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arsen [322]
3 years ago
11

Find the value of x and y.

Mathematics
1 answer:
zysi [14]3 years ago
8 0

Answer:

<em>x = 9</em>

<em>y = 36</em>

Step-by-step explanation:

<u>Lines and Angles</u>

Triangle CDE is isosceles. This means the two angles of the base DE are congruent (have the same measure):

7x + 1 = 4x + 28

Subtracting 4x + 1:

3x = 27

Dividing by 3:

x = 9

Substituting in the expression for the angles:

7x + 1 = 7*9 + 1 = 64°

The angles are 64° and 64°. The other internal angle at vertex C is 180°-64°-64°=52°. This angle is congruent with its vertical angle in the triangle ABC. We are given another angle of 43°. Thus the measure of angle A is 180°-52°-43°=85°

This last angle is equal to the expression of y:

-2(3 - y) + 19 = 85

Subtracting 19:

-2(3 - y) = 66

Removing the parentheses:

-6 + 2y = 66

Adding 6:

2y = 72

Dividing by 2:

y = 36

Final answer:

x = 9

y = 36

You might be interested in
The city's central library has 72,864 books. The library has 72 bookcases. If each bookcase has room for the same number of book
solong [7]

Answer:

There are 1012 books per bookcase

Step-by-step explanation:

To find the number of books per bookcase take the number of bookcases (72) divided by the number of books (72,864)

So;

72,864 / 72 = 1012

Hope this helps!

5 0
3 years ago
The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.
iris [78.8K]

Answer:

  • L(t) = 727.775 -51.875cos(2π(t +11)/365)
  • 705.93 minutes

Step-by-step explanation:

a) The midline of the function is the average of the peak values:

  (675.85 +779.60)/2 = 727.725 . . . minutes

The amplitude of the function is half the difference of the peak values:

  (779.60 -675.85)/2 = 51.875 . . . minutes

Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.

Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.

Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.

Our formula is ...

  L(t) = 727.775 -51.875cos(2π(t +11)/365)

__

b) L(55) ≈ 705.93 minutes

8 0
3 years ago
PLEASE HELP!! 20 POINTS!!
luda_lava [24]

Answer:

yea

Step-by-step explanation:

8 0
2 years ago
CORRECT ANSWER GETS BRAINLIEST
kati45 [8]

Answer:

2.5

Step-by-step explanation:

t = 0.25d^{1/2}

Substitute d with 100

t = 0.25 x (100^{1/2})

A number to the half power is equal to the square root of a number.

Square root of 100 is 10: \sqrt{100} = 10

t = 0.25*10

t = 2.5

Hope this helps :)

Have an awesome day!

7 0
2 years ago
anyone know how to do this?
Ugo [173]

Answer: A reasonable estimate of the minimum is 20.

8 0
2 years ago
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