Mathematics, 13.02.2021 22:10 jonesmegan526

the line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,-6) what is the value of k ?

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Answer from: bazzy94

The value of k is:

$k=-\frac{31}{4}$

Step-by-step explanation:

Given

The line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,-6).

To determine

what is the value of k?

To determine the value of k, the first step we need to do is to find the slope of the line containing the points (5,3) and (1,-6) using the formula

$\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}$

Here:

$\left(x_1,\:y_1\right)=\left(5,\:3\right)$ $\left(x_2,\:y_2\right)=\left(1,\:-6\right)$

now substituting (x₁, y₁) = (5, 3) and (x₂, y₂) = (1, -6) in the formula

$m=\frac{-6-3}{1-5}$

$m=\frac{-9}{-4}$

Apply the fraction rule: $\frac{-a}{-b}=\frac{a}{b}$

$m=\frac{9}{4}$

Thus, we conclude that the slope of the line containing the points (5,3) and (1,-6) will be:

$m=\frac{9}{4}$

Importing Tip:

We know that the parallel lines have the same slopes, so the slope of the line containing the points (-3,k) and (4,8) will also be 9/4.

Thus, using the slope formula for the line containing the points (-3,k) and (4,8).

$\mathrm{Slope}=m=\frac{y_2-y_1}{x_2-x_1}$

Here:

$\left(x_1,\:y_1\right)=\left(-3,\:k\right)$ $\left(x_2,\:y_2\right)=\left(4,\:8\right)$

As we know that the parallel lines have the same slopes.

Thus, the second step we need to do is to substitute m = 9/4 in the slope formula

$\frac{9}{4}=\frac{y_2-y_1}{x_2-x_1}$

now substituting (x₁, y₁) = (-3, k) and (x₂, y₂) = (4, 8) in the formula

$\:\:\:\frac{9}{4}=\:\frac{8-k}{4-\left(-3\right)}$

switch sides

$\frac{8-k}{4-\left(-3\right)}=\frac{9}{4}$

Multiply both sides by 7

$\frac{7\left(8-k\right)}{4-\left(-3\right)}=\frac{9\cdot \:7}{4}$

Simplify

$8-k=\frac{63}{4}$

Subtract 8 from both sides

$8-k-8=\frac{63}{4}-8$

Simplify

$-k=\frac{31}{4}$

Divide both sides by -1

$\frac{-k}{-1}=\frac{\frac{31}{4}}{-1}$

Simplify

$k=-\frac{31}{4}$

Therefore, the value of k is:

$k=-\frac{31}{4}$

VERIFICATION:

As the value of k = -31/4.

So the first line will contain the points:

(-3, -31/4)(4, 8)

Finding the slope between (-3, -31/4) and (4, 8) using the slope formula

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Here:

$\left(x_1,\:y_1\right)=\left(-3,\:-\frac{31}{4}\right)$ $\left(x_2,\:y_2\right)=\left(4,\:8\right)$

so substituting (x₁, y₁) = (-3, -31/4) and (x₂, y₂) = (4, 8) in the formula

$m=\frac{8-\left(-\frac{31}{4}\right)}{4-\left(-3\right)}$

Apply rule: $-\left(-a\right)=a$

$m=\frac{8+\frac{31}{4}}{4+3}$

Add the numbers: 4+3=7

$m=\frac{8+\frac{31}{4}}{7}$

$m=\frac{\frac{63}{4}}{7}$ ∵ $8+\frac{31}{4}=\frac{63}{4}$

Apply fraction rule: $\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$m=\frac{63}{4\cdot \:7}$

$m=\frac{63}{28}$

Cancel the common factor: 7

$m=\frac{9}{4}$

So, the slope of the line containing the points (-3,k) and (4,8) is m = 9/4. It means both lines have the same slopes. Hence, they are parallel.

Therefore, we conclude that the value of k = -31/4 is true.

Answer from: Quest

asdsaddsa

step-by-step explanation:

Answer from: Quest

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

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