S thus measures around 2.77 centimetres in length.
What is the purpose of law of sines?The law of sines is frequently used to find the elusive side or angle of a triangle. This law can be used if precise triangle measurement combinations are given. ASA The objective is to identify the unknown side given two angles and an included side.
The Law of Sines can be used to determine the length of side s: s/sin(mS) = q/sin(mQ).
replacing the specified values:
s/sin(10°) = 3.9/sin(74°)
s ≈ sin(10°) × 3.9 ÷ sin(74°)
s ≈ 0.684 × 3.9 ÷ 0.961
s ≈ 2.77 cm (rounded to the nearest 10th)
S thus measures around 2.77 centimetres in length.
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Find the length of the missing side.
Answer:
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)
If leg b is unknown, then: b = √(c² - a²)
For hypotenuse c missing, the formula is: c = √(a² + b²)
Step-by-step explanation:
Answer:
[tex]\huge\boxed{\sf P= 9 \ in. }[/tex]
Step-by-step explanation:
Given is a right-angled triangle.
So, we can use Pythagorean Theorem to find the missing length.
It is:
[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]
Here,
Hypotenuse = 41 in.
Base = 40 in.
Perpendicular = P
So, the above equation becomes:[tex](41)^2=(40)^2+P^2\\\\1681 = 1600 + P^2\\\\Subtract \ 1600 \ from \ both \ sides\\\\1681-1600=P^2\\\\81 = P^2\\\\Take \ square \ root \ on \ both \ sides\\\\\sqrt{81} = \sqrt{P^2} \\\\P= 9 \ in. \\\\\rule[225]{225}{2}[/tex]
Let a=4,b=4 and angle C=120 degrees. Find the length of side c and measure of the angles, angles A and B(in degrees). Give your answer to at least 3 decimal places.
c=
Angle A=
Angle B=
Step-by-step explanation:
law of cosine
c² = a² + b² - 2ab×cos(C)
c is the side opposite of the C angle. a and b are the other 2 sides.
AB² = 4² + 4² = 16 + 16 = 32
AB = c = sqrt(32) = 5.656854249...
since a and b are equal (isoceles triangle), so must be the angles at A and B.
the sum of all angles in a triangle is always 180°.
180 = angle A + angle B + angle C
= angle A + angle B + 120
since angle A = angle B we get
180 = 2×angle A + 120
2×angle A = 60°
angle A = angle B = 30°.
8) For a given area of a triangle, the base varies inversely as its height. When the height is
10 in the base is 5 in. Find the base if the height is increased to 20 in.
Answer:
2.5
Step-by-step explanation:
If the areas stay the same, then 10*5=20*h
So, 20h=50
h=2.5
simplify these expressions 13xyz +9 +2xyz + 3 and 6ab + (-2ab) + 4 + 6
The expressions are simplified to give;
15xyz + 12
4ab + 10
What are algebraic expressions?
Algebraic expressions are simply defined as mathematical expressions that are known to contain variables, constants, coefficient, factors and terms.
These algebraic expressions are also known to be made up of mathematical operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFloor division, etcFrom the information given, we have that;
13xyz +9 +2xyz + 3
Now, collect the like terms, we have;
13xyz + 2xyz + 9 + 3
Add the values
15xyz + 12
6ab + (-2ab) + 4 + 6
expand the bracket and collect like terms
4ab + 10
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The area of a square is represented by 9x2 - 42x + 49. Find the length of each side.
O (9x-7)
O (3x-7)(3x+7)
O (3x-7)
O (3x+7)
O cannot be determined
Answer:
3x-7
Step-by-step explanation:
A square’s area represents (ax+b)^2. Let’s expand that. [tex]a^2x^2+2abx+b^2[/tex] now, we can notice this fits perfectly when a=3 and b=-7. Therefore one side length of the square is 3x-7.
3. A board of directors consists of twelve men and ten women. A 5-member search
committee is randomly chosen to recommend a new company president. What is the
probability that all five members of the search committee will be in order of man,
man, man, woman, and woman (without replacement)?
The probability of selecting the committee in the order of man, man, man, woman, woman, without replacement is; 5/133
What is the probability of an event?The probability of an event is the ratio of the number of desired outcome to the number of possible outcome.
The number of men in the board = 12
The number of women in the board = 10
The probability of selecting a man in the first position = 12/22
The number of men remaining is 11 and the number of women remaining is 10.
The probability of selecting a man in the second position is therefore = 11/21
In the same order, the probability of selecting a man in the third position = 10/20
The probability of selecting a woman next = 10/19
The probability of selecting another woman = 9/18
The probability of selecting the committee of five members in the specified order is therefore;
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Which chart has an equation of y = 2.75x?
Answer:
None of it.
Step-by-step explanation:
Notice the slope is 2.75 this means for EVERY X the graph goes up by 2.75 in the Y axis. For example.
If at X=1 y=0
Then for X=2 y=2.75
and for X=3 y=2.75+2.75=5.5
also the graph must pass thought point (0,0), the origin, and none of the graph follow this.
You can also compare the slopes of each equations
for graph A, from x=1 to x=2 the height Y goes from 3 to 3.5, this is a slope of 0.5 (not the 2.75 we are looking for)
for graph A, from x=1 to x=2 the height Y goes from 1 to 2.5, this is a slope of 1.5 (not the 2.75 we are looking for)
for graph A, from x=1 to x=2 the height Y goes from 1 to 2.75 this is a slope of 1.75 (not the 2.75 we are looking for)
notice the last is similar to equation y=1.75X+b, just in case.
Answer:
none
Step-by-step explanation:
a. 15
b. 25
c. 88.5
d. not enough information
Answer:
B
Step-by-step explanation:
assuming DF is the diameter of the circle , then
the angle in a semicircle is 90° , that is
∠ DCF = 90° and Δ CDF is a right triangle
using Pythagoras' identity in the right triangle
CD² + CF² = DF²
CD² + 60² 65²
CD² + 3600 = 4225 ( subtract 3600 from both sides )
CD² = 625 ( take square root of both sides )
CD = [tex]\sqrt{625}[/tex] = 25
I been struggling with this answer for 30 mins now can someone please help me
Bobbi owes a total of $10,455.75 in taxes.
What is taxes?Taxes are compulsory financial charges imposed by governments on individuals or entities based on income, property, or goods/services.
To compute the tax owed by Bobbi, we can use the following steps:
Calculate Bobbi's taxable income by subtracting the standard deduction and personal exemption from her total income:
Taxable income = $68,000 - $6,350 (standard deduction) - $4,050 (personal exemption) = $57,600
Determine the tax bracket in which Bobbi's taxable income falls:
Bobbi's taxable income of $57,600 falls in the 25% tax bracket.
Calculate the tax owed by Bobbi by applying the marginal tax rates to her taxable income. We can use the following formula:
Tax owed = (Taxable income - Previous tax bracket limit) x Marginal tax rate + Previous tax amount
In Bobbi's case, we need to calculate the tax owed in three steps, since her taxable income falls in the 10%, 15%, and 25% tax brackets:
For the first $9,325 of her taxable income, Bobbi owes 10% in taxes:
Tax owed = ($9,325 - $0) x 0.10 + $0 = $932.50
For the next $28,625 of her taxable income (up to $37,950), Bobbi owes 15% in taxes:
Tax owed = ($37,950 - $9,325) x 0.15 + $932.50 = $3,825.75
For the remaining $19,650 of her taxable income (up to $57,600), Bobbi owes 25% in taxes:
Tax owed = ($57,600 - $37,950) x 0.25 + $3,825.75 = $5,697.50
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A certain forest covers an area of 2100 km sq. Suppose that each year this area decreases by 4%. What will the area be after 10 years?
round your answer to the nearest square kilometer.
The area of the forest will be approximately 1396 km sq. after 10 years.
What will the area be after 10 years?Given that, a forest covers an area of 2100 km sq and that each year this area decreases by 4%..
Initial value = 2100rate = 4%Elapsed time = 10 yearsIf the area of the forest decreases by 4% each year, then after one year it will be 96% of the original size.
After two years, it will be 96% of 96% of the original size, or 0.96² of the original size.
After ten years, it will be 96% of itself ten times, or 0.96¹⁰ of the original size.
So the area of the forest after 10 years will be:
Area = Initial area × 0.96¹⁰
Area = 2100 km sq × 0.96¹⁰
Area = 1396 km sq
Therefore, the area of the forest cover in 10 years will be 1396 km sq.
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2 1/3 x 9 the product is approximately
Answer:
21
Step-by-step explanation:
2 1/3 ×9=7/3 × 9=21
Rectangle abcs is the image of rectangle abcs after t abcs if a is (6,-8) a is (-2,4) and (4,-6)what are coordinates of b
In the rectangle , the cοοrdinate οf b is (0,2).
What is rectangle?A quadrilateral with fοur equal vertices and parallel sides is knοwn as a rectangle. Because οf this, it is alsο knοwn as an equiangular quadrilateral.
The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.
Here In the given rectange abcd, Let cοοrdinates οf b be (x, y)
then, ac and bd are diagοnals οf the rectangle.
Coordinates of midpoints of ac and bd must be same.
Coordinates of midpoint of ac = [tex](\frac{6-2}{2},\frac{-8+4}{2})[/tex] = [tex](\frac{4}{2},\frac{-4}{2})[/tex] = (2,-2)
Coordinates of midpoint of bd = [tex](\frac{x+4}{2},\frac{y-6}{2}) = (2,-2)[/tex]
=> [tex]\frac{x+4}{2}=2 , \frac{y-6}{2}=-2[/tex]
=> x+4=4 , y-6=-4
=> x=4-4, y=-4+6
=> x=0,y=2
Hence the coordinate of b is (0,2).
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determine the value of b²- 4ac
12x² + 5x -2=0
27 km
12 km
40 km
Find the area of the SHADED region. Round to the nearest hundredth when necess
A =
km²
The area of the shaded portion is solved to be
426.89 km²How to find the area of the shaded portionThe area of the shaded portion is solved by finding the whole area of the triangle and subtracting the area of the circle
Area of the whole shape
The shape is a triangle and the area of the triangle is
= 0.5 * base * height
where
base = 40 km
height = 27 km
plugging in the values
Area = 0.5 * 40 * 27
Area = 540 square km
Area of the circle
= π * radius^2
= 3.142 * 6^2
= 113.112 square km
Area of the shaded portion is
= 540 - 113.112
= 426.888
= 426.89 km²
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hailey invested $940 with an interest rate of 8.25 % that is compounded quarterly and Justin invested $940 with an interest rate of 7.625% that is compounded monthly
To the nearest dollar, how much money would Hailey have in her account when Justin's money has tripled in value?
To solve this problem, we need to first determine how long it will take for Justin's money to triple in value. We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For Justin, we have:
P = $940
r = 0.07625
n = 12 (monthly compounding)
t = unknown
We want to solve for t when A = 3P = $2820. We can rearrange the formula and plug in the values:
A = P(1 + r/n)^(nt)
3P = P(1 + r/n)^(nt)
3 = (1 + 0.07625/12)^(12t)
ln(3) = 12t * ln(1 + 0.07625/12)
t = ln(3) / (12 * ln(1 + 0.07625/12))
t ≈ 15.8 years
So it will take Justin about 15.8 years for his money to triple in value.
Now we can use the same formula to find how much money Hailey will have in her account after 15.8 years:
P = $940
r = 0.0825
n = 4 (quarterly compounding)
t = 15.8
A = P(1 + r/n)^(nt)
A = $940(1 + 0.0825/4)^(4*15.8)
A ≈ $3501
Therefore, Hailey will have about $3,501 in her account when Justin's money has tripled in value
help 50 pts .. brainliest
1. Choose two animals with different speeds. You can choose from the chart
that starts at the bottom of this page or do research to choose your own.
2. Design a fair race in which the two animals have an equal chance of winning
if they race at their top speed. Here are a few tips for your design:
a. The race is fair if the two animals could finish the race in the same
amount of time.
b. You can give the slower animal a shorter distance to race.
c. Since this is a video game, the race does not need to be realistic—it
can be any length, and the animals can run at a constant speed.
3. Write a system of two linear equations showing the distance each animal can
travel to model the fair race. Be sure to define all variables.
4. Graph the system to prove that the two animals have an equal chance of
winning the race. Explain how the graph proves the race is fair
The animals I chose are the squrriel and mouse. the linear equation for the squrriel is y = 12x
and for the mouse its y = 8x
Can I please get help with number 4? Im not sure how to graph it
The linear equation that can be given for squirrel y is the value of 12x.
How to solveAccording to the question,
Animal Mouse Squirrel
Speed(mph) 8 12
SInce "x" the time goes along with x-axis and "y" is the distance covered by the animal.
The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....
The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....
Let us consider the track is a straight line and the shorter distance is 50 meters.
The formula for straight line equation y = mx + b where 'b' is the base value, 'x' is the time and 'y' is the distance.
The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.
The linear equation for mouse y = 8x + b and the mouse starts at 0 meters. so the equation becomes y = 8x.
Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by the mouse and the squirrel.
y =12x
y = 12(3)
y = 36.
The distance covered by the squirrel is 36km at time 3hours.
For mouse, at time x = 3 hours.
y = 8(3)
y=24.
The distance covered by the squirrel is 24km at time 3hours.
Hence, The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
Thus:
The linear equation for mouse y = 8xThe distance covered by the squirrel is 36km at time 3hours.The distance covered by the squirrel is 24km at time 3hours.Read more about fair race here:
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15 ) Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t² + 6t+ 3, with h(t) measured in feet, and time, t,
measured in seconds. The number 3 in h(t) represents
(1) the maximum height of the ball
(2) the height from which the ball is thrown
(3) the number of seconds it takes for the ball to reach the ground
(4) the number of seconds it takes for the ball to reach its maximum
height
The number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
The equation h(t) = -16t² + 6t+ 3 models the height of the ball thrown in the air, with h(t) measured in feet and time, t, measured in seconds. The number 3 in this equation refers to the height from which the ball is thrown. This is represented by the constant term 3, which is added to the equation after the sum of the variables. The formula h(t) = -16t² + 6t+ 3 can be broken down into three parts. The first part is the constant term, 3, which denotes the initial height of the ball. The second part is the linear term, 6t, which represents the acceleration of the ball due to gravity. Lastly, the quadratic term, -16t², is used to describe the rate at which the ball’s acceleration slows down due to air resistance. Therefore the number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.
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-8x+6>-30 what is the answer
Answer: x< 4.5
Step-by-step explanation:
-8x+6>-30
-8x>-36
x<4.5
The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image.
( please explain how to do it and what i have to plot)
Answer:
Step-by-step explanation:
Ok so basically, what I would do is make note of each of the points of the triangle, and them multiply them by four, or the scale factor.
The speed of light is 299,792,458 meters per second. How would you write the approximate speed in scientific notation
Answer:
3 * 10^8 m/s.
Step-by-step explanation:
The given number is close to 300 million so an approximate speed is
3 * 10^8.
which expression does not belong? explain
The expression that does not belong with the other three is B. x ² - 8 ˣ because C. The different expression is the one that is not a polynomial.
How to find the expression ?Expression 2 is not a polynomial because it contains a term (8^x) with a variable in the exponent, which is not allowed in a polynomial. All the other expressions are polynomials. This expression therefore does not belong.
Polynomials are mathematical expressions that consist of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.
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Maria Fay bought four Dunlop tires at a local Goodyear store. The salesperson told her that her mileage would increase by 6%. Before this purchase, Maria was getting 24 mpg. What should her mileage be with the new tires?
Note: Round to the nearest hundredth.
Aubrey wants to know how students in her school feel about the new intramural sports program being developed. She randomly selects the names of 100 students and e-mails them a survey. She waits for responses and records data from the 32 surveys that are returned to her. Is her sample biased? Explain.
Her sample is in fact biased, as the sampling method used was voluntary sampling, which results in self-selection bias.
What is voluntary sampling and why it is biased?Voluntary sampling is a type of sampling method in which individuals are invited to participate in a study or survey based on their willingness or availability to do so. In other words, individuals choose to participate in the study, rather than being selected randomly by the researcher.
Voluntary sampling is chosen for this problem as the students had the option to answer the e-mail or not.
A limitation of voluntary sampling is that the individuals who choose to participate in the study may not be representative of the larger population from which they were drawn, leading to biased results.
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One of your co-workers is giving a presentation on the results of an analysis the two of you have been working on. Someone in the audience points out that the data system you used has frequent errors. How should you deal with this comment?
Answer:
As a co-worker, you should support your colleague by offering to address the question. Here are some steps to consider:
Acknowledge the concern: Begin by thanking the person for their comment and acknowledging their concern about the data system. This will help to show that you are open to feedback and willing to listen.
Provide context: If appropriate, offer some context about the data system that was used. For instance, if the system was chosen due to budget or resource constraints, you can explain why that decision was made.
Offer a solution: Explain what steps were taken to ensure the accuracy of the data, despite the known issues with the system. If there were steps taken, share those with the audience. Alternatively, offer to follow up with the audience member after the presentation with more information on how the team plans to address the issue.
Stay professional: Be calm, professional, and open-minded throughout the conversation. Avoid getting defensive or argumentative. Instead, focus on addressing the issue in a constructive manner.
By following these steps, you can help to address the concern in a professional and effective manner.
Which expression is equal to the product of 1/3 and 2 1/4?
1/3*4/9
3/1*4/9
1/3*9/4
1/3*1/4
3/1*9/4
Answer:
the answer is 1/3*9/4
Answer: 1/3*9/4
Step-by-step explanation: I did a test.
Help Please, I dont know what to do.
Answer: B: y=5x-5
Step-by-step explanation:
Lisa is going on a 3 1/2 mile hike. She has already hiked 2 3/4 miles How many miles does she have left?
Answer:
3/4 miles
Step-by-step explanation:
Parameters
Total distance = 3 1/2 miles
Covered distance = 2 3/4 miles
To make things easier let's convert our parameters from fraction to decimal,
Therefore,
Total distance= 3.5 miles
Covered distance = 2.75 miles
Remaining distance = Total distance - Covered distance
Remaining distance = 3.5 miles - 2.75 miles
Remaining distance= 0.75 miles
Converting back to fraction,
Remaining distance = 3/4 miles
Therefore,
Lisa has 3/4 miles left to hike.
Please mark brainliest.
Thanks.
a stable has 27 horses each one of eats 9 pounds how many pounds will the horses eat in 8 weeks
Using the multiplication operation, the total quantity that the 27 horses consume in 8 weeks is 1,944 pounds.
What is the multiplication operation?The multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication operation involves the multiplicand (the number multiplied), the multiplier (the number multiplying), and the product (the result).
The number of horses in a stable = 27
The quantity of food eaten per horse per week = 9 pounds.
The number of weeks involved = 8 weeks.
The total quantity eaten by the 27 horses in 8 weeks = 1,944 pounds (27 x 9 x 8)
With multiplication, we can conclude that the total quantity is 1,944 pounds.
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Complete Question:A stable has 27 horses. Each one eats 9 pounds per week. How many pounds will the horses eat in 8 weeks?
SUPER EASYYY PLEASE ANSWER THIS
Answer:
The y-intercept represents a starting salary of $32,500.
The slope represents an additional $2,500 in salary for each additional year of employment.
If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
[tex]y=2500x+35000[/tex].
If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
[tex]y = 3000x + 32500[/tex].
Step-by-step explanation:
Answer:
The y-intercept represents a starting salary of $32,500.
The slope represents an additional $2,500 in salary for each additional year of employment.
If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
y=2500x+35000y=2500x+35000 .
If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
y = 3000x + 32500y=3000x+32500 .