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natita [175]
3 years ago
8

Find the value of each variable

Mathematics
1 answer:
mina [271]3 years ago
7 0

Answer:

x = 16  y= 16√3

Step-by-step explanation:

we know that a angle is 60 degrees. Thanks to this information we can say that x is half the hypothenuse, so is value is 16.

y can be express as √3/2 x 32 = 16√3

You might be interested in
Find four consecutive integers such that if the sum of the first and third is increased by 10, the result is 6 greater than 4 ti
kap26 [50]
Four consecutive integers are four numbers in a row, with a difference of one between each of them.

x= first integer
x+1= second integer
x+2= third integer
x+3= fourth integer

sum= add
increased by 10= add 10
the result is= equal sign
6 greater than= add 6
4 times= multiply


EQUATION
(x + x + 2) + 10= (4(x + 3)) + 6
combine like terms on the left side

2x + 12= (4(x + 3)) + 6
multiply 4 by terms in parentheses

2x + 12= 4x + 12 + 6
combine like terms on right side

2x + 12= 4x + 18
subtract 4x from both sides

-2x + 12= 18
subtract 12 from both sides

-2x= 6
divide both sides by -2

x= -3 first integer


x+1= -2 second integer
x+2= -1 third integer
x+3= 0 fourth integer


ANSWER: The four consecutive integers are -3, -2, -1 and 0.

Hope this helps! :)
6 0
3 years ago
If ΔMNO ≅ ΔXYZ, then what corresponding parts are congruent?
8090 [49]

Answer:

∠N and ∠Y

Step-by-step explanation:

When two triangles are congruent then there corresponding parts ( angle or sides ) are also congruent or equal, ( CPCTC )

In triangles MNO and XYZ,

Side MN, NO and OM are corresponding to XY, YZ and ZX respectively,

And, angles M, N and O are corresponding to angles X, Y and Z respectively,

Thus, if ΔMNO ≅ ΔXYZ

By CPCTC,

MN ≅ XY

NO ≅ YZ

OM ≅ ZX

Also, ∠M ≅ ∠X, ∠N ≅ ∠Y and ∠O ≅ ∠Z

Hence, THIRD OPTION is correct.

4 0
3 years ago
Read 2 more answers
Elliott’s backyard is 4800 square feet. His dad is going to pave 15% of this area to use as a patio. How many square feet will b
Gennadij [26K]

Step-by-step explanation:

\frac{15}{100}  \times 4800 \: ft {}^{2}

15 \times 18

720 \: ft {}^{2}

the answer is B

3 0
3 years ago
A gardener is planting two types of trees: Type A is 9 feet tall and grows at a rate of 6 inches per year. Type B is 6 feet tall
xenn [34]

It will take exactly 3 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees

  • Type A is 9 feet tall and grows at a rate of 6 inches per year.
  • Type B is 6 feet tall and grows at a rate of 18 inches per year.

We need to find exactly how many years it will take for these trees to be the same height

To solve this problem let us make an equation of each type and then equate the two equations to find the number of years

Assume that the two types will have the same heights in x years

∵ Type A is 9 feet tall and grows at a rate of 6 inches per year

- Change the feet to inches

∵ 1 foot = 12 inches

∴ 9 feet = 9 × 12 = 108 inches

The height of the tree after x years is the sum of the initial height and the product of the rate of growth and the number of years

∵ The rate of growth = 6 inches per year

∵ The number of years = x

∵ The initial height = 108 inches

∴ The height of tree A = 108 + 6 x

∵ Type B is 6 feet tall and grows at a rate of 18 inches per year

∵ 1 foot = 12 inches

∴ 6 feet = 6 × 12 = 72 inches

∵ The rate of growth = 18 inches per year

∵ The number of years = x

∵ The initial height = 72 inches

∴ The height of tree B = 72 + 18 x

Now equate the two equations to find x

∵ 72 + 18 x = 108 + 6 x

- Subtract 72 from both sides

∴ 18 x = 36 + 6 x

- Subtract 6 x from both sides

∴ 12 x = 36

- Divide both sides by 12

∴ x = 3

It will take exactly 3 years for these trees to be the same height

Learn more:

You can learn more about the linear equations in brainly.com/question/9801816

#LearnwithBrainly

4 0
3 years ago
A translation is applied to the rectangle formed by the points A(−2, 6) , B(2, 6) , C(2, 4) , and D(−2, 4) . The image is the re
Natasha_Volkova [10]
So basically from (-2,6) to (1,6)
The up and down translations applies to the y values 
So from 6 to 6 nothing happened! so wasn't translated neither up nor down 

And left and right applies to x values. 
from -2 to 1 
3 units positive that means 3 units right..
Hope it helps 
4 0
3 years ago
Read 2 more answers
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