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Rus_ich [418]
3 years ago
7

What two rational expressions sum to

mula1" title="\frac{4x+2}{x^{2}-9+8 }" alt="\frac{4x+2}{x^{2}-9+8 }" align="absmiddle" class="latex-formula"> Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

Mathematics
2 answers:
Darina [25.2K]3 years ago
8 0

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

bulgar [2K]3 years ago
3 0

Answer:

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

Step-by-step explanation:

Given

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

Required

Fill in the gaps

Going by the given parameters, we have that

\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}

x^2 - 9x + 8, when factorized is (x-1)(x-8)

Hence; the expression becomes

\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}

Combine Fractions

\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}

Simplify the denominators

4x + 2 = A + B

By direct comparison

A = 4x

B = 2

Hence, the complete expression is

\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}

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8090 [49]

Answer:

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0
3 years ago
A single gram of a certain metallic substance has 0.52 g of copper and 0.25 g of zinc the remaining portion of the substance is
andrezito [222]
Ben's estimate gives 7 g of nickel; the actual amount is 8.03 g.

In 1 g of the substance, there is 0.52 g of copper and 0.25 g of zinc; this gives 
0.52+0.25 = 0.77 g of the substance.

The remaining part of the substance is nickel:
1-0.77 = 0.23 g of nickel.

Using Ben's estimate, 0.2 g of nickel per gram of substance, we have
0.2(35) = 7 g of nickel in 35 g of the substance.

The actual amount is 0.23(35) = 8.03 g of nickel in 35 g of the substance.
6 0
3 years ago
Evaluate (4/25) 1/2<br><br> A 4/5<br><br> B 4/25<br><br> C2/5<br><br> D2/25
Phantasy [73]
(4/25) 1/2 = 4/50 = 2/25

D. 2/25
8 0
3 years ago
Read 2 more answers
4x-10=30<br> 2n-7=30 <br> S/3+2=4
emmasim [6.3K]

Answer:

x=10 n=18.5 s=6

Step-by-step explanation:

4x-10=30

Add 10 to both sides

4x-10+10=30+10

4x=40

Divide by 4 on both sides

(4x)/4=40/4

x=10

2n-7=30

Add 7 to both sides

2n-7+7=30+7

2n=37

Divide by 2 on both sides

(2n)/2=37/2

n=18.5

(s/3)+2=4

Subtract 2 from both sides

(s/3)+2-2=4-2

(s/3)=2

Multiply by 3 on both sides

3s/3=2*3

s=6

6 0
3 years ago
Find the missing length of the triangle
kondaur [170]

Answer:

35/3 yd

Step-by-step explanation:

first convert the hypotenuse into 37/3, then you can write (37/3)^2-(4)^2=a^2. solve to get 35/3

3 0
3 years ago
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