If 4 − 7x is 5 less than 23, what is the value of 3x ?

In Val's class, the ratio of students who ate enchiladas for lunch to the students who ate tacos was 14:20. Which of the followi

fgiga [73]

An equivalent ratio would be 7:10 or 70:100 or 42:60 and so on...

6 0

2 years ago

Simplify. 14a^2bc^4/21abc^6

kramer

14a^2bc^4/21abc^6 = 2a/3b^2

7 0

3 years ago

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What is the simplified form of each expression? 7x^–8 × 6x^3

klio [65]

7*6*x^-8*x^3
42x^-8+3 (bases same powers add)
42x^-5
1/42x^5
so the simplified form of 7x^-8*6x^3 is=1/42x^5

7 0

3 years ago

A rectangular garden has a walkway around it. The area of the garden is 6(6.5x + 2.5). The combined area of the garden and the w

Rasek [7]

According to the information given in the exercise, the following expression represents the area of the rectangular garden:

$6\mleft(6.5x+2.5\mright)$

And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:

$6.5\mleft(8x+6\mright)$

You can identify that the word "combined" indicates that that expression was obtained by adding both areas.

Knowing the above, you can set up the following equation:

$6(6.5x+2.5)+A=6.5(8x+6)$

Where "A" is the area of the walkway around the rectangular garden.

Solving for "A", you get the following expression:

$\begin{gathered} A=6.5(8x+6)-6(6.5x+2.5) \\ A=52x+39-39x-15 \\ A=13x+24 \end{gathered}$

The answer is:

$13x+24$

7 0

10 months 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

3 years ago

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