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3 years ago

On his afternoon jog Chris took 42 minutes to run 3.75 miles. How many miles can he run in 90 minutes?

Mathematics

1 answer:

Troyanec [42]3 years ago

7 0

Answer:

8.03

Step-by-step explanation:

43 min = 3.75 miles

90 min = X

99 min×3.75÷42=8.03

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In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

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

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

$g(x)=f(x+2)$

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

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

$g(0)=1$

Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

$g(x)=f(x)+2$

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

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

$g(x)=f(x)-3$

$g(x)=(x-2)^{2}+1-3$

$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}-2$

$g(2)=-2$

Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!

8 0

3 years ago

Which number is NOT in the solution set of the inequality x>-15?

Ipatiy [6.2K]

Answer:

Step-by-step explanation:

if x has to be greater than -15 and -20 = x than its not true because -20 isn't greater than -15

5 0

3 years ago

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PLEASE HELP I HAVE A TEST!!!!!!!!! Show all work to factor x4 − 17x2 + 16 completely

Finger [1]

Answer:

Step-by-step explanation:

Here you go mate,

step 1

x^4 − 17x^2 + 16 equation/question

step 2

x^4 − 17x^2 + 16 factor completely

answer

(x+1)(x-1)(x+4)(x-4)

8 0

2 years ago

HELP ASAP!!! IM BEING TIMED. Use synthetic division to test one potential root. Enter the numbers that complete the division pro

Diano4ka-milaya [45]

Step-by-step explanation:

1 * (-5) = -5 a = -5

6 + (-5) = 1 b = 1

1 * (-5 ) = -5 c = -5

-7 + -5 = -12 d = -12

3 0

3 years ago

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Stonehenge is a circular arrangement of massive stones near Salisbury, England. A viewer at V observes the monument from a point

Marysya12 [62]

We are given the following measures:

mAB = 48°

mDC = 180°

In the given figure above, we can say that angle AVB is an exterior angle which intercepts two arcs, arc AB and arc DC, therefore in this case to solve for the measure of angle mAVB, we have to make use of the formula which is in words:

Find the difference between the measures of the two intercepted arcs and divide by 2, or expressed mathematically in this case as:

mAVB = (mDC – mAB) / 2

Substituting the given values into the equation:

mAVB = (180° - 48°) / 2

mAVB = 66°

8 0

3 years ago

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