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3 years ago

If h(x) = x-7 and g(x)

Mathematics

1 answer:

shtirl [24]3 years ago

8 0

Answer:

If you would like to find the equivalent expression to (g*h)(5), you can do this using the following steps:

h(x) = x - 7

g(x) = x^2

(g*h)(x) = g(h(x)) = g(x - 7) = (x - 7)^2

(g*h)(5) = g(h(5)) = g(5 - 7) = (5 - 7)^2 = (-2)^2 = 4

The correct result would be (5 - 7)^2.

Step-by-step explanation:

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Identify the ordered pair that represents the vector from a(1,6) to b(2,-3) and the magnitude of ab

aliina [53]

Answer: magnitude ab = 9.06

Step-by-step explanation:

The vector coordinates will be represented with ( X , Y )

Magnitude of ab will be

ab^2 = (X2 -X1)^2 + (Y2 -Y1)^2

ab^2 = (2 -1)^2 + (-3 -6)^2

ab^2 = 1^2 + 9^2

ab^2 = 1 + 81

ab = 9.06

3 0

3 years ago

The number of bacteria in a refrigerated food product is given by N ( T ) = 27 T 2 − 180 T + 100 N(T)=27T2-180T+100, 7 < T &l

NeX [460]

Answer:

$N(T(t))=432t^2-374.4t-118.88$

The number of Bactria after 5.8 hours is 12242.

Step-by-step explanation:

The number of bacteria in a refrigerated food product is given by

$N(T)=27T^2-180T+100$

where, T is the temperature of the food.

When the food is removed from the refrigerator, then the temperature is given by

$T(t)=4t+1.6$

We need to find the composite function N(T(t)).

$N(T(t))=N(4t+1.6)$

$N(T(t))=27(4t+1.6)^2-180(4t+1.6)+100$

$N(T(t))=432t^2+345.6t+69.12-720t-288+100$

$N(T(t))=432t^2-374.4t-118.88$

where N(T(t)) is the number of bacteria after t hours.

Substitute t=5.8 in the above function.

$N(T(5.8))=432(5.8)^2-374.4(5.8)-118.88$

$N(T(5.8))=14532.48-2290.4$

$N(T(5.8))=12242.08$

$N(T(5.8))\approx 12242$

Therefore, the number of Bactria after 5.8 hours is 12242.

7 0

4 years ago

Prove algebraically that (m + 2)2 – m 2 – 12 is always a multiple of 4

Julli [10]

Answer:

$(m + 2)^{2} - m^{2} - 12 = 4(m - 2)$

Step-by-step explanation:

Step 1:

Write the expression

$(m+2)^{2} - m^{2} - 12$

Step 2: Expand $(m + 2)^{2}$

$(m+2)^{2} - m^{2} - 12\\(m+2)(m+2) - m^{2} - 12\\m^{2} + 2m + 2m + 4 - m^{2} - 12$

Step 3: Collect similar terms

$m^{2} - m^{2} + 4m + 4 - 12\\4m - 8$

Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.

$Therefore\\4m - 8 = 4(m - 2)\\Hence,\\(m+2)^{2} - m^{2} - 12 is a multiply of 4 because the expression is equal to 4(m-2)$

3 0

3 years ago

Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation , where represents the height o

tigry1 [53]

Answer:

2.5 second

Step-by-step explanation:

The equation is missing in the question.

The equation is, $h=-8t^2+40t$ , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

$\frac{dh}{dt} =0$

Now the differentiating the equation with respect to time t, we get

$\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)$

$\frac{dh}{dt}=-16t+40$

For maximum height, $\frac{dh}{dt} =0$

So, $-16t+40=0$

$\Rightarrow 16t=40$

$\Rightarrow t=\frac{40}{16}$

$\Rightarrrow t = 2.5$

Therefore, the ball takes 2.5 seconds time to reach the maximum height.

7 0

3 years ago

Is 3/2 greater than 1? Or Less than

Simora [160]

Answer:

3/2 is greater than 1

Step-by-step explanation:

A little trick to immediately know if a number is more or less than when it involves fractions versus whole numbers is that improper fractions will always be greater than 1.

If you want to confirm this, dividing 3/2 equals 1.5, ergo 1.5 > 1.

In essence, improper fractions will always represent a number greater than one contrasted to proper fractions because if you put it on a perspective (let's say you have 13 pie slices but you only needed 12, that means there is a pie slice that's extra that makes it greater than the original pie slices).

Hope that helps :)

6 0

3 years ago