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Archy [21]
3 years ago
5

FOR 12 POINTS I NEED HELP ASAP! Consider the system of linear equations. 5 x + 10 y = 15. 10 x + 3 y = 13 To use the linear comb

ination method and addition to eliminate the x-terms, by which number should the first equation be multiplied? –2 Negative one-half One-half 2
Mathematics
1 answer:
Romashka [77]3 years ago
8 0

Answer:

Do you mean which equation should the 5x+10=15 be multiplied to?

it would be -2

Step-by-step explanation:

This is because 5 times -2 is -10

and so when you add the (now) x value of the first equation to the x value of the second equation, it gets 0

which makes it eliminated!

-10x+10x=0

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Write a rule to describe the function shown. x y −6 −4 −3 −2 0 0 3 2 y equals start fraction two over three end fraction x y equ
sertanlavr [38]

Answer:

y=\frac{2}{3} x (y equals start fraction two over three end fraction x)

Step-by-step explanation:

Lest's organize the table values of our function first:

x    y

-6  -4

-3  -2

0   0

3   2

The simplest kind of of function is a linear function of the form y=mx+b where m is the slope and b is the y-intercept. Let's us check if our function is a linear one finding its equation and checking that all points are in the line.

The first step to find a linear equation is find the slope of the line; to do it, we are using the slope formula:

m=\frac{y_2-y_1}{x_2-x_1}

where

m is the slope of the line

(x_1,y_1) are the coordinates of the first point

(x_2,y_2) are the coordinates of the second point

We know from our table that the first and second points are (-6, -4) and (-3, -2) respectively, so x_1=-6, y_1=-4, x_2=-3, and y_2=-2.

Replacing values:

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-2-(-4)}{-3-(-6)}

m=\frac{-2+4}{-3+6)}

m=\frac{2}{3)}

Now that we have the slope of our line we can use the point slope formula to complete our linear function:

y-y_1=m(x-x_1)

where

m is the slope

(x_1,y_1) are the coordinates of the first point

Replacing values:

y-y_1=m(x-x_1)

y-(-4)=\frac{2}{3)}(x-(-6))

y+4=\frac{2}{3)}(x+6)

y+4=\frac{2}{3} x+4

y=\frac{2}{3} x+4-4

y=\frac{2}{3} x

Now, to check if our function is valid, we can either check if each point satisfies the rule y=\frac{2}{3} x, or we can graph it and check if each lies is in the graph.

Let's check both:

We already know that points (-6, -4) and (-3, -2) satisfy the rule (after all, those were the point we used to came out with the rule in the first place), so we just need to check the points (0, 0) and (3, 2)

- For (0, 0):

y=\frac{2}{3} x

0=\frac{2}{3}(0)

0=0

The point satisfies the rule.

- For (3, 2):

y=\frac{2}{3} x

2=\frac{2}{3} (3)

2=2

The point satisfies the rule.

Since all the points of our table satisfies the rule y=\frac{2}{3} x, we can conclude that the rule describing the function shown is y=\frac{2}{3} x.

4 0
3 years ago
Read 2 more answers
What is the proportional relationship between 200 and 500?
goldenfox [79]

Answer:

Step-by-step explanation:

300 hundred no explaination

6 0
3 years ago
A quiz has 1 true-false question and 2 multiple choice questions that each have 4 answers what is the probability that someone q
Anit [1.1K]
1 true and false question = 1 / 2 chances
2 multiple choice question = 2/8
1/2 + 2/8 =
4/8 + 2/8 = 6/8.

6/8 = 3/4

you have a 75% chance of getting all 3 answers correct and getting a 100% on the quiz

hope this helps :D


8 0
3 years ago
A third-grade class has 12 girls and 13 boys. A fourth-grade class has 10 boys and 11 girls. When picking teams for PE, one capt
Nuetrik [128]
Probability that the first captain's first pick is a girl = 11/21
Probability that the first captain's second pick is a girl = 12/25

<span>the probability that the first captain will pick two girls before picking any boys = 11/21 x 12/25 = 132/525 = 44/175</span>

5 0
3 years ago
Danielle had a slime party and each friend got to take home 6/10 of a pound of slime. If 4 friends attend her party, between whi
Wewaii [24]

Answer:

24/10 or 2 and 4/10

Step-by-step explanation:

5 0
3 years ago
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