Which of the following is the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers?

x2 - 14x + 41 + 8 = 0 + 8

x2 - 14x + 41 + 9 = 0 + 9

x2 - 14x + 41 - 8 = 0 - 8

x2 – 14x + 41 - 9 = 0 - 9

Answer:

**Answer:**

*The correct answer is the first option*

**Step-by-step explanation:**

__Quadratic Equation__

The standard form of a quadratic equation is

Sometimes we need to change the expression of the same equation to the form

To accomplish that change, we usually modify the left-hand expression to make it look like the square of a binomial.

The given quadratic equation is

Recall the square of a binomial is

The first term is already present. The second term gives us the value of p:

Solving

Now we need to produce the third term . We only have 41, thus we need to add 8 to both sides of the equation:

The correct answer is the first option

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Catherine's employer matches 25% of her 401(k) contributions — up to $2000. Catherine's salary is $50,000, and last year she contributed $10,000 to her 401(k) plan. What was her employer's contribution to the 401(k)?

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

The director of student health at a large university was concerned that students at his school were consuming too many calories each day. For a certain population of college-age students, it is recommended to consume around 2,000 calories/day. The director would like to test the hypothesis that H0:μ=2000 vs. HA:μ>2000. In a random sample of 50 students the director found that the average was 2105 calories/day with a standard deviation of 288 calories/day. Calculate the appropriate test statistic for this situation. Round your answer to 3 decimal places.

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.

Catherine's employer matches 25% of her 401(k) contributions — up to $2000. Catherine's salary is $50,000, and last year she contributed $10,000 to her 401(k) plan. What was her employer's contribution to the 401(k)?

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

The director of student health at a large university was concerned that students at his school were consuming too many calories each day. For a certain population of college-age students, it is recommended to consume around 2,000 calories/day. The director would like to test the hypothesis that H0:μ=2000 vs. HA:μ>2000. In a random sample of 50 students the director found that the average was 2105 calories/day with a standard deviation of 288 calories/day. Calculate the appropriate test statistic for this situation. Round your answer to 3 decimal places.

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.

Given the x or y value of a 2-variable equation solution, find the value for the other variable in the solution. Practice solving one-variable equations like 20 - 7x

**Answer:**

the answer is 8a

**Step-by-step explanation:**

becuase the numbers are simply being added, you can just add 3+5.

for example, say a=3

3(a)+5(a)=3(3)+5(3)

9+15=24

but 3+5(a)=8(a)

8(3)=24

**Answer:**

8a2

**Step-by-step explanation:**

**Answer:**

nothing actually Iteursitskysjtskydjtsitsitsitskgditdkgd elhsitdlhclufluclydlhcogogjdy

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Sum of the interior angles of any triangle equal 180° .

Thus ;

The angle which facing to the side 4 is 45°.

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**Hint****:**

In a right triangle, the side facing the 45° angle is √2 / 2 times the hypothenuse .

Thus ;

Multiply sides by **2**

Divide sides by **√****2**

Done...

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y= 3x/5 - 2/5 .i think

**Answer:**

**45 units**

**Step-by-step explanation:**

Since both figures are similar, the ratio of their similar sides will be equal to a constant. Hence;

8/10 = 12/EH

8EH = 12 * 10

8EH = 120

EH = 120/8

EH = 15

Perimeter of EFGH = 15 + 10 + 5 + 15 = **45 units**

B) 5

C)8

D) 20

**Answer:**

A)2

**Step-by-step explanation:**

2×x + 3=7

2x+3=7

2x=7-3

2x=4

divide both sides by the coefficient of x which is 2

2x=4

x=2