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2 years ago

Complete the equation to show two equivalent expressions. g2 – 4g – 21 = (g – )(g + )

Mathematics

2 answers:

Misha Larkins [42]2 years ago

6 0

Answer:

$g^2-4g-21=(g-7)(g+3)$

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

$(g-a)(g+b)$

expanding this expression we get:

$g^2+bg-ag-ab$

$g^2+(b-a)g-ab$

Thus we have

$g^2-4g-21=g^2+(b-a)g-ab$

from here we see that for both sides of the equation to be equal, it must be that

$b-a=-4$

$-ab=-21$ .

Getting rid of the negative signs we get:

$a-b=4$

$ab=21$

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for $a$ and $b$ systematically.

The solutions to this set are $a=7$ and $b=3$ . (you have to guess on this—it's easier)

Therefore, we have

$(g-a)(g+b)=(g-7)(g+3)$

which completes our equation

$\boxed{ g^2-4g-21=(g-7)(g+3)}$

sergejj [24]2 years ago

3 0

Answer:

I think that the answer is -7&3

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The table shows weights for different US coins. Allen has one of each coin in his hand

Sever21 [200]

Penny- 3g
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6 0

2 years ago

Read 2 more answers

Which value of a would make the expression 5 1/3 ÷ 4/a equivalent to a whole number?

nordsb [41]

Answer:

a is any number that is multiples of 3

3, 6, 9, 12, etc...

Step-by-step explanation:

5 1/3 ÷ 4/a

16/3 * a/4

16a/12

$\frac{4}{3} a$

since denominator is 3, a can be any whole number that is a multiple of 3

$\frac{4}{3}(3) = 4$

$\frac{4}{3}(6) = 8$

$\frac{4}{3}(9) = 12$

so on and so on....

8 0

2 years ago

Pat's ending balance on his debit card last month was $233.55. This month he had $542 worth of purchases and $710 worth of depos

ad-work [718]

Answer:

$401.55

Step-by-step explanation:

Given:

Pat's ending balance on his debit card last month was $233.55, we can consider it as opening balance for this month as carry forwarded.

This month he had $542 worth of purchases.

This month he had $710 worth of deposits.

Question asked:

What is his ending balance for this month ?

Solution:

We can easily find the ending balance by subtracting purchase amount as it will reduce the balance and we will add deposits as it increase the balance of debit card.

Opening balance of debit card = $233.55

Purchases worth of = $542

Deposit worth of = $710

Ending balance for this month = Opening balance of debit card + Deposit - Purchases

Ending balance for this month = $233.55 + $710 - $542

= $943.55 - $542 = $401.55

Therefore, the ending balance for this month in his debit card is $401.55

4 0

2 years ago

In a study of hormone supplementation to enable oocyte retrieval for assisted reproduction, a team of researchers administered t

olchik [2.2K]

Answer:

Note: This question is incomplete and complete question is posted down below with multiple choice questions and from Option 3 is correct

Step-by-step explanation:

Note: This question is incomplete and it is a multiple choice question. With the following multiple choices to select from.

1. The researchers expect that 80% of all similarly constructed intervals will contain the true mean number of oocytes that could be retrieved from the population of women aged 36-40 years.

2. The researchers expect that 80% of all similarly constructed intervals will contain the mean number of oocytes retrieved in the sample of 98 women aged 36-40 years.

3. There is a 80% chance that the the true mean number of oocytes that could be retrieved from the population of women aged 36-40 years is uniquely contained in the reported interval.

4. The researchers expect that 80% of all similarly constructed intervals will contain the range of the number of oocytes that could be retrieved from the population of women aged 36-40 years.

we have to select the appropriate answer from the above options.

So, in order to choose the correct option, first we need to understand the confidence interval.

Confidence Interval is a range of value for which are pretty sure our true values will lie in that interval. For example, in this question, we have 80% confidence interval and it means there is a 80% confident chance that our true values will lie in that 80% interval. Let's calculate it.

We have following data given from the question.

Sample = 98

Mean = 9.7

Confidence Interval = 80%

Z = 1.282

And formula for confidence interval is :

Mean ± Z x SD/ $\sqrt{n}$

For this equation, we have all quantities except SD which is standard deviation. Let's calculate it first.

Standard deviation is square root of variance and so we need to calculate variance first.

Mean = Sum/ total number

9.7 = Sum/ 98

Sum = 950.6

For variance we will use this sum.

s² = (950.6 (1 - 9.7)²) ÷ (98-1)

s² = 741. 762 = Variance.

Let's calculate Standard deviation

SD = $\sqrt{variance}$

SD = $\sqrt{741.762}$

SD = 27.23 = Standard Deviation.

Now, we have complete data to calculate range of values for the confidence interval of 80%

Mean ± Z x SD/ $\sqrt{n}$

Here, Z is the Z-score and it has predetermined value for different confidence intervals and here in our case for 80% , Value of Z = 1.282

Now, by just plugging in the values in to above formula we will get range of values or confidence interval of 80% in which our true value will likely to lie.

9.7 ± 1.282 x 27.23/ $\sqrt{98}$

9.7 ± 3.52 Or

9.7 + 3.52 = 13.22

9.7 - 3.52 = 6.18

Rangle of Values with confidence interval of 80% = (6.18 to 13.22).

Which means that, our true mean will most likely lie in this interval.

So, the option 3 is correct which meets the correct definition and interpretation of the problem.

6 0

2 years ago

PLEASE HELP!

melamori03 [73]

Answer:

The answer is C.

Step-by-step explanation:

The $13 he started off with is the y-intercept or the initial value, which is the point where x=0.

The x-intercept, or rate of change, is $8.50.

The slope intercept formula is y=mx+b, where m=8.5 and b=13.

The equation for this problem is y=8.5x+13.

So the answer is C

4 0

2 years ago