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2 years ago

For ΔABC, the measure in degrees of angles A, B, and C are 30, 4x, and 50 respectively. What is the value of x?

Mathematics

1 answer:

Luba_88 [7]2 years ago

6 0

Answer:

x=25

Step-by-step explanation:

The area of a traingle is 180 degrees, so we subtract 30 and 50 from 180. we are then left with 100 degrees, divide by 4 and we get that x=25.

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Consider the arithmetic sequence 13, 24, 35, ....

Nostrana [21]

Answer: 27

Step-by-step explanation:

The given sequence : 13, 24, 35, ....

Here, first term : a= 13

Common difference: d=24-13 =11

The nth term of arithmetic sequence is given by :-

$a_n=a+(n-1)d$

It is given that the nth term is 299, so put $a_n=299, a=13 ; d=11$

$299=13+(n-1)11$

Subtract 13 from both sides , we get

$286=(n-1)11$

Divide both sides by 11, we get

$26=n-1$

Add 1 on both sides , we get

$n=27$

Hence, the value of n= 27

4 0

3 years ago

Find the slope of the line passing through the two points.<br><br> (2.1, 3.8), (3.1, 7.6)

bixtya [17]

Answer:

3.8

Step-by-step explanation:

Slope formula- m = y2 - y1

x2 - x1

x1, y1

2.1, 3.8

7.6 - 3.8

3.1 - 2.1 = 3.8

x2,y2

3.1, 7.6

3 0

3 years ago

A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

Tom has 7 more silver dollars than Jimmy. Together they have a total of 71 silver dollars. How many silver dollars does Tom have

Eddi Din [679]

Tom has 39 silver dollars. You can do this on your head. Jimmy has 32, and Tom 39.

4 0

3 years ago

If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the larg

vlabodo [156]

Consider all employees.

gross pay $32,600 - 100%,
total job benefits $33,600 - x%.

Then

$\dfrac{32,600}{33,600}=\dfrac{100}{x},\\ \\32,600\cdot x=33,600\cdot 100,\\ \\x=\dfrac{33,600\cdot 100}{32,600}=\dfrac{33,600}{326} \approx 103.07.$

Employee A receives 3.07% of gross pay in employee benefits.

gross pay $32,900 - 100%,
total job benefits $34,000 - x%.

Then

$\dfrac{32,900}{34,000}=\dfrac{100}{x},\\ \\32,900\cdot x=34,000\cdot 100,\\ \\x=\dfrac{34,000\cdot 100}{32,900}=\dfrac{34,000}{329} \approx 103.34.$

Employee B receives 3.34% of gross pay in employee benefits.

gross pay $33,400 - 100%,
total job benefits $33,900 - x%.

Then

$\dfrac{33,400}{33,900}=\dfrac{100}{x},\\ \\33,400\cdot x=33,900\cdot 100,\\ \\x=\dfrac{33,900\cdot 100}{33,400}=\dfrac{33,900}{334} \approx 101.50.$

Employee C receives 1.50% of gross pay in employee benefits.

gross pay $33,700 - 100%,
total job benefits $34,700 - x%.

Then

$\dfrac{33,700}{34,700}=\dfrac{100}{x},\\ \\33,700\cdot x=34,700\cdot 100,\\ \\x=\dfrac{34,700\cdot 100}{33,700}=\dfrac{34,700}{337} \approx 102.97.$

Employee D receives 2.97% of gross pay in employee benefits.

Answer: correct choice is B.

7 0

3 years ago

Read 2 more answers