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2 years ago

Solve the equation using square roots. 7x2 + 6 = 13

Mathematics

2 answers:

m_a_m_a [10]2 years ago

8 0

Answer:

The solution of the equation $7x^2+6=13$ is:

x=1 or -1

Step-by-step explanation:

$7x^2+6=13$

subtracting by 6 on both sides

$7x^2+6-6=13-6$

$7x^2=7$

dividing by 7 on both sides, we get

$x^2=1$

taking square roots on both sides, we get

x=±√1

⇒ x=1 or -1

Elis [28]2 years ago

4 0

Move all terms not containing xx to the right side of the equation.
Since 66 does not contain the variable to solve for, move it to the right side of the equation by subtracting 66 from both sides.7x2=−6+137x2=-6+13Add −6-6 and 1313 to get 77.7x2=77x2=7Divide each term by 77 and simplify.
Divide each term in 7x2=77x2=7 by 77.7x27=777x27=77Reduce the expression by cancelling the common factors.
x2=77x2=77Divide 77 by 77 to get 11.x2=1x2=1Take the squaresquare root of both sides of the equationequation to eliminate the exponent on the left side.x=±√1x=±1The complete solution is the result of both the positive and negative portions of the solution.
Any root of 11 is 11.x=±1x=±1The complete solution is the result of both the positive and negative portions of the solution.
x=1,−1

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Suppose that in a survey of 1,000 U.S. residents, 721 residents believed that the amount of violent television programming had i

Art [367]

Answer: 0.813

Step-by-step explanation:

Let A be the event describes the number of residents believed that the amount of violent television programming had increased over the past 10 years.

& B be the event describes the number of residents believed that the amount of violent television programming had decreased over the past 10 years.

Given : n(A)=721 ; n(B)=454 ; n(A∩B)=362

We know that ,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

i.e. $n(A\cup B)=721+454-362=813$

Also, the total number of U.S. residents surveyed n(S)= 1,000

Then, the proportion of the 1,000 U.S. residents believed that either the amount of violent programming had increased or the overall quality of programming had decreased over the past 10 years will be :-

$P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}=\dfrac{813}{1000}=0.813$

Hence, the required answer = 0.813

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2 years ago

Leslie started last week with $1200 in her checking account. During the week, she wrote the checks below.

kifflom [539]

Answer: B
Look at the line where it says 935 54
Leslie goes to the salon and pays $30
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However, the line after the $30 says $900.59, which is incorrect.

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An obtuse angle which is greater than 90 degrees and less than 180 degrees.

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According to a survey, 10% of Americans are afraid to fly. Suppose 1100 Americans are sampled. a) What is the probability that 1

JulijaS [17]

Answer:

a) 14.46%

b) 0.00%

c) 1.54%

Step-by-step explanation:

According to the survey, 10% of Americans are afraid to fly.

This means $p=0.10$ and $q=1-0.10=0.90$ .

If 1100 Americans are sampled, then the sample size is $n=1100$ .

The mean of the distribution is $\mu=np$ .

This means $\mu=1100\times 0.10=110$

The standard deviation is $\sigma=\sqrt{npq}$

We substitute the values to get:

$\sigma=\sqrt{1100\times 0.1\times 0.9}=9.95$

a) We want to find the probability that 121 or more Americans in the survey are afraid to fly.

We first apply the continuity correction factor to get: $P(X\ge121)=P(X\:>\:121-0.5)\\P(X\ge121)=P(X\:>\:120.5)$

We now convert to Z-scores to get:

$P(X\:>\:120.5)=P(z\:>\:\frac{120.5-110}{9.95})=1.06\\$

From the standard normal distribution table P(z>1.06)=0.1446

As a percentage, the probability is 14.46%

b) We want to find the probability that 165 or more Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\ge165)=P(X\:>\:165-0.5)\\P(X\ge165)=P(X\:>\:164.5)$

We convert to z-scores:

$P(X\:>\:164.5)=P(z\:>\:\frac{164.5-110}{9.95})=5.48$

From the normal distribution, P(z>164.5)=0

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We want to find the probability that 88 or less Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\le88)=P(X\:$

We convert to z-scores:

$P(X\:$

From the normal distribution, P(z>\:-2.16)=0.0154

As a percentage, we get 1.54%

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