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2 years ago

Which of the following graphs represents the solution set for y< -2x – 4?

Mathematics

1 answer:

Katen [24]2 years ago

3 0

Given:

The inequality is $y$ .

To find:

The graph of the given inequality.

Solution:

The inequality is

$y$

The related equation is

$y=-2x-4$

For x=0,

$y=-2(0)-4$

$y=0-4$

$y=-4$

For y=0,

$0=-2x-4$

$4=-2x$

$\dfrac{4}{-2}=x$

$-2=x$

So, the related line passes through two points (0,-4) and (-2,0).

Sign of inequality is <, so the related line is a dotted line and shaded region is below the related line.

Therefore, the correct option is B.

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2 years ago

Help! Ill mark you as brain! 15 points!

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Answer:

35 in²

Step-by-step explanation:

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2 years ago

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 − x 2 . What are the dimensions

kherson [118]

Answer:

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola

y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?

Width =

Height =

Width =√10 and Height $= \frac{10}{4}$

Step-by-step explanation:

Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)

are (h,k) and (-h,k).

Hence, the area of the rectangle will be (h + h) × k

Therefore, A = h²k ..... (2).

Now, from equation (1) we can write k = 5 - h² ....... (3)

So, from equation (2), we can write

$A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}$

For, A to be greatest ,

$\frac{dA}{dh} =0 = 10h-4h^{3}$

⇒ $h[10-4h^{2} ]=0$

⇒ $h^{2} =\frac{10}{4} {Since, h≠ 0}$

⇒ $h = ±\frac{\sqrt{10} }{2}$

Therefore, from equation (3), k = 5 - h²

⇒ $k=5-\frac{10}{4} =\frac{10}{4}$

Hence,

Width = 2h =√10 and

Height = $k =\frac{10}{4}.$

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2 years ago

Jasmine mixes 37 ounces of grape juice and 13 ounces of apple juice to make a fruit punch. She will pour the punch into 6-ounce

Anastaziya [24]

First we have to figure out how much fruit punch Jasmine has.
To do this, we just have to add the number of ounces of grape juice she mixes with the number of ounces of apple juice.

37 + 13 = 50.

Jasmine is pouring the punch into 6 ounce cups. To find out how many cups of punch she can make, you have to divide the number of ounces of punch she has (50) by the number of ounces she can put in a cup (6).

50/6 ≈ 8.33

Therefore, Jasmine can

A. make 8 full cups of punch with the apple juice and grape juice.

and

B. Yes, there will be juice left over, because the amount of cups Jasmine could fill had a decimal, or a remainder.

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2 years ago

What is the solution to the inequality 2 + 5x > 12?

Alexxx [7]

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3 years ago

Read 2 more answers

Which of the following graphs represents the solution set for y< -2x – 4? ​

Which of the following graphs represents the solution set for y< -2x – 4?