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2 years ago

Determine if the following system of equations has no solutions 4x+3y= -8 -8x-6y= 16

1 answer:

3 0

$\begin{cases} 4x+3y=-8\\\\ -8x-6y=16 \end{cases}~\hspace{10em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$4x+3y=-8\implies 3y=-4x-8\implies y=\cfrac{-4x-8}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3} \\\\[-0.35em] ~\dotfill\\\\ -8x-6y=16\implies -6y=8x+16\implies y=\cfrac{8x+16}{-6} \\\\\\ y=\cfrac{8}{-6}x+\cfrac{16}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3}$

one simple way to tell if both equations do ever meet or have a solution is by checking their slope, notice in this case the slopes are the same for both, meaning the lines are parallel lines, however, notice both equations are really the same, namely the 2nd equation is really the 1st one in disguise.

since both equations are equal, their graph will be of one line pancaked on top of the other, and the solutions is where they meet, hell, they meet everywhere since one is on top of the other, so infinitely many solutions.

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What letter stays the same when reflected over the x-axis

valina [46]

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.p explanation:

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3 years ago

Using the simple random sample of weights of women from a data set, we obtain these sample statistics: nequals45 and x overbar

Tomtit [17]

Answer: (141.1, 156.48)

Step-by-step explanation:

Given sample statistics : $n=45$

$\overline{x}=148.79\text{ lb}$

$\sigma=31.37\text{ lb}$

a) We know that the best point estimate of the population mean is the sample mean.

Therefore, the best point estimate of the mean weight of all women = $\mu=148.79\text{ lb}$

b) The confidence interval for the population mean is given by :-

$\mu\ \pm E$ , where E is the margin of error.

Formula for Margin of error :-

$z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given : Significance level : $\alpha=1-0.90=0.1$

Critical value : $z_{\alpha/2}=z_{0.05}=\pm1.645$

Margin of error : $E=1.645\times\dfrac{31.37}{\sqrt{45}}\approx 7.69$

Now, the 90% confidence interval for the population mean will be :-

$148.79\ \pm\ 7.69 =(148.79-7.69\ ,\ 148.79+7.69)=(141.1,\ 156.48)$

Hence, the 90% confidence interval estimate of the mean weight of all women= (141.1, 156.48)

3 0

3 years ago

But how is is it 1 hour and 45 minutes(someone please respond this is due tomorrow)I need work

astraxan [27]

Because it is every hour there's 60min so that's and hour the the next 45 min are different

4 0

3 years ago

If a triangle has sides 4, 6 and 10 and a 2nd similar triangle has a perimeter of 60, find the 2nd largest side of the 2nd trian

algol13

The first triangle has a perimeter of 4+6+10 = 20.

The 2nd longest side is 6/20 = 3/10 of the perimeter. In the larger triangle, the 2nd longest side will have length (3/10)*60 = 18.

_____
These side lengths mean the "triangle" is a line segment. That is, it has zero area.

8 0

3 years ago

Yolanda used a reconciliation worksheet provided by her bank. Line 5 should equal line 6 at the end of the reconciliation, but i

forsale [732]

Answer is 19.99 dollars

Explanation:

Let us draw the reconciliatin done by Yolanda linewise

Banking reconciliation Worksheet Amount of Mega

1) Closing balance $ 345 89

2) the sum of any outstanding deposits or credits. 0.00

3) Sum of 1 and 2 345.89

4. sum of any outstanding checks or debits. $ 37 51 5.

5) (3)-(4) $ 308 38

6) checkbook balance. $ 328 37

7) Difference (6)-(5) $ 19.99

SInce difference is exactly 19.99 dollars Yolanda should look for the amount 19.99 dollars to find a solution to the problem i.e. to see the reason for the difference between lines 5 and 6

4 0

3 years ago

Read 2 more answers