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Vadim26 [7]
3 years ago
14

If the graph of the function h is defined by = h(x)+x^2+9 is translated vertically downward by 9 units, it becomes the graph of

a function g. Find the expression for
gx
Mathematics
1 answer:
natulia [17]3 years ago
6 0
The answer is g(x) = x².
Solution:
The graph of h(x) = x²+9 translated vertically downward by 9 units means that each point (x, h(x)) is shifted onto the point (x, h(x) - 9), that is, 
     (x, h(x)) → (x, h(x) - 9)
The translated graph that represents the function is defined by the expression for g(x):
     g(x) = h(x) - 9 = x² + 9 - 9 = x²

h(x) = x²+9 → g(x) = x² shows that the graph of the equation g(x) = x² moves the graph of h(x) = x²+9 down nine units.
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Is the dilation from A to B a reduction or enlargement?
WITCHER [35]

Answer:

This is actually a reduction, and the scale factor of this dilation is 0.5.

8 0
2 years ago
Read 2 more answers
Y=6x-11 -2x-3y=-7 solve each system of equation by substitution
Anit [1.1K]

Answer:

(2, 1 )

Step-by-step explanation:

Given the 2 equations

y = 6x - 11 → (1)

- 2x - 3y = - 7 → (2)

Substitute y = 6x - 11 into (2)

- 2x - 3(6x - 11) = - 7 ← distribute and simplify left side

- 2x - 18x + 33 = - 7

- 20x + 33 = - 7 ( subtract 33 from both sides )

- 20x = - 40 ( divide both sides by - 20 )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = 6(2) - 11 = 12 - 11 = 1

Solution is (2, 1 )

5 0
3 years ago
The reproduction function for a sardine is f(p) = −0.0005p2 + 4p, where p and f(p) are in hundred metric tons. Find the populati
tensa zangetsu [6.8K]

Answer:

Population (p) = 4,000 hundred metric tons

Size of the yield (f(p)) = 8,000 hundred metric tons

Step-by-step explanation:

The population of sardines 'p', for which the derivate of the function f(p) is zero, is the population that gives the maximum sustainable yield:

f(p) = -0.0005p^2 + 4p\\\frac{df(p)}{dp}=-0.0010p+4\\-0.0010p+4 =0\\p=4,000

The size of the maximum sustainable yield is:

f(p) = -0.0005p^2 + 4p\\f(4,000) = -0.0005(4,000^2) + 4*4,000\\f(4,000) = 8,000

Population = 4,000 hundred metric tons

Size of the yield = 8,000 hundred metric tons

3 0
3 years ago
What is the surface area of the triangular prism?
FrozenT [24]

Answer:

252

Step-by-step explanation:

if you go around the faces, 20*5 is 100, 20*4 is 80, 20*3 is 60, 2*3 is 6 and another 2*3 is 6. add these together

3 0
2 years ago
Which expressions are polynomials??
GrogVix [38]

Answer:

Options (1) and (2)

Step-by-step explanation:

Properties of a polynomial,

1). A polynomial having division by a variable can't be defined as a polynomial.

  Example:

   (y² + \frac{x}{1+x})

2). A polynomial can't have a negative exponent.

  Example : (x^{-2}+y-6)

3). Polynomials don't have the radicals.

  Example : y² + x√3

4). A polynomial can't have a fraction exponent.

   Example : x^2+x^{\frac{1}{2}}-1

By these properties, Options (3) and (4) are not the polynomials.

Options (1) and (2) are the correct options.

5 0
3 years ago
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