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Alona [7]
3 years ago
10

Solve each system by substitution. y = 2x + 5 3x - y= -6

Mathematics
1 answer:
castortr0y [4]3 years ago
7 0
X=-1 and y=3

To solve this, because y is equal to 2x+5, you can substitute 2x+5 into the bottom equation for y.

You now have 3x - (2x + 5) =-6

This can be solved like a normal equation. Multiply each term in the parenthesis by -1.

3x - 2x - 5 = -6

Subtract 2x from 3x

x - 5 = -6

Add 5 to both sides

x=-1

Now you can solve for y by plugging -1 in for x in either equation. Im going to use the top one.

y= 2(-1)+5
y= -2+5
y=3

You can check your answer by plugging in the values for x and y into both equations and making sure both sides equal each other.
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What is the cross-sectional area of a cement pipe 2 in. thick with an inner diameter of 5 ft? Use pie 3.14.
Paul [167]

Answer:

1.60 ft^{2}

Step-by-step explanation:

Assuming that this is a cylindrical pipe, the area can be determined by applying the formula for calculating the area of a circle.

i.e Area = \pir^{2}

So that,

for the inner part of the pipe,

r = \frac{diameter}{2}

 = \frac{5}{2}

 = 2.5 feet

Area of the inner part of the pipe = \pir^{2}

                                 = 3.14 x (2.5)^{2}

                                 = 19.625

Are of the inner part of the pipe is 19.63 ft^{2}.

Total diameter of the pipe = 5 + 0.2

                                           = 5.2 feet

r = \frac{5.2}{2}

 = 2.6 feet

Area of the pipe = \pir^{2}

                            = 3.14 x (2.6)^{2}

                            = 21.2264

Area of the pipe is 21.23 ft^{2}.

Thus the cross sectional area = Area of the pipe - Area of the inner part of the pipe

                                           = 21.2264 - 19.625

                                           = 1.6014

The cross sectional area of the cement pipe is 1.60 ft^{2}.

6 0
2 years ago
Define a substitution method to solve the followingsysten of equation of y=2x-3, x+y=1
Ivan
I will solve you system by substitution

y = 2x - 3 ; x + y = 1

→Step 1: Solve y = 2x - 3 for y

→Step 2: Substitute 2x - 3 for y in x + y = 1:

x + y = 1 

x + 2x- 3 = 1

3x - 3 = 1 (Simplify both sides of the equation)

3x - 3  + 3 = 1 + 3 (Add 3 both sides)

3x = 4 
 
3x ÷ 3 = 4 ÷ 3 (Divide each side by 3)

x = 4/3

→Step 3: Substitute 4/3 for x in y = 2x - 3:  

y = 2x - 3 

y = 2 (4/3) -3 

y = -1/3 (Simplify both sides of the equation)

Answer: 

x = 4/3 and y = -1/3

∫Hope that helps∫
7 0
2 years ago
Find the first five terms of the sequence below <br> a1=3<br> An=an-1+6
mihalych1998 [28]
The first dove terms are:3,9,12,15,18
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1) solve for y.
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12. A population of carpenter ants is called a(n) _______ ___________________
gregori [183]

Answer:

swarmers

Step-by-step explanation:

hope this helps

5 0
2 years ago
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