A) The vertex (h, k)=(9, 0) if p(x)=[x-9]
B) The vertex (h, k)=(0, 9) if q(x)= [x]+9
What is meant by a function?The earliest known treatment of the idea of function can be found in the writings of the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally merely a simplified illustration of the relationship between two varying quantities. The position of a planet is just one example of how time is used. The concept was historically developed towards the end of the 17th century with infinitesimal calculus, and the functions that were taken into consideration up until the 19th century. The concept of a function was formalised in terms of set theory at the end of the 19th century, greatly extending its range of applications.
Given,
A) p(x)=[x-9]
We have to compare with f(x)=a|x-h|+k
Therefore, the vertex (h, k)=(9, 0)
B) Given,
q(x)= [x]+9
We have to compare with the above equation we get,
The vertex (h, k)=(0, 9)
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Mugs can be packed with up to 6 mugs in each box how many boxes are needed to pack 1528
The function f(x) = -x + 2 can be formed by
shifting the function y = -2/3x in which way?
A. vertical shift up 2
B. reflection over the x-axis
C. vertical shift down 2
D. horizontal shift to the left 2
Please Show the Work & thank u
Answer:
A) vertical shift up 2------------------------------
The difference of the functions is:
f(x) - y = - 2/3x + 2 - (- 2/3x) = 2The difference between functions is positive, therefore it is a vertical shift up by 2 units.
Choose the slope-intercept form of 3x + 2y = 5. y =
Answer: [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Given: [tex]3x + 2y = 5[/tex]
We are needed to find the slope-intercept form.
We know that the slope-intercept form of an equation is given by
[tex]y = mc + c[/tex]
[tex]3x + 2y = 5[/tex]
[tex]2y = 5 -3x[/tex]
[tex]2y = -3x + 5[/tex]
[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]
What is the distance between the points (-2,3) and (5, -1)?
Answer:
√65
Step-by-step explanation:
Compute the Euclidean distance between the following points:
p_1 = (-2, 3) and p_2 = (5, -1)
The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:
sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)
Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):
= sqrt((-2 - 5)^2 + (--1 + 3)^2)
(-1)^2 = 1:
= sqrt((-2 - 5)^2 + (1 + 3)^2)
-2 - 5 = -(2 + 5):
= sqrt((-(2 + 5))^2 + (3 + 1)^2)
2 + 5 = 7:
= sqrt((-7)^2 + (3 + 1)^2)
Multiply each exponent in -7 by 2:
= sqrt((-1)^2×7^2 + (3 + 1)^2)
7^2 = 49:
= sqrt((-1)^2×49 + (3 + 1)^2)
(-1)^2 = 1:
= sqrt(49 + (3 + 1)^2)
3 + 1 = 4:
= sqrt(49 + 4^2)
4^2 = 16:
= sqrt(49 + 16)
| 1 |
| 4 | 9
+ | 1 | 6
| 6 | 5:
Answer: √65
Find a formula for the exponential function passing through the points(-1,4/5) and (1 , 20)
y=
The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
How to derive the exponential function containing two given points
In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:
y = A · [tex]e^{B\cdot x}[/tex]
Where:
x - Independent variable.y - Dependent variable. A, B - Constants.If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:
4 / 5 = A · [tex]e^{-B}[/tex]
20 = A · [tex]e^{B}[/tex]
If we divide the latter expression by the former, then:
25 = [tex]e^{2\cdot B}[/tex]
㏑ 25 = 2 · B
B = (1 / 2) · ㏑ 25
B ≈ 1.609
And the value of A is:
A = 20 / [tex]e^{1.609}[/tex]
A ≈ 4.002
The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
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Suppose you want to have $800,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
b) How much interest will you earn?
$1,556.72 is required to deposit in the account each month.
72% of interest is earned.
a)
It is a classic Ordinary Annuity saving plan. The general formula is
FV = P((1+r)^n-1)/r)--------(1)
where
FV is the future value of the account.
P is the monthly payment (deposit).
r is the monthly percentage yield presented as a decimal.
n is the number of deposits (= the number of years multiplied by 12, in this case).
From this formula, you get the monthly payment:
P=FV(r/(1+r)^-1)----------(2)
Under the given conditions,
FV = $800,000
r = 0.04/12
n = 25*12.
So, according to formula (2), the monthly payment is
P=800000(0.04/12(1+0.04/12)^25*12-1)
P=800000(0.003/1.713)
P=$1.556.72
Note that of the projected $800,000 the total you deposit will be only 25*12 times $1.556.72 i.e. about 25*12*1.556.72 = 467016 dollars.
The rest is what the account will earn/accumulate over the 25 years.
b)
You will earn:
(8000000-467016/467016)*100
72% of interest is earned.
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A transversal runs across two parallel lines, forming two angles. One measures 80 degrees. How large is the other angle
Answer:
100°
Step-by-step explanation:
180°- 80°= 100°
The angles are supplementary, meaning that they have to add up to 180.
Hope this helps!!! :)
Find the value of x. Leave your answer in simplest radical form.
The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]
Explain Pythagoras theorem.
The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.
The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.
Using Pythagoras theorem in both the triangles,
Find the hypotenuse in above triangle
[tex]h^2=P^2+B^2[/tex]
[tex]h^2=4+4=8[/tex]
h = [tex]2\sqrt{2}[/tex]
Now, using Pythagoras theorem in below triangle,
[tex]h^2=P^2+B^2[/tex]
[tex]5^2 = x^{2} + 8[/tex]
25 = [tex]x^{2}[/tex] + 8
[tex]x^{2}[/tex] = 25 - 8 = 17
x = [tex]\sqrt{17}[/tex]
Therefore, x = [tex]\sqrt{17}[/tex]
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A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
The number of liters in the tank after 109 seconds is 60.5 liters.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
2.5 liters = 1 minute
2.5 liters = 60 seconds
Multiply 109/60 on both sides.
109/60 x 2.5 liters = 109 seconds
4.5 liters = 109 seconds
This means,
4.5 liters is drained after 109 seconds
Now,
The liters of water in the tank.
= 65 - 4.5
= 60.5 liters
Thus,
There are 60.5 liters in the tank.
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Nicholas is typing a book report at an average speed of 40 words per minute. Which equation could Nicholas use to find t, the amount of time in minutes he will spend typing, if his report has [w] words?
A. t = 40w
B. w = 40t
C. t = w + 40
D. w = t + 40
Choose the best answer. For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3
\times
×
weight. Which of the following is not correct? (a) The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length. (b) The predicted tail length of a mouse that weighs 38 grams is 134 millimeters. (c) By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive. (d) If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3. (e) One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is -7.
The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.
What is Regression analysis ?
Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".
Given, tail length = (3 × weight) + 20
(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.
(b) If weight is 38 gm, then
tail length = 38 × 3 + 20
= 114 + 20 = 134mm.
So, the statement is correct.
(c) We've tail length = (3 × weight) + 20
we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.
So, the given statement is correct.
(d) The slope is 3 when the tail length is being measured in millimeters.
Now, If we measure it in centimeter = 3/10 = 0.3 cm
∵ 1 mm = 1/10 cm.
So, the given statement is correct.
(e) when a mouse has weight of 29 grams and tail length of 100 mm.
When the weight is 29 grams, it should have tail length as :
tail length = 29 × 3 + 20
= 107 mm.
but, tail length is given as 100 mm.
So, the residual for the mouse is -7 i.e. (100 - 107)
Hence, The given statement is correct.
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How many reflection symmetries does a twelve-pointed star have? How many rotational symmetries does a twelve-pointed star have?
Answer: 12 symmetries
Step-by-step explanation:
just draw the lines on the star.
5 and square root of 4
Answer:
7-------------------
It is assumed you need to add 5 and square root of 4:
[tex]5+\sqrt{4} =5+\sqrt{2^2} =5+2=7[/tex]Please help ASAP I've been stuck on this question
The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.
What is coordinate of a point?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.
The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).
The scale factor is k = 3.
The x-coordinate of A is 1.
The y-coordinate of A is 2.
The x-coordinate of B is 3.
The y-coordinate of B is -1.
The x-coordinate of C is -4.
The y-coordinate of C is 2.
To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.
The x-coordinate of A' is 1 × 3 = 3.
The y-coordinate of A' is 2 × 3 = 6.
The x-coordinate of B' is 3 × 3= 9.
The y-coordinate of B' is -1 × 3 = -3.
The x-coordinate of C' is -4 × 3 = -12.
The y-coordinate of C' is 2 × 3 = 6.
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You have $108,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.0 percent. Stock X has an expected return of 12.6 percent and a beta of 1.15, and Stock Y has an expected return of 9.8 percent and a beta of .86.
The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Data provided in the question:
Total amount to be invested = $140000
Stock X Y
Expected return 14% 10%
Beta 1.42 1.18
Expected return of portfolio = 17.6%
Now,
let the weight invested n stock X be W
therefore,
Weight of Stock Y = 1 - W
thus,
( W × 14% ) + (1 - w) × 10% = 17.6 %
14W + 10% - 10W = 17.6%
4W = 7.6
W = 1.9
Therefore,
weight of Y = 1 - 1.9 = -0.9
Amount investment in Sock Y = Total amount to be invested × Weight
= 140,000 × ( - 0.9 )
= - $126,000 i.e short Y
Beta of portfolio = ∑ (Beta × Weight)
Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]
Beta of portfolio= 2.698 - 1.062
Beta of portfolio= 1.636
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HELP PLEASEEE
A party rental company has chairs and tables to rent. There were two customers who rented both chairs and tables last week. The table below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.
By setting up the equation, we get the system of linear equations are
9x + 7y = 77
3x + 5y = 49
solving these equation Cost to rent a chair = $1.75
cost to rent a table = $8.75
What is system of linear equation?A system of linear equations is a collection of one or more linear equations involving the same variables.
What are the method to solve system of linear equations?There are several methods for solving systems of linear equations, including:
Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.
Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.
Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.
etc.
To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.
First, solve the first equation for y:
9x + 7y = 77
7y = -9x + 77
y = (-9/7)x + 11
Now substitute this expression for y into the second equation:
3x + 5((-9/7)x + 5(11) = 49
3x - (45/7)x + 55 = 49
solving for x :
x = 1.75
Now substitute this value for x back into the first equation to find y:
y = 8.75
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Solve 5(2m + 1) − 3m = −16.
m equals negative 16 over 30
m equals negative 21 over 30
m = −3
m = −0.33
Answer:
m= -3
Step-by-step explanation:
5(2m+1)-3m=-16
5(2m)+5(1)-3m= -16
10m+5-3m= -16
7m+5= -16
-5. -5
7m= -21
/7. /7
m= -3
Hopes this helps please mark brainliest
And :-3
process:
5(2m + 1) - 3m = - 16
10m+5-3m=-16
7m=-16-5
m=-21/7
m=-3
Write a function describing the relationship of the given variables.
A, varies directly with, r, and when r = 4, A = 8
A=______
The relation between a and r is 2r
How to write a function describing the relationship of the given variables?According to the given information
a varies directly with r
a = 8
r = 4
a is directly proportional to r
a ∝ r
a = k r
where k is constant of proportionality
k = [tex]\frac{a}{r}[/tex]
k = [tex]\frac{8}{4}[/tex]
k = 2
so,
a = k r
putting the value of k in the above equation
we get
a = 2r
The relation between a and r is 2r
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Solve 3x + 2 = 5. hurry pls
Answer: 1
Let's solve your equation step-by-step.
3x+2=5
Step 1: Subtract 2 from both sides.
3x+2−2=5−2
3x=3
Step 2: Divide both sides by 3.
3x/3 = 3/3
(3x divided by 3 cancels the 3 in 3x making it just x)
x=1
Write an explicit formula for a_n, the n^{\text{th}}n th term of the sequence 6, -24, 96, ...
The explicit formula for the geometric sequence 6, -24, 96, ... is
6 * -4^(n - 1)How to find the formula for the geometric sequenceEvery term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio
The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.
For the given sequence the first term is a = 6
The common ratio is solved as follows
a * r = second term
6 * r = -24
r = -24/6
r = -4
check
-24 * -4 = 96 correct
The nth term of a geometric sequence
= ar^(n - 1)
= a * -4^(n - 1)
checking for the third term
= a * -4^(n - 1)
= 6 * -4^(3 - 1)
= 6 * -4^(2)
= 6 * 16
= 96
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Write this number in scientific notation.
.0000149
Answer: 1.49 x [tex]10^{-5}[/tex]
Step-by-step explanation:
If η. is an even positive integer, the double factorial notation represents the product of all the even integers from to η. For example 8! = 2 . 4. 6. 8 . What is the units digit of the following sum?
a. 0
b. 2
c. 4
d. 6
e. 8
The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.
What is meant by the term factorials?Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.
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To test m for an x distribution that is mound-shaped using
sample size n 30, how do you decide whether to use the normal or the
Student’s t distribution?
To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:
Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.
It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.
What is t distribution?For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.
Hence t-distribution is suitable when the variance which is standard deviation squared is unknown
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Graph this line y+4=1/4(x+10)
Answer:
goes from(6,0),(10,1),(14,2) in +ve
Answer to these required:
For what value of x would 3 (3x − 1)− 3 (5x − 3)= − (x + 6)?]
Answer:
x = 12/5
Step-by-step explanation:
3 (3x − 1) − 3 (5x − 3) = − (x + 6)
9x − 3 − 15x + 9 = − x − 6
9x − 15x + x = 3 − 9 − 6
− 5x = − 12
5x = 12
x = 12/5
Answer:
[tex]x=\dfrac{12}{5}[/tex]
Step-by-step explanation:
Given equation:
[tex]3(3x-1)-3(5x-3)=-(x+6)[/tex]
Distribute:
[tex]\implies 3 \cdot 3x + 3 \cdot (-1) - 3 \cdot 5x - 3 \cdot (-3)=-x-6[/tex]
[tex]\implies 9x-3-15x+9=-x-6[/tex]
Collect and combine like terms on the left side of the equation:
[tex]\implies 9x-15x+9-3=-x-6[/tex]
[tex]\implies -6x+6=-x-6[/tex]
Add 6x to both sides:
[tex]\implies -6x+6+6x=-x-6+6x[/tex]
[tex]\implies 6=5x-6[/tex]
Add 6 to both sides:
[tex]\implies 6+6=5x-6+6[/tex]
[tex]\implies 12=5x[/tex]
[tex]\implies 5x=12[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5x}{5}=\dfrac{12}{5}[/tex]
[tex]\implies x=\dfrac{12}{5}[/tex]
At a baseball game, a vender sold a combined total of 246 sodas and hot dogs. The number of hot dogs sold was 34 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
The vendor sold 212 sodas and 34 hot dogs.
Step-by-step explanation:
Subtract 34 from 246 for the number of sodas sold.
If f(x) = 4x - 5 and g(x) = 6 - 3x, what is f (x) + g(x)?
If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
We know f(x) + g(x) = (f + g)(x).
Given, f(x) = 4x - 5 and g(x) = 6 - 3x.
∴ f(x) + g(x) = (4x - 5) + (6 - 3x).
f(x) + g(x) = 4x - 3x - 5 + 6.
f(x) + g(x) = x + 1.
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What is the correct to this answer ???????( answers only)
Answer:
x > 24 goes to the bottom
x < 24 goes to the 3rd slot
x ≤ 24 goes to the 1st slot
x ≥ 24 goes to the 2nd slot
Step-by-step explanation:
Hope this helps.
Aspen incorrectly converted 15/8 to a decimal using long division. Check her work carefully to find the error. Select the digit where she first made a mistake.
The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.
The correct long division is shown below.
This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.