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3 years ago

Factor completely: 10x2 + 2x − 8

2 answers:

7 0

The answer is 2(5x - 4)(x + 1)

10x² + 2x - 8 = 2*5x² + 2*x - 2*4 =
= 2(5x² + x - 4) =
= 2(5x² + 5x - 4x - 4) =
= 2(5x *x + 5x*1) - (4*x + 4*1) =
= 2(5x(x + 1) - 4(x + 1)) =
= 2(5x - 4)(x + 1)

melomori [17]3 years ago

3 0

Answer:

The answer is 2(5x - 4)(x + 1)

Step-by-step explanation:

In this case, use the shortcut, since (a - b + c) = 0. One factor is (x + 1) and the other is (x + c/a = - 8/10).

y = (x + 1)(10x - 8) = 2(x + 1)(5x - 4)

You may also use the new AC Method.

Converted

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)

(

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)

Factor pairs of (-80) -> ...(-4, 20)(-8, 10). This sum is 2 = b. Then p' = -8 and q' = 10.

Then,

−

and

y = 10(x - 8/10)(x + 1) = (10x - 8)(x + 1)= 2(5x - 4)(x + 1)

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What is the confidence interval estimate of the population mean percentage change in the price per share of stock during the fir

I am Lyosha [343]

Answer:

(-0.1059 ; - 0.0337)

Step-by-step explanation:

The data table is attached in the picture below:

These is a matched pair design ; which requires taking the difference of the two values for each sample :

The mean and standard deviation of the difference will be used to construct the confidence interval :

The mean of difference, dbar = Σx/n = - 0.0698

The standard deviation of difference, Sd ;

Sd = [√Σ(d - dbar)²/(n-1)] = 0.1054

n = sample size = 25

The confidence interval :

dbar ± [TCritical * Sd/√n]

Tcritical at 90% ; df = n -1 = 25 -1

Tcritical(90% , 24) = 1.1711

C.I = - 0.0698 ± (1.711 * 0.1054/√25)

C.I = - 0.0698 ± 0.0361

C.I = (-0.1059 ; - 0.0337)

5 0

3 years ago

Need help with this confusing

Dahasolnce [82]

Answer:

The blanks are 18 and 20

equivalent ratios

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the volume of a square pyramid with a base side length of 9 and a height of 11.

andre [41]

V = 297 for a square pyramid, I hope its right..

3 0

3 years ago

Read 2 more answers

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

Jane has a bag of candy, she gives 8 to her friend. Then jane's grandmother buys 5 more pieces than jane had originally. Now jan

goblinko [34]

Answer:

12 Pieces

Step-by-step explanation:

Number of candies in Jane's bag = x

she gives 8 to her friend;

x - 8

Then jane's grandmother buys 5 more pieces than jane had originally; add (x + 5)

x - 8 + x + 5

Now jane has 27 pieces of candy

x - 8 + x + 5 = 27

Solve for x;

x - 8 + x + 5 = 27

2x - 3 = 27

2x = 27 -3

2x = 24

x = 12

4 0

3 years ago