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miskamm [114]
2 years ago
12

Indicate the equation of the given line in standard form. Write the answer in the equation box below.

Mathematics
1 answer:
denis-greek [22]2 years ago
5 0

Answer:

x + 8y - 35 = 0.

Step-by-step explanation:

The hypotenuse is the line joining A and C.

Slope = (4-5) / (3 + 5)

= -1/8.

Equation is:

y - 4 = -1/8(x - 3)

y - 4 = -1/8x + 3/8

1/8x + y - 35/8 = 0

x + 8y - 35 = 0

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Population 78500
Increased by 2%
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3 years ago
For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x
Alla [95]
The <u>correct answer</u> is:

D) \left \{ {{2x-y=7} \atop {2x+7y=31}} \right..

Explanation:

We solve each system to find the correct answer.

<u>For A:</u>
\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.

Since we have the coefficients of both variables the same, we will use <u>elimination </u>to solve this.  

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. &#10;\\&#10;\\6x=23

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.

<u>For B</u>:
\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.

For this equation, it will be easier to isolate a variable and use <u>substitution</u>, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.

<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.  

<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>.  We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. &#10;\\&#10;\\-8y=-24

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate  Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so <u>D is the correct answer</u>.
7 0
3 years ago
please help me and before you try to answer the height is not 8 in but the volume is 25.12 in if that helps thank you &lt;3
DochEvi [55]

Answer:

25.12 in^3.

Step-by-step explanation:

Volume of the cylinder = 3.14 * r^2 * h

= 3.14 * 2^2 * 8

The volume of the preserve

= 1/4 * 3.14 * 4 * 8

= 25.12 in^3.

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3 years ago
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Help me plzzzzzzz with this question
Sergio039 [100]

Answer:

625/17

Step-by-step explanation:

-5 times -5 is 25 because if you times a negative to a negative you get a positive, so do that to both sides and 25 times 25 is 625....... you may have to simplify, hope this helps :)

8 0
3 years ago
Choose the best graph that represents the linear equation: -2y = x + 6 Graph A On a coordinate plane, a line goes through (negat
Aleksandr-060686 [28]

Answer:

i think its A

Step-by-step explanation:

divide both sides by -2 which makes the y int -3 and A has a negative slope

6 0
2 years ago
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