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german
3 years ago
15

Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

Mathematics
1 answer:
True [87]3 years ago
7 0
Question 1:

--------------------------------------------------------------------
Find Slope
--------------------------------------------------------------------
Equation: y = 5x - 2
Slope = 5
Slope of parallel line = 5

--------------------------------------------------------------------
Insert slope into the general equation y = mx + c
--------------------------------------------------------------------
y = 5x + c

--------------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------------
At point (2, -1)
y = 5x + c
-1 = 5(2) + c
c = -1 - 10
c = -11

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 5x + c
y = 5x - 11

--------------------------------------------------------------------
Answer: y = 5x - 11
--------------------------------------------------------------------

Question 2:

--------------------------------------------------------------------
Find Slope
--------------------------------------------------------------------
y = 9x 
Slope = 9 
Slope of the parallel line = 9

--------------------------------------------------------------------
Insert slope into the equation y = mx + c
--------------------------------------------------------------------
y = 9x + c

--------------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------------
y = 9x + c
At point (0, 5)
5 = 9(0) + c
c = 5

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 9x + c
y = 9x + 5

--------------------------------------------------------------------
Answer: y = 9x + 5
--------------------------------------------------------------------
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A rectangle is 6yards longer than it is wide. Find the dimensions of the rectangle if it’s area is 187 square yards
emmasim [6.3K]

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where <em>w</em> is width, and <em>l</em>, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

187 = w^{2} +6w

w^{2} +6w-187 =0,

Using the quadratic formula w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a} where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}

w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}

We have two options: w=\frac{-6+28}{2}=\frac{22}{2}=11  yards

Or

w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length l =\frac{187}{11}=17 yards

6 0
3 years ago
6-2/3(x+5)=4x solve for x
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Answer:

3x^2+15x-1=0

Step-by-step explanation:

4/(3x+15)=4x

4=12x^2+60x

12x^2+60x-4=0

3x^2+15x-1=0

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2 years ago
Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages d
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Given:

Reese read twice as many pages Saturday than she read Sunday.

She read a total of 78 pages over the weekend.

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The number of pages she read on Sunday.

Solution:

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Reese read twice as many pages Saturday than she read Sunday. So, the number of pager she read on Saturday is 2x.

Total number of page she read over the weekend is:

Total=x+2x

Total=3x

She read a total of 78 pages over the weekend.

3x=78

x=\dfrac{78}{3}

x=26

Therefore, Reese read 26 pages on Sunday.

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