All categories

3 years ago

The measures of all of the interior angles of a triangle are in the extended ratio 1 : 2 : 3. The value of the smallest angle is

1 answer:

7 0

The sum of the interior angles of a triangle is 180°.

Let's suppose that all 3 angles in the ratio are divisible by a value x.

So the three angles become 1x, 2x and 3x.

1x + 2x + 3x = 180°

6x = 180°

x = 30° [ By dividing both sides by 6 ]

Thus the three angles are: 1x = 30° ; 2x = 2*30 = 60° ; 3x = 3*x = 90°

Hence the smallest angle is 30°.

You might be interested in

Write an equation of a circle that has the center at the origin and goes through (-3,-6)

dexar [7]

Answer:

$x^{2} +y^{2} = 45$

Step-by-step explanation:

General Equation of circle is

$(x-x_1)^{2} +(y-y_1)^{2} = r^{2}$ ----------- (1)

Here

$(x_1, y_1)= (0, 0)$

Radius r is distance from origin (x1, y1) to point (x2, y2)=(-3, -6)

$r=\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2} }$

$r= \sqrt{(-3-0)^{2} + (-6-0)^{2} }$

$r= \sqrt{9+36}$

$r=\sqrt{45}$

Substituting values in equation (1)

$(x-0)^{2} +(y-0)^{2} =( \sqrt{45})^{2}$

$x^{2} +y^{2} = 45$

6 0

2 years ago

A cell phone company has a basic monthly plan of $40 plus $0.45 for any minutes used over 700. Before receiving his statement, J

fgiga [73]

Ok so we know he used over 700 because he was charged more than 40. Then we take the $8.10 and divide 0.45 into it. This then gives you 18 more minutes. Then add 18 to 700 and you get 718 min.

4 0

3 years ago

Pleaseee helpppp:)))

matrenka [14]

Answer:

<h2>Option B:</h2><h3>112 families </h3>

Step-by-step explanation:

Given,

No. of families = 75

Out of 75 no. of families had cars = 42

Out of 1, no. of families can have cars

$= \frac{42}{75}$

Therefore, 

Out of 200 families, no. of families had cars

$= 200 \times \frac{42}{75}$

$=200 \times \frac{14}{25}$

= 8 × 14

= 112

Hence, 

option B is correct as 112 families have cars out of 200 families (Ans)

5 0

2 years ago

The ratio of workers to supervisors and factories 32 to 2. The ratio of male workers to female workers is 6 to 5. If there are 8

Margarita [4]

Answer:

The number of supervisor in the factory is 9 .

Step-by-step explanation:

Given as :

The ratio of workers to supervisors and factories 32 : 2

let the number of workers = 32 x

And The number of supervisors = 2 x

The ratio of male workers to female workers is 6:5

Let The number of male workers = 6 y

And The number of female worker = 5 y

The number of female workers at the plant = 80

So, 5 y = 80

∴ y = $\frac{80}{5}$

I.e y = 16

So, The number of male workers = 6 y = 6 × 16 = 96

Thus The Total number of worker in the factory = The number of male workers + The number of female workers at the plant

Or, The Total number of worker in the factory = 96 + 80 = 146

Now , Again

∵ The ratio of workers to supervisors in factories 32 : 2

So, The number of workers = 32 x

I.e 146 = 32 x

∴ x = $\frac{146}{32}$ = 4.5

So, The number of supervisors = 2 x = 2 × 4.5 = 9

Hence The number of supervisor in the factory is 9 . Answer

3 0

3 years ago

Read 2 more answers

What is the equation of the line through (-6, -5) and (-4, -4)?

Norma-Jean [14]

Answer:

y = 1/2x -2

Step-by-step explanation:

The 2-point form of the equation for a line is useful for answering questions like this.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . equation of a line through (x1, y1) and (x2, y2)

Filling in the given points, the equation becomes ...

y = (-4 -(-5))/(-4 -(-6))/(x -(-6)) -5

y = 1/2(x +6) -5

y = 1/2x -2

3 0

3 years ago