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hammer [34]
3 years ago
8

What is the value of x

Mathematics
1 answer:
Sedbober [7]3 years ago
8 0

Step-by-step explanation:

Pythagorus theorum:

17² = 15² + x²

289 - 225 = x²

√64 = x

∴ x= 8

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The change in water vapor in a cloud is modeled by a polynomial function, C(x). C(x) = x^3+ 5x^2+3x+30 Describe how to find the
kari74 [83]

Answer:

Suppose the equation that describes the change in water vapor in a cloud (y) with respect to temperature (x): C(x) = x³ - 4x² - 7x + 10

You find the x-intercepts of the cubic equation by finding the roots. Let y be zero:

x³ - 4x² - 7x + 10 = 0

Now, find possible factors of the constant term in the equation: 10. These could be 1, 2, 5, and 10. Suppose we choose 1. We substitute x=1. If the answer is zero, then x=1 is one of the roots.

(1)³ - 4(1)² - 7(1) + 10 = 0

Hence, x=1 or x-1 = 0 is one of the roots. We use this to manipulate the rest of the terms in the original equation, such that you can factor out (x-1). Substitute -x² - 3x² to -4x³ because they are just equal. Same is true for +3x - 10x for -7x:

x³ -x² - 3x²+3x - 10x + 10 = 0

Factor out like terms such that they have a common factor of (x-1) as much as possible.

x³ -x² = x²(x-1)

- 3x²+3x = -3x(x-1)

- 10x + 10 = -10(x-1)

The factored equation is:

x²(x-1)-3x(x-1)-10(x-1) = 0

Factor out (x-1):

(x-1)(x²-3x-10) = 0

Now, we have the quadratic equation left to be solved:x²-3x-10

Use the quadratic formula to find the roots:

x = [-b +/- √(b²-4ac)]/2a,

The a, b and c coefficients are based on the general form of the quadratic equation: ax² + bx + c. Hence, a=1, b=-3 and c=-10. Substituting the values:

x = [-(-3) +/- √((-3)²-4(1)(-10))]/2(1)

x = 5, -2

Therefore, the roots of the cubic equations are x = 1, x = 5 and x =- 2. These are the x-intercepts of the equation. At temperatures °C, 5°C and -2°C, there is no change in water vapor in a cloud. The graph is shown in the attached picture

Step-by-step explanation:

7 0
3 years ago
(HELP ASAP PLEASE!!)
Doss [256]

Answer:

Each shirt cost $<u>7</u>  and each pair of shorts cost $<u>17</u> .

Step-by-step explanation:

let shirts be represented as x

let shorts be represented as y

Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.

4 x + 3 y = $79    .......equation 1

Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.

7 x + 8 y = $185  .......equation 2

multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.

7 × (4 x + 3 y = $79)     ⇒             +28 x + 21 y = $553

-4 × (7 x + 8 y = $185)  ⇒             <u> -28 x - 32 y = - $740</u>

                                                          0   - 11 y   = - $187     ⇒  -11 y   = - $187

y = \frac{- $187}{- 11}   ⇒   y = $17

shorts = y = $17

put value of y in equation 1

4 x + 3 ( $17 ) = $79  ⇒    4x + $51 = $79   ⇒   4x = $79 - $51

4x = $28   ⇒  x = \frac{$28}{4}   ⇒   x = $7

Shirts = x = $7

8 0
3 years ago
Help please
erastovalidia [21]
A = a+b/ 2 h the / is a fraction btw.
6 0
2 years ago
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Which is greater 0.8 or 3/4
Illusion [34]
3/4 is equivalent to 0.75  Therefore 0.8 is greater
7 0
3 years ago
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Divide. Write the quotient in the lowest terms.
oee [108]

Answer:

12/1\frac{1}{5} = 10

8 0
3 years ago
Read 2 more answers
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