return over the same rod at 30 miles per hour, and spends 8 hours away from home, including a 1 hour stop for luch
Given the time, the distance that the.womn drives will be 240 miles.
How to calculate the distance?From the information illustrated, the woman drives out at 40 miles per hour, return over the same road at 30 miles per hour, and spends 8 hours away from home.
It should be noted that the average speed will be illustrated as:
= (2 × r1 × r2) / +r1 + r2)
= (2 × 40 × 30) / (40 + 30)
= 240/7
Since she drive for 7 hours, the distance will be:
= 240/7 × 7
= 240 miles.
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I’m confused on this and don’t know what to do please help
Answer:
83
Step-by-step explanation:
3x³+2y-6
x= 3 and y = 4, we will plug in what x equals to for the x value, then we will plug in what y equals to for the y value
3(3³) + 2(4) - 6
now let's use order of operations (PEMDAS: parenthesis exponent multiplication division addition subtraction)
parenthesis first
3³ = 3·3·3= 27
3(27) + 2(4) - 6
there are no exponents so we will use multiplication
3·27 = 81
2·4=8
81 + 8 - 6
83
A $300 fax machine is on sale for 45% off. Find the amount of the discount and the sale price.
The amount of discount is $
The sale price is $
The length of a parking lot is 4 yards more than the width. If the area of the parking lot is 117 square yards, find the dimensions of the parking lot.
A parking lot's length is 4 yards longer than its width. The dimensions of the parking lot are width=9 and length =12.
Given that,
A parking lot's length is 4 yards longer than its width.
We have to determine the parking lot's measurements if the area is 117 square yards.
Let us take the width as x and we get the length as x+4.
We can write as,
x(x+4)=117
x²+4x=117
x²+4x-117=0
x²+13x-9x-117=0
x(x+13)-9(x+13)=0
(x+13)(x-9)=0
x+13=0 and x-9=0
x=-13 and x=9
Therefore, The dimensions of the parking lot are width=9 and length=12.
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If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph?
4
8
12
16
Answer: y-intercept is 12
Step-by-step explanation:
y = mx +b
m = slope
b = y-intercept
y | = | x | + | b
f(x) | = | 4x | + | 12
b = y-intercept
Suppose there are 17 jelly beans in a box-2 red, 6 blue, 4 white, and 5 green.
What part of the jelly beans is blue? Express your answer in each of the forms requested.
8. Rectangle R's perimeter remains 180 feet when
the length is halved and the width is doubled.
What are the dimensions of rectangle R?
(Hint: Perimeter = 2(l+w)
rectangle
The perimeter of 180, the length and width of the rectangle with maximum area are 45 and 45.
What is the maximum-area rectangle?The difference in length and breadth of any rectangle must be minimal for the area to be maximum. As a result, the length must be ceil (perimeter / 4) and the breadth must be floor (perimeter /4). As a result, the maximum area of a rectangle with a given perimeter is ceil(perimeter/4) * floor(perimeter/4). As a result, the area is greatest when the rectangle is square.Let x= the length and y= the width of the rectangle.
The area of the rectangle A=x y
2 x+2 y=180 because the perimeter is 180.
Solve for y
[tex]$&2 y=180-2 x \\[/tex]
[tex]$&y=90-x[/tex]
Substitute for y in the area equation.
[tex]$&A=x(90-x) \\[/tex]
[tex]$&A=90 x-x^2[/tex]
This equation describes a parabola that extends down. The maximum value of the area is at the vertex.
Rewriting the area equation in the form [tex]$a x^2+b x+c$[/tex]
[tex]$A=-x^2+90 x \quad a=-1, b=90, c=0$[/tex]
The formula for the x coordinate of the vertex is
[tex]$x=\frac{-b}{2 a}=\frac{-90}{2 \cdot-1}=45[/tex]
The maximum area exists found at x=45
and [tex]$y=90-x=90-45=45$[/tex]
Given a perimeter of 180, the proportions of the rectangle with the maximum area are 45 × 45
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jamies bought 23 cases of soda for her party. each case contain dozes cans
if her guest drank 223 can of soda how many cases were used
Answer:
4.416 or rounded just 4
Step-by-step explanation:
23×12=276
276-223=53
53÷12=4.416
87 billion 295 million written out
Answer: 87, 295,000,000 or eighty-seven two hundred ninety-five Billion
Im pretty sure
im stuck on this question
a) g(3) = -182
b) g(0) = 7
c) g(-1) = 70
Explanation:[tex]\begin{gathered} \text{Given:} \\ g(x)\text{ = }7\text{ - 63x} \end{gathered}[/tex]a) g(3): To get this, we will substitute 3 for x in the function g(x)
[tex]\begin{gathered} \text{x = 3} \\ g(3)=\text{ 7 - 63(3) = 7 - 189} \\ g(3)\text{ = }-182 \end{gathered}[/tex]b) g(0): To get this, we will substitute 0 for x in function g(x)
[tex]\begin{gathered} x\text{ = 0} \\ g(0)\text{ = 7 - 63(0) = 7 - 0} \\ g(0)\text{ = 7} \end{gathered}[/tex]c) g(-1): To get this, we will substitute -1 for x in function g(x)
[tex]\begin{gathered} x\text{ = -1} \\ g(-1)\text{ = 7 - 63(-1)} \\ mu\text{ltiplication of same signs give positive sign} \\ g(-1)\text{ = 7 + 63} \\ g(-1)\text{ = 70} \end{gathered}[/tex]Find the value of each variable.
7
(4x + 8)
x=
Answer:
x=-1/4 or -.25
Step-by-step explanation:
I took the test and double checked it
7. If f(x) = -x + 7, what is f(15)?Of(15) = 22f(15) = -22Of(15) = -8f(15) = 8
the fuction f(x) is equal to:
[tex]f(x)=-x+7[/tex]now, to evaluate f(15) we have to replace x=15 so the equation is going to be equal to:
[tex]f(15)=-15+7=-8[/tex]What i5 divided by 312
The value derived when 5 is divided by 312 is 62.40.
What is the value of the division?Division is the process of putting a number into distinct equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other mathematical operations include addition, subtraction and multiplication.
312 ÷ 5 = 62.40
The long division is:
62.4
5[tex]\sqrt{312}[/tex]
- 30
12
- 10
20
- 20
00
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Consider the system of equations x+2y=8 -3x-2y=12 How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer'
The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
The given system of equations:
x + 2y = 8 (Equation - 1)
-3x - 2y = 12 (Equation - 2)
This can be written in matrix form as shown:
[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]
Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]
We can use cross multiplication,
= (-2)(1) - (-3)(2)
= -2 + 6
= 4 ≠ 0
So the system has a unique solution,
Then,
[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]
[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]
So, they can solve the X and Y values,
X = D1 / D
X = -40/4
X = -10
Y = D2 / D
Y = 36/4
Y = 9
Therefore,
The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
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I need help with this question
Probability that first three price winners are omar, kira and elsa is [tex]\frac{1}{84}[/tex]
Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is [tex]\frac{1}{504}[/tex]
What is permutation and combination ?When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.
(i)First 3 prizes must be given to 3 persons regardless of order
Hence they can also be arranged in 3! ways.
est 6 can be arranged in 6! ways.
positions ___ ___ ___ ___ ___ ___ ___ ___ ___
number of ways 3 2 1 6 5 4 3 2 1
total number of ways to arrange 9 people = 9!
[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]
(ii)Event A
In event A three positions are fixed .
Omar -1 Kira -2 Elsa -3
Therefore there is only 1 way to fill the 1st,2nd and 3rd position
Permutations can only be made among the other positions.
Positions - ___ ___ ___ ___ ___ ___ ___ ___ ___
Number of ways- 1 1 1 6 5 4 3 2 1
Total number of ways of arranging 9 people =9×8×7×6×5×4×3×2×1
Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1
P(A)= [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]
P(A)= [tex]\frac{1}{504}[/tex]
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What is the probability of flipping a coin 7 times and getting heads 4 times?Round your answer to the nearest tenth of a percent.A. 27.3%B. 0.8%C. 5.5%D. 16.4%
We know that
• The probability of a head is 1/2.
,• The probability of a tail is 1/2.
Notice that the number of times they flip a coin is 7. Since both probabilities are the same, we just have to multiply 1/2 seven times by itself.
[tex]P=(\frac{1}{2})^7[/tex]Now, we multiply the probability with 7 since there are 7 possibilities.
[tex]P=7\cdot(\frac{1}{2})^7=7(0.0078125)=0.0546\approx0.055[/tex]Then, we multiply by 100 to express it as a percentage.
[tex]0.055\cdot100=5.5[/tex]Therefore, the answer is C. 5.5%.
[tex]\rm \int_{-\infty}^0\sqrt{1+2^2}e^{2\theta}d\theta=\phi-\frac12\\[/tex]
Nothing tricky here:
[tex]\displaystyle \int_{-\infty}^0 \sqrt{1+2^2} \, e^{2\theta} \, d\theta = \sqrt5 \int_{-\infty}^0 e^{2\theta} \, d \theta \\\\ ~~~~~~~~ = \frac{\sqrt5}2 \left(e^0 - \lim_{\theta\to-\infty} e^{2\theta}\right) \\\\ ~~~~~~~~ = \frac{\sqrt5}2[/tex]
Recall that
[tex]\phi = \dfrac{1+\sqrt5}2[/tex]
and this is exactly 1/2 more than the value of the integral.
8. There were a total of 117 football games in
the season, and 33 were played at night. The
season was nine months long. How many
games were played each month, if each month.
had the same number of games?
So, 13 games were played each month, if each month had the same number of games.
What is division?Compared to multiplication, division is the opposite. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. It is referred to as a method of division to divide anything. According to the degree of difficulty, there are three different sorts of division procedures. These include the bus stop approach, the chunking method, and the long division method. The chunking method is also known as division by repeated subtraction.
Given Data
A total of 117 football games in the season, and 33 were played at night.
The season was nine months long.
Each month same numbers of game were played.
So,
117 ÷ 9
13
So, 13 games were played each month, if each month had the same number of games.
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