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3 years ago

What is the value of (g o f)(3)?

Mathematics

1 answer:

Phantasy [73]3 years ago

4 0

Answer:

- 13

Step-by-step explanation:

To evaluate (g ￮ f)(3), evaluate f(3) then use this value to evaluate g(x)

f(3) = 3 - 7 = - 4, then

g(- 4) = 4(- 4) + 3 = - 16 + 3 = - 13

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Susan's math teacher assigned x homework problems on Monday. On Tuesday, she assigned 13 more problems. Over the two days, a tot

lana66690 [7]

we can find the answer to this problem by thinking about it logically for a minute:

we know that she assigned "x" homework problems on Monday, so,

x=Monday

we also know that she assigned 13 more problems on Tuesday, so,

13=Tuesday

over the course of the two days she assigned a total of 23 homework problems.

to get the answer of how many problems she assigned on Monday, we have to do the total number of problems she assigned(23) minus the number of problems we know she assigned on Tuesday(13), so,

23-13=10

she assigned 10 problems on Monday.

4 0

3 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$

$\frac{d(D^{2})}{dt} = \frac{d(90^{2} + x^{2})}{dt}$

$D\frac{dD}{dt} = x\frac{dx}{dt}$ (3)

We have that D is:

$D = \sqrt{x^{2} + 90^{2}} = \sqrt{(45)^{2} + 90^{2}} = 100.63$

By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:

$\frac{dD}{dt} = \frac{45*31}{100.63} = 13.9 ft/s$

Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.

I hope it helps you!

4 0

2 years ago

Read 2 more answers

I'll make you brainlist and 40 points (2z²)^-3 please hurry

gladu [14]

Is the goal to simplify? You just need to multiply the exponents for each factor:

(2z^2)^(-3)
= 2^(-3) x z^(2 x -3)
= (1/2)^3 x z^(-6)
= (1/8) x (1/z)^6
= 1/(8z^6)

7 0

3 years ago

Read 2 more answers

Hey can you please help me posted picture of question :)

IRINA_888 [86]

If you observe carefully, you can see that the graph is crossing x-axis at the points 1 and 9. This means x = 1 and x = 9 are the roots of the polynomials and x - 1 and x - 9 are thus the factors of the polynomial.

We can express the polynomial as the product of its factors. So the above polynomial can be expressed as (x - 1)(x - 9)

Thus, the answer to the question is option D

4 0

3 years ago

Which ordered pair is a solution to the linear inequality below

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

3(6)-5(-3)≥10

18-(-15)≥10

18+15≥10

33≥10

8 0

2 years ago