How would you write 3 divided by 5 as a percent?

The diagonals of a rectangle enclose an angle of measure 78 degree

katrin2010 [14]

The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².

<h3>What is the Area of a Rectangle?</h3>

Area of a rectangle = (length)(width).

<h3>Given the following:</h3>

Angle of measure 78 degree enclosed by the diagonals of the rectangle

Perimeter = 36 cm

To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.

A side of the rectangle = x cm

The other side = (36 - 2x)/2 = (18 - x) cm

Angle of the diagonal base = (180 - 78)/2 = 51°

Apply the tangent ratio to find x:

Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,

∅ = 51°

Opposite side = x cm

Adjacent side = (18 - x) cm

Tan 51° = x/(18 - x)

1.235 = x/(18 - x)

1.235(18 - x) = x

22.23 - 1.235x = x

22.23 = x + 1.235x

22.23 = 2.235x

22.23/2.235 = 2.235x/2.235

x = 9.946 cm (one side length)

The other side length = 18 - x = 18 - 9.946 = 8.054 cm

Area of the rectangle = (9.946)(8.054)

Area of the rectangle = 80.1 cm²

Learn more about the area of rectangle on:

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3 0

1 year ago

The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered

Margaret [11]

Answer:

The pair of equations which has (2,12) as its solution is,

equation B and equation C.

Step-by-step explanation:

According to the question,

equation of line A is $\frac {y - 16}{x + 6} = \frac {16 + 4}{-6 - 9}$

or, $\frac {y - 16}{x + 6} = \frac {-4}{3}$

or, $3y - 48 = -4x - 24$

or, 3y + 4x = 24 ------------------(1)

Now, the point (2, 12) doesn't satisfy (1). Hence, (2,12) is not a solution for the line A.

Equation of line B is, $\frac {y - 20}{x + 2} = \frac {20 - 0}{-2 - 8}$

or, $\frac {y - 20}{x + 2} = -2$

or, $y - 20 = -2x - 4$

or, y + 2x = 16 -----------------------------(2)

The point (2,12) is satisfied by (2). Hence, (2, 12) is a solution for line B.

Equation of line C is, $\frac {y + 6}{x + 7} = \frac {20 + 6}{6 + 7}$

or, $\frac {y + 6}{x + 7} = 2$

or, y + 6 = 2x + 14

or. y - 2x = 8 -----------------------------------(3)

The point (2, 12) is satisfied by (3). Hence, (2 , 12) is a solution for the line C.

Equation of line D is, $\frac {y - 20}{x - 7} =\frac {20 + 7}{7 - 0}$

or, $\frac {y - 20}{x - 7} = \frac {27}{7}$

or, 7y - 140 = 27x - 189

or, 7y - 27x = -49----------------------------------------(4)

The point (2, 12) is not satisfied by (4). hence, (2, 12) is not a solution of the line D

Hence, the pair of equations which has (2,12) as its solution is,

equation B and equation C.

6 0

3 years ago

Can anyone help me with this. Click to see

IgorLugansk [536]

Answer: mean = 6

median = 7

mode = 8

Step-by-step explanation:

8 0

3 years ago

Widget Wonders produces widgets. They

navik [9.2K]

Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50

7 0

3 years ago

Fifty students were eating lunch in the school cafeteria. The ratio of boys to girls was 25:25. Mrs. White asked Kym to explain

Studentka2010 [4]

42 percent of the people would because the answer to everything is 42

4 0

3 years ago

Read 2 more answers