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3 years ago

Evaluate the function f(x)=−4x^2+6x−4 Find f(5)

Mathematics

1 answer:

Tamiku [17]3 years ago

8 0

Hey there!

1. How to find f(5)?

To find f(5) - simply substitute x = 5 in the function. f(5) means the value of f(x) at x = 5.

2. Substitution and Evaluate

$\large{f(5) = - 4( {5})^{2} + 6(5) - 4}$

Remember to follow the PEMDAS/BODMAS rules! Exponent comes before multiplication.

$\large{f(5) = - 4(25) + 30 - 4} \\ \large{f(5) = - 100 + 30 - 4} \\ \large{f(5) = - 74}$

3. Final Answer

f(5) = -74

If you have any questions regarding the question or my answer, feel free to ask!

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Nastasia [14]

Answer:

We conclude that the rule for the table in terms of x and y is:

y = 3x+2

Step-by-step explanation:

The table indicates that there is constant change in the x and y values, meaning the table represents the linear function the graph of which would be a straight line.

We know the slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept.

Taking two points

(-2, -4)

(-1, -1)

Finding the slope between (-2, -4) and (-1, -1)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)$

$m=\frac{-1-\left(-4\right)}{-1-\left(-2\right)}$

$m=3$

We know that the y-intercept can be determined by setting x = 0 and finding the corresponding y-value.

Taking another point (0, 2) from the table.

It means at x = 0, y = 2.

Thus, the y-intercept b = 2

Using the slope-intercept form of the linear line function

y = mx+b

substituting m = 3 and b = 2

y = 3x+2

Therefore, we conclude that the rule for the table in terms of x and y is:

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3 years ago

Maria is installing gutters on her rectangular shed that measures 10 ft by 9 ft she has 23 ft of gutter already and need to purc

Paha777 [63]

Answer:

Maria needs 3 lengths of gutter of finish the shed.

Step-by-step explanation:

We need to calculate the perimeter of the rectangular shed to know how much 5 feet gutter is needed.

The perimeter of the shed is p = 2(l + b) where l = 10ft and b = 9 ft

p = 2(10 + 9) = 2(19) = 38 ft

Now, the perimeter of the shed also equal 23 ft of gutter already installed plus 5x ft gutter where x = number of gutters.

So 23 + 5x = 38

collecting like terms, we have

5x = 38 - 23

5x = 15

dividing through by 5 we have

5x/5 = 15/5

x = 15/5

x = 3

So, Maria needs 3 lengths of gutter of finish the shed.

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