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DanielleElmas [232]
3 years ago
14

3valuate the diagram below. Find the values of m and n.

Mathematics
1 answer:
Pepsi [2]3 years ago
5 0

Answer:

m = 20 and n = 35

Step-by-step explanation:

The triangle on the right has 2 congruent sides and is isosceles

Thus the 2 base angles are congruent, that is

n = \frac{180-110}{2} = \frac{70}{2} = 35

The external angle of a triangle is equal to the sum of the 2 opposite internal angles.

110 is an external angle to the triangle on the left, thus

m + 90 = 110 ( subtract 90 from both sides )

m = 20

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Naddik [55]

Answer:

All are correct there are just disorganized.

8 0
3 years ago
If I can run 5 miles per hour, how far is this in feet per hour?
stiv31 [10]

Answer:

26,400 feet is 5 miles, so 5,280 fph.

Step-by-step explanation:

1 foot is equal to 0.000164 mile.

If you need an explanation, let me know. Hope this helps!!

4 0
2 years ago
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Jeremy is cutting a board into pieces that are 1 2/3 feet long . The board is 14 1/4 feet long . How many 1 2/3 -feet long piece
Solnce55 [7]

Answer:

Total number of 1 2/3 feet long pieces that will be cut=8 pieces

Step-by-step explanation:

This can be expressed as;

Total length of the board=length per piece×number of pieces

where;

Total length of board=14 1/4 feet

Length per piece=1 2/3 feet

Number of pieces=n

Replacing;

14 1/4=1 2/3×n

(57/4)=(5/3)n

n=(57/4)×(3/5)=8.55

Total number of 1 2/3 feet long pieces that will be cut=8 pieces

7 0
3 years ago
Read 2 more answers
A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.
melisa1 [442]
Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°. 

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

\overline{OB}:\overline{AB} = 1:2
\overline {OB}:10 = 1:2
\overline{OB} = \frac{1}{2}(10) = 5

Similarly, we have

\overline{AO}:\overline{AB} = \sqrt{3}:2
\overline {AO}:10 = \sqrt{3}:2
\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}

Now, to find the lengths of the diagonals, 

\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}
\overline{BC} = 2(\overline{OB}) = 10

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0
3 years ago
What is the solution to the equation
Elis [28]

Answer:

x = -13

Step-by-step explanation:

Distribute:

8 - 6x + 10x - 15 = 20 - 5x

Combine like terms:

4x - 7 = 20 - 5x

Isolate Variable

-x = 13

-1(-x) = -1(13)

x = -13

8 0
3 years ago
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