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Kisachek [45]
1 year ago
15

find the equation of the line which passes through the point (-5,5) and is parallel to the given line. express your answer in sl

ope-intercept form. simplify your answer.

Mathematics
1 answer:
Softa [21]1 year ago
5 0

The given equation of a line is:

7y-14=-3(5-x)

It is required to find the equation of a line that is parallel to this line and passes through the point (-5,5).

Recall that the equation of a line in point-slope form is given as:

y-y_1=m(x-x_1)

Where m is the slope of the line, and the line passes through the point (x₁,y₁).

Rewrite the given equation in the point-slope form:

\begin{gathered} 7y-14=-3(5-x) \\ Distribute\text{ -1 into the parentheses in the right-hand side:} \\ \Rightarrow7y-14=3(-5+x) \\ \text{Rewrite the expression in the parentheses using the co}mmutative\text{ property of addition:} \\ \Rightarrow7y-14=3(x-5) \\ \text{Divide both sides of the equation by 7:} \\ \Rightarrow y-2=\frac{3}{7}(x-5) \end{gathered}

Compare this equation with the standard point-slope form written above, it can be seen that the slope of the line is 3/7.

Recall that the slopes of parallel lines are the same or equal<em>.</em>

It follows that the slope of the required parallel line is also 3/7.

Substitute m=3/7 and the point (x₁,y₁)=(-5,5) into the point-slope form of the equation of a line:

y-5=\frac{3}{7}(x-(-5))

Rewrite the equation in the slope-intercept form and simplify as required:

\begin{gathered} \Rightarrow y-5=\frac{3}{7}(x+5) \\ \Rightarrow y-5=\frac{3}{7}x+\frac{15}{7} \\ \Rightarrow y=\frac{3}{7}x+\frac{15}{7}+5 \\ \Rightarrow y=\frac{3}{7}x+\frac{50}{7} \end{gathered}

The required equation of the line is y=3/7 x + 50/7.

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For this case we have that the cost of each pizza is given by the following function:

S (r) = 0.1 \pi * r ^ 2

Where:

r: It's the radius of the pizza

IF a pizza cost $26.32 we have:

26.32 = 0.1 \pi * r ^ 2

We cleared the radius, using \pi = 3.14:

\frac {26.32} {0.1} = \pi * r ^ 2\\263.2 = 3.14r ^ 2\\\frac {263.2} {3.14} = r ^ 2\\83.82 = r ^ 2\\r = \pm \sqrt {83.82}

We choose the positive value:

r = 9.15

So, the radius of the pizza is 9.16 \ in

Then, the diameter is: 2r = 2 * 9.15 = 18.30 \ in

Finally, the diameter of the pizza is:18.30 \ in

Answer:

Option B

4 0
3 years ago
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True or false. to solve y in the equation 2x y=5, subtract 2 from both sides of the equation
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True. To solve for y you have to subtract 2 from both sides of the equation.
3 0
3 years ago
Krystal bought a refrigerator from a rental center for $1,050. She makes 16 monthly payments of $112.75 with her credit card. Th
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The total cost of the refrigerator was $1,824
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wanting to cut down his television-watching time slowly, Vince decides to watch 30 fewer minutes of television each week after t
Effectus [21]

Answer:

f(n) = - 0.5n + 6

Step-by-step explanation:

Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.

Slope-intercept form is y=mx+b. In this case, we are choosing to use f(n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f(n)=mn+b.

We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or -0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of -0.5 and is represented by m.

We substitute b=6 and m=0.5 into our form to get f(n)=-0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.

f(n)=-0.5(1)+6=-0.5+6=5.5

We can substitute for any n week and find the amount.


7 0
3 years ago
I NEED HELP WITH THIS (GEOMETRY)
denis23 [38]

Answer:

x=30

Step-by-step explanation:

5x+x=180

6x=180

x=30

5x=150

x=30

3x=90

2x=60

5 0
3 years ago
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