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malfutka [58]
3 years ago
13

What is the slope of the line that passes through the points ( 5 , − 10 ) (5,−10) and ( 11 , − 12 ) ? (11,−12)? Write your answe

r in simplest form.
Mathematics
1 answer:
yan [13]3 years ago
4 0

The slope of the line that passes through (5,−10) and ( 11 , − 12 ), in simplest form is: -1/3

<em><u>Recall:</u></em>

  • The slope of a line passing across through two points can be calculated using: m = \frac{y_2 - y_1}{x_2 - x_1}

<em><u>Given two points:</u></em>

(5,−10) and ( 11 , − 12 )

  • Let,

(5,-10) = (x_1, y_1)\\\\( 11 , - 12) = (x_2, y_2)

  • Substitute

m = \frac{-12 - (-10)}{11 - 5}

Slope (m) = -2/6

Slope (m) = -1/3

Therefore the slope of the line that passes through (5,−10) and ( 11 , − 12 ), in simplest form is: -1/3

Learn more about slope of a line on:

brainly.com/question/3493733

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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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How does mathematics connect to the everyday life of an individual?
mr_godi [17]

Answer:

Math is considered to be a part in everyones life, for example, you use math to throw a ball, like the force you use, or the height of the ball. Math is an important concept, and is lingering in our everyday lives, but the reason we take math is to find out of its exsitence, and use it for engineering, etc.

Step-by-step explanation:

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2 years ago
Write the quadratic equation whose roots are 2 and -2, and whose leading coefficient is 4
chubhunter [2.5K]

Answer:

4x^2-16=0

Step-by-step explanation:

We want to write the quadratic equation whose roots are 2 and -2, and whose leading coefficient is 4.

Since 2 and -2 are roots,   x+2\\and\\x-2  are factors of this quadratic function.

The factored form is given as: a(x-2)(x+2)=0

Since the leading coefficient is 4, a=4

Therefore the equation becomes:

4(x-2)(x+2)=0

Recognize and expand using difference two squares.

4(x^2-4)=0

The required equation is:

4x^2-16=0

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Answer:

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Step-by-step explanation:

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Gabriel went to Los Angeles, California, for the summer to visit his cousins. He used a map of bus routes to get from the airpor
irina [24]

Answer:

Scale factor = 1/8

Step-by-step explanation:

The formula would be

Number of miles × scale factor = 5 inches

Number of miles = 40 miles

Hence,

40 miles × scale factor = 5 inches

Scale factor = 5/40

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