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alexandr1967 [171]
3 years ago
8

What is the answer using either the substitution method or elimination method

Mathematics
1 answer:
Sophie [7]3 years ago
8 0

To solve this problem, I am going to use the substitution method.  To do this, we use our first equation given (s=4r-1) and substitute this given value for s (4r-1) and substitute it into the second equation so that we have an equation with only one variable.  This is modeled below:

s = 4r - 1

6r - 5s = -23

6r - 5(4r-1) = -23

Now, we can solve this equation as we would any other equation, using the order of operations outlined by PEMDAS.  To begin, we will distribute the factor of -5 through the parentheses on the left side of the equation.

6r - 20r + 5 = -23

Next, we should combine like terms on the left side of the equation:

-14r + 5 = -23

Next, we should subtract 5 from both sides of the equation to get the variable term alone on the the left side of the equation.  We get:

-14r = -28

Finally, we should divide both sides by -14 to get the variable r alone on the left side of the equation.

r = 2

Now that we know that value for the variable r, we can substitute this value into one of our original equations (either one will work, but I am choosing to use the first one):

s = 4r - 1

s = 4(2) - 1

Now, we can find the value for s by using multiplication and then subtraction to simplify the right side of the equation.

s = 8-1

s = 7

Therefore, your answer is s = 7 and r = 2.

Hope this helps!

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-8+12=4 is the correct answer

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A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The
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Answer:

a) [-0.134,0.034]

b) We are uncertain

c) It will change significantly

Step-by-step explanation:

a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.

Since we assume that the variances are equal, we use the pooled variance given as

s_p^2 = \frac{ (n_1 -1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2},

where n_1 = 40, n_2 = 30, s_1 = 0.16, s_2 = 0.19.

The mean difference \mu_1 - \mu_2 = 10.85 - 10.90 = -0.05.

The confidence interval is

(\mu_1 - \mu_2) \pm t_{n_1+n_2-2,\alpha/2} \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}} = (-0.05) \pm t_{68,0.025} \sqrt{\frac{0.03}{40} + \frac{0.03}{30}}

= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]

b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.

c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.

6 0
3 years ago
Complete the remainder of the<br> table for the given function rule:
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Answer:

-3=2

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3 0
2 years ago
A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. S
Lubov Fominskaja [6]

Realize that since 2x and 3x - 1 are equal to each other, they are also equal to y. This means that we can craft two equations, y = 2x and y = 3x - 1.


When you want to solve a systems of equations via a graph, you need to plot both equations on a graph and determine the x- and y-value of where the lines intersect. In this case, we would plot both y = 2x and y = 3x - 1. These lines intersect at the point (1, 2).


Since we are trying to find the day the bullfrog will be able to eat the entire population, or x, we are going to use the x-value of our point as our answer. Thus, our answer is 1 day.

3 0
3 years ago
The length of a rectangle is 5 more than twice the width. the perimeter is 130. what is the area?
vekshin1
<span>L the length     W the width 

The length of a rectangle is 5 more than twice the width</span>
L = 5+ 2W

<span>the perimeter is equal the sum of sides =130
</span>
L+L+W+W =130

by subtitution we replace L by <span>L = 5+ 2W

</span>5+ 2W+<span>5+ 2W +W+W = 130
</span>
6W= 120

w= 20              <span>L = 5+ 2W= 5+ 40=45</span>
7 0
3 years ago
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