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3 years ago

Solve for x. Use the completing the square method. x² + 10x = 6

Mathematics

1 answer:

wel3 years ago

6 0

Answer:

x =5 ±sqrt( 31)

Step-by-step explanation:

x² + 10x = 6

b = 10

Take b/2 and square it

(10/2) = 5 5^2 = 25

Add 25 to each side

x² + 10x+25 = 6+25

The left side will be (x+b/2)^2

(x+5)^2 = 31

Take the square root of each side

sqrt((x+5)^2) = ±sqrt( 31)

x+5 = ±sqrt( 31)

Subtract 5 from each side

x+5-5 = -5 ±sqrt( 31)

x =5 ±sqrt( 31)

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Kim, Laura and Molly share £385 The ratio of the amount of money Kim gets to the amount of money Mollly gets is 2:5 Kim gets £10

Thepotemich [5.8K]

Molly: 105 x 05/02 = 42
Kim: 105-42 = 63
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280 x 100/385 = 72%
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3 years ago

What is the answer for -4 (-6x + 3 ) =12

liq [111]

Answer:

x=1

Step-by-step explanation:

Simplify:

24x-12=12

add 12 on both sides:

24x=24

divide both sides by 24

x=1

Hope this helps!

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3 years ago

What all sets does 4/5 belong too? Natural, whole, integer, rational, irrational, real?

Lera25 [3.4K]

Answer:

Real, rational

Step-by-step explanation:

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4 years ago

Read 2 more answers

Help me please !!!!!!!! I DON'T KNOWWWWWWWWWW

r-ruslan [8.4K]

Answer:

m<1= 120

Step-by-step explanation:

1. we know supplementary angles equals 180. the angle 130 is part of a supplementary angle so we can subtract it by 180 to see that missing angle.

2. we also know that all triangles three angles add up to 180. So if we add the number we know 70+50 (50 is from subtracting 130 from 180), Once we find that answer, we subtract it from 180 to find angle 2 which is 60 degrees

3. Last step, angle 2 is part os a supplementary angle in which the two angles add up to 180. So, subtracting 60 from 180 will get you the degree of the angel one which his 120 degrees.

7 0

4 years ago

23. A certain type of gasoline is supposed to have a mean octane rating of at least 90. Suppose measurements are taken on of 5 r

Nostrana [21]

Answer:

a) $p_v =P(Z$

b) Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

c) $P(\bar X >90)=1-P(Z$

$1-P(Z$

d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

Step-by-step explanation:

Previous concepts and data given

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".

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$\bar X=88.96$ represent the sample mean

$s=1.011$ represent the sample standard deviation

n=5 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 90, the system of hypothesis would be:

Null hypothesis: $\mu \geq 90$

Alternative hypothesis: $\mu < 90$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{88.96-90}{\frac{0.8}{\sqrt{5}}}=-2.907$

Part a

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=5-1 = 4$

Then since is a left tailed test the p value would be:

$p_v =P(Z$

Part b

Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

Part c

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >90)=1-P(Z$

$1-P(Z$

Part d

For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

7 0

3 years ago