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3 years ago

Given: △DMN, DM=10 3 m∠M=75°, m∠N=45° Find: Perimeter of △DMN

Mathematics

1 answer:

OlgaM077 [116]3 years ago

5 0

Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...

... 30-60-90: 1 : √3 : 2

... 45-45-90: 1 : 1 : √2

The long side of ΔMDX is 10√3, so the other two sides are

... MX = MD(√3/2) = 15

... DX = MD(1/2) = 5√3

The short side of ΔMNX is MX = 15, so the other two sides are

... NX = MX(1) = 15

... MN = MX(√2) = 15√2

Then the perimeter of ΔDMN is ...

... P = DM + MN + NX + XD

... P = 10√3 +15√2 + 15 + 5√3

... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN

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There are 18 female students and 16 male students in a class. Which of the following expresses the ratio of female students to m

fiasKO [112]

Hey!

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Solution:

The ratio is FEMALES to MALES.

So its 18/16, 18:16, or 18 to 16.

~Now we need to simplify.

18:16 → 18/2:16/2 → 9:8

*Note* When you have a ratio you need to know which comes first. If you put males to females that incorrect. It has to be correct according to the question.

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Answer:

$\large\boxed{B)~9~to~8}$

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Hope This Helped! Good Luck!

4 0

3 years ago

Which graph shows the solution to this system of inequalities?<br> y>-1/3x+1<br> y>2x-3

Mademuasel [1]

Given:

The system of inequalities is:

$y>-\dfrac{1}{3}x+1$

$y>2x-3$

To find:

The graph of the given system of inequalities.

Solution:

We have,

$y>-\dfrac{1}{3}x+1$

$y>2x-3$

The related equations are:

$y=-\dfrac{1}{3}x+1$

$y=2x-3$

Table of values for the given equations is:

$x$ $y=-\dfrac{1}{3}x+1$ $y=2x-3$

0 1 -3

3 0 3

Plot (0,1) and (3,0) and connect them by a straight line to get the graph of $y=-\dfrac{1}{3}x+1$ .

Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of $y=2x-3$ .

The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.

Therefore, the graph of the given system of inequalities is shown below.

6 0

2 years ago

The diameter of a sphere is 6 cm. What is the volume of the sphere?

irinina [24]

Answer:

36pi

Step-by-step explanation:

the volume of a sphere is equal to 4/3 x pi x r^3

the radius is half of the diameter

3^3=27

27x4/3=36

36pi

6 0

2 years ago

Please help me ......................

jekas [21]

Answer:

n = 18

Step-by-step explanation:

The formula for angle sum of a polygon is S = 180 (n - 2), where S is the sum and n is the sides.

We are given that the sum is 2880, and are trying to find n.

Simply sub in S = 2880,

2880 = 180 (n - 2)

Divide by 180 to get (n - 2) by themselves on the right side,

16 = n - 2

Now add 2 to the other side to get n by itself

18 = n

n = 18

Hope this helped!! Please feel free to ask me if there's anything you don't understand from this working

3 0

3 years ago

Read 2 more answers

A coin will be tossed three times, and each toss will be recorded as heads (H) or tails (T). Give the sample space describing al

cricket20 [7]

Answer:

Sample space:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Third toss is heads:

{HHT, HTT, THT, TTT}

First toss is heads, second tails and third heads:

{HTH}

Explanation:

In order to find the sample space we need to write all the possible outcomes from tossing the coin three times.You can start by writting all the possible outcomes for the first toss being a head and finish with all the possible outcomes for the first toss being Tails. The number of elements in the sample space can be found by multiplying the possible outcomes of each toss together, so 2*2*2=8

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For the third toss being heads we will have one restriction this time. Which is that the third toss is Tails. You can take the elements from the sample space where the third element is a tails. In this case, the number of elements can be calculated by multiplying the possible outcomes for only the first two tosses 2*2=4

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

For first toss is heads, second tails and third heads there is only one possible way for you to get this outcome so there is only one element to this set.

{HTH}

4 0

2 years ago