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3 years ago

Need help and will be giving Brainliest

Mathematics

1 answer:

Katena32 [7]3 years ago

6 0

Answer:

x-intercept (s):

For this case h (x) = 0

x2 - 2x - 8 = 0

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

x1 = 4

x2 = -2

y-intercept:

For this case x = 0

h (0) = (0)2 - 2 (0) - 8

h (0) = - 8

vertex:

We derive the equation:

h '(x) = x2 - 2x - 8

h (x) = 2x - 2

We match zero:

2x-2 = 0

x = 2/2

x = 1

We evaluate the function for x = 1

h (1) = (1)2 - 2 (1) - 8

h (1) = 1 - 2 - 8

h (1) = -9

The vertex is:

(1, -9)

axis of symmetry of the function:

x = 1

Step-by-step explanation:

hope it helps

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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

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3 years ago

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PLEASE HELP

Aliun [14]

Hello from MrBillDoesMath!

Answer:

(x^4-2) (x^4 -1)

Discussion:

Let u = x^4, then

x^8 - 3x^4 + 2

= u^2 - 3u + 2

= (u -2) ( u -1)

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Answer:

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