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ASAPPP!!!! HELP I WILL GIVE 100POINTS AND BRAINLIST Question 9 (Essay Worth 10 points)

Luda [366]

Answer:

Part A)

The x-intercepts are (-1/4, 0) and (4, 0).

Part B)

The vertex is a maximum because the leading coefficient is negative.

The vertex is (1.875, 72.25).

Part C)

We can plot the zeros and the vertex, and connect them with a curve.

Step-by-step explanation:

The function given is:

$f(x)=-16x^2+60x+16$

Part A)

To find the x-intercepts of the function, set the function equal to 0 and solve for x:

$0=-16x^2+60x+16$

We can divide both sides by negative four:

$0=4x^2-15x-4$

Factor:

$0=(4x+1)(x-4)$

Zero Product Property:

$x-4=0\text{ or } 4x+1=0$

Solve for each case:

$\displaystyle x=-\frac{1}{4}\text{ or }x=4$

Hence, our zeros are:

$\displaystyle \left(-\frac{1}{4}, 0\right)\text{ and } \left(4, 0\right)$

Part B)

Note that the leading coefficient of our function is negative.

So, our function will be concave down.

Hence, our vertex will be the maximum.

The vertex is given by:

$\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 60, and c = 16.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(60)}{2(-16)}=\frac{15}{8}=1.875$

Substitute this back into the function to find the y-coordinate:

$f(1.875)=-16(1.875)^2+60(1.875)+16=72.25$

Hence, our vertex is:

$(1.875, 72.25)$

Part C)

Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.

The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the y-intercept.

7 0

3 years ago

How do I find Trig ratios

nadya68 [22]

Trig ratios can only be used on right triangles with acute measures.

If given an angle and there are adjacent and opposite sides, then use tan(opposite/adjacent)

If given an angle and there is an adjacent side and a hypotenuse, then use cosine(adjacent/hypotenuse)

If given an angle and there is an opposite and adjacent side, then use sin(opposite/hypotenuse)

A common mnemonic device used to memorize the trig rules is SOH-CAH-TOA

8 0

4 years ago

What is the equation of the line that passes through the point (-5,5) and has a slope of -1

max2010maxim [7]

Answer:

y - 5 = -(x + 5)

y - 5 = -x - 5

y = -x

7 0

4 years ago

What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time)

bekas [8.4K]

Answer:

The interest after 3 years is $360

Explanation:

Given the principal amount (P) = $3000

Rate of interest (R) = 0.04

Time period (T) is given as 3 years

The Simple Interest is calculated by the formula;

$SI = Principal \times Rate of Interest \times Time$

Substituting the values in the above formula,

$SI = 3000 \times 0.04 \times 3$

SI = $360

Therefore, the interest after 3 years is $360

5 0

3 years ago

Which matrix equation represents the system of equations? {-x+ 2y = 0 y= -2

Snowcat [4.5K]

We are given a system of equations,

$\begin{cases}-x+2y=0\\y=-2\\ \end{cases}$

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}$

The matrix will then be applied to the vector (lower dimensions on top),

$\begin{bmatrix}x\\y\\ \end{bmatrix}$

And the result vector will be whats on the other side of equals sign,

$\begin{bmatrix}0\\-2\\ \end{bmatrix}$

So to put everything together,

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}$

Hope this helps :)

6 0

3 years ago