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3 years ago

What are the endpoint coordinates for the midsegment of △PQR that is parallel to PQ¯¯¯¯¯?

Mathematics

2 answers:

Svetlanka [38]3 years ago

8 0

Answer:

did you ever find the answer because im so stuck on this one and i dont know where to get help from

Step-by-step explanation:

sergey [27]3 years ago

5 0

Answer:

$m_{PR} (-3.5; 0.5)$

$m_{RQ}(-1;-0.5)$

Step-by-step explanation:

The midsegment that is being asks has endpoints on PR and RQ, exactly from midpoint of one side to the midpoint of the other side.

So, to find the coordinates of this midsegment, we just have to find the mid point between PR and RQ.

$m_{PR} (\frac{x_{1}+x_{2}}{2}; \frac{y_{1}+y_{2}}{2} )\\m_{PR} (\frac{-3-4}{2}; \frac{3-2}{2})\\m_{PR} (\frac{-7}{2}; \frac{1}{2})\\m_{PR} (-3.5; 0.5)$

Therefore the midsegment starts at $m_{PR} (-3.5; 0.5)$

Now, we calculate the other coordinate, which is the mid point of RQ:

$m_{RQ}(\frac{-4+2}{2} ;\frac{-2+1}{2} )\\m_{RQ}(\frac{-2}{2} ;\frac{-1}{2} )\\m_{RQ}(-1;-0.5)$

Therefore, the endpoint coordinates for the midsegment are:

$m_{PR} (-3.5; 0.5)$

$m_{RQ}(-1;-0.5)$

You might be interested in

What is the radius and diameter of 7

Aleks04 [339]

<h3>Answer:</h3>

The radius would be 3.5 units.

Step-by-step explanation:

This is because a radius is always half of a diameter.

By using that,

7 ÷ 2 = 3.5 units

Since there was no measurement listed in the question, the answer would be in "units."

8 0

3 years ago

Tea is made up of milk and tea ratio of 2 to 9. how much tea can be made using 1 litre of milk

Ilya [14]

You can solve it like this

2=milk (a); 1=milk (b)
9=tea (a); x= tea (b)

2:9=1:x (then multiply means and the extremes)
(means are 9 and 1; extremes are 2 and x)

9=2x
9/2= x
4.5 or 4 1/2=x

Therefore, using 1 litre of milk, we can have 4 1/2 tea.

3 0

3 years ago

Need help filling in the blanks: selling price using markup.

Xelga [282]

Answer:

Refer to the explanation.

Step-by-step explanation:

Let's take each one at a time.

To solve for the complement, we simply subtract our markup rate by 100%.

100% - 30% = 70%

Now to solve for the selling price, we use the formula

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{86.74}{0.70}$

Selling Price = $123.91

We do the same process with the first number.

100% - 40% = 60%

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{220.00}{0.60}$

SellingPrice = $366.67

The same as the first two.

100% - 20% = 80%

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

$SellingPrice=\dfrac{89.50}{0.80}$

SellingPrice = $111.88

Now to solve for the markup rate, we use the formula:

$MarkupRate=\dfrac{Markup}{SelingPrice}$

In this case we first need to find the markup. The markup is the difference between the selling price and the cost.

Selling Price = $235.28

Cost = $199.99

Markup = $235.28 - $199.99

Markup = $35.29

Now the we know our markup, we can then solve for the markup rate using the formula.

$MarkupRate=\dfrac{Markup}{SelingPrice}$

$MarkupRate=\dfrac{35.29}{235.28}$

MarkupRate = 0.1499 x 100 = 14.99% or 15%

Now for the last one, we need to find for the cost. Let's use the selling price formula to find for the cost.

$SellingPrice=\dfrac{Cost}{ComplementOfMarkupRate}$

Selling Price = $30.77

Complement = 65% or 0.65

This will then give us.

$30.77=\dfrac{Cost}{0.65}$

We multiple both sides of the equation by 0.65 to leave our cost alone.

30.77 x 0.65 = Cost

Cost = $20

4 0

3 years ago

41. Assuming that a man can complete the work alone in x days, his work in four days would be: a) b) X X C d) 4x x 42. If a man

Schach [20]

Percentage and ratio word problems require understanding of the relationship between variables from which the question is formed

The options that give the correct values of the duration of the work are;

$41. \ c) \ \dfrac{4}{x}$

$42. \ d) \ \dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

43. a) 35 days

44. c) 21·a + 28·b = 1

45. c) (42, 56)

Reasons:

41. Number of days it takes a man to complete the work alone = x days

Therefore;

$The \ work \ done \ by \ the \ man \ in \ one \ day = \dfrac{1}{x}$

$The \ work \ done \ in \ four \ days \ by\ the \ man = 4 \times \dfrac{1}{x} = \dfrac{4}{x}$

The correct option is $c) \ \dfrac{4}{x}$

42. Number of days it takes a man to complete the work alone = x days

$Work \ done \ by \ a\ man \ in \ one \ day = \dfrac{1}{x}$

$Work \ done \ by \ four \ men \ in \ one \ day = \dfrac{4}{x}$

Number of days it takes a boy to complete the work alone = y days

$Work \ done \ by \ a \ boy \ in \ one \ day = \dfrac{1}{x}$

$Work \ done \ by \ six \ boys \ in \ one \ day = \dfrac{6}{y}$

4 men and 6 boys work for 5 days to complete the work

Therefore, work done by 4 men and 6 boys in 1 day is therefore;

$\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

The correct option is therefore;

$d) \ \dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

43. As per the case study, we have;

Case 1

$\dfrac{4}{x} + \dfrac{6}{y} = \dfrac{1}{5}$

Which gives;

$\dfrac{6\cdot x + 4\cdot y}{y \cdot x} = \dfrac{1}{5}$

30·x + 20·y = y·x

Case 2

$\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$

Which gives;

$\dfrac{4\cdot x + 3\cdot y}{y \cdot x} = \dfrac{1}{7}$

28·x + 21·y = y·x

Therefore;

30·x + 20·y = 28·x + 21·y

∴ 2·x = y

Plugging in the value of y = 2·x, in Case 1 gives;

$\dfrac{4}{x} + \dfrac{6}{2 \cdot x} = \dfrac{1}{5}$

$\dfrac{2 \times 4 + 6}{2 \times x} = \dfrac{14}{2 \times x} =\dfrac{7}{x} = \dfrac{1}{5}$

7 × 5 = x

x = 7 × 5 = 35

The number of days, x, it takes a man to complete the work alone, is given by option; a) 35 days

44. For the equation $\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$ , if $a = \dfrac{1}{x}$ , and $b = \dfrac{1}{y}$ , we have;

$3 \cdot a+ 4\cdot y = \dfrac{1}{7}$

21·a + 28·y = 1

The correct option is option C. 21·a + 28·b = 1

45. A solution to the equation $\dfrac{3}{x} + \dfrac{4}{y} = \dfrac{1}{7}$ , is given by the values of x, and y, that gives;

$\dfrac{1}{14} + \dfrac{1}{14} = \dfrac{1}{7}$

We have;

3 × 14 = 42

4 × 14 = 56

Therefore, a solution to the equation is (42, 56)

The correct option is $c) \ \underline{ (42, \ 56)}$

Learn more here:

brainly.com/question/11825953

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3 0

2 years ago

Factor completely x3 – 3x2 - 9x + 27

lakkis [162]

Answer:

x³ - 3x² - 9x + 27

= x²(x - 3) - 9(x - 3)

= (x² - 9)(x - 3)

= (x -3)(x + 3)(x - 3)

= (x + 3)(x - 3)²

Step-by-step explanation:

7 0

3 years ago