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2 years ago

Solve the system, enter the smallest x coordinate first

Mathematics

1 answer:

uranmaximum [27]2 years ago

8 0

The solutions to the system of equations are given as follows: (1, -3) and (-4,2).

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The equations are given as follows:

(x + 3)² + (y + 2)² = 17.

x + y = -2.

From the second equation:

y = -2 - x.

Replacing in the first:

(x + 3)² + (y + 2)² = 17.

(x + 3)² + (-2 - x + 2)² = 17

x² + 6x + 9 + x² = 17

2x² + 6x - 8 = 0

2(x² + 3x - 4) = 0

2(x + 4)(x - 1) = 0.

Then the solutions for x are:

x + 4 = 0 -> x = -4.

x - 1 = 0 -> x = 1.

The solutions for y are:

When x = 1, y = -2 - 1 = -3.

When x = -4, y = -2 -(-4) = 2.

Hence the solutions are:

(1, -3) and (-4,2).

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

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What is the constant proportionality for the relationship on the graph

tankabanditka [31]

<h3>Answer: Choice A) 3.5</h3>

Work Shown:

The point (8,28) is the furthest to the right on the graph. We have x = 8 and y = 28 pair up here. Divide the y over the x

y/x = 28/8 = 3.5

side note: the tickmarks on the y axis go up by 4 each time

5 0

3 years ago

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Stacie is choosing between two careers. Working for company A, Stacie will make $45,000 the first year and will receive an addit

fomenos

The expression in company B represents that is is in arithmetic progression where first term is 42000 and common difference is 1800 . So we have to use the formula of sum of n terms which is

$S=\frac{n}{2}(2a +(n-1)d)$

Where a is the first term, n is the nth term, d is the common difference

On substituting there values,we will get

$S =\frac{30}{2}(2*42000+(30-1)1800)$

= 15(84000+52200) = 15*136200 =2043000

And for company A, it is

$S= \frac{30}{2}(2*45000+(30-1)1500 ) = 15(90000+43500)=2002500$

Difference between them =2043000-2002500= 40500

So the correct option is the second option .

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3 years ago

Boris drove 240 miles using 9 gallons of gas. At this rate, how many gallons of gas would he need to drive 216 miles?

satela [25.4K]

Use proportion to solve this.
240 miles needs 9 gallons
216 miles needs (9÷240) × 216 = 8.1 gallons

Hope it helped!

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3 years ago

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Which algebraic expression represents “the quotient of a number and thirty”?

Anestetic [448]

Answer: 30/a

Step-by-step explanation:

Quotient means to divide. So the quotient of 30 and another number would be 30/a

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3 years ago

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At the farmer's market, there is a scale that measures the weight of fruit and vegetables. The needle is 16 cm long, and it rota

Eddi Din [679]

It may help to draw a picture as you start planning this problem and draw a circle, showing a circle which represents the scale needle's range of motion 360 degrees around. The needle length will then be the radius of that circle.

We know that the needle rotated 68 degrees and are trying to find the distance it traveled in cm. To find out how far the needle traveled, we need to find the arc length - in this case, the distance between the needle's starting point and where it ended up after the oranges were placed on the scale on the circle.

There is a formula you can easily use to find the arc length
arc length = 2* $\pi$ *r ( $\frac{c}{360}$ )

We need to input the radius, r into this formula, as well as the central angle measure c, which in this case is 68 degrees.

2 $\pi$ (16) ( $\frac{68}{360}$ )

If you multiply the above formula components all together using a calculator, you will get ~18.99. (When rounded to the second decimal place.)

So, the answer is around 19 cm. (Your answer may vary depending on how your teacher usually wants you to round answers.)

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3 years ago

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