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2 years ago

Find the slope and y-intercept of the line that is parallel to y = -x - 3 and passes through the point (3, -2)

1 answer:

3 0

Use point slope formula y-y1=m(x-x1)
You are told that y=-x+3. This equation is of the form y=mx+b. Where m=-1. m is the slope. And you have a point (x1,y1) that is (3,-2). With all of this in mind, you then plug all of these details into the point slope formula y-y1=m(x-x1)

In point slope form, you have the following:

y-(-2)=-1(x-3).

To turn this into slope intercept form, simplify y-(-2) to get y+2 and distribute in the -1 to get:

y+2=-x+3

Subtract 2 from both sides to get

y=-x+1

In slope intercept form, the answer is
y=-x+1 and in point slope form, the answer is y+2=-x+3

Hope this helps!!!

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If f(x) = 3x^2 – 2 and g(x) = 2x + 4, find (f- g)(x).

Andreas93 [3]

Answer:

(f - g)(x) = 3x² - 2x - 6

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 2

g(x) = 2x + 4

(f - g)(x) is f(x) - g(x)

Step 2: Evaluate

Substitute: (f - g)(x) = 3x² - 2 - (2x + 4)
Distribute -1: (f - g)(x) = 3x² - 2 - 2x - 4
Combine like terms: (f - g)(x) = 3x² - 2x - 6

5 0

2 years ago

35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Find the area of the larger circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

7 0

3 years ago

interest rate on a credit card is 15% if we charge $200 to the card, how much will we pay including the interest

san4es73 [151]

Answer:

$230

Step-by-step explanation:

15 percent of 200 is 30, add 30 to 200 which is 115%,

so 230.

5 0

3 years ago

PLEASE HELP! I know the top part I just need the bottom!

Zolol [24]

slope = (y2-y1)/(x2-x1)

= (70-52)/(8-1)

= 18/7

=2.6

point slope form

y-y1 = m(x-x1)

y-52 = 2.6(x-1)

distribute

y-52 = 2.6x-2.6

add 52 to each side

y = 2.6x+49.4

y = 2.6x +49

the initial temperature is 49.4 or about 49

and it increases about 2.6 degrees each week

7 0

3 years ago

PLEASE HELP I WILL GIVE BRAINLIEST:)

DedPeter [7]

Answer: uhhhh try the first one

Step-by-step explanation:

5 0

2 years ago