Which of these professionals most directly uses geometry? Choose the best answer.

Answer:   k = -15

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Explanation:

Let p(x) = 4x^2+4x+k be the polynomial function.

Also, let r and s be the two roots of the polynomial p(x).

By definition of what it means to be a root, we know that

p(r) = 0

p(s) = 0

So this means p(r) = p(s).

Because one root exceeds another by 4, we can say s = r+4.

So the equation p(r) = p(s) updates to p(r) = p(r+4).

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Let's compute p(r) and p(r+4)

So,

p(x) = 4x^2+4x+k

p(r) = 4r^2+4r+k

and

p(x) = 4x^2+4x+k

p(r+4) = 4(r+4)^2+4(r+4)+k

p(r+4) = 4(r^2+8r+16)+4(r+4)+k

p(r+4) = 4r^2+32r+64+4r+16+k

p(r+4) = 4r^2+36r+80+k

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Now equate those results

p(r) = p(r+4)

4r^2+4r+k = 4r^2+36r+80+k

4r+k = 36r+80+k        ...... the 4r^2 terms cancel

4r = 36r+80                ..... the k terms cancel as well

4r-36r = 80

-32r = 80

r = 80/(-32)

r = (16*5)/(-16*2)

r = -5/2 = -2.5 is one of the roots

s = r+4

s = -2.5+4

s = 1.5 = 3/2 is the other root.

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With this in mind, we can use either r or s to find the value of k

p(x) = 4x^2 + 4x + k

p(r) = 4r^2 + 4r + k

p(r) = 4(-2.5)^2 + 4(-2.5) + k

p(r) = 15+k

0 = 15+k

k+15 = 0

k = -15

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To confirm this answer, you can use the quadratic formula to solve 4x^2+4x-15 = 0. You should get the two roots r = -5/2 = -2.5 and s = 3/2 = 1.5

Then note how s-r = 4 which is the same as saying s = r+4.

The equation of the line x + 2y = 6 in slope-intercept form is y = - (1/2)x + 6.

What is slope?

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.

The equation of the given line is x + 2y = 6.

We know equation of a line in slope intercept form is,

y = mx + b.

Therefore,

x + 2y = 6.

2y = - x + 6.

y = - (1/2)x + 6.

learn more about linesand slopes here :

brainly.com/question/16180119

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Answer:

y= -1/2x+3

Step-by-step explanation:

Answer:

Conditional frequencies offer more specific information to analyse certain data set.

Step-by-step explanation:

A conditional frequency is a type of relative frequency which involves a condition to be defined.

For example, the conditional frequency of having a house given that the person is female. Notice that this example shows the condition "being female", so the conditional frequency would be all females who own a house.

On the other hand, the relative frequency is just a ratio between the frequency of the data and the total number of  data. It's doesn't includes a condition to be defined, that's the difference.

Therefore, conditional frequencies offer more specific information to analyse certain data set.