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2 years ago

Determine the intercepts of the line. -5x-4y=10

Mathematics

1 answer:

storchak [24]2 years ago

8 0

Answer:

$x-intercept:(-2,0)\\\\y-intercept:(0,-\frac{5}{2})$

Step-by-step explanation:

The y-intercept is where x is 0 (0,y)

The x-intercept is where y is 0 (x,0)

Insert 0 as the value for x to find the corresponding y value:

$-5(0)-4y=10$

Simplify multiplication:

$0-4y=10\\\\-4y=10$

Isolate the variable. Divide both sides by 4:

$\frac{-4y}{4}=\frac{10}{4} \\\\-y=\frac{10}{4} \\\\-y=\frac{5}{2}$

Make the variable positive. Multiply both sides by -1:

$-1(-y)=-1(\frac{5}{2})\\\\y=-\frac{5}{2}$

The y-intercept is at $(0,-\frac{5}{2})$ .

Insert 0 as the value for y to determine the value of x:

$-5x-4(0)=10$

Simplify multiplication:

$-5x-0=10\\\\-5x=10$

Isolate x. Divide both sides by 5:

$\frac{-5x}{5} =\frac{10}{5} \\\\-x=2$

Multiply both sides by -1:

$-1(-x)=-1(2)\\\\x=-2$

The x-intercept is at $(-2,0)$ .

:Done

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Last year a business had profits of $8,000.This year its profits are 5 times as great.This are this year's profits?

Solnce55 [7]

$40,000 in profits this year

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2 years ago

Find the area of the triangle.

BabaBlast [244]

Answer:

17.7 cm^2

Step-by-step explanation:

Use trig to find the height of the triangle. Then the area is bh/2.

Extend side BC to the right until it is vertically below point A. Draw a segment from point A vertically down until it intersects the extension of side BC. Call the point of intersection D. <D is a right angle.

Use triangle ABD to find the height, AD, of triangle ABC.

For <B of 37 deg, AD is the opposite leg. AB is the hypotenuse. The trig ratio that relates the opposite lefg to the hypotenuse is the sine.

sin B = opp/hyp

sin 37 deg = AD/13.1

AD = 13.1 * sin 37 deg

AD = 7.9

AD is the height of triangle ABC. BC is the base. We can find the area of triangle ABC.

area = bh/2

area = (4.5 cm)(7.9 cm)/2

area = 17.7 cm^2

5 0

3 years ago

Jason wants to add a fence to his yard to make it the shape of a rectangle. What is the measure of angle MKJ in the portion of t

alex41 [277]

Answer:

$\angle MKJ = 34$

Step-by-step explanation:

Given

$\angle LKJ = 124$

Required

Find $\angle MKJ$

From the attachment:

The measure of $\angle MKJ$ is calculated using the following expression:

$\angle MKJ + \angle LKM = \angle LKJ$

Where

$\angle LKM = 90$ -- right-angled.

The expression becomes

$\angle MKJ + 90 = 124$

$\angle MKJ = 124 - 90$

$\angle MKJ = 34$

3 0

2 years ago

can anyone help tech me how to solve for tax and tip. im going to 6th grade and trying to get into the advanced group but I don'

baherus [9]

If something isn't clear or you're still confused about, let me know in the comments.

Step-by-step explanation:

Okay, here's my best try.

Suppose you have a bill for $8.45

If you are asked to add, say, 8% tax, you must calculate 8 percent of 8.45 and then add it to 8.45.

Begin by converting 8% to decimals by dividing by 100.

$\frac{8}{100}=0.08$ 8% is 0.08 in decimal form.

To calculate a percentage of a number, you multiply the decimal percent by the number; example:

$0.08(8.45)$ 8.45 is being multiplied by 0.08. The result is: 0.676. (this is the tax; however you have to round up to two decimal places: $0.68)

After finding the tax amount, if you are asked to add it to the bill, you have to add it to the original bill; in this case, $8.45

This would be: 0.68+8.45=9.13.

Therefore, the total bill after tax is for $9.13

----------------------------------------------------------------------------------------------------

With tips is the same thing, however, you can have 2 situations.

Situation 1: You are asked to calculate 15% tip of total bill.

In this situation, you can do the same we do to calculate tax.

Convert the percentage to decimal by dividing by 100.

$\frac{15}{100}=0.15$

and multiply it by the original bill.

$0.15(8.45)=1.2675$ . Rounding up, this would be $1.27 for tip.

If you were to add it to the original bill, simply sum.

$8.45+1.27=9.72$

The total bill after tips is for $9.72

Situation 2: You are asked to calculate 15% tip of the total bill with a tax of 8% included.

In this situation, you must first calculate the total bill with the tax added, like we did above; we got a bill for $9.13 (Tax included)

Then you can calculate 15% tip of this new bill that has tax included.

Convert

$\frac{15}{100}=0.15$

Multiply by the new bill (because this is the one that includes tax)

$0.15(9.13)=1.3695$ Round up.... $1.37 for tips.

If you are asked to give a total amount of money including tax and tips, add this to the bill.

9.13+1.37=10.50

This bill would be for $10.50

3 0

3 years ago

An artist wants to frame a square painting with an area of 400 square inches . she wants

Artemon [7]

(a) $x^{2}$ = 400
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(c) Only the positive solution makes sense because you cannot have a negative side length.
(d) Since one side of the painting is 20 inches, all four sides together will be 20*4 = 80 inches

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3 years ago