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kompoz [17]
3 years ago
11

Please help me solve this thanks

Mathematics
1 answer:
WINSTONCH [101]3 years ago
8 0

Answer:

A

Step-by-step explanation:

let r represent rate and d distance.

Given that r varies directly as d² then the equation relating them is

r = kd² ← k is the constant of variation

To find k use the condition r = 4 when d = 15, then

4 = k × 15² = 225k ( divide both sides by 225 )

k = \frac{4}{225}

r = \frac{4}{225} d²  ← equation of variation

When r = 9, then

9 = \frac{4}{225}d² ( multiply both sides by 225 )

2025 = 4d² ( divide both sides by 4 )

506.25 = d² ( take the square root of both sides )

d = \sqrt{506.25} = 22.5 = 22 \frac{1}{2} → A

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8 0
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gizmo_the_mogwai [7]

Answer:

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P (0,5)

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3 0
3 years ago
1. Find the domain of the given function. (1 point)
Vika [28.1K]
1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.
 using a graphical tool    see the attachment  
the answer is C) x ≥ -3, x ≠ 2  
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g(x) = 2 - (x - 7)2
 using a graphical tool     
see the attachment
 the answer is  C) Increasing: x < 7; decreasing: x > 7
3. Perform the requested operation or operations.
f(x) = 4x + 7, g(x) = 3x2
Find (f + g)(x).
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(f + g)(x) = 4x + 7 + 3x^2 
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 f(x)=(x-5)/8    g(x)=8x+5
g(f(x))=8((x-5)/8)+5=x-5+5=x
the answer is  B) g(f(x)) = x   
5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five. 
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let do
g(x)=5x+5...........so
f(x)= 9/( x^1/2)
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6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Original size- >4km*4km=16 km2
4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km
Therefore
3km----------------------------- 1 sec
(8km-4km)---------------------x
X=4/3=1.33 sec
The answer is D) 1.33 sec

7. Find the inverse of the function.
f(x) = the cube root of quantity x divided by seven. - 9
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f(x)=((x/7)-9) ^(1/3)
replace f(x) with y
y=((x/7)-9) ^(1/3)
switch x and y
x=((y/7)-9) ^(1/3)
solve for y
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8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

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9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

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using a graphical tool     see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x5 - 7x4 – 6
The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7 

Complete the square on the right side of the equation
Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=7
Consider the vertex form of a parabola.
a(x+d)2+e
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d=4/(2*1)=2
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(x+2)2+3
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We have to only consider the factors of the constant (leading coefficient = 1)

The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24

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6 0
3 years ago
I don't know the transformation
NeX [460]
The original was expanded...
3 0
3 years ago
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