How to find the area of region composed of rectangles and/or right triangles?

Answers

Answer 1

To determine the area of a region that is composed of rectangles and triangles, you should just calculate for the individual area of each of the rectangles and the triangles. Then, after determining the areas, you add them all up. The sum would represent the total area of the region. The area is the number of square units in a shape. It is one way of describing the size of a particular surface. For a rectangle, it is calculated from the product of its length and its width. For a triangle, it obtained from one half the product of its base and the height.

Related Questions

List all your possibility of outcomes (there are 36 outcomes) if you roll a dice containing numbers 1-6 two times. Determine the probability of each outcome.

Answers

Check the table attached.

The first coordinates of each pair represent the 1.roll, and the second coordinates the 2nd, roll.

All the possible outcomes are {(1, 1), (1, 2).... (6, 5), (6, 6)}, a total of 36, as can be seen in the table.

Each outcome has a chance of 1 out 36 total possible outcomes of occurring.

So the probability is 1/36=0.02778

On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.

Answers

We have the fixed cost of $2.20
For every mile travelled the fare is 5 × 30cents = $1.50

If the fare was $17.20, the number of miles travelled is [tex] \frac{17.20-2.20}{1.50} = 10 [/tex] miles

The fare for travelling 16.8 miles is [tex]2.20+1.5(16.8)=$27.40[/tex]

The fare for travelling n miles is [tex]C=2.20+1.5n[/tex]

The relationship is a linear relationship as there is a constant increase of $1.50 for every mile travelled. The graph of the relationship is shown below

In triangle abc, the measure of angle b is 29 degrees° more than three times the measure of angle

a. the measure of angle c is 61 degrees° more than the measure of angle

a. find the measure of each angle.

Answers

Answer:

∠a = x

∠b = 3x + 29

∠c = x + 61

x + 3x + 29 + x + 61 = 180

5x = 180 - 29 - 61

5x = 90

x = 90/5

x = 18° ← ∠a

∠b = 3x + 29 = 3*18 + 29 = 83°

∠c = x + 61 = 18 + 61 = 79°

Step-by-step explanation:

Jared is in charge of production in a factory that makes lightbulbs. The factory made 2,648 lightbulbs over the weekend. Jared wants to pull a sample of these bulbs for testing. Which sample would give Jared the most-accurate test results? a sample consisting of every 20th lightbulb a sample consisting of every 40th lightbulb a sample consisting of every 50th lightbulb a sample consisting of every 100th lightbulb

Answers

Ideally, the smaller the sample population, the more accurate is the sampling result, but it will take longer time if the number of samples is huge.

The answer to the above question is ideally 20 light bulbs per sampling.

in how many ways can a judge award first, second, and third place in a contest with 10 entries

Answers

Since order is important, this is a problem solved by:

n!/(n-k)!, where n=total choices available, k=number of choices made.

10!/(10-3)!

10!/7!

720

720. just multiply 10 9 and 8 because first, second, and third, that is means three and that's how many numbers you multiply from 10,so it equals 720.

hope this helps

cheers!

AB and BC are tangent to circle D. Find x if AB = 2x + 9 and BC = 3x + 6. Find x.

Answers

it woulds be x+15 because if you take 2x and subtracted from the 3x then you get x and then you add the 9 and 6 witch you get 15

Answer:

the value of X comes out to be equal to 3

Step-by-step explanation:

since AB and BC are tangent to the circle D

then the length of the tangent will be same

AB will be equal to BC

where,

AB = 2 x + 9

and

BC = 3 x + 6

2 x + 9 = 3 x + 6

3 x - 2 x = 9 - 6

x = 3

hence, the value of X comes out to be equal to 3

Find the take home percent of the gross pay: net pay $298.76, gross pay $402.38. round to the nearest percent.

Answers

298.76 / 402.38 = 0.742 = 74%

In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.

Answers

rectangle and square.
Consecutive angles are next to each other. squares and rectangles are the only to that has angles with the same values that are next to each other

Answer:

Rectangle and Square.

Step-by-step explanation:

To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.

In other words, two or more angles are said congruent if and only if they have the same measurement.

Find the value of x to the nearest tenth. See linked picture below. Thanks!

Answers

Answer: Choice D) 11

----------------------------

Work Shown:

cos(angle) = adjacent/hypotenuse
cos(35) = 9/x
x*cos(35) = 9
x = 9/cos(35)
x = 10.9869712988531 ... make sure your calculator is in degree mode
x = 11 ... rounding to the nearest tenth

Helpppppppppp me!!!!!!!!!

Answers

A) w/9=6

w=9*6

w=54

B) 5q=15

q=15/5

q=3

C)2s-3s=20

-1s=20

s=20/-1 = -20

s=-20

D)4-a=-12

a= 4+12 = 16

a=16

What is the slope of the line below

Answers

Answer: m = 2
The formula for slope can be found by finding the difference in y between two values divided by the difference in x between the same two values. In this case, you would subtract 4 from 8 and 2 from 4, to get 4/2, or 2. The slope is represented by the variable m, so m = 2.

BARNEY'S BICYCLE SHOP IS SELLING T-SHIRTS AT THE LOCAL HEALTH FAIR. THEY PLAN ON SELLING SHIRTS FOR $8 EACH. TO HAVE THE SHIRTS MADE, BARNEY'S BICYCLE SHOP PAYS THE SHIRT MAKER $3.50 PER SHIRT PLUS AN INITIAL FEE OF $63. HOW MANY SHIRTS MUST BARNEY'S BICYCLE SHOP SELL BEFORE THEY CAN MAKE A PROFIT?

A. 9 SHIRTS
B. 8 SHIRTS
C. 14 SHIRTS
D. 11 SHIRTS

Answers

STOP SHOUTING, WHOSE SHOUTING, I'M NOTTTTT

so

shirts are being sold 8 doolars each
shirts cost 3.5 to make plus initial fee of 63

how much to make a profit

ok, amount they make=cost per shirt times number of shirts=8 times x where x is number of shirts of 8x

cost he needs to pay=3.5x+63

when will his profit be more than what he's paying

8x>3.5x+63
solve
mnus 3.5x both sides
4.5x>63
divide both sides by 4.5
x>14

needs to sell at least 14 shirts
hmm, ok, 14 is the answer then

C is answer

Barney's Bicycle Shop must sell at least 14 shirts before they can make a profit. Among the given options, the correct answer is C. 14 shirts.

To determine the number of shirts Barney's Bicycle Shop must sell before making a profit, we need to consider the cost of producing the shirts and the revenue generated from selling them.

For each shirt sold, the shop earns $8 in revenue. However, they incur costs to have the shirts made. The shirt maker charges $3.50 per shirt and an initial fee of $63.

Let's calculate the total cost per shirt:

Cost per shirt = $3.50 + ($63 / number of shirts)

To break even or make a profit, the revenue from selling the shirts must exceed the cost per shirt.

Let's calculate the revenue per shirt:

Revenue per shirt = $8

Now we can set up the equation to find the number of shirts needed to break even or make a profit as inequality:

Revenue per shirt ≥ Cost per shirt

$8 ≥ $3.50 + ($63 / number of shirts)

To solve this inequality, we can subtract $3.50 from both sides:

$4.50 ≥ $63 / number of shirts

Multiplying both sides by the number of shirts:

$4.50 x number of shirts ≥ $63

Simplifying the equation:

Number of shirts ≥ $63 / $4.50

Number of shirts ≥ 14

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2. A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?
Part I: Sketch a figure to illustrate the scenario above. Label the vertices and the lengths that are given in the question. (3 points)

Part II: Using your sketch from Part I, write an equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. Round your answer to the nearest 100th. Show your work. (2 points)

3. Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ∠ABC, what is the perimeter of the deck area to the right of the beam of light (△BDC)?

Part 1: What other angles or sides of △BDC can you label given that side AB is 10 feet, BE and BD trisect ∠ABC? Label the diagram accordingly, and explain your reasoning. (4 points)

Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of △BDC. Show your work. (3 points)

Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points)

Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)

4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first?

Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2 points

Part II: Use to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour. (1 point)

Part III: Use to determine the time necessary for Car B to reach the intersection. (1 point)

Part IV: Which car reaches the intersection first, and by how many hours? (2 point

5. Solve for the missing length and the other two angles in the triangle below.

Part I: Use the law of cosines to find the missing third side. (2 points)

Part II: Use either the law of cosines or the law of sines to find the measure of angle C. (2 points)

Part III: Use any method you like to find the measure of angle B. (1 point)

6. Solve the triangle below.

Part I: Use the law of cosines to find the measure of angle B. (2 points)

Part II: Use the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle A. (1 point)

7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and Suzie to be . Suzie approximates the angle formed by the lead boat, herself, and Swanson to be . How far is the boat from Swanson?

Part I: What is the missing angle in this triangle? (1 point)

Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)

8. Solve the following triangle for all missing sides and angles.

Part I: Find the measure of angle B. (1 point)

Part II: Use the law of sines to find the length of side a. (2 points)

Part III: Use any method to find the length of side c. (2 points)

Answers

You are given the mountain that has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. You are asked to find how many yards will a tourist travel from the base of the mountain to its peak. You can solve this using trigonometric function. More importantly, imagine that the mountain has a 90 - degree vertical height so that when you connect the peak of the mountain down to its base and then connected to the ski, you can form a right triangle.

Use the sine function.
sine β = opposite side / hypotenuse side
the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain

sine 40° = 100 yards / hypotenuse side
hypotenuse side = 100 yards / sine 40°
hypotenuse side = 156 yards

Answer:

156

Step-by-step explanation:

Use the sine function.

sine β = opposite side / hypotenuse side

the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain

sine 40° = 100 yards / hypotenuse side

hypotenuse side = 100 yards / sine 40°

hypotenuse side = 156 yards

How do I do this someone please explain I need help

Answers

so.. she washes cars and charges 15 bucks per car...ok... Revenue( sales income), in this case is how much she gets in total income from the car washing.. .well, if she washes, say "a" automobiles, then she makes 15*a, or 15a in income, or Revenue.

now, she pays in advertising 145 bucks... and for cleaning products, she spends 3 bucks for each washed car... ok.. .so if she washes say "a" automobiles, then she spends 3*a or 3a, ok.... so, her costs for the washing cars business is 145 for ads plus 3a, or 145 + 3a is her Cost.

now, Profit is the surplus amount after you remove the cost expenses, and can only happen if the Revenue is higher or greater than the Cost.

Revenue > Cost
15a > 145 + 3a

when will she turn a profit?

[tex]\bf 15a \ \textgreater \ 145 + 3a\implies 15a - 3a\ \textgreater \ 145\implies 12a \ \textgreater \ 145 \\\\\\ a\ \textgreater \ \cfrac{145}{12}\implies a\ \textgreater \ 12\frac{1}{12}[/tex]

she will turn a profit after washing 12 cars and 1/12 of a car, maybe just the windshield =).... anyhow..... namely, the revenue then is greater than the cost after that, or one can say, after the 13th car washed.

Factor the expression.

4r^2 – 64

1)(4r + 5)(r – 16)
2)4(r – 4)(r – 4)
3)(4r – 5)(r + 16)
4)4(r + 4)(r – 4)

Answers

4r^2-64
4(r^2-16)
4(r+4)(r-4)
First factor out the gcf. Because (r^2-16) has perfect squares, you can factor it out one more time.
Final answer: D

Hey!

First, let's write the problem,
[tex]4r^2-64[/tex]
Factor out the common term, which is 4,
[tex]=4\left(r^2-16\right)[/tex]
Then, let's factor this part: [tex]r^2-16[/tex]
We are going to factor it using the difference of squares rule.
[tex]=\left(r+4\right)\left(r-4\right)[/tex]
Our final factored answer would be,
[tex]=4\left(r+4\right)\left(r-4\right)[/tex]

Thanks!
-TetraFish

Today Javier put a cabinet on layaway by making a down payment of $80 and agreeing to pay $24 a month starting next month for 36 months. When will Javier receive the cabinet ?
A. 1 month
B. Today
C in 24 months
D in 36 months

Answers

Answer:

Option D is the answer.

Step-by-step explanation:

A layaway is a system of paying a deposit to secure an item that is meant to be purchased later. In this purchasing method, a buyer places a deposit on an item to lay it away. He can pick the item later when he pays the balance. The balance can also be paid in smaller installments until the full amount is paid.

So, here Javier will be paying for 36 months, hence, he will get the cabinet after 36 months.

Harry Hoodeen made $24,567.00 net pay last year. His monthly expenses averaged $1,980.00. How much was left over for savings for the year?

Answers

24,567 - 12(1980)
24,567 - 23760
807

His left over savings was $807.

Which correlation should be used to measure the relationship between gender and grade point average for a group of college students??

a. ?point-biserial correlation

b. ?pearson correlation

c. ?phi-coefficient

d. ?spearman correlation?

Answers

I believe the correct answer would be A. The best correlation to use to measure the relationship between gender and grade point average for a group of college students would be the point-biserial correlation. It is coefficient that is used when a variable is dichotomous or that the variable is part of a whole set. It is used in measuring the direction of the correlation that is present between a dichotomous variable and a continuous variable. From the question, the dichotomous variable would be the grade point average for a group of college students while the other variable is the continuous one.

PLEASE HELP ME AND TRY TO ANSWER THIS PLS PLS PLS AND IF YOU CAN DO THIS ONE AND HELP ME CAN YOU PLEASE GO BACK TO MY LAST PROBLEM AND TRY TO SOLVE IT IF IT HASNT ALREADY BEEN SOLVED I AM RUSHING SO FAST RIGHT NOW PLEASE TRY TO HELP AND ANSWER IT ASAP IT WOULD BE A HUGE HELP!

Answers

The solution is (4.75,-22)

Angle C is an inscribed angle of circle P. Angle C measures (5x-7) degrees and arc AB measures (2x) degrees. Find x.

Answers

This is the concept of geometry, the vale of x can be found as follows;
angle C and arc BC are supplementary angles, therefore:
(5x-7)+2x=180
7x-7=180
7x=187

x=187/7
x=26 5/7

Let f(x) = 27x5 − 33x4 − 21x3 and g(x) = 3x2. Find f of x over g of x

Answers

The answer is 9x3 − 11x2 − 7x

Answer: 9x^3 − 11x^2 − 7x

What is the inverse of f(x)=70x^3/4 ?

Answers

y/70=x^3/4
x=(y/70)^(4/3)

Final answer:

The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].

Explanation:

The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.

Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]

Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]

Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]

Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].

Two trucks leave a warehouse at the same time. one travels due north at an average speed of 4747 miles per hour, and the other travels due south at an average speed of 5050 miles per hour. after how many hours will the two trucks be 388388 miles apart?

Answers

the combined speed are 47 + 50 = 97 mph

required number of hours = 388/97 = 4 hours

Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.

Answers

check the picture below.

make sure your calculator is in Degree mode.

From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet

How to work with trigonometric ratios?

We are told that you are standing 30 ft from the base of a tree.

Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.

Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;

h/30 = tan 37

h = = 30 * tan 37

h = 22.61 ft

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How can you tell whether a rational expression is in simplest form? Include an example with your explanation.

Answers

a rational in its most simple an be written as a fraction a/b where a and b are co-prime. Which means that there are no common factors in a and b

for example 4/6 is not simplest form because 2 is a factor of 4 and 6
In its simplest form 4/6 is 2/3.

Rational numbers are numbers that are written as a ratio of two integers.

Let a and b be integers, hence a rational expression can be expressed as a/b

In order to tell whether a rational expression is in its simplest form, we need to ensure no integer can go in both the numerator and the denominator.

For instance, given the rational number 10/15, the simplest form of the rational number will be expressed as (5*2)/(5*3) = 2/3

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An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is cubic inches. This is cubic inches less than the volume of the new chamber. NextReset

Answers

Original chamber:
Length, L = 12 in.
Base diameter, d = 5.7 in.
The volume is
V = (1/3)*(πd²/4)*L = (1/3)*(π/4)(5.7 in)²*(12 in) = 102.07 in³

Scaled chamber:
Because the scale factor is 1.5, obtain
Length = 1.5*12 = 18 in.
Base diameter = 1.5*5.7 = 8.55 in
The new volume is
V (1/3)*(π/4)*(8.55 in)²*(18 in) = 344.49 in³

Differenc in volumes = 344.49 - 102.07 = 242.42 in³

Answer: 242.4 in³ (nearest tenth)

Answer:

added pictures of all the questions on this test

Step-by-step explanation:

What is another name for angle 2?

Answers

The rays MR and MP intersects at the point M, this means the point M is the vertex of the ∠2.

Another name for ∠2 is ∠PMR.

Final answer:

Angle 2 could refer to different things, such as an angular velocity, a direction angle, or a contact angle, depending on its context within a mathematical or physical scenario.

Explanation:

In mathematical terms, angle 2 refers to a particular position or orientation, typically specified in degrees. For instance, if points 1 and 2 rotate through the same angle (AO), angle 2 might move through a greater arc length because it is farther from the center of rotation. This concept is related to the mathematical definition of angular velocity, defined as radians per unit time.

Alternatively, angle 2 could also refer to the direction angle, which is the angle measured counterclockwise from the positive direction on the x-axis to a vector. This term is often used when calculating vector components. In this context, a positive angle indicates a counterclockwise rotation, whereas a negative angle implies a clockwise rotation.

Finally, angle 2 might specify the contact angle, which is the angle between the tangent to the liquid surface and the surface itself. To figure out the precise name for angle 2 in your particular context, I would need further information about the specific scenario or diagram you're referring to.

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At a certain university the student to teacher ratio is 16:1. If there are 2,000 students enrolled, how many teachers must be employed to maintain this ratio?

A. 28,000 B. 200 C. 215 D. 125

Mark for review (Will be highlighted on the review page)

Answers

Answer:

D. 125

Step-by-step explanation:

Ratio between students and teacher = 16:1 , 16/1 =2000 /x , x = 2000/16 = 125 teachers

The number of teachers in the school will be 125. The correct option is D.

What are ratios and proportions?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3.

Given that at a certain university the student-to-teacher ratio is 16:1. If there are 2,000 students enrolled.

The number of teachers will be calculated as,

16 / 1 = 2000 / t

t = 2000 / 16

t = 125 teachers

Therefore, the count of teachers in the school is 125.

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Statistics??? Construct a 95% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.

Answers

Given:
μ = $3120, population mean
σ = $677, population standard deviation.
The population is normally distributed.
n = 20, sample size.

At the 95% confidence level, the confidence interval is
[tex]( \mu - 1.96\frac{\sigma}{ \sqrt{n} } ,\, \mu + 1.96\frac{\sigma}{ \sqrt{n} }) [/tex]

1.96(σ/√n) = 1.96(677/√20) = 296.71
Th confidence interval for the mean is
($2823.29, $3416.71)

Answer: ($2823.29, $3416.71)

1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!

Answers

The first one is a disjunction, an "or", meaning that the solution set shares no numbers on the number line. That's how you graph these...on a number line. Solving the first one, multiply both sides by 8 to get
[tex]3x\ \textless \ -48[/tex] and divide to get x<-16. Now the second one, just divide both sides by 5 to get
[tex]x\ \textgreater \ \frac{2}{5} [/tex]
On a single number line, make 0 your center, put -16 where it belongs in reference to the 0 and put 2/5 where it belongs in reference to the 0. The numbers to the left of -16 are those that are less than -16, and the circle above the -16 is an open one, not including the -16. The numbers to the right of 2/5 are those numbers that are greater than 2/5, so put an open circle above the 2/5 and go to the right with that line. And you can see that you have a big open space between the -16 and the 2/5 where the solution set is not the same at all. For b, solve this one simultaneously. It is a conjunction, an "and", where there will be a solution set that is shared by both values for x. Solve it like this...start by subtracting 10 from both sides:
-8< -4d < -4 Now, when you divide by the negative 4, you have to change the signs to greater than: 2 > d > 1. That means, in words, that "d is less than 2 and greater than 1". On a single number line you will have open circles above the 1 and the 2 and the numbers in between 1 and 2 are shared solutions.

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