Simplify and state the restrictions on the domain:
The simplification of the given expression is (x - 1)²/ (x-2)(x+3) which restrictions on the domain of this expression are x ≠ 1, 2, -3.
The expression is given in the question as:
(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)
To simplify the expression (x+3)(x-1)/(x-2) ÷ (x+3)/(x-1), we can start by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction:
(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)
= (x+3)(x-1) / (x-2) × (x-1) / (x+3)
Then, we can simplify the expression by combining like terms:
= (x - 1)² (x+3)/ (x-2)(x+3)
= (x - 1)²/ (x-2)(x+3)
The restrictions on the domain of this expression are that x cannot be equal to 2 or -3, because these values would make the denominator equal to zero, which is not allowed in a fraction.
Therefore, the domain of the expression is all real numbers except x = 1, x = 2, and x = -3. We can express this as:
Domain: x ∈ R, x ≠ 1, x ≠ 2, x ≠ -3
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Describe and correct error
Dave opens a savings account that has an annual simple interest rate of 0.1%. If he initially deposits $1500, find the amount in the savings account after 5 years. PLEASE HELP WILL GIVE 20 POINTS
The amount in his savings after 5 years will be $1507.5.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P = 1500, r = 0.1, t = 5 years.
∴ SI = (1500×0.1×5)/100.
SI = $7.5.
Now, We know Amount = principle + SI.
∴ Amount = 1500 + 7.5 = $1507.5
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A fair coin is to be tossed 10 times. Let i/j, in lowest terms, be the probability that heads never occur on consecutive tosses. Find i+j.
The probability that there are 89/1024 ways in which heads never happen on consecutive tosses.
Explain the definition of probability?Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.For the stared question;
Think of the flips as either a string of [Head first Tail] or [Tail]. Let x stand for the quantity of [Head followed by Tail] and y for the quantity of [Tail]. If 2x + y = 10, then.Then, for every value of x, I completed casework:
The number of configurations of AAAAAAAAAA is bijective to x=0 and is 1.
The number of configurations of AAAAAAAAB is then bijective to x=1, which really is 9 and so forth.
These variables add up to 89, and there are 1024 different ways to flip them.
P(i + j) = 89/1024
Thus, there are 89/1024 ways in which heads never happen on consecutive tosses.
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Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at least $20.00 on his card at the end of this month.To determine how many bus rides he can take between now and the end of this month, Soro wrote and solved the following inequality:
50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
What error, if any, did Soro make when writing or solving this inequality?
The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is :
50 - 2.5y ≥ 20.
What is an inequality ?Inequality is defined as the unequal distribution of income and opportunity among various groups in society.In this case, y represents the number of bus rides that Soro will be able to take from the start of the week to the end of the week.The amount she will have to pay for y tickets is 2.5y. The amount she will have left over after the purchase will then be= 50 - 2.5y
This number must be at least 20. The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is 50 - 2.5y ≥ 20.To learn more about inequalities refer to :
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is the expression 16x⁸ equivalent to (16x⁴)²?
Answer:
Yes
Step-by-step explanation:
16x^4 x 16x^2= 16x^8
Determine the work to empty a parabolic tank filled with water which can be seen as the rotation about the y-axis of the function Y=(x^2)/9 on the interval 0≤x≤8. Water weights 62.4 lb/ cubic feet.
It is necessary to compute in the volume of the rotated region while taking into account that each cross section piece is raised up by a height of h = 4 - y. Scale the results by 62.4 lb/ft3 as well.
The given parabolic region's volume of revolution about the y-axis is a parabolic cylinder. This solid is revolved, and it has circular disks as its cross section. The differential volume of one such disk situated at a differential height y above the x-axis must be determined. The weight of water in this volume can then be calculated by multiplying this volume by the density of water. The depth of this volume is then determined from the tank's top surface. Determine how much differential work is needed to lift this water layer to the top surface. Integrate this differential work now to calculate the overall effort needed to empty the tank.
Rotating the curve x=3y about the y-axis creates the region. Keep in mind that 62.5 = (125 / 2) As a result, using the disk method,
[tex]\int_{0}^{3} \left(\frac{125}{2} \pi (4-y) (3\sqrt{y})^2\right)\, dy \\ &=\int_{0}^{3} \left(\frac{1125}{2} \pi (4-y) y\right)\, dy &\text[/tex]
Integrate in relation to:
[tex]y\text{]} \\ &=\left(-\frac{1125}{2} \pi \left(\frac{y^3}{3}-2 y^2\right)\right)\bigg|_{0}^{3} \\ &=\frac{10125 \pi }{2} \\ &\approx 16045.7 \end{align*} \)[/tex]
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Fully simplify.
16x^5y^4(14x^2y^2)
16x
5
y
4
(14x
2
y
2
)
The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.
What is the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² )?It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.
Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).
As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;
The expression can be simplified as follows using the laws of indices as follows;
[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]
It follows from the quotient of exponents law of indices; we have that;
[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]
= 8x³ y² / 7
Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.
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Suppose that you wish to obtain a confidence interval for a population mean. Under the
conditions described below, should you use the z-interval procedure, the t-interval
procedure, or neither?
- The population standard deviation is unknown.
The data contain outliers.
- The sample size is small.
To obtain a confidence interval for a population mean under the t-interval procedure.
What is meant by population mean?The major trend discovered from the sample data is the sample mean. The population is used to create the sample data. In statistics, the sample mean is denoted by the letter "x." The population mean, on the other hand, is the average value of all observations within a certain population or group.The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign stands for the population mean.The population is the total number of people residing in a certain area. Estimating the population enables us to determine how many beings there are and how best to respond.To learn more about population mean refer to:
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help meeeeeeeeeee pleaseee
The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.
What is an algebraic expression?An algebraic expression is formed by variables, constants, and arithmetic operations.An algebraic expression provides the relation between the input and output variables i.e., x and f(x) respectively.Calculation:It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,
C(x) = 270 ln(x+1) + 1900
The average intake of calories consumed per day is given by C(x) = 2200
Here x is the number of acres of land. Then, the required number of acres of land is
C(x) = 270 ln(x+1) + 1900
⇒ 2200 = 270 ln(x+1) + 1900
⇒ 270 ln(x+1) = 2200 - 1900
⇒ 270 ln(x+1) = 300
⇒ ln(x+1) = 300/270 = 10/9
Applying base 'e' on both sides, we get
⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]
⇒ x+1 = 3.0377
⇒ x = 3.0377 - 1 = 2.0377
When rounding the final answer to the nearest tenths, we get x = 2 acres.
When rounding the final answer to the nearest thousand, we get x = 2.038 acres.
Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.
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If the value of a commodity decreases at a monthly rate of 0.8%, by what percentage does it decrease in a year?
If the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that, the value of a commodity decreases at a monthly rate of 0.8%,
We have to find by what percentage the rate decreases in a year.
If there are 12 months in a year, the rate decrease in a year obtained as,
=0.8 × 12
=9.6 %
Thus, if the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
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In a year, the value of commodity decreases by 9.6%, at the monthly rate of 8%.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Monthly decrease rate of change in commodity = 0.8 %,
To find the percentage decrease in year,
Use ratio property,
In 1 month, commodity decreases 0.8%
In 12 months commodity decreases = 12 x 0.8 = 9.6 %
The value of commodity will decrease by 9.6% in a year.
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What is 10% of 20? Hint: We can think of 10% as a common fraction. HELP ME PLS
Answer:
Step-by-step explanation:
10% of 20 is equal to 2. To calculate 10% of a number, we can multiply the number by 10% expressed as a decimal, which is 0.1. For example, 10% of 20 is equal to 20 * 0.1 = 2.
Alternatively, we can calculate 10% of a number by dividing the number by 100 and then multiplying the result by 10. For example, 10% of 20 is equal to (20 / 100) * 10 = 2.
Use the formula A=P[1+r/n]nt to solve the compound interest problem.
Find how long it takes for $900 to double if it is invested at 6% interest comp
The money will double in value in approximately $\square$ years.
(Do not round until the final answer. Then round to the nearest tenth as need.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as need
It will take around 0.24 months for the invested money to get doubled.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The formula to calculate the amount is as follows,
A = P[tex](1 + r)^{(nt)}[/tex]
Substitute all the corresponding values in the above expression to obtain,
A = P[tex](1 + 6/100)^{nt}[/tex]
1800 = 900[tex](1 + 6/100)^{nt}\\[/tex]
=> [tex](1 + 6/100)^{nt}[/tex] = 1800/900
=> [tex]1.06^{nt}[/tex] = 2
Since, there are 12 months in one year, n = 12.
[tex]1.06^{12t}[/tex] = 2
=> 12t = log(2) ÷ log(1.06)
=> 12t = 0.275
=> t = 0.02
Which is equivalent to 12 × 0.02 = 0.24 months.
Hence, it will take 0.24 months to double the invested money.
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Which point would not be a solution to the system of linear inequalities shown
below?
y > 2x - 2
O (-5,3)
O (-5, 10)
O (-10,8)
O(-10,-9)
Y >
6
5+8
The solution to the linear inequality y > 2x - 2 and y > 5x + 8 is -3.33 and -8.67
Graph of Linear InequalityThe graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
Using a graphing calculator, the solution of y > 2x - 2 and y > 5x + 8 is
This will give us a value of x is -3.33 and y is -8.67
Kindly find attached graph below
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Which of the following algebraic steps will solve the equation -6t = 2/3
Answer:
t= 0.1 or t= 1/9Step-by-step explanation:
divide each term in 6t = 2/3 by 6,6t/6 = 2/3/6
simplify the left sidecancel out the common factor of 6.6t/6 = t while were left with 2/3 /6
divide t by 1.t = 2/3 / 6.
simplify the left sidemultiply the numerator by the reciprocal of the denominator.t = 2/3 x 1/6
cancel the common factor of 2.Factor 2 out of 6.t = 2/3 x 1/2(3)
Cancel the common factor which is 2,and then rewrite the expression.t = 1/3 x 1/3
Multiply the expression like this:t = 1 / 3 x 3
multiply 3 by 3 to get...t=1/9
decimal form: 0.1
help me please thank youuuu
Answer:
B. g(x) = -x² - 2
Step-by-step explanation:
f(x) = x²
g(x) = -x²
The graph now has a maximum of (0, 0) and is curving downwards. To make the graph go down by -2 subtract 2 from the equation
g(x) = -x² - 2
I hope this helps!
what is the value of the logarithm? round answer to nearest ten thousand IN (175)
The logarithm value for the expression → ln(175) is equivalent to 5.17.
What is logarithm?Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -
[tex]$\log_{b}({b^x})=x[/tex]
Given is the following logarithmic expression, as follows -
ln(175)
We have the expression as -
ln(175)
Solving the expression further, we get -
ln(25 x 7)
ln(25) + ln(7) {Property : log(A x B) = log(A) + log(B)}
ln(5)² + ln(7)
2 x ln(5) + ln(7)
2 x 1.61 + 1.94
5.17
Therefore, the logarithm of the number 175 is equivalent to 5.17.
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11. Lourdes is making a square pattern. Each
side is 7 centimeters. Is the perimeter of
the pattern the same as the area of the
pattern?
The perimeter of the pattern the same as the area of the pattern is 20 cm.
Perimeter of a square is the total length (distance) of the boundary of a square
In a square all the sides are of equal lengths.
Hence, perimeter of a square = 4l
We know that all the sides of a square are equal.
Perimeter of a Square
Perimeter of the square ABCD
= AB + BC + CD + AD
= 2 cm + 2 cm + 2 cm + 2 cm
= (2 × 4) cm
= 8 cm
Perimeter of a square is 4 times of s side.
Perimeter of a square = 4 × length of a side..
1st method:
Perimeter of a square PQRS
= side + side + side + side
= 5 cm + 5 cm + 5 cm + 5 cm
= 20 cm:
2nd method
Perimeter of a square = 4 times side
= 4 × side
= 4 × 5 cm
= 20 cm
Therefore, Perimeter of a square = 4 × length of one side.
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Determine the slope of the line represented by the equation: 1 x − 3 y = − 14
Answer:
The slope is 1/3
Step-by-step explanation:
The equation is equivalent to
x - 3y = -14
x = 3y - 14
x + 14 = 3y
(x + 14)/3 = y
The population of Orange County is represented by the function f(x)=87,000(0.9), where x is the number of years since 2010 The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year
How do the populations of these counties compare in 2015?
Drag a value or word to the boxes to correctly complete the statements
Question 1
In 2015, [tex]x=5[/tex]. [tex]P(5)=87000(0.9)^5 \approx \boxed{51373}[/tex]
Question 2
[tex]78000(1-0.08)^5 \approx \boxed{51408}[/tex]
Question 3
[tex]51408 > 51373[/tex], so Greene county was more populous.
What is a formula for the nth term of the given sequence 16,8,4
That is a geometric progression.
the common ratio is 1/2.(t2÷t1)
nth term= ar^n-1
16×1/2=8
tn=8^n-1
i need help especially for #4
The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively
How to determine the values of x in the triangle?
To solve this problem, we need some angle geometry knowledge:
For the first triangle:
x = 4 (All sides in a rhombus are identical)
For the second triangle:
The missing side is also equal to x (base of isosceles triangles)
x + x + 40 = 180 (sum of angles in triangle)
2x+40 = 180
2x = 180-40
2x = 140
x = 70°
For the third triangle:
x = 76° (base of isosceles triangles are equal)
For the fourth triangle:
Check the image attached for labeling
m = 180-110 = 70° (angle on a straight line)
y = 70° (base of isosceles triangles are equal)
z = 180-70-70 = 40°
t = 90-40 = 50°
L = 50° (base of isosceles triangles are equal)
Thus, x = 180-50-50 = 80°
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A
07
06
O15
09
B
15 m
2x+3
Given that
ABCD is a parallelogram, find the x.
Given that ABCD is a paralle log ram, find the value of x.
D
C
Answer:
x = 6
Step-by-step explanation:
the opposite sides of a parallelogram are congruent , then
2x + 3 = 15 ( subtract 3 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
-3≤2x-1≤5
Step by step
Answer:
-1≤x≤3
Step-by-step explanation:
-3≤2x-1≤5
add 1 to all sides
-2≤2x≤6
divide all sides by 2
-1≤x≤3
math 1 , answer plssssssss
a balance of $11,670. The bank statement indicated a balance of $13,640 on April 30. Comparing the bank statement and the accompanying canceled checks and memos with the records revealed the following reconciling items:
Checks outstanding totaled $4,910.
A deposit of $5,120, representing receipts of April 30, had been made too late to appear on the bank statement.
The bank collected $2,660 on a $2,520 note, including interest of $140.
A check for $770 returned with the statement had been incorrectly recorded by Lakeshore Gelato as $700. The check was for the payment of an obligation to Sprinkles Supply Co. for the purchase on account.
A check drawn for $40 had been erroneously charged by the bank as $400.
Bank service charges for April amounted to $50.
The balance of the bank reconciliation statement is $3,640
How to prepare a bank reconciliation statement?A bank reconciliation is is defined as the process by which the bank account balance in an entity’s books of account is reconciled to the balance reported by the financial institution in the most recent bank statement
The bank Reconciliation statement appears thus
Bank reconciliation statement
$ $
Cash book balance 11,670
Add unpresented cheque 5,120
Over cast (400-40) 360
17,150
Cheque not credited 5120
Less Uncredited cheque 4910
Notes collected 2660
Dishonored cheque 770
Bank charges 50
bank interest 140
13500
Balance as per bank statement 3640
In conclusion the balance of the Statement is $3640
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What is the greatest common factor between 24, 56, and 72? 01 2 5 08
Answer: The common factor is 8
Step-by-step explanation:
Each is a variant of the number 8 and 2 but it called for the greater common factor so 8
A number is such that it is as much greater than 112 as it is less than it Find the number.
Answer:: 111
Step-by-step explanation:
111 is greater than 112 I hope it helps!!!!
Z is the midpoint of XY. Complete the proof that ∠Y ≅ ∠X .
Statement Reason
Z is the midpoint of overline XY Given
WZ ⊥ XY Definition of perpendicular lines
angle WZX ≅ angle WZY Definition of isosceles triangle
line XA ≅ line YZ Definition of bisection
line WZ ≅ line WZ Reflexive Property of Congruence
Δ WXZ ≅ Δ WYZ Side - Angle - Side (SAS)
< Y ≅ < X Corresponding Parts of Congruent Triangles are Congruent
What is congruency in triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent
The SAS have it that the two triangles being compared should have their two sides and the included angle equal
Using Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠Y ≅ ∠X .
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Can you help me fast please