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vlabodo [156]
3 years ago
5

If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a paralle

logram. The diagram is not drawn to scale.

Mathematics
1 answer:
posledela3 years ago
7 0

Answer:

x=12\\y=\frac{13}{3}


Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

  • OL = NM, and
  • ON = LM

Using the expressions given, we can make 2 equations:

<u>Equation 1:</u>

OL=NM\\3y-6=x-5\\-x+3y=1


<u>Equation 2:</u>

ON=LM\\8x-8=7x+4\\


<em>Solving equation 2, we have x:</em>

8x-8=7x+4\\8x-7x=4+8\\x=12

<em>Plugging this value of x into equation 1, we can solve for y:</em>

-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}

So,

x=12\\y=\frac{13}{3}



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as a gift, you fill the calendar with packets of chocolate candy. Each packet has a volume of 2 cubic inches. Find the maximum n
qaws [65]
The picture of the calendar is shown in the attached image.

Now, first we will get the volume of the calendar itself, we can note the calendar has the shape of a triangular prism.
Volume of triangular prism = area of base * depth
The area of base = area of triangle = 1/2 * base * depth 
Therefore:
Volume of prism = 1/2 * base * height * depth
where:
base = 4 in
height is he height of the base = 6 in
depth is the depth of the calendar = 8 in
Therefore:
Volume of calendar = 1/2 * 4 * 6 * 8 = 96 in^3

Now, we are given that the volume of each candy is 2 in^3, this means that:
number of candies to fill the calendar = volume of calendar / volume of candy
                                                            = 96/2 
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Hope this helps :)

4 0
3 years ago
Suppose we take two different random samples from the same population of test scores. The population mean and standard deviation
Leto [7]

Answer:

The 95% confidence interval obtained with a sample size of 64 will give greater precision.            

Step-by-step explanation:

We are given the following in the question:

A 95% confidence interval is calculated with the following sample sizes

n_1 = 25\\n_2 = 64

The population mean and standard deviation are unknown.

Effect of sample size on confidence interval:

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  • As the margin of error decreases the width of the confidence level decreases.
  • Thus, with increased sample size the width of confidence level decreases.

If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.

Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.

3 0
3 years ago
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soldier1979 [14.2K]

Perform the indicated multiplication first:  -15 + 5q + 4 = 5q - 11

Note that 5q appears on both sides of this equation.  Cancelling, we get :

-11 = -11.  This is always true.  Thus, -5(3-q) +4=5q-11 is true for all q.

4 0
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How many seconds equals 54 minutes
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60x54=3240
8 0
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Afina-wow [57]
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