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2 years ago

For what value of x is P|| BC? A. 5 B. 6 C. 7 D. 8

Mathematics

1 answer:

77julia77 [94]2 years ago

4 0

Answer:

Option C. x=7

Step-by-step explanation:

we know that

If PQ is parallel to BC

then

triangles APQ and ABC are similar

Remember that

If two figures are similar them the ratio of its corresponding sides is proportional

$\frac{AP}{AB}=\frac{AQ}{AC}$

substitute the values

$\frac{x}{x+7+x}=\frac{x-3}{x-3+x+1}$

Solve for x

$\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units$

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178 rounded to the nearest hundred

Reika [66]

In order to round to the nearest 100 you look at the 10s place.

It's 7 which means we round up. So 178 rounded to the nearest 100 is 200.<span />

6 0

2 years ago

Read 2 more answers

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

2 years ago

Jessica pours 1/3 of a cup of water into a pot. She does this 5 times. How many

nydimaria [60]

She poured 1 full cup and 2/3 of another cup. The answer would be 1 and 2/3 cups.

5/3= 1 and 2/3

4 0

2 years ago

A cookie factory uses ½ of a bag of flour in each batch of cookies. The factory used 2 ½ bags of flour yesterday. How many batch

ankoles [38]

Answer:

5 batches

Step-by-step explanation:

1/2 can go into 1, 2 times. so 1/2 can go into 2, 4 times. Add the extra 1/2 and you get 5. Hope this helps.

please give me brainliest it would help(✿◠‿◠)

4 0

2 years ago

A self-service car wash has 3 individual car wash stalls. Customers wait in a single line before choosing the next available sta

jeka94

Answer:

single-channel, multi -phase

Step-by-step explanation:

The concept known as '' Queuing'' is not only important in the mathematical aspect alone but it is also useful in economic matters as signifies the abundance of resources that is when we have queues it means the reason for it is that the available resources is not enough.

From the question above we have that there are 3 individual car wash stalls, it is also given that the customers wait in a single line before choosing the next available stall. This means that there is only a single-channel.

Then, we have that from the single line initially, the queues then moves to multi -phase that is to 3 individual car wash stalls.

3 0

2 years ago