All categories

3 years ago

HELP. SUPER EASY MATH PROBLEM. 20 POINTS

Mathematics

2 answers:

Stells [14]3 years ago

7 0

The area of the shaded = the area of the sector - the area of the isosceles triangle.

Split the isosceles triangle in half, each of those triangles is a 30-60-90 triangle, where the radius is the hypotenuse.

Ratio of short leg: long leg: hypotenuse= x : x√3 : 2x

Given hypotenuse = radius = 27.8 in

so short leg = 27.8 / 2 = 13.9 in

long leg = 13.9 √3 = 24.1 in

Area of this isosceles triangle = 24.1 x 13.9 = 334.99 in^2

Area of sector = (150 / 360) π r^2

= (150 / 360) (3.14) (27.8)^2

= 0.4 * (3.14) (772.84)

= 970.7 in^2

Area of shaded = 970.7 in^2 - 334.99 in^2 = 635.71 in^2

= 635.7 in^2 (nearest tenth)

Answer:

635.7 in^2

Stells [14]3 years ago

6 0

First find the area of the sector of 150 degrees:

150/360 x PI * 27.8^2 = 1011.6452 in^2

Now find the area of the triangle formed by the 150 degrees and the radius 27.8

first find the length of the chord ( the base of the triangle)

c^2 = 27.8^2 + 27.8^2 - 2 * 27.8 * cos(150) = 53.71

now find the height by using half the chord length as the base and using the Pythagorean theorem:

26.855^2 - 27.8^2 = height^2

height = 7.19

The area of the triangle is 1/2 x base x height = 1/2 x 26.855 x 7.1952 = 96.605

multiply by 2 because we made 2 right triangles: 96.54 x 2 = 193.21 square inches.

Now the area of the shaded region is the area of the sector minus the area of the triangle:

1011.6452 - 193.21 = 818.4352

Rounded to nearest tenth = 818.4 in^2

You might be interested in

Use the order of operations to simplify the given expression. 4−6+2⋅7

andrezito [222]

Answer:

Step-by-step explanation:

PEMDAS

no parenthesis

no exponents

4-6+2 x 7

4-6+ 17

no division

4-6=2

2+17

19 is the answer

6 0

3 years ago

Read 2 more answers

A salesperson is paid a flat rate plus a fixed percentage of her sales. Last month, she sold $16,000 worth of goods and was paid

Feliz [49]

Answer:

She will be paid $1,350

Step-by-step explanation:

Linear Modeling

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

y=mx+b, where m and b are constants.

The payments for a salesperson will be linearly modeled. There are two known points: When the sales were $16,000, the payment was $1,600. This makes the point (16,000;1,600).

We also know when the sales were $12,000, the payment was $1,400. The point is (12,000;1,400)

Let's use the points to find the values of m and b.

Using (16,000;1,600):

1,600=m*16,000+b

Using (12,000;1,400):

1,400=m*12,000+b

Subtracting both equations:

200=16,000m-12,000m

200=4,000m

Solving:

m=200/4,000=0.05

Using the first equation and the value of m:

1,600=0.05*16,000+b

1,600=800+b

Solving:

b=800

The equation is now complete:

y=0.05x+800

She sold $11,000 this month, so the payment is:

$y=0.05\cdot 11,000+800$

Y=550+800=1,350

She will be paid $1,350

3 0

2 years ago

What is 19.6 divided by 7

Lemur [1.5K]

19 divided by 7 = 2.8

7 0

3 years ago

Real numbers include

Travka [436]

D. All of the above
is the correct answer.

I hope you like this answer and have a good night and life! :D

4 0

2 years ago

Read 2 more answers

Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in

Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.$

Divide both sides of equation (II) by 5 so our numbers become smaller

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.$

Rearrange (I) to solve for y so that we can substitute into (II)

$\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}$

Substituting this into equation (II) for the y:

$\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}$

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

$y = 38 - 32 = 6$

32 five-dollar bills and 6 ten-dollar bills

7 0

3 years ago