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Delicious77 [7]
4 years ago
5

Solve the system of equations using elimination. 2x + y = 9 8x – 2y = 6

Mathematics
2 answers:
sp2606 [1]4 years ago
7 0
2x+y=9 (*2) __ 4x+2y=18 name it 1.  8x-2y=6 name it 2. Now add both equations, 1 & 2. 4x+2y+8x+-2y=18+6. 2y will be cancelled out. You'll be left with 12x=24, x=2. Then replace the value of x which is 2 in either equation 1 or 2. I'll go with 1 equation 4(2)+2y=18  2y=18-8=10 y=5. Using the equation 2 should provide the same result of y.




givi [52]4 years ago
3 0
For the first equation:
Let's solve for x.<span><span><span>2x</span>+y</span>=9</span>Step 1: Add -y to both sides.<span><span><span><span>2x</span>+y</span>+<span>−y</span></span>=<span>9+<span>−y</span></span></span><span><span>2x</span>=<span><span>−y</span>+9</span></span>Step 2: Divide both sides by 2.<span><span><span>2x/</span>2</span>=<span><span><span>−y</span>+9/</span>2</span></span><span>x=<span><span><span><span>−1/</span>2</span>y</span>+<span>9/2</span></span></span>Answer:<span>x=<span><span><span><span>−1/</span>2</span>y</span>+<span>9/<span>2

For the second equation:
</span></span></span></span>Let's solve for x.<span><span><span>8x</span>−<span>2y</span></span>=6</span>Step 1: Add 2y to both sides.<span><span><span><span>8x</span>−<span>2y</span></span>+<span>2y</span></span>=<span>6+<span>2y</span></span></span><span><span>8x</span>=<span><span>2y</span>+6</span></span>Step 2: Divide both sides by 8.<span><span><span>8x/</span>8</span>=<span><span><span>2y</span>+6/</span>8</span></span><span>x=<span><span><span>1/4</span>y</span>+<span>3/4</span></span></span>Answer:<span>x=<span><span><span>1/4</span>y</span>+<span>3/<span>4
Hope I helped!:)</span></span></span></span>
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The national average for the number of students per teacher for all U.S. public schools in 15.9. A random sample of 12 school di
Nady [450]

Answer:

The 95% confidence interval for the true mean number of students per teacher is (17.9, 20.5). The lower bound of the interval is above the national average, which means that this estimate is higher than the national average.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.201

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.201\frac{\sqrt{4.41}}{\sqrt{12}} = 1.3

In which s is the standard deviation of the sample(square root of the variance) and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 19.2 - 1.3 = 17.9 students.

The upper end of the interval is the sample mean added to M. So it is 19.2 + 1.3 = 20.5 students

The 95% confidence interval for the true mean number of students per teacher is (17.9, 20.5). The lower bound of the interval is above the national average, which means that this estimate is higher than the national average.

5 0
3 years ago
- 2/3 (x+12)+2/3 x=-5/4 x+2
bogdanovich [222]

We will have the following:

-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10\Rightarrow5x=40\Rightarrow x=8

So, the value of x is 8.

5 0
1 year ago
During a review game, Mr. TooMuch's class correctly answered 68 questions on the first try. If there were 74 questions in the ga
anygoal [31]
I'm not sure but maybe the answer is :
68 / 74 = 0.919
3 0
3 years ago
The measurement of an angle is 40°, and the length of a line segment is 8 centimeters.
natima [27]

Answer:

I'm assuming it's a triangle of some sort. I'll assume it's a right triangle. All the angles and sides are there. I would need 2 angles and 1 side or 2 sides and 1 angle to get a specific triangle.

Step-by-step explanation:

4 0
3 years ago
HELP PLS A=45 help and how
MA_775_DIABLO [31]

Answer:

<h2>a=18.5</h2>

Step-by-step explanation:

the value of c angle is 35°

according to the question

\frac{a}{ \sin( {45}^{o} ) }  =  \frac{15}{ \sin(35°) }

a =  \frac{15 \times  \frac{ \sqrt{2} }{2} }{ \sin({35}^{o} )}

a= 18.5

7 0
3 years ago
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