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3 years ago

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Which is the BEST estimate of the average rate of change for the function given in the table, over the interval 2 ≤ x ≤ 4?

2 answers:

ladessa [460]3 years ago

3 0

Answer:

6

Step-by-step explanation:

Use the slope formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Picking x = 2 and x = 4 as my two points (since the interval is 2 ≤ x ≤ 4), we get:

$m = \frac{15-3}{4-2} = \frac{12}{2} = 6$

So, the BEST estimate of the average rate of change for the function given in the table is 6.

Mice21 [21]3 years ago

3 0

4 is bigger but if times maybe it’s will = to 8

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In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm

jeyben [28]

Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

$AB = 17$

$PAMC = 32$

$PBMC = 25$

From the attachment, we have:

$y + z = AB$

Since, M is the Midpoint

$y = z = \½AB$

Substitute 17 for AB

$y = z = \½ * 17$

$y = z = 8.5$

Also, from the attachment

$v + x + z = PAMC$

$v + x + y = 32$

Substitute 8.5 for y

$v + x + 8.5 = 32$

$v + x = 32 - 8.5$

$v + x = 23.5$ --------- (1)

Also, from the attachment

$v + w + z = 25$

Substitute 8.5 for z

$v + w + 8.5 = 25$

$v + w = 25 - 8.5$

$v + w = 17.5$ ----------- (2)

Subtract (2) from (1)

$v - v + x - w = 23.5 - 17.5$

$x - w = 6$

Make x the subject

$x = 6 + w$

Apply Pythagoras Theorem:

We have that:

$AB^2 = AC^2 + BC^2$

The above can be replaced with

$17^2 = x^2 + w^2$ (see attachment)

$289 = x^2 + w^2$

Substitute 6 + w for x

$289 = (6 + w)^2 + w^2$

$289 = 36 + 12w + w^2 + w^2$

$289 - 36 = 12w + 2w^2$

$253 = 12w + 2w^2$

Reorder

$2w^2 + 12w - 253 = 0$

Solve using quadratic equation:

$w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 2$

$b = 12$

$c = -253$

$w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}$

$w = \frac{-12 \± \sqrt{144 + 2024}}{4}$

$w = \frac{-12 \± \sqrt{2168}}{4}$

$w = \frac{-12 \± 46.56}{4}$

Split:

$w = \frac{-12 + 46.56}{4}$ or $w = \frac{-12 - 46.56}{4}$

$w = \frac{34.56}{4}$ or $w = \frac{-58.56}{4}$

$w = 8.64$ or $w = -14.64$

But length can't be negative

So:

$w = 8.64$

Recall that: $x = 6 + w$

$x = 6 + 8.64$

$x = 14.64$

<em>Hence, the length of the legs is 8.64cm and 14.64cm respectively</em>

5 0

3 years ago

Eduardo is painting a rectangular wall that is 96 inches high and 110 inches long. What is the area of the wall?

EastWind [94]

<h3><u>Required</u><u> Answer</u><u>:</u><u>-</u></h3>

Here the height and length are the sides of the rectangular wall and we have to find the area.

Area of rectangle is given by:

$= l \times b$

where l is the length and b is the breadth/width according to the question. Plugging the given values:

$= 110 \times 96 \: {inch}^{2}$

$= 10560 \: {inch}^{2}$

<h3><u>Hence:</u><u>-</u></h3>

The area of the wall is <u>1</u><u>0</u><u>5</u><u>6</u><u>0</u><u> </u><u>inch²</u>

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Find the area of a rectangle with the length of 1 3/4 foot and a width of 1 1/2 foot.

Stolb23 [73]

To find the Area you need to use the formula L x W!! Anyways, You have to multiply the Length x the width. Your Length is 1 3/4 and your width is 1 1/2. So 1 3/4 x 1 1/2 is 2 5/8!!

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3 years ago

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If k=3 then the answer is 5

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3 years ago

A drug trial is testing the effectiveness of two drugs. If 80 patients are given Drug A, 10 patients are given Drug B, and 20 pa

KiRa [710]

Answer:

The answer is 9/11.

Step-by-step explanation:

To find the answer you'd first add up how many patients you have:

80+10+20 = 110.

Now find out that how many patients are taking a real drug, which is represented by 80+10 = 90.

So, the probability of a patient NOT getting a placebo is 90/110

Simplified would be 9/11

Thus the answer is 9/11....

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3 years ago