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2 years ago

Which expression represents the perimeter of the rectangle below?

Mathematics

1 answer:

Contact [7]2 years ago

8 0

Perimeter = combine length and width of all the sides
2(8x - 43) + 2(5x + 12)
16x - 86 + 10x + 24
26x -62

The solution is C

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When Ms. Lawrence goes to the doctor’s office, they have patients wait 30 minutes. She found a new doctor that has 15% less wait

baherus [9]

Answer:

25.5 minutes

Step-by-step explanation:

3 0

2 years ago

98 POINTS! PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked f

Colt1911 [192]

See the attached picture.

Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

The resulting box has a volume

$V(x)=x(8-x)(12-x)=x^3-20x^2+96x$

because the volume of a box is the product of its width $(12-x)$ , length $(8-x)$ , and height $(x)$ .

find the zeroes

You know right away from the factored form of $V(x)$ that the zeroes are $x=0,8,12$ . (zero product property)

sketch the graph of the function

Easy to plot by hand. You know the zeroes, and you can check the sign of $V(x)$ for any values of $x$ between these zeros to get an idea of what the graph of $V(x)$ looks like. See the second attached picture.

Here's what I mean by "check the sign" in case you don't follow. We know $V(x)=0$ when $x=0$ and $x=8$ . So we pick some value of $x$ between them, say $x=1$ , and find that

$V(1)=1(8-1)(12-1)=7\cdot11=77$

which is positive, so $V(x)$ will be positive for any other $x$ between 0 and 8. Similarly we would find that $V(x)$ for $x$ between 8 and 12, and so on.

What is the size of the cutout he needs to make so that he can fit the most marbles in the box?

It's impossible to answer this without knowing the volume of each marble...

If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?

Thomas wants $V(x)=12$ , so you solve

$x^3-20x^2+96x=12$

While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions

$x\approx0.1284$

$x\approx7.6398$

$x\approx12.2318$

but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.

What would be the dimensions of this box?

The box's dimensions are ( $x$ in) x ( $8-x$ in) x ( $12-x$ in).

If $x\approx0.1284$ , then $8-x\approx7.8716$ and $12-x\approx11.8716$ .

If $x\approx7.6398$ , then $8-x\approx0.3602$ and $12-x\approx4.3602$ .

8 0

2 years ago

Analyze the diagram below and complete the instructions that follow.

lora16 [44]

Answer:

$\displaystyle y=2\sqrt{6}$

$\displaystyle x=2\sqrt{2}$

Step-by-step explanation:

<u>Trigonometric Ratios </u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

$\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}$

Solving for y:

$y=4\sqrt{2}\cos 30^\circ$

Since:

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}$

Simplifying:

$\displaystyle y=2\sqrt{6}$

Now we use the sine ratio:

$\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}$

Solving for x:

$x=4\sqrt{2}\sin 30^\circ$

Since:

$\sin 30^\circ=\frac{1}{2}:$

$\displaystyle x=4\sqrt{2}\frac{1}{2}$

Simplifying:

$\displaystyle x=2\sqrt{2}$

The choices are not clear, but it seems like the correct answer is C.

$\boxed{\displaystyle y=2\sqrt{6}}$

$\boxed{\displaystyle x=2\sqrt{2}}$

6 0

3 years ago

A student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests. She scored 78% on the final exam and 86% on

Anna71 [15]

Her weighted mean grade is 81.2% if the student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have a student who earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests. She scored 78% on the final exam and 86% on her class projects.

The weighted mean can be calculated as:

$\rm = 0.4\times\dfrac{[(84+78+84+72)]}{4} + 0.3\times 78 + 0.1\times 86+ 0.2\times 87$

After calculating, we get:

= 81.2%

Thus, her weighted mean grade is 81.2% if the student earned grades of 84, 78, 84, and 72 out of 100 on her four regular tests.

Learn more about the mean here:

brainly.com/question/22871228

#SPJ1

8 0

2 years ago

Am I right? Doing a quiz.

love history [14]

Yea you’re right
Xcjdejwhwh

4 0

2 years ago