Consider a triangle ABC like the one below. Suppose that B=103 degrees ,C=28 degrees , and b=52 . (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
Answers
Given:
Angle B = 103 degrees
Angle C = 28 degrees
Side b = 52 units
Find: measures of Angle A, side a, and side c.
Solution:
First, let's solve for the measure of Angle A.
Recall that the sum of the interior angles of a triangle is 180°. This means:
\(AngleA+AngleB+AngleC=180\degree\)Since we already know the measure of angles B and C, we can subtract it from the total measure which is 180° to solve for the measure of Angle A.
\(\begin{gathered} AngleA=180\degree-103\degree-28\degree \\ AngleA=49\degree \end{gathered}\)Therefore, the measure of Angle A is 49°.
Next, let's solve for the measure of side c using Sine Law.
\(\frac{sinB}{b}=\frac{sinC}{c}\)Let's plug into the equation above the value of B, C, and b.
\(\frac{sin103}{52}=\frac{sin28}{c}\)Then, solve for the value of c.
Cross multiply.
\((c)(sin103)=(52)(sin28)\)Divide both sides by sin 103.
\(\frac{(c)(sin103)}{(sin103)}=\frac{(52)(sin28)}{(sin103)}\Rightarrow c=\frac{52sin28}{sin103}\)Evaluate the value of "c" using a calculator.
\(c=25.0546\approx25.1\)The measure of side c is approximately 25.1 units.
Lastly, to solve for the measure of side "a", we will still use sine Law.
\(\frac{sinA}{a}=\frac{sinB}{b}\)Let's plug into the equation above the value of A, B, and b.
\(\frac{sin49}{a}=\frac{sin103}{52}\)\(a=\frac{52sin49}{sin103}\)\(a=40.277\approx40.3\)The measure of side a is approximately 40.3 units.
Related Questions
Whats 150 x 2 divided by 2?
Answers
Answer:
150 ?
Step-by-step explanation:
150*2 = 300 / 2 = 150
Answer:
the answer is 150
Step-by-step explanation:
150×2÷2
150×1
150
PLEASE HELP I HAVE TO GET THIS DONE
Answers
Answer: so the answer is A
Step-by-step explanation: -3/2
if you ever have a question like that again go to Math-way it is every helpful and easy.
What is the central angle(pic included)
Answers
Answer:
72
Step-by-step explanation:
circumference = 20
arc = 4
4/20 =1/5
a circle = 360°
1/5 * 360 = 72
For which conditions is p V q false?
p is true and q is false.
p is true and q is true.
p is false and q is true.
Opis false and q is false.
Answers
Answer:
opis is false and q is false
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
Two increased by the product of a number and 7 is at most -29
Answers
The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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10 workers can create 20 products in 40days. all workers are equally productive. A company has only 5 workers.
how many days will it take to create all 20 products?
Answers
The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days
What is the work rate of 1 worker?Work rate is the rate at which a specified work is completed.
The number of days it will take 10 workers to create 20 products = 40 days
Therefore;
The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days
Where 1 worker can create 20 products in 400 days, then;
The work rate for one worker indicates;
The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5
5 workers will take = 400 days ÷ 5 = 80 days
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A group of 6 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: Queen of Clubs, 10 of Hearts. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.)
Recall, while using your calculator, that E10 means to move the decimal place 10 places to the righ
Answers
a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.
b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.
Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52
Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,
a) Number of cards are in the deck that are not one of the designated cards
= 52 - 2 = 50
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.
b) Number of cards are in the deck = 52
Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35
Thus total possible number of ways
= ⁵²C₃₅ = 21945588357420
Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards
= 2250829575120/21945588357420
= 0.10256410256
Hence, required probability is 0.1026.
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Find the inequality represented by the graph
Answers
Answer:all you need to do is Times everything
Step-by-step explanation:
Answer:
y >= -2x - 5
Step-by-step explanation:
slope = rise / run
slope = -2
y >= -2x - 5
Explain what went wrong.
Please solve both.
75 points
Answers
John’s grocery bill totaled $200. After he used his coupons, the cash register showed the total bill as $20. Which statement is true?
The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.
The grocery bill after the coupons were used was 10 times as much as the bill before the coupons were used.
The grocery bill before the coupons were used was 100 times as much as the bill after the coupons were used.
The grocery bill after the coupons were used was 100 times as much as the bill before the coupons were used.
Answers
Answer:
The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.
Step-by-step explanation:
The price after coupons were used is 20, and the price before was 200. 20x10 =200
Set up expression solve for x 3x^3+20x^2+26x-27 / X+4
Answers
The expression and the solution for x is the quotient of 3x² + 8x + 2 and the a remainder of -35
How to set up the expression and the solution for xThe quotient expression is given as
(3x³ + 20x² + 26x - 27)/(x + 4)
To set up the expression is to evaluate the quotient
Using a synthetic method of quotient, we have the following set up
-4 | 3 20 26 -27
|__________
Bring down the first coefficient, which is 3:
-4 | 3 20 26 -27
|__________
3
Multiply 3 by -4 to get -12, and write it below the next coefficient and repeat the process
-4 | 3 20 26 -27
|___-12_ -24__-8__
3 8 2 -35
So, the quotient is 3x² + 8x + 2 and the remainder is -35
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A rain gutter is made from sheets of
aluminum that are 24 inches wide by
turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-
sectional area and allow the greatest
amount of water to flow. What is the
maximum cross-sectional area?
Flat sheet 24 inches wide
1 Write a quadratic function for the Area in terms of x: A(x) =
2 The cross-sectional area is maximized when the depth of the gutter is
3 The maximum cross-sectional area is square inches.
Answers
1. The quadratic function for the Area in terms of x: A(x) = 24x.
2. The cross-sectional area is maximized when the depth of the gutter is 0.
3. The maximum cross-sectional area is square inches 0.
To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.
1. Write a quadratic function for the area in terms of x:
The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.
2. The cross-sectional area is maximized when the depth of the gutter is:
To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.
3. The maximum cross-sectional area is square inches:
Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.
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5 points
In a survey, 13 out of 20 teachers respond yes to a proposal for a new
after-school club. In the same survey, 37 out of 50 students respond yes.
Which group is more in favor of the new after-school club, teachers or
students? *
New after school club students or teachers
Answers
Answer:
Students
Step-by-step explanation:
Teachers: 13/20= 0.65 = 65%
Students: 37/50= 0.74 = 74%
74% > 65%
Students are more in favor of the new club than teachers
Solve the given proportion X/4 = 3/6 X=
Answers
Answer:
X/4=3/6
Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.
6X=12 X=2
Answer:
2
Step-by-step explanation:
Cross Multiple and Divide
X. 3
----. = ----
4. 6
So what you want to do is multiply diagonally:
(6)(X) = 6X
(3)(4) = 12
Now that we have our two answers, we put an equal sign between them.
6X = 12
Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.
So remember to divide on both sides to get rid of the 6.
6X divided by 6 is just X.
12 divided by 6 is 2
We got our answers, put the equal sign in-between
X = 2
(q1) Find the length of the curve described by the function
Answers
The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:
L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2
The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.
Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:
L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral be solved.
We can, however, find a general solution. We use the above formula and substitute the limits of integration.
Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
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sally used all of the paint shown below to make a certain tint of orange paint.
Answers
Answer:
We can't see the paint, and what's the question?
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. the result is120 grams 15% sugar syrup. how many grams of 25% sugar syrup did samantha use?
Answers
Answer:
Final mixture is 120 gm
x = 10% then (120-x) = 25%
.25(120-x) + .1 (x) = .15 (120) solve for x= 10% amount
then 25% amount = 120-x
Step-by-step explanation:
Plzz help will mark brainleast
Answers
Answer:
A-1 central nervous system
b- peripheral nervous
Chau will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $44 and costs an
additional $0.11 per mile driven. The second plan has an initial fee of $49 and costs an additional $0.07 per mile driven.
for what amount of driving to the two plans cost the same amount?
What is the cost when the two plans cost the same?
Answers
Answer:
I don't know
Step-by-step explanation:
i don't know
PLEASE HELP
Does anybody remember that game people used to play as kids on the computers. When I was in 1st grade there would be this game where I placed like a number or something and then a circle or stuff would be drawn. If you know that game pls tell me.
Answers
Answer:
ABC ya?
Step-by-step explanation:
I think its in a minigame
If two opposite sides of a square are increased by 12 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 66 square meters. Find the area of the original square.
Answers
Answer:
100
Step-by-step explanation:
Let us Assume x as the original sides of the square
As we know that
Area of rectangle is
\(= Length \times width\)
where,
Length is 12 meters
And, the width is 7 meters
Moreover, the area of the rectangle is 66 square meters
Now since the length is increased by 12 meters and the width is decreased by 7 meters
So, the equation would be
(x + 12) (x - 7) = 66
x^2 + 5x - 84 = 66
x^2 + 5x - 150 = 0
Now, we compute the factor of the above equation
(x - 10) (x + 15) = 0
We do not consider the negative root
Therefore the area of original square is
= Side^2
= 10^2
= 100
Please awnser asap I will brainlist
Answers
Answer:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Step-by-step explanation:
Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.
Write the equations:
V + S + L = 310 (total number of vehicles)
V = 2S (twice as many vans as small trucks)
35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)
Substitute equation 2) into equation 1):
2S + S + L = 310
3S + L = 310
Simplify equation 3) by substituting V = 2S:
70,000S + 70,000S + 60,000L = 15,000,000
140,000S + 60,000L = 15,000,000
Set up a system of equations:
3S + L = 310
140,000S + 60,000L = 15,000,000
Eliminate L by multiplying equation 1) by 60,000:
60,000(3S + L) = 60,000(310)
180,000S + 60,000L = 18,600,000
Subtract equation 2) from the new equation:
(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000
40,000S = 3,600,000
Solve for S:
S = 90
Substitute the value of S into equation 1) to solve for L:
3(90) + L = 310
270 + L = 310
L = 40
Substitute the values of S and L into equation 2) to solve for V:
V = 2S
V = 2(90)
V = 180
The final answer is:
V = 180 (vans)
S = 90 (small trucks)
L = 40 (large trucks)
Answer:
180 Vans 90 Small trucks and 40 Large trucks
Step-by-step explanation:
Help please i donit know the answer
Answers
Answer:
96°
Step-by-step explanation:
Opposite angles in a parallelogram are equal.
Answer:
hi
Step-by-step explanation:
2(3 + m)
How to expand and simplify ?
Answers
Hope attachment helps (✿^‿^)
6+2m
Step-by-step explanation:
To simplify 2(3 + m), you just use the distributive property (search the web for more). For example, when x(y ± z), the simplification is xy ± xz.
So in this case, 2(3 + m) would be (2×3) + (2×m), which is 6 + 2m.
PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answers
Answer:
Not equal to.
Step-by-step explanation:
Students who score within 14 points of the number 88 will pass a particular test. Write this statement using absolute value notation and use the variable x for the score.
Answers
Answer:
|88-x| ≤ 14
Step-by-step explanation:
their score has to be within 14 points of 88.
if their score is above 88, the number will be negative, but the absolute value makes the number positive. if that number is still within 14 of 88, they pass.
if their score is below 88, the number will be negative, and the absolute value keeps the number positive. if that number is still within 14 of 88, they pass.
the foundation of a house has 1600 termites. The termites grow at a rate of 4.2% each day. How would this be written out?
Answers
The number of terminates are 2,384.78.
An exponential function can be used to illustrate the daily growth of termites.
If "t" represents the number of days, then "N" represents the number of termites.
⇒ N = \(1600(1 + 0.042)^{t}\)
Where 0.042 is the decimal form of 4.2%.
Using this formula,
It can be calculate the number of termites after any number of days t.
For example,
After 10 days, the number of termites would be:
⇒ N = \(1600(1 + 0.042)^{10}\)
⇒ N = \(1600(1.042)^{10}\)
⇒ N ≈ 2,384.78 termites
Hence,
⇒ N = 2,384.78 termites
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how can you find the area and perimeter?
Answers
After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:
1. Rectangle:
• Area: A = length x width
• Perimeter: P = 2(length + width)
2. Square:
• Area: A = side x side (οr A = side²)
• Perimeter: P = 4 x side
3. Circle:
• Area: A = π x radius²
• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)
4. Triangle:
• Area: A = (base x height) / 2
• Perimeter: P = side1 + side2 + side3
5. Trapezοid:
• Area: A = ((base1 + base2) x height) / 2
• Perimeter: P = side1 + side2 + side3 + side4
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A manufacturer knows that their items have a normally distributed length, with a mean of 18.1 inches, and standard deviation of 3.7 inches. If one item is chosen at random, what is the probability that it is less than 28.9 inches long
Answers
Answer:
Step-by-step explanation:
z = (X - μ) / σ, where X = date, μ = mean, σ = standard deviation
z = (28.9 - 18.1) / 3.7
z = 18.6
0.06681 is the area for this z.
6.681% shall be shorter than 18.6 inches.
The following is a data set of five quiz scores.
92, 88, 90, 96, 84
What is the mean absolute deviation of the scores?
Answers
Answer:
The mean absolute deviation is 36.8. Hope this was helpful
Step-by-step explanation: