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3 years ago

Given ∆ABC≅∆DEF, m∠A=5x+12 and m∠D=8x, find m∠A and m∠D.

Mathematics

1 answer:

Alona [7]3 years ago

7 0

Given :

Two triangle ∆ABC and ∆DEF are congruent.

m∠A=5x+12 and m∠D=8x.

To Find :

m∠A and m∠D.

Solution :

Since, both the triangle are congruent.

m∠A = m∠D

5x + 12 = 8x

3x = 12

x = 4

m∠A = 5(4) + 12 = 32°

m∠D = 8(4) = 32°

Therefore, value of m∠A and m∠D is 32°.

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A school play sells adult and child tickets. On Friday they sold 55 child tickets and 20 adult tickets for $200. On Saturday the

Anarel [89]

Answer:

Step-by-step explanation:

Let, price of individual child ticket is $x, and price of individual adult ticket is $y.

Now, on Friday we can write an equation is 55x+20y=200....(1).

and on Saturday we can write an equation is 72x+36y=306.....(2).

so, Equation 1: 55x+20y=200

Equation 2: 72x+36y=306

now, we are going to solve both equations.

after solving you will find x=2 and y=4.5

Hence, we can say that the cost of child ticket is $2, and the cost of adult ticket is $4.50.

4 0

3 years ago

If the figure shown on the grid below is dilated by a scale factor of

shepuryov [24]

The coordinate of point N after the dilation is N' = (-8/3, 8/3)

<h3>Dilation of coordinates</h3>

Dilation is a transformation technique for changing the size of an object using a scale factor.

Given the coordinate of N from the figure as (-4, 4). If this coordinate point is dilated by a factor of 2/3, then the resulting coordinate will be:

N' = (2/3(-4), 2/3(4))

N' = (-8/3, 8/3)

Hence the coordinate of point N after the dilation is N' = (-8/3, 8/3)

Learn more on scale factor here: brainly.com/question/10253650

#SPJ1

7 0

2 years ago

You are standing 40 meters from the base of a tree that leans 8o away from you. The angle of elevation from you to the top of th

Y_Kistochka [10]

Answer:

the height of the tree is 15.49 m

Step-by-step explanation:

Step 1:

From the figure, we can determine ∠ATB by using the fact that the sum of all the angles in a triangle add up to 180°:

∠ ATB = 180° - 98° - 20°

∠ ATB = 62°

Step 2:

Therefore, using the law of sines, we can determine the height of the tree.

TB / sin(20°) = 40 / sin(62°)

TB = 40 × (sin(20°) / sin(62°))

TB = 15.49 m

Therefore, the height of the tree is 15.49 m

3 0

3 years ago

To speed the process of surveying, surveyors use brass metal plates to record important information. The benchmarks, as they are

Agata [3.3K]

Answer:

Feet Above Sea Level

Step-by-step explanation:

A benchmark is a term in Surveying and Geo informatics, that describes a point of reference established at a known elevation which serves as basis in which other elevation or topographical point can be measured.

Therefore, when determining the benchmark, it's height is calculated relative to the vertical datum of the area, typically mean sea level, which is then recorded in FEET ABOVE SEA LEVEL.

Hence, Benchmarks measurements refer to FEET ABOVE SEA LEVEL.

5 0

3 years ago

A cyclist rides a bike at a rate of 24 miles per hour. What is this rate in miles per minute? How many miles will the cyclist tr

BlackZzzverrR [31]

there are 60 minutes per hour

24/60 = 0.4 miles per minute

0.4*5 = 2

they will ride 2 miles in 5 minutes

4 0

3 years ago