All categories

3 years ago

Find two integers whose product is 138 such that one of the integers is seven less than five times the other integer.

Mathematics

1 answer:

Oksana_A [137]3 years ago

4 0

Answer: the integers are 6 and 23

Step-by-step explanation:

Let x represent one of the integers.

Let y represent the other integer.

The product of the integers is 138. This means that

xy = 138 - - - - - - - - - -1

One of the integers is seven less than five times the other integer. This means that

x = 5y - 7

Substituting x = 5y - 7 into equation 1, it becomes

y(5y - 7) = 138

5y² - 7y = 138

5y² - 7y - 138 = 0

5y² + 23y - 30y - 138 = 0

y(5y + 23) - 6(5y + 23)

y - 6 = 0 or 5y + 23 = 0

y = 6 or y = - 23/5

The only possible value of y is 6

x = 138/y = 138/6

x = 23

You might be interested in

Using the simple random sample of weights of women from a data set, we obtain these sample statistics: nequals45 and x overbar

Tomtit [17]

Answer: (141.1, 156.48)

Step-by-step explanation:

Given sample statistics : $n=45$

$\overline{x}=148.79\text{ lb}$

$\sigma=31.37\text{ lb}$

a) We know that the best point estimate of the population mean is the sample mean.

Therefore, the best point estimate of the mean weight of all women = $\mu=148.79\text{ lb}$

b) The confidence interval for the population mean is given by :-

$\mu\ \pm E$ , where E is the margin of error.

Formula for Margin of error :-

$z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given : Significance level : $\alpha=1-0.90=0.1$

Critical value : $z_{\alpha/2}=z_{0.05}=\pm1.645$

Margin of error : $E=1.645\times\dfrac{31.37}{\sqrt{45}}\approx 7.69$

Now, the 90% confidence interval for the population mean will be :-

$148.79\ \pm\ 7.69 =(148.79-7.69\ ,\ 148.79+7.69)=(141.1,\ 156.48)$

Hence, the 90% confidence interval estimate of the mean weight of all women= (141.1, 156.48)

3 0

3 years ago

You go to the store and buy some pencils and sweet tarts. ( $.35 per pencil & $.10 per sweet tart) You purchased a total of

blondinia [14]

Answer:

7 pencils

8 sweet tarts

Step-by-step explanation:

7*0.35=2.45

8*0.10=0.80

2.45+0.80=3.25

7+8=15

8 0

3 years ago

Which graph represents a function with a rate of change of 0.5?

stiks02 [169]

Answer:

C.)On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (1, 1).

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

CE and FI are parallel, give reasons to prove that DGH is isosceles

Tresset [83]

Answer:

DGH has a different number than Ce and FI

4 0

2 years ago

Huilan is years 15 younger than Thomas. The sum of their ages is 73 . What is Thomas's age?

UNO [17]

thomas age:44

huilan age: 29

7 0

2 years ago

Read 2 more answers