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3 years ago

What are the properties used to solve 4(x+3)=20

Mathematics

1 answer:

ryzh [129]3 years ago

4 0

Answer:

Multiproperty

Step-by-step explanation:

To solve this problem, we use different properties to arrive at our answer.

Given expression;

4(x + 3) = 20;

First we use the distributive property to expand;

4x + 12 = 20

Now use subtraction property by adding (-12) to both sides;

4x + 12 + (-12) = 20 + (-12)

4x = 8

you can now divide by 4,

x = 2

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Convert 720º to radians.

Luba_88 [7]

Answer:

$720 \cdot \frac{\pi }{180} = 4\pi = 12.56637 rad$

5 0

4 years ago

A phone company offers two monthly plans. Plan A costs $19 plus an additional $0.11 for each minute of calls. Plan B costs $10 p

Aloiza [94]

Answer:

Part 1) When the amount of calling is 450 minutes the two plans cost the same

Part 2) When the two plans cost the same , the cost is $68.50

Step-by-step explanation:

Part 1) For what amount of calling do the two plans cost the same?

Let

x ---> the number of minutes

y ----> the total cost

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

Plan A

The slope is equal to

$m=\$0.11\ per\ minute$

The y-intercept is

$b=\$19$

substitute

$y=0.11x+19$ ----> equation A

Plan B

The slope is equal to

$m=\$0.13\ per\ minute$

The y-intercept is

$b=\$10$

substitute

$y=0.13x+10$ ----> equation B

Equate equation A and equation B

$0.13x+10=0.11x+19$

solve for x

$0.13x-0.11x=19-10\\0.02x=9\\x=450$

therefore

When the amount of calling is 450 minutes the two plans cost the same

Part 2) What is the cost when the two plans cost the same?

substitute the value of x=450 minutes in equation A or equation B and solve for y

$y=0.11(450)+19=68.5$

therefore

When the two plans cost the same , the cost is $68.50

4 0

3 years ago

If the center of the locket is at the origin of a

cluponka [151]

Answer: I believe it is D, y2/1444+x2/676=1

Step-by-step explanation:

6 0

3 years ago

Convert the Cartesian equation x^2 + y^2 = 16 to a polar equation.

RideAnS [48]

Answer:

Problem 1: $r=4$

Problem 2: $r=-2\sin(\theta)$

Problem 3: $r\sin(\theta)=3$

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

$x=r \cos(\theta)$

$y=r \sin(\theta)$

$\frac{y}{x}=\tan(\theta)$

So if we make those substitution into the first equation we get:

$x^2+y^2=16$

$(r\cos(\theta))^2+r\sin(\theta))^2=16$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)=16$

Factor the $r^2$ out:

$r^2(\cos^2(\theta)+\sin^2(\theta))=16$

The following is a Pythagorean Identity: $\cos^2(\theta)+\sin^2(\theta)=1$ .

We will apply this identity now:

$r^2=16$

This implies:

$r=4 \text{ or } r=-4$

We don't need both because both of include points with radius 4.

Problem 2:

$x^2+y^2+2y=0$

$(r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0$

Factoring out $r^2$ from first two terms:

$r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0$

Apply the Pythagorean Identity I mentioned above from problem 1:

$r^2(1)+2r\sin(\theta)=0$

$r^2+2r\sin(\theta)=0$

or if we factor out r:

$r(r+2\sin(\theta))=0$

$r=0 \text{ or } r=-2\sin(\theta)$

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

$y=3$

$r\sin(\theta)=3$

8 0

4 years ago

A moving company is trying to store boxes in a storage room with a length of 5 m, width of 3 m and height of 2 m. How many boxes

Lostsunrise [7]

Volume of room = 500 * 300 * 200 cm

= 30000000 cm³

Volume of 1 box = 10 * 6 * 4

= 240 cm³

Thus, number of boxes in the room

= 30000000/ 240
= 125000 boxes ;

Thus, 125000 boxes can be stored in the room.

5 0

3 years ago