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3 years ago

-2(x-5)=6(2- 1/2x) Please show your work. Distributive property, remove variable

Mathematics

1 answer:

schepotkina [342]3 years ago

6 0

The solution of given equation is x=2

Further explanation:

In order to solve the given equation we have to isolate the variable x on one side of the equation. The process will involve distributive property and simplification.

Given:

$-2(x-5)=6(2-\frac{1}{2}x)\\Apply\ distributive\ property\\-2x-2(-5)=(6)(2)-(6)(\frac{1}{2}x)\\-2x+10=12-\frac{6}{2}x\\-2x+10=12-3x\\-2x+3x=12-10\\x=2$

The solution of given equation is x=2

Keywords: Linear Equation, Distributive property

Learn more about linear equations at:

#LearnwithBrainly

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Identify the percent of change as an increase or decrease. Then find the percent of change. Round to the nearest tenth of a perc

bazaltina [42]

I'll do the first two problems to get you started. All problems shown will use the same formula.

===========================================

Problem 4

The formula to use is

C = 100*(B-A)/A

where

A = old value

B = new value

C = percent change

In this case, A = 12 and B = 36, so

C = 100*(B-A)/A

C = 100*(36-12)/12

C = 100*(24/12)

C = 100*2

C = 200%

We have a 200% increase. It is an increase because the value of C is positive.

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Problem 5

Use the same formula as in the previous problem. This time,

A = 75 is the old value

B = 25 is the new value

C = 100*(B-A)/A

C = 100*(25-75)/75

C = 100*(-50/75)

C = 100*(-2/3)

C = -66.6667%

C = -66.7%

The value of C is negative, so we have a percent decrease of roughly 66.7%

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2 years ago

Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of

yuradex [85]

Answer:

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

Step-by-step explanation:

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining side c and ∠B and ∠C

Using Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c = 4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

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2 years ago

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1 year ago

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Answer:

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2 years ago

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AVprozaik [17]

Answer:

The 99% confidence interval would be given by (196.2;283.8)

We are 99% condident that the true mean is between 196.2 and 283.8

We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.

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".

$\bar X=240$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=15 represent the sample standard deviation

n=4 represent the sample size

Part a

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=4-1=3$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,3)".And we see that $t_{\alpha/2}=5.84$

Now we have everything in order to replace into formula (1):

$240-5.84\frac{15}{\sqrt{4}}=196.2$

$240+5.84\frac{15}{\sqrt{4}}=283.8$

So on this case the 99% confidence interval would be given by (196.2;283.8)

We are 99% condident that the true mean is between 196.2 and 283.8

What assumption about the data is necessary for the inference derived from the analysis to be valid?

We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.

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2 years ago