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4 years ago

What is the equation of a line that is parallel to y=47x−3 and passes through (14, 4)?

Mathematics

1 answer:

Shtirlitz [24]4 years ago

6 0

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where

m = slope

c = intercept

The equation of the given line is

y = 47x - 3

Comparing with the slope intercept equation, m = 47

If two lines are parallel, it means that they have equal slope. This means that the slope of the line passing through (14, 4) is 47

We would determine the intercept, c by substituting m= 47, x = 14 and y = 4 into y = mx + c. It becomes

4 = 47× 14 + c

4 = 658 + c

c = 4 - 658 = - 654

The equation becomes

y = 47x - 654

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MAVERICK [17]

Answer:

$d.\:ellipse;\:3x^2+y^2+6x-6y+3=0$ .

Step-by-step explanation:

The given conic has equation;

$3x^2+y^2=9$

Divide through by 9.

$\Rightarrow \frac{3x^2}{9}+\frac{y^2}{9}=\frac{9}{9}$

$\Rightarrow \frac{x^2}{3}+\frac{y^2}{9}=1$ .

This is an ellipse centered at the origin;

This ellipse has been translated so that the center is now at;

$(-1,3)$

The translated ellipse has equation;

$\frac{(x+1)^2}{3}+\frac{(y-3)^2}{9}=1$ .

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Expand;

$3(x^2+2x+1)+(y^2-6y+9)=9$ .

$3x^2+6x+3+y^2-6y+9=9$ .

Write in general form;

$3x^2+y^2+6x-6y+9-9+3=0$ .

$3x^2+y^2+6x-6y+3=0$ .

The correct choice is D

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3 years ago

Read 2 more answers

If x= 19 feet and y = 12 feet, what is the area and perimeter of the figure above?

Delicious77 [7]

All we need to do to solve this problem is calculate the area of a rectangle and the area of a circle, then add them!

____________________________

First, let's do the rectangle!

Area of a rectangle = length x width

or in this case... Area = "x" times "y"

Area = 19 × 12 = 228 square feet!

________________________________

Now, let's do the circle!

Area of a circle = πr² ... (r = radius)

* In this diagram, the diameter of the circle is also the same length as "y"!

* And remember that radius is half of the diameter.

radius = 6

Now, let's actually calculate the area

Area = π(6)² ⇒ 36π

Area = 113.1 (I rounded up the decimals!)

_______________________________________

*But wait! Look at the figure! It looks like HALF of the circle's area was included when we calculated the area of the rectangle! This means that we should divide the area of the circle (that we just calculated) in half!

Area of the HALF CIRCLE = 113.1 ÷ 2 = 56.5

Now let's add the area of the rectangle to the area of the half-circle to find the area of THE ENTIRE FIGURE!

228 + 56.5 = 284.5

284.5 square feet is our answer!

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2 years ago

Convert 7.5 to a decimal

julsineya [31]

7.5 is already in decimal form.

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