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3 years ago

Triangle sum (3x+1)^0+(10x-11)^0+(3x-2)^0=180

Mathematics

1 answer:

svetlana [45]3 years ago

4 0

Answer:

x = 12
3x+1 = 37°
10x-11 = 109°
3x-2 = 34°

Step-by-step explanation:

Perhaps you want to know the value of x or the measures of the angles?

Simplifying the given equation, you get ...

(16x -12)° = 180°

16x = 192 . . . . . . . divide by °, add 12

x = 12

(3x+1)° = (3·12+1)° = 37°

(10x-11)° = (10·12-11)° = 109°

(3x-2)° = (3·12-2)° = 34°

x is 12, and the angle measures are 37°, 109°, 34°.

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Answer:

-27

Step-by-step explanation:

6^2=36

36/-4=-9

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3 years ago

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Answer:

Step-by-step explanation:

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2 years ago

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

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Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

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2 years ago

Louie is trying to find a rectangular canvas for his art project. Its height

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The length of the diagonal of the canvas is approximately 27 degrees.

The height of the rectangular canvas must reach 18 inches. It must form a 48 degrees angle with the diagonal at the top of the canvas.

<h3>Length of the diagonal Canvas</h3>

Therefore, the length of the diagonal can be found as follows:

Using trigonometric ratio,

cos ∅ = adjacent / hypotenuse

where

∅ = 48°

adjacent side = Height of the rectangle = 18 inches

hypotenuse = Length of the diagonal

Therefore,

cos 48° = 18 / h

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h = 18 / cos 48°

h = 18 / 0.66913060635

h = 26.9005778976

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learn more on rectangle here: brainly.com/question/26099609?referrer=searchResults

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2 years ago

Carolina y su mamá compraron tres tortas de sabores diferentes para la reunión con sus amigos del colegio. De la torta de naranj

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Answer: 2 1/5 partes de torta

Step-by-step explanation:

Para contestar esta pregunta debemos sumar cada parte de torta:

0.7+9/12+6/8 =

Convertimos las fracciones en decimales, para tener todos los valores expresados de la misma forma. Dividiendo:

9/12=0.75

6/8=0.75

Sumamos :

0.7+0.75+0.75 = 2.2 partes = 2 1/5 partes

En conclusión, Carolina y sus amigos comieron 2 1/5 partes de torta.

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3 years ago