The value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is defined as a function.
Given functions
f(x) = -5x − 9
g(x) = 8x − 4
we have to determine which equation defines function h
f(x) = -5x − 9
g(x) = 8x – 4
(f x g) (x) = (-5x –9)(8x – 4)
(f x g) (x) = -40x2 + 20x – 72x + 36
(f x g) (x) = -40x2 – 52x + 18
Therefore the value of h(x) = -40x2 – 52x + 18. Option (b) is correct.
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A regular pentagon with sides of 7 cm. What is the area of this pentagon?
The area of the regular pentagon with sides of 7 cm is 84.30 cm²
How to calculate the area of a regular pentagon?
The area of a regular pentagon can be determined if the side length (s) is given. The formula used for calculating the area of a regular pentagon is:
[tex]A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}[/tex]
Given: side length (s) = 7 cm
Area (A) = 1/4×√( 5(5+2√5) ×7² = 84.30 cm²
Therefore, the area of the pentagon is 84.30 cm²
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Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. the ordered pair (2, - 2) y = -x - 2.
The equation of the parallel line is y = -x
How to determine the line equation?The equation is given as
y = -x - 2
The point is also given as
point = (2, -2)
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = -1
This means that the slope of y = -x - 2 is -1
The slopes of parallel lines are equal
This means that the slope of the other line is -1
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -1
(x₁, y₁) = (2, -2)
So, we have
y = -1(x - 2) - 2
Open the brackets and evaluate
y = -x
Hence, the parallel line has an equation of y = -x
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Please I need help please
Show that a quadrilateral with vertices (0,0), (5,0), (8,4) and (3,4) is a rhombus using distance
formula.
The quadrilateral with vertices (0,0), (5,0), (8,4), and (3,4) is a rhombus.
What is a rhombus?
A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
What is a distance formula?
D = √(x₂ - x₁)² + (y₂ - y₁)²
Here, we have
Given vertices A(0,0), B(5,0), C(8,4), and D(3,4)
By applying the distance formula, we get
AB = √(5 - 0)² + (0 - 0)² = 5
BC = √(8 - 5)² + (4 - 0)² = 5
CD = √(3 - 8)² + (4 - 4)² = 5
Hence, it's all sides are equal so it is a rhombus.
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8.26 cats, part i. the following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). the coefficients are estimated using a dataset of 144 domestic cats
The correlation coefficient is the square root of the coefficient of determination.
A. The linear model is y' = -0.357+4.034x
Where y' is the predicted heart weight and X is the body weight
B. The intercept of -0.357 is actually showing the non existence of the heart weight when the body weight is absent, ie. When X=0
C. The slope indicates that with each unit increase in the body weight x, the heart weight y increases 4.034 times.
D. R^2 = 64.66% indicates that 64.66% variation in the dependent variable that is explained by our model.
E. Given that the coefficient of determination = 0.6466
Thus the correlation coefficient is the square root of the coefficient of determination
Thus, R = √0.6466 = 0.8041
( Since the slope is positive the correlation ought to be positive)
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The question was incomplete. Check below the complete question.
The following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using dataset of 144 domestic cats_ Estimate Std. Error t value Pr(> /tl_ 20 (Intercept _ -0.357 0.692 -0.515 0.607 body wt 4.034 0.250 16.119 0.000 ? 15 1.452 R2 64.66% Radj 64.41% 1 Write out the linear model. [ 10 Interpret the intercept_ Interpret the slope. Interpret R?_ 2.0 Calculate the correlation coefficient 2.5 3.0 3.5 Body weight (kg) 4.0.
The table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
A) Write an equation that models the amount of storage as a function of the number of songs
B) Interpret the slope and t-intercept of the line of fit
pls include work
a) An equation that models the amount of storage as a function of the number of songs is y = -0.005x + 16
b) Slope of the equation is -0.005 and the intercept of the equation is 16
Slope intercept form
Slope intercept form presents the graph of a straight line and is represented in the form of
y = mx + c.
where
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Given,
Here we have the table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
Now, we have to find the following:
a) Equation of the table
b) Slope and intercept.
In order to find the equation, we have to identify the slope an intercept of the table.
So, to find that we have to take two points from the table.
Then the selected points are
(0, 16), (242, 14.8)
By using these point we have to calculate the slope as,
m = (14.8 - 16) / (242 - 0)
m = -1.2/242
m = -0.005
Now, the intercept is calculated by using the point (0, 16) and the slope -0.005, then we get,
16 = -0.005(0) + c
c = 16
Therefore, the equation is y = -0.005x + 16.
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What is the equation of a circle with center (-3, -5) and radius 4?
O A. (x+3)2 + (y + 5)² = 16
O B. (x-3)2 + (y- 5)² = 4
O C. (x+3)2 + (y + 5)² = 4
O D. (x-3)2+(vy- 5)² = 16
The equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.
In the given equation we have to find the equation of circle with center and radius.
The given center is (-3, -5).
Radius = 4
The standard equation of a circle with center and radius.
(x−a)^2+(y−b)^2=r^2
where a and b represent a point of center and r represent a radius.
So a=-3, b=-5 and r=4.
Putting the value in the standard equation.
(x−(-3))^2+(y−(-5))^2=(4)^2
Simplifying
(x+3)^2+(y+5)^2=16
Hence, the equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.
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A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.
The given linear function is [tex]f (h) = - \frac{1}{5} x + 3[/tex]. The graph is attached at the end.
Let the independent variable be x.
It is given in the question:
Value of the function, h at 0 = 3
Thus, h(0) =3
Also, when the independent variable decreases by 5, the dependent variable increases by 1.
So, slope = -[tex]\frac{1}{5}[/tex]
y-intercept = 3
We know the linear equation is-
y = mx + b ... (i)
where y ⇒ linear function
m ⇒ slope of the line
x ⇒ independent variable
b ⇒ y-intercept
Putting the values of each term in equation (i), we get:
[tex]h (x) = - \frac{1}{5} x + 3[/tex]
We can plot this equation in a graph, as attached below.
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The complete question is:
Graph the function with the given description. A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.
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If p + q = 11 and 2p + q = 1 it says that 3p + 2q = 12 but I can't understand how they got to the answer. Please can someone explain? Thank you!
The value of p and q in the equation are -10 and 21 respectively.
How to solve system of equation?The value of p and q will be found in the equation before we can form another equation with p and q.
Therefore,
p + q = 11
2p+ q = 1
using elimination method
p = 1 - 11
p = -10
q = 11 + 10
q = 21
Therefore,
3p + 2q = 12 (let's check if its correct)
3(-10) + 2(21) = -30 + 42 = 12
Therefore, 3p + 2q = 12 is correct.
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What is the argument of (1+i)^4
The fourth power of the complex number 1 + i has an argument of π radians.
How to determine the argument of the power of a complex number
In this problem we find a complex number of the form z = (a + i b)ⁿ, where n is the grade of the power of the complex number, whose expanded form is obtained by the De Moivre's theorem:
(a + i b)ⁿ = rⁿ · (cos nθ + i sin nθ)
Where:
r - Norm of the complex number.θ - Argument of the complex number, in radians.And the norm and the argument of the complex number are, respectively:
Norm
r = √(a² + b²)
Argument
θ = tan⁻¹ (b / a)
First, determine the components of the complex number and its power:
a = b = 1; n = 4
Second, calculate the argument of the complex number:
θ = tan⁻¹ 1
θ = π / 4 rad.
Third, find the argument of the power of the complex number according to De Moivre's theorem:
θ' = 4 · (π / 4)
θ' = π
The argument of the power of the complex number is π radians.
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An object is dropped from a height of 1, 600 feet. The amount of time, in seconds, the object takes to hit the ground can be
Found by solving the equation -16r2+1, 600 = 0. How many seconds will it take to hit the ground?
10?,50?,10 or -10?,100?
The time taken by the object to hit the ground is 10 seconds , the correct option is (a) .
In the question ,
it is given that ,
the object is dropped from the height of 1600 feet ,
So , the height h(t) = 1600
the equation representing the height of the object at time t is ,
h(t) = 16t² + 155
Substituting the height h(t) = 1600
16t² + 155 = 1600
16t² = 1600 - 155
16t² = 1445
t² = 1445/16
t² = 90.31
t = √90.31
t = 9.503
t ≈ 10 seconds
Therefore , The time taken by the object to hit the ground is 10 seconds .
The given question is incomplete , the compete question is
An object is dropped from a height of 1,600 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation 16t² + 155 = h(t) . How many seconds will it take to hit the ground ?
(a) 10
(b) 50
(c) 100
(d) 500
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Write an equation to determine the number of friends (x) at Jack's party.
Answer:
x = 48/3
when Jack got 50 chocolates and has left 2, then Jack gave away 50-2=48 chocolates. When each friend got 3 chocolates, the number of friends x is equal to 48 divided by 3.
What is an equation of the line that passes through the point (-4,-7) and is parallel to the line 3x-y=4.
The admission fee to a museum is $12.50 per nonsenior adult, $8 per child, and $6.50 per senior citizen. A tour group consists of m nonsenior adults, (5/4m +6) children, and 8n senior citizens. What is the total admission fee of the group
The total admission fee of the group is 22.5m + 51n + 48.
How to calculate the total cost?Given that the admission fee to a museum is $12.50 per nonsenior adult, $8 per child, and $6.50 per senior citizen.
Also, it was further stated that the tour group consists of m nonsenior adults, (5/4m +6) children, and 8n senior citizens.
The total amount for the fees will be:
= Non senior adults + Children + Senior citizen
= 12.5(m) + 8(1.25m + 6) + 6.50(8n)
= 12.5m + 10m + 48 + 51n
= 22.5m + 48 + 51n
= 22.5m + 51n + 48
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A salesman bought a computer from a manufacturer. The salesman then sold the computer for $15600 making a loss of 25%. What amount did the salesman pay the manufacturer for the computer?
The amount that the salesman pay the manufacturer for the computer is $20800.
How to calculate the value?From the information, the salesman sold the computer for $15600 making a loss of 25%.
The amount that the salesman pay the manufacturer for the computer will be illustrated thus:
Since a 25% loss was made, the cost price will be: = 100% + 25% = 75%
Therefore, the cost price will be:
= Sales price / 125%
= $15600 / 0.75
= $20800
The amount is $20800.
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note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the expression in factored form? 9x^2-4
Answer: (3x-2)(3x+2)
I knew the answer it was just hard to explain all of it. Sorry if this doesn't help
Is 8/20 equal to 4/5
Answer: no
Step-by-step explanation:
8 and 20 can both be divided by 4
8 divided by 4 = 2
and 20 divided by 4 = 5
based on this, we can tell that 8/20 is not equivalent to 4/ but rather 2/5
I hope that helps
Answer:
No
Step-by-step explanation:
Because if you divide the numerator by something you have to do the same for the denominator. This means the if you do 8÷2 to get 4 then you do 20÷2 you get. 8/20=4/10/2/5
A ramp is elevated to a height of 7 inches from the base. The horizontal distance between the lower end of the ramp and the base is 19 inches, as shown in the figure. What is the length of the ramp?
The length of the ramp is [tex]\sqrt{410}[/tex] inches.
According to the question,
We have the following information:
A ramp is elevated to a height of 7 inches from the base. The horizontal distance between the lower end of the ramp and the base is 19 inches.
So, it will be a right-angled triangle.
Now, we can use Pythagoras theorem to find the length of the ramp which is the hypotenuse of the triangle.
Let's denote the length of the ramp to be l, elevated height to be p and horizontal distance to be b.
[tex]l^{2} =p^{2} +b^{2}[/tex]
[tex]l^{2} =7^{2} +19^{2}[/tex]
[tex]l^{2}[/tex] = 49+361
[tex]l^{2}[/tex] = 410
l = [tex]\sqrt{410}[/tex] inches
Hence, the length of the ramp is [tex]\sqrt{410}[/tex] inches.
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What is the equation of the function
The equation of line will be given as y = 3x + 24
Given,
The graph of a linear function passes through the points (4, 24) and (6, 30).
The equation of the line will be given as:-
y - y₁ = m ( x - x₁)
Slope m will be calculated as:-
m = (y₂ - y₁) / (x₂ - x₁) = (30 - 24) / (6 - 4) = 6/2 = 3
The equation will be:-
y - 24 = 3 ( x - 4 )
y = 3x - 12 + 24
y = 3x + 24
Therefore the equation of the line will be given as y = 3x + 24.
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Each time that Daniel runs an obstacle course, he can run it 2 seconds faster than the last time.
He ran the course in 57 seconds the first time. How fast will he run the course the seventh time?
OA. 43 seconds
B. 45 seconds
O C. 47 seconds
OD. 55 seconds
alex and ben go to a cafe with some friends.
alex buys 4 cups of coffee and 3 cups of tea. he paid a total of £6.95.
Ben buys 5 cups of coffee and 2 cups of tea. He pays a total of £7.20.
work out the total cost of each cup of coffee in the cost of each cup of tea
Answer:
Step-by-step explanation:
Assume the cost for a cup of coffee is x and the cost for a cup of tea is y.
For Alex: 4x+3y=6.95
For Ben 5x+2y=7.20
Then multiply Alex's cost by 2 and Ben's by 3 to cancel y.
8x+6y=13.90
15x+6y=21.60
Equation 2 minus equation 1 would be
15x+6y-(8x+6y)=15x+6y-8x-6y=7x
21.60-13.90=7.70
7x=7.70
Then x=1.10 and plugging it one of the equations,
y= 0.85
A cup of coffee costs 1.10 pounds and A cup of tea is 0.85 pounds
:)
How many angles are formed by the intersection of the diagonals
Answer:
[tex]4 \alpha ngles[/tex]
4 angles
hope it help!
have a nice night
alexander has 418 songs on his MP3 player. he divides the songs into 11 equal groups. About how many songs are in each group. (round the numbers)
Answer:
38 songs in each group.
Step-by-step explanation:
Alexander has 418 songs on his MP3 player. he divides the songs into 11 equal groups. About how many songs are in each group. (round the numbers)
418/11 = 38 songs in each group.
What’s the equation of the function?
Hi again! The equation to the function would be..
y = 1/2x + 1 (assuming that the initial value is one)
the goal of the least-squares regression is to compute a line that
Answer: you did not put in the full equation but i got this right out of the box.
ˉx 28
r 0.82
Solve it find the slope!
t
f(t) = t - 8
h(t) = −2t
f(h(-5)) =
⇒Let us first find the expression of f(h(t))
⇒It means in the expression of f in the place of t you will plug in the value of what h is equal to.
[tex]f(h(t))=(-2t)-8\\f(h(t))=-2t-8[/tex]
Now f(h(-5)) means in the place of t you will plug in -5 and simplify.
[tex]f(h(-5))=-2(-5)-8\\\\f(h(-5))=10-8\\f(h(-5))=2[/tex]
write a coordinate rule for the composition.blue quadrilateral w x y z and green quadrilateral s t u v are graphed on a coordinate plane. quadrilateral w x y z has vertex w at ordered pair negative 1 comma negative 2, vertex x at ordered pair negative 2 comma 0, vertex y at ordered pair 1 comma 2, and vertex z at ordered pair 1 comma negative 1. quadrilateral s t u v has vertex s at ordered pair negative 2 comma negative 4, vertex t at ordered pair negative 2 comma 2, vertex u at ordered pair 2 comma 4 and vertex v at ordered pair 4 comma 0.$\left(x,\ y\right)\rightarrow$ ( , )skip to navigation
Coordinate rule for the composition is w(-1,-2) → s(-1-1,-2-4) → s(-2,-4) , x(-2,0) → t(-2+0,0+2) → t(-2,2), y(1,2) → u(1+1,2+2) → u(2,4) , z(1,-1) → v(1+3,-1+1) → v(4,0).
Given:
w x y x has vertices w(-1,-2) , x(-2,0), y(1,2) and z(1,-1).
s t u v has vertices s(-2,-4) , t(-2,2) , u(2,4) and v(4,0).
The coordinate rule for transformation is:
w(-1,-2) → s(-1-1,-2-4) → s(-2,-4)
x(-2,0) → t(-2+0,0+2) → t(-2,2)
y(1,2) → u(1+1,2+2) → u(2,4)
z(1,-1) → v(1+3,-1+1) → v(4,0)
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If you can help me that would be great
Answer:
x - 6 = -45y = -5Step-by-step explanation:
For the first one, find the value of x:
[tex]3x-8=-2\\3x=8-2=6\\x=2[/tex]
Then, use the value of x to find the answer:
[tex]x-6=2-6=-4[/tex]For the second one, find the value of y:
[tex]-2(3y+5)=-4\\-6y-10=-4\\-6y=10-4=6\\y=-1[/tex]
Then, use the value of y to find the answer:
[tex]5y=5(-1)=-5[/tex]
Rewrite the value of each expression without using absolute value notation
|2b| where b<0
The rewritten form of the given expression such that it is without absolute value notation is; 2b.
What is the rewritten form of the given expression?It follows from the task content that the rewritten form of the given expression; | 2b | is to be determined.
On this note, since it is given that the variable b is less than zero; i.e b < 0.
It follows that the expression evaluation of 2b yields a negative number.
However, the rewritten form of the expression without the absolute value notation since the value of b is unknown still remains; 2b.
Therefore, the required rewritten form is; 2b.
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