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3 years ago

Solve the following quadratic equation by factoring.

Mathematics

2 answers:

saveliy_v [14]3 years ago

8 0

<h3>Answer: x = -2 or x = 7 (choice D)</h3>

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Work Shown:

x^2 - 5x = 14

x^2 - 5x - 14 = 0

(x-7)(x+2) = 0 .... this step is further explained below

x-7 = 0 or x+2 = 0

x = 7 or x = -2

The order of the solutions does not matter.

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To factor x^2-5x-14, we need to find two numbers that multiply to -14 and add to -5. This is done through trial and error. I recommend making a table to help organize everything. See the diagram below.

After a bit of guess work, you should find that -7 and 2 are the two values we're after

-7 + 2 = -5

-7 * 2 = -14

This is why x^2-5x-14 = (x-7)(x+2)

tekilochka [14]3 years ago

6 0

Answer:

x = 7, -2

Step-by-step explanation:

<h2>Factor and set each factor equal to 0</h2>

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8 0

3 years ago

What is the value of the expression:

inna [77]

54 I hope this helps

6 0

3 years ago

Read 2 more answers

(CO6) From a random sample of 68 businesses, it is found that the mean time that employees spend on personal issues each week is

satela [25.4K]

Answer:

(1) (4.82, 4.98)

(2) Large sample size

(3) Yes, the temperature is within the confidence interval of (37.40, 37.60)

(4) (15.083, 15.117)

Step-by-step explanation:

Confidence Interval (CI) = mean + or - (t×sd)/√n

(1) mean = 4.9, sd = 0.35, n = 68, degree of freedom = n-1 = 68 - 1 = 67

t-value corresponding to 67 degrees of freedom and 95% confidence level is 1.9958

CI = 4.9 + (1.9958×0.35)/√68 = 4.98

CI = 4.9 - (1.9958×0.35)/√68 = 4.82

CI is (4.82, 4.98)

(2) Error margin = (t-value × standard deviation)/√sample size

From the formula above, error margin varies inversely as the square root of the sample size. Since the relationship between the error margin and sample size is inverse, increase in one (sample size) will conversely lead to a decrease in the other (error margin)

(3) mean = 37.5, sd = 0.6, n= 100, degree of freedom = n-1 = 100-1 = 99

t-value corresponding to 99 degrees of freedom and 90% confidence level is 1.6602

CI = 37.5 + (1.6602×0.6)/√100 = 37.5 + 0.10 = 37.60

CI = 37.5 - (1.6602×0.6)/√100 = 37.5 - 0.10 = 37.40

37.53 is within the confidence interval (37.40, 37.60)

(4) mean = 15.10, sd =0.08, n = 104, degree of freedom = n-1 = 104-1 = 103

t-value corresponding to 103 degrees of freedom and 97% confidence interval is 2.2006

CI = 15.10 + (2.2006×0.08)/√104 = 15.10 + 0.017 = 15.117

CI = 15.10 - (2.2006×0.08)/√104 = 15.10 - 0.017 = 15.083

CI is (15.083, 15.117)

4 0

3 years ago

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2 years ago

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2 years ago