Martin is building a sandcastle at the

Which ratio correctly compares 2 feet to 48 inches, when the lengths are written using the same units?

guajiro [1.7K]

Answer: OPTION D

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:

$(48inches)(\frac{1foot}{12inches})=4feet$

- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that correctly compares 2 feet to 48 inches, you can write:

$ratio=\frac{2feet}{4feet}$

- Reduce the fraction, then:

$ratio=\frac{1}{2}$

- You can rewrite it as following:

$ratio=1:2$

3 0

3 years ago

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat

NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

35x = -0.05(x² - 800x + 160000) + 9492

35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

35x = -0.05x² +40x - 8000 + 9492

35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

$x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492} }{2X0.05} = \frac{5 +/- \sqrt{25 + 298.4} }{0.1} = \frac{5 +/- \sqrt{323.4} }{0.1}\\= \frac{5 +/- 17.983 }{0.1}\\= \frac{5 - 17.983 }{0.1} or \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or \frac{22.983 }{0.1}\\= -129.83 or 229.83$

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0

4 years ago

Read 2 more answers

PLEASE HELP

Studentka2010 [4]

<span>The side length for a cube
with volume 8000cm3 = 8000^(1/3)= 20 m
Cheers,
Stan H.</span>8000=S^3<span>8000=20^3
so the answer will be B</span>

3 0

3 years ago

How do i ask the community?

postnew [5]

just do whatever you did now

3 0

3 years ago

Read 2 more answers

Compare properties of squares and rhombi to properties of other quadrilaterals by answering each question. Write a brief explana

GuDViN [60]

Hey there! Hello!

Not sure if you still need these answers, but I'd love to help out if you do!

Now, I want you to go ahead and think of some stuff that's true for squares. To name a few, the opposite sides are going to be parallel to one another, all the angles are 90°, all the sides are the same length, and both diagonals are going to be perpendicular and equal in length. I'm sure there's even more, but I'll leave that to you. (BTW, by diagonals, I mean the lines that go through the the opposite diagonal corners).

What about rectangles? The opposite sides are going to be parallel to one another, the diagonals are going to be equal in length, and the angles are going to be 90°.

Now, rhombi. All sides are going to be equal, opposite sides are going to be parallel, the diagonally opposite angles will be equal to each other, and the diagonals bisect each other at 90°.

And lastly, parallelograms. Pretty similar to rhombi in that they have parallel opposite sides and that the opposite diagonal angles are equal to each other, but there's one thing that makes a parallelogram not a rhombus.

If you differentiate the stuff I described, you'll be golden. There's a lot to choose from, and I personally like to have options. Hope this helped you out, feel free to ask me any additional questions you have! :-)

3 0

3 years ago