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miv72 [106K]
2 years ago
14

The points P(2, 1), Q(4, 5), and R(7, 4) are the midpoints of the sides of a triangle. Graph the three midsegments to form the m

idsegment triangle. Then use your graph and the properties of midsegments to draw the original triangle.
Mathematics
1 answer:
MariettaO [177]2 years ago
7 0

Answer:

  see attached

Step-by-step explanation:

We followed instructions to create the attached graph of the two triangles.

Each mid-segment is parallel to the side of the triangle whose midpoint is the vertex opposite that segment. So, we used a graphing tool to draw, for example, a line parallel to PQ through point R. The vertices of the original triangle are at the intersection points of these lines (or 1 mid-segment length from the midpoint).

__

Analytically, we can make use of the fact that each mid-segment is effectively a diagonal of a parallelogram. For example, PQ is a diagonal of APRQ. The other diagonal is AR. The two diagonals cross at the midpoint of each. This means we can find point A using the midpoint relation:

  midpoint AR = midpoint PQ

  (A +R)/2 = (P +Q)/2 . . . use the midpoint formula

  A +R = P +Q . . . . . . . . multiply by 2

  A = P +Q -R . . . . . . . . subtract R to get an expression for A

  A = (2, 1) +(4, 5) -(7, 4) = (2+4-7, 1+5-4) = (-1, 2)

The other vertices of ΔABC can be found in similar fashion:

  B = R +P -Q = (7, 4) +(2, 1) -(4, 5) = (7+2-4, 4+1-5) = (5, 0)

  C = Q +R -P = (4, 5) +(7, 4) -(2, 1) = (4+7-2, 5+4-1) = (9, 8)

So, the original triangle's vertices are ...

  A(-1, 2), B(5, 0), C(9, 8)

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Find the missing number.
DENIUS [597]

Answer:

20%

Step-by-step explanation:

In the graph, there is a cycle of increasing and decreasing. First, the original circle increases by 25% into the new, larger circle. Then, the circle does back to its original size. So, to solve we can assign a value to the smaller circle, increase it by 25%, and then find what percentage brings this back to the original value.

It is easiest to assign the value of 100 because it is easy to work with. So, let's say the smaller circle is 100; this increased by 25% is 125. The next step is to find what percentage of 125 brings us back to 100. There are multiple ways to do this such as guess and check or proportions/fractions. Either way, the correct percentage is 20%. If you decrease 125 by 20% you get the correct value of 100. This means that the missing number must be 20%.

6 0
2 years ago
Please help! can you explain it to me?
Semenov [28]

Answer:

It is increasing before x = -2 and from x = 0 to x = 2

Step-by-step explanation:

Option 1 - you can see the line going down starting at -2 and that means the line is decreasing but the choice says "It is increasing before x = 0". This contradicts the actual graph.

Option 2 - The line isn't increasing before x= -1, it's actually decreasing as seen in the graph.

Option 3 - The line doesn't even touch the point before x = -3 so this choice makes no sense.

Option 4 - Since all the other choices were eliminated this is the only choice standing. Looking at the line it is increasing before x = -2.

7 0
2 years ago
Torrance is shopping for a school party. His donation to the party is snack bags and juice boxes. Snack bags come in packages of
lara [203]

Answer:

Torrance must purchase 5 packages of snack bags and 6 packages of juice boxes.

Step-by-step explanation:

Given that:

Snack bags come in packages of 12.

Juice bags come in packages of 10.

To find:

Fewest number of packages of each product so that there are same number of snack bags and juice boxes.

Solution:

Number of snack bags when 1 package is bought = 12

Number of snack bags when 2 package is bought = 24

Number of snack bags when 3 package is bought = 36

Number of snack bags when 4 package is bought = 48

Number of snack bags when 5 package is bought = 60

Number of snack bags when 6 package is bought = 72

Number of juice bags when 1 package is bought = 10

Number of juice bags when 2 package is bought = 20

Number of juice bags when 3 package is bought = 30

Number of juice bags when 4 package is bought = 40

Number of juice bags when 5 package is bought = 50

Number of juice bags when 6 package is bought = 60

Number of juice bags when 7 package is bought = 70

We can see that when 5 packages of snack bags are bought and 6 packages of juice bags are bought, 60 bags of each are bought.

This can be found by finding the LCM as well.

LCM of 10 and 12 is 60.

It means we need to buy 60 bags of each item.

And we can easily find the number of packages for each.

Number of packages of snack bags to be bought = \frac{60}{12} =5

Number of packages of juice bags to be bought = \frac{60}{10} = 6

Torrance must purchase 5 packages of snack bags and 6 packages of juice boxes.

4 0
3 years ago
There are 376 students in 8th grade at Samuel's school. There are 47 8th graders trying out for football last Thursday. What per
statuscvo [17]

Answer:

87.5%

Step-by-step explanation:

There are 376 students in 8th grade at Samuel's school. There are 47 8th graders trying out for football last Thursday.

The number is students not trying out for football last Thursday is calculated as:

376 students - 47 students

= 329 students

The percent of 8th graders that did not try out for football is calculated as:

329 students/376 students × 100

= 329/376 × 100

= 87.5 %

8 0
2 years ago
How to solve this problem?
valentinak56 [21]

Very nice handwriting but the math and English are confusing.

Let's assume we're told

\displaystyle 45 = \sum_{i=1}^9 (x_i - 10)^2

The subscript is important.

I think we're told the similar sum with 11 gives the smallest possible value for the sum. This is a rather cagey way of telling us 11 is the mean of the nine points. The mean is the number which minimizes the sum of squared deviations.

\displaystyle 45 = \sum_{i=1}^9 (x_i - 10)^2 = \sum x_i^2 - 20 \sum x_i + 9(100)

\displaystyle  \sum x_i^2=  20 \sum x_i  - 900

If 11 is the mean, the sum of the points is 9(11)=99.

\displaystyle  \sum x_i^2=  20 (99)  - 900 = 1080

Answer: 1080

6 0
3 years ago
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