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Margaret [11]
3 years ago
5

Solve using elimination PLEASE I NEED HELP!!! IT WOULD REALLY MEAN A LOT IF ANYONE CAN ANSWER THIS! 16 POINTS!!!

Mathematics
1 answer:
Marysya12 [62]3 years ago
4 0

Answer:

  (x, y) = (2, -3/4)

Step-by-step explanation:

The point of the "elimination" technique is to combine the equations in a way that eliminates one of the variables. Sometimes this involves multiplying one or both of the equations by constants before you add those results together. In any event, the first step is to look at the coefficients of the variable terms to see if there is a simple combination of them that will result in zero.

The y terms have coefficients that are opposites of each other (4, -4), so you can simply add the two equations to eliminate y as a variable.

  (2x +4y) +(x -4y) = (1) +(5)

  3x = 6 . . . . . simplify

  x = 2 . . . . . . divide by 3

Now, you find y by substituting this value into one of the equations. I would choose the equation with the positive y-coefficient:

  2(2) +4y = 1

  4y = -3 . . . . . . subtract 4

  y = -3/4

Then the solution is ...

  (x, y) = (2, -3/4)

_____

A graphing calculator confirms this solution.

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What is the coefficient of the variable in the expression 4 − 3x − 7 + 6?
liberstina [14]
-3.

Coefficients are numbers that have a variable next to it, thus leading it to be -e of the -3x.

Hope this helps!
3 0
3 years ago
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What is the greatest common factor of 14 56 63?
olga55 [171]
14: 1 × 14
      2 × 7

56: 1 × 56
      2 × 28
      4 × 14
      7 × 8

63: 1 × 63
      3 × 21
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GCF(14, 56, 63) = 7
6 0
3 years ago
X^2+y^2=169, 3x+2y=39 please answer using substitution and each step
Oksanka [162]

Answer:

x=13,y=0

Step-by-step explanation:

We are given a system of equations

{x}^{2}  +  {y}^{2}  = 169 -  - eqn \: 1 \\ 3x + 2y = 39 -  - eqn \: 2

For equation 1,square all terms to reduce it

√x²+√y²=169

x+y=13

Make x the subject as required by the question to use substitution method

x=13-y

Plug x=13-y into eqn 2

3(13-y)+2y=39

39-3y+2y=39

39-y=39

y=39-39=0

Plug y=0 into equation 1

x+0=13

x=0

7 0
2 years ago
An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w
zzz [600]

Answer:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

df=n-1=12-1=11

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \leq 0

Alternative hypothesis: \mu_y -\mu_x >0

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference d_i=y_i-x_i and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

The next step is calculate the degrees of freedom given by:

df=n-1=12-1=11

Now we can calculate the p value, since we have a right tailed test the p value is given by:

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0
2 years ago
20 POINTS QUESTION IN PICTURE
Serga [27]
Domain includes all the x-values in the function. Range includes all the y-values in the function.

The first table has x-values of -1, 3, and 6, and y-values of 4, 5, and 6. This means that the domain and range would be given by the following sets:
Domain: {-1, 3, 6}
Range: {4, 5, 6}

The second set of points has x-values of -4, -4, -3, and 1, and y-values of 1, 1, 3, and 4. Duplicate points are not listed within the domain and range, so the domain and range would be given by the following sets:
Domain: {-4, -3, 1}
Range: {1, 3, 4}
7 0
2 years ago
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