If B=80°, a=4.1, c=7.1, find the area of the triangle.
Answers
Answer:
14.2 squared units
Step-by-step explanation:
Always draw a diagram for the question. Capital letters are usually angles, and their opposite side is the same letter as a lowercase. (See diagram) The opposite side of angle B is side b.
The formula for area of a triangle is A = bh/2
"A" is for area.
"b" is for base (usually bottom side)
"h" is for height (perpendicular to base).
We know the measurement for the base c = 7.1. We need to find the height.
Notice when you draw in the height, it form two right triangles. We can use trigonometric ratios for right triangles.
Remember the trigonometric ratios using SohCahToa:
sinθ = opposite/hypotenuse;
cosθ = adjacent/hypotenuse and;
tanθ = opposite/adjacent, where θ means the angle of reference.
Focus on the triangle on the left side. We know one angle (∠B = 80°) and one side (a = 4.1). We can find "h", the missing side.
Since ∠B is our angle of reference, "h" is opposite. Since "a" is a longest side, it's the hypotenuse. Use the sine ratio because it uses the opposite and hypotenuse sides.
sinθ = opp/hyp General sine ratio formula
sinB = h/a Variables you use in this problem
sin80° = h/4.1 Isolate "h". Multiply both sides by 4.1
h = 4.1(sin80°) Multiply with calculator
h = 4.1(0.98480775...) Unrounded sin80
h = 4.03771178... Round this number
Note the number of decimal places given in the question.
h ≈ 4.0 Round to one decimal place
Now we can use the formula for the area of a triangle.
A = bh/2 Don't confuse side "b" with the base in this question
A = (7.1)(4.0)/2 Simplify the division
A = (7.1)(2.0) Multiply
A = 14.2 Final answer for area
Since we don't know what the units are, you can say the answer is:
A = 14.2u² or 14.2 squared units
Related Questions
Solve: 6x = -24 and x/7 = 3
Answers
Answer:
1) x = -4
2) x = 21
Step-by-step explanation:
6x = -24
6/6x=-24/6
x=-4
and
x/7 = 3
x/7*7=3*7
x=21
Please answer number 1
Answers
Step-by-step explanation:
[tex] \triangle \: ABC \cong \triangle \: FED[/tex]
Here, all the sides or angles of triangle ABC are congruent to the corresponding sides or angles of triangle FED. As both triangles are reflections of each other.
Evaluate the function. F(x)=3/x-1/. F(-3)
Answers
On a scale drawing the scale is 1/2 inch=1 foot what are the dimensions on the scale drawing for a room that is 22 feet by 17 feet
Answers
Hey there! I'm happy to help!
We have a room that is 22 by 17 feet. We know that for every foot, we draw a 1/2 inch. This means that we need multiply our dimensions by 1/2 to find the dimensions of the drawing.
22×1/2=11
17×1/2=8.5
Therefore, the dimensions of the room are 11 feet by 8.5 inches. These are the dimensions of a normal white paper!
Have a wonderful day! :D
To convert the actual room dimensions of 22 feet by 17 feet to a scale drawing with a scale of 1/2 inch equals 1 foot, the length becomes 11 inches, and the width becomes 8.5 inches in the drawing.
When creating a scale drawing, the dimensions of the actual room need to be converted into scale dimensions. According to the scale given, which is 1/2 inch equals 1 foot, the actual room dimensions of 22 feet by 17 feet should be converted using this scale ratio.
To do this conversion, each actual dimension must be divided by the scale factor. The scale factor is determined by the number of feet that are represented by 1/2 inch. Since 1/2 inch is equivalent to 1 foot, the scale factor is 1 foot per 1/2 inch. Therefore, we calculate the dimensions as follows:
Length: 22 feet / 1 foot per 1/2 inch = 22 x 1/2 inches = 11 inches
Width: 17 feet / 1 foot per 1/2 inch = 17 x 1/2 inches = 8.5 inches
Thus, the dimensions on the scale drawing for a room that is 22 feet by 17 feet would be 11 inches by 8.5 inches.
Mary has 15 points with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there
Answers
Answer:
The number of nickel coins is 10 and the number of quarter coins is 5
Step-by-step explanation:
The correct question is
Mary has 15 coins with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there
Let
x ----> the number of nickel coins
y ----> the number of quarter coins
Remember that
[tex]1\ nickel=\$0.05[/tex]
[tex]1\ quarter=\$0.25[/tex]
we know that
Mary has 15 coins
so
[tex]x+y=15[/tex] -----> equation A
The total value of the coins is $1.75
so
[tex]0.05x+0.25y=1.75[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (10,5)
therefore
The number of nickel coins is 10 and the number of quarter coins is 5
Solve for k.
6 1
2k - 6 - 3
Answers
Answer:
k = 6.
Step-by-step explanation:
k = 6
2k = 12
12 - 6 - 3 = 3
k = 1
2k = 2
2 - 6 - 3 = -7
So, the answer is k = 6 because it makes more sense.
Marco buys a certain brand of shampoo from a supplier at 7.25 dollars per bottle .He sells it at a markup of 25 percent. What is the markup .
Answers
Final answer:
Marco buys shampoo at $7.25 per bottle and sells it with a 25% markup, making the markup $1.81 per bottle. The selling price, therefore, is $9.06 per bottle.
Explanation:
The question is about calculating the markup applied by Marco on a bottle of shampoo. Marco buys the shampoo at $7.25 per bottle and sells it at a markup of 25 percent. The markup is calculated based on the cost price of the product. In this case, to find the markup amount, we use the formula: Markup = Cost Price * Markup Percentage. So, the markup on each bottle of shampoo is $7.25 * 0.25 = $1.81. Therefore, Marco applies a $1.81 markup on each bottle of shampoo.
To determine the selling price, one can add the markup to the cost price, which would be $7.25 + $1.81 = $9.06. This is Marco's selling price per bottle after applying the 25 percent markup.
if I know A B C equals d e f can you stay B C equals ef
Answers
there are 45 green cars and bkack cars. the green cars are 27 more than the black. how many are green cars?
Answers
Answer:
18
Step-by-step explanation:
45-27=18
Answer:
18
Step-by-step explanation:
subtract 45 and 27 it gives u 18
What numbers are divisible by 2 and 5 but not 3
Answers
Answer:
10 20 40
Step-by-step explanation:
How is the Distributive Property used to simplify operations with scientific notation
Answers
Answer:
See explanation
Step-by-step explanation:
Let a,b, and c be real numbers.
The distributive property says that:
[tex]a(b + c) = ab + ac[/tex]
Assuming we want to simplify:
[tex]10(5*10^{-1}+150*10^{-3})[/tex]
We apply the distributive property to get:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10[/tex]
We can now use rules of exponents to simplify further:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0} [/tex]
An apartment complex has a total of 175 units. Of these, 154 units are occupied. What percent of the apartment are unoccupied?
Answers
Answer:
12%
Step-by-step explanation:
There are a total of 175 units in an apartment complex.
Out of which, 154 units are occupied.
Now, we have to find the percentage of the apartment which are unoccupied.
So, the number of units that are not occupied is (175 - 154) = 21.
Hence, the percentage of the number of unoccupied units of the apartment complex will be [tex]\frac{21}{175}\times 100 \% = 12 \%[/tex] (Answer)
Two people bought a 13-inch sandwich to share. How many inches of sandwich does each person get if they split it evenly? Choose the correct answer from the choices below.
Answers
Answer:
6.5
Step-by-step explanation:
13/2 = 6.5 inches or 6 1/2 inches
Answer:
6 2/4ths
Step-by-step explanation:
VERY VERY VERY VERY VERY URGENT!!?!!???
These triangles are similar.
True
False
Answers
Answer:
True
Step-by-step explanation:
I am interested in a new van that costs $32,500. The salesman says he will give it to me for $27,950. What is the percent discount he is giving me?
Answers
Answer:
The salesman is giving you a 14% discount
Step-by-step explanation:
Do 27950/32500 to get 0.86
Then do 1-0.86=0.14
Multiply by 100 to get 14%
Hope this helped!
Population in Millions
World: 7,691
Canada: 37.4
What percent of the 2019 world population lives in Canada? Round the percentage to three decimal places.
Answers
Answer:
0.486% of world population lives in Canada.
Step-by-step explanation:
Given: World Population= 7691 million.
Canada Population= 37.4 million.
Now, finding the percentage of world population lives in Canada.
[tex]Population\ percentage= \frac{Canada\ population}{World\ population} \times 100[/tex]
⇒ [tex]Population\ percentage= \frac{37.4}{7691} \times 100[/tex]
⇒ [tex]Population\ percentage= 0.00486\times 100[/tex]
∴ [tex]Population\ percentage= 0.486\%[/tex]
Hence, 0.486% of world population lives in Canada.
Each pair of polygons is similar. Find the values of x and y
Answers
x = 14 and y = 10
Explanation:Two shapes are similar if they have the same form but not necessarily the same size. In other words, when shapes are similar they are in proportion. Since you haven't provided any diagram, I'll choose two irregular polygon that are similar as indicated in the figure below. So we can calculate both x and y with proportions as follows:
[tex]For \ x: \\ \\ \frac{x}{7}=\frac{16}{8} \\ \\ x=\frac{7\times 16}{8} \\ \\ x=14 \\ \\ \\ For \ y: \\ \\ \frac{y}{20}=\frac{8}{16} \\ \\ y=\frac{8\times 20}{16} \\ \\ y=10[/tex]
Learn more:Translation: https://brainly.com/question/11131466
#LearnWithBrainly
2 Kate biked 9 miles north to the park, then 4
miles west to the mall. How far is Kate
from her starting point?
Answers
if the interior angle ofa regular polygon is 162° how many sides does it have
Answers
Answer:
20 sides.
Step-by-step explanation:
The exterior angle = 180 - 162 = 18 degrees.
Since the sum of the exterior angles = 360 degrees the number of sides
= 360 / 18
= 20 sides.
Given m angle A = 35°, and b = 4.2, find c. Show all work.
Answers
Answer:
[tex]c=5.1\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the measure of angle B
we know that
In the right triangle ABC
[tex]m\angle A+m\angle B=90^o[/tex] ---> by complementary angles in a right triangle
we have
[tex]m\angle A=35^o[/tex]
substitute
[tex]35^o+m\angle B=90^o[/tex]
[tex]m\angle B=90^o-35^o=55^o[/tex]
step 2
Find the length side c
Applying the law of sines
[tex]\frac{c}{sin(C)}=\frac{b}{sin(B)}[/tex]
substitute the given values
[tex]\frac{c}{sin(90^o)}=\frac{4.2}{sin(55^o)}[/tex]
[tex]c=\frac{4.2}{sin(55^o)}=5.1\ units[/tex]
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answers
Answer- You can get 10 Small rafts
12 x 100+ 1200
1600-1200=400
400/40 =10 Rafts
A linear equation representing the given situation and the number of small rafts is required.
The required equation is [tex]100x+40y=1600[/tex]
The number of small rafts will be [tex]10[/tex]
Cost of one large raft = $100
Cost of one small raft = $40
Total amount to spend = $1600
Let the number of large rafts be [tex]x[/tex]
and small rafts be [tex]y[/tex]
The equation will be
[tex]100x+40y=1600[/tex]
The number of large rafts [tex]x=12[/tex]
[tex]100\times 12+40y=1600\\\Rightarrow y=\dfrac{1600-100\times 12}{40}\\\Rightarrow y=10[/tex]
Learn more:
https://brainly.com/question/8449665
https://brainly.com/question/16135223
The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Answers
Answer:
Part 1) Option a. TZY
Part 2) Option c. YZX
Step-by-step explanation:
The question is as following and see the attached figure
The minor arc measures of circle Z are shown in the figure.
Use the drop-down menus to complete each statement.
1) Angle UZT is congruent to angle _____
2) Angle VZW is congruent to angle____
Answer choices
1) a. TZY, b. XZW, c. VZW
2) a. UZV, b. TZY, c. YZX
===============================================
Solution:
Part 1) Angle UZT is congruent to angle______
From the attached figure, we can deduce that:
∠UZT = 54°
∠TZY = 54°
So,
∠TZY = ∠UZT ⇒ both angles are congruent.
1. Angle UZT is congruent to angle TZY
===========================================
Part 2) Angle VZW is congruent to angle_____
From the attached figure, we can deduce that:
∠VZW = 71°
∠YZX = 71°
So,
∠YZX = ∠VZW ⇒ both angles are congruent
2. Angle VZW is congruent to angle YZX
Answer: correct answer is TZY for first one and YZX for second
Step-by-step explanation:
Just chose those and got it correct :)
erin makes $18 an hour. she works 40 hours a week. she found an apartment for $1,000 a month. Should erin rent the apartment?
Answers
Answer:
Based on her monthly income YES
Step-by-step explanation:
18 × 4 = $720 a week and 720 × 4 = $2,880 a month
The rent for the apartment is $1,000 if Erin rent this place she will have an extra =1,880 for her living expenses after she pays for the rent so there would be no problem of her renting the place.
How many times does 5 go into 236
Answers
Answer:
47.2
Step-by-step explanation:
236/5
47.5
47.2
Step-by-step explanation:
Because,
= 236/5
= 47.2
Therefore, 47.2 tines 5 goes into 236.
What is 7 3/8 + 3 1/4?
Answers
Answer:
10 5/8
Step-by-step explanation:
1/4 = 2/ 8
7 3/8 + 3 1/4 = 7 3/8 + 3 2/8
7 3/8 + 3 2/8 = 10 5/8
Answer:
10.675
Step-by-step explanation:
Two joggers run 8 miles north and 5 miles west . what is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point ?
Answers
Answer:9.4 miles
Hope this helps
Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 4 to 2. Tia
wants to sell a total of 54 apples and oranges. How many apples should she sell?
A.
52 apples
B. 36 apples
C. 9 apples
D. 32 apples
Answers
Answer:
[tex]\large \boxed{\text{B. 36 apples}}[/tex]
Step-by-step explanation:
Let a = the number of apples
and o = the number of oranges
You have two conditions:
[tex]\begin{array}{lrcl}(1) & \dfrac{a}{o} & = & \dfrac{4}{2} \\\\(2) & a+ o & = & 54\\\end{array}[/tex]
Solve the equations for a
[tex]\begin{array}{rcll}2a & = & 4o & \text{Multiplied each side of (1) by 2o}\\\(3) \,2a - 4o& = & 0 &\text{Subtracted 4o from each side}\\a + o & = & 54& \text{This is equation (2)}\\(4) \, 4a +4o& = &216&\text{Multiplied each side by 4} \\6a& = &216&\text{Added (3) and (4)} \\a & = &\mathbf{36}&\text{Divided each side by 6} \\\end{array}\\\text{Tia should sell $\large \boxed{\textbf{36 apples}}$}[/tex]
A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $40. What was her profit or loss?
Answers
Answer:loss 20
Step-by-step explanation:
She lost 20
Step-by-step explanation:
60 take away 40 is 20
Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest?
Answers
Answer:$1200
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The student council at Princeton High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $9 per shirt, plus a setup fee of $140. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
Selling shirts will cover the $ in costs.
Answers
To cover costs, the student council needs to sell 70 T-shirts, which will cover the $770 in costs.
Explanation:To solve the student council's problem, we need to find the number of T-shirts that must be sold so that the total revenue equals or exceeds the costs associated with making the T-shirts. Let's define x as the number of T-shirts to be sold. The total revenue from selling the T-shirts at $11 apiece can be represented as 11x. The costs consist of a setup fee of $140 and $9 per shirt, so the total cost is 9x + 140. To determine when the revenue will cover the costs, we can set up the following equation:
11x = 9x + 140
Solving this equation for x, we subtract 9x from both sides:
2x = 140
Then divide both sides by 2:
x = 70
Therefore, the student council needs to sell 70 T-shirts to cover their costs, which will be $770 ($11 per shirt multiplied by 70 shirts).