The sum of four consecutive integers is 106. What is the largest number?

The size of the largest angle in a triangle is 3 times the size of the smallest angle.

tamaranim1 [39]

The sizes of the angles are 34° , 44° , 102°

Step-by-step explanation:

The given is:

The size of the largest angle in a triangle is 3 times the size of the smallest angle
The third angle is 10° more than the smallest angle
The size of the third angle is x

We need to find the size of each angle in the triangle

∵ The size of the smallest angle = x°

∵ The size of the largest angle is 3 times the size of the smallest angle

∴ The size of the largest angle = x × 3 = (3x)°

∵ The third angle is 10° more than the smallest angle

∴ The size of the third angle = (x + 10)°

Add the size of the three angles and equate the sum by 180°

∵ The sum of the sizes of the interior angles of a Δ is 180°

∴ x + (3x) + (x + 10) = 180

∴ x + 3x + x + 10 = 180

- Add like terms

∴ 5x + 10 = 180

- Subtract 10 from both sides

∴ 5x = 170

- Divide both sides by 5

∴ x = 34

∵ x is the size of the smallest angle

∴ The size of the smallest angle is 34°

∵ 3x is the size of the largest angle

∴ The size of the largest angle = 3(34) = 102°

∵ x + 10 is the size of the third angle

∴ The size of the third angle = 34 + 10 = 44°

The sizes of the angles are 34° , 44° , 102°

Learn more:

You can learn more about the triangles in brainly.com/question/1479138

#LearnwithBrainly

6 0

2 years ago

What is the value of (2x^2-5x+4)if x =7

Troyanec [42]

<span>We have to use PEMDAS for this expression.

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

</span>(2x^2 - 5x + 4) Original Mathematical Expression

[2(7)^2 - 5(7) + 4] Plugging the value of x, 7 into expression.

There are parentheses, so that means we have to work in them.

There are exponents, so we have to do those first.

[2(49) - 5(7) +4] Exponents.

There is multiplication, that we can do, so we do that left to right.

[98 - 35 + 4] Multiplication.

There is no division.

There is addition and subtraction, so we do those left to right.

[63 + 4] Subtraction.

67 Addition.

Final Answer: 67

6 0

2 years ago

Read 2 more answers

A 40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. how far away from the building is the b

zaharov [31]

The distance between the building and the ladder is 34.876 foot.

<h3>What is a Right Triangle?</h3>

A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.

The ladder forms a right triangle with the building and the ground,

The length of the triangle is 40 foot

The angle made by the ladder is 29.32 degree

By using Trigonometric Ratios

cos 29.32 = Base / Hypotenuse

cos 29.32 = Base / 40

0.8718 × 40 = Base

Base = 34.876 foot

Base is the distance between the building and the ladder.

Base of the ladder = 34.876 foot

To learn more about trigonometric functions from the given link

brainly.com/question/24336684

#SPJ4

8 0

1 year ago

I nedd help please.....

oksian1 [2.3K]

(-3,4)(0,-3)
slope = (-3 - 4) / (0 - (-3) = -7/3 <=

3 0

3 years ago

I need help please helppppppppppppppppppppppp

Marrrta [24]

Given:

A figure of a circle and two secants on the circle from the outside of the circle.

To find:

The measure of angle KLM.

Solution:

According to the intersecting secant theorem, if two secant of a circle intersect each other outside the circle, then the angle formed on the intersection is half of the difference between the intercepted arcs.

Using intersecting secant theorem, we get

$\angle KLM=\dfrac{1}{2}(Arc(JON)-Arc(KM))$