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2 years ago

If f(x) = x2 - 1, and g(x) = x + 2, then f(g(x)) = [? ]x2+[?]x+[?]

Mathematics

1 answer:

klio [65]2 years ago

4 0

Step-by-step explanation:

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

=(x+2)2 -1

=(x2+2*x*2+4)-1

=x2+4x+4-1

=x2+4x+3

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the perimeter of an equilateral triangle is 39 centimeters. What is the length of an altitude of the triangle ?

victus00 [196]

Answer: $h = 11.26cm$

Step-by-step explanation:

Equilateral triangle has equal sides, let the side be $xcm$ , then the perimeter is $3x$

Therefore:

$3x = 39$

$x = 39/3$

$x = 13cm$

To find the altitude , we will apply Pythagoras theorem , that is

$13^{2}=h^{2}+6.5^{2}$

Therefore:

$h^{2}=13^{2}-6.5^{2}$

$h^{2}=169-42.25$

$h^{2}=126.75$

take the square root of both sides

$h = 11.26cm$

8 0

2 years ago

The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 se

Ksenya-84 [330]

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope $m$ of the graph from 16 to 24:

$m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s$

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope $m$ :

$m= \dfrac{45-5}{28-24}= 10mph/s$

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

7 0

3 years ago

Read 2 more answers

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x)

Verdich [7]

Answer:

g(x)=(x+7)^2-3

Step-by-step explanation:

Given:

f(x)= x^2

Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).

As per the rules of translation

when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)

Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a

Translating f(x), 7 units to the left

f(x+7)= (x+7)^2

Translating f(x+7), 3 units down

f(x+7)-3 = (x+7)^2-3

Hence new function g(x)=(x+7)^2-3!

7 0

3 years ago

The owner of a store buys wooden benches for $50 each. She marks up the

Sliva [168]

Answer:

$98.75

Step-by-step explanation:

50×75÷100 = 37.5 + 50 = 87.5

87.5 × 30 ÷ 100 = 26.5

87.5 - 26.5 = 61.25

87.5 + 61.25 = 148.75

148.75 - 50 = 98.75

i hope i am right

5 0

2 years ago

What is the bisector of RS

Inessa05 [86]

Step-by-step explanation: A line, ray, or line segment (referred to as segment) that is perpendicular to a given segment at its midpoint is called a perpendicular bisector. ... In the diagram above, RS is the perpendicular bisector of PQ, since RS is perpendicular to PQ and PS≅QS. Additionally, since PS≅QS, point S is the midpoint of PQ.

8 0

2 years ago