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devlian [24]
3 years ago
14

Solve these two equations using the Addition Method (also known as the elimination method).

Mathematics
1 answer:
Brums [2.3K]3 years ago
4 0

Answer:

(-2, 3)

Step-by-step explanation:

5/2(3/4x + 1/3y = -1/2)

1/2x - 5/6y = -7/2

15/8x + 5/6y = -5/4

19/8x = -19/4

x = -2

1/2(-2) - 5/6y = -7/2

-1 -5/6y = -7/2

-5/6y = -5/2

y = 3

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3. Is the relationship shown by the data linear? If so, model the data with an equation X | Y 1 ,5| 5,10| 9,15| 13,20|
son4ous [18]

Answer:

y=\frac{5}{4}x+\frac{15}{4}

Step-by-step explanation:

x | y

-------

1     5

5   10

9    15

13   20

This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.

So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,

( 1    ,   5)

-( 5   ,  10)

----------------

-4          -5

So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.

So we have m=5/4. Let's plug that into our y=mx+b.

y=5/4 x+b

To find b, we need to use y=5/4 x+b along with one of the given points.

Choose; it doesn't matter.  I like (1,5) I guess.

y=5/4 x +b with (1,5)

5=5/4 (1)+b

5=5/4    +b

Subtract 5/4 on both sides:

5-5/4=b

20/4-5/4=b  (Found a common denominator)

15/4=b

The y-intercept is 15/4 so b=15/4.

So the equation for the line in slope-intercept form is y=5/4 x +15/4.

y=\frac{5}{4}x+\frac{15}{4}

4 0
3 years ago
Read 2 more answers
IS MY ANSWER CORRECT??? If not what’s the correct answer
Kazeer [188]

Answer:

yes

Step-by-step explanation:

your answer is correct

4 0
2 years ago
Read 2 more answers
Its all one big question
Nostrana [21]
1)5 2)6 3)17 because h(x)+k(x)=3x-1
6 0
3 years ago
Read 2 more answers
Find the values for a and b that would make the equality true.
Crank

Answer:

a = - 4, b = 5

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms on the right side.

- 3(2x² + ax + b)

= - 6x² - 3ax - 3b

Comparing like terms with - 6x² + 12x - 15

x - term → - 3a = 12 ( divide both sides by - 3 )

                    a = - 4

constant term → - 3b = - 15 ( divide both sides by - 3 )

                               b = 5

6 0
3 years ago
Selena was comparing the flying speeds of different birds in science class. Which of the three birds flies fastest? Why?
Mashcka [7]

Answer:

Option C. The robin flies fastest because its rate is 15 m/s

Step-by-step explanation:

Let

x -----> the time in seconds

y ----> the distance in meters

The speed is equal to divide the distance by the time

In this problem, the slope or unit rate of the linear equation is the same that the speed

<em>Robin's Flight</em>

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

take two points from the table

(2,30) and (3,45)

substitute in the formula

m=\frac{45-30}{3-2}

m=\frac{15}{1}

m=15\frac{m}{sec}

<em>Cardinal's Flight</em>

y=10x

m=10\frac{m}{sec}

<em>Blue Jay's Flight</em>

take two points from the graph

(0,0) and (2,20)

substitute in the formula

m=\frac{20-0}{2-0}

m=\frac{20}{2}

m=10\frac{m}{sec}

Compare

The robin flies fastest because its rate is 15 m/s

4 0
3 years ago
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