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shutvik [7]
3 years ago
15

Solve and graph this system of equations x+2y=5 and 3x=15-6y

Mathematics
1 answer:
Bogdan [553]3 years ago
3 0

Answer:

(x,y)=(5-2y,y), y belongs to all real numbers

Step-by-step explanation:

x=5-2y

3x=15-6y

3(5-2y)=15-6y

15-6y=15-6y

y∈All Real Numbers

(x,y)=(5-2y,y), y∈All Real Numbers

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The formula for the circumference, C, of a circle with radius r is given.
kolezko [41]
The formula for the circumference, C, of a circle with radius r is given.

C=2pi

Amanda made a circular toy hoop using a plastic tube. The circumference of the hoop is 125.6 inches. What is the radius of the hoop? Use 3.14 for pi.

The answer is
D.
40 inches
8 0
3 years ago
Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushe
maria [59]

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34       Eq. 1

c + 3t + b = 22           Eq. 2

3c + 2b = 17               Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7            Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17      Eq. 3

c + b = 7          Eq. 4

Solve Eq. 4 for b.

b = 7 - c        Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22           Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4

7 0
3 years ago
Paige lives 3 miles east of her school. Diego lives 8 miles wes of the school. Which expression represents the distance, in mile
True [87]

Answer: |3-(-8)|


Step-by-step explanation:

Given: Paige lives 3 miles east of her school. Diego lives 8 miles west of the school.

From the picture , the number line represents the position of the houses of the two friends such that position of Paige is 3 but position of Diego is (-8) [since east and west are opposite directions]

We know that, Distance between any two points from A to B= B-A

Since distance is a positive quantity, thus

The distance between them = |3-(-8)| miles=11 miles


5 0
3 years ago
Read 2 more answers
Product in standard form (explain)<br> (3+6i)(4+9i)
ololo11 [35]
First you have to factor (aka, multiply) your binomial (which is what you have written) usually it helps to organize your thinking, and help tell what you need to multiply, to use the binomial chicken(or crab claw, what ever you want to call it) which basically you draw two arches, one arch connecting the 3 and 4, and then the other the 3 and 9i. on the opposite side (depending on wheater you connected then from the top or bottom) you connect (with an arch) the 6i and the four, and then the 6i to the 9i.

so now you multiply each piece you've connected:
3 x 4= 12
3 x 9i= 27i 
6i x 4= 24i
6i x 9i= 54i^2 

after  you've done this you can move on to  putting it into standard form, which just means you put things in descending order, depending on how many exponents the x (or in this case i) has.
your largest exponent is 54i^2, so that's first in out equation, next 27i, and 24i (you can combine these because they are like term) which equals 51i, after that you just add the 12 on the end, so the final equation looks like this:

54i^2+51i+12


4 0
3 years ago
What are the domain and range of the function f(x)= 3^x+5
rewona [7]

Answer:

Step-by-step explanation:

Domain:all real values

Range:[5,∞)

5 0
3 years ago
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