Answers
Using the law of cosines, the missing angles are:
A = 34.1°, B = 44.4°, C = 101.5°
What is the Law of Cosines?The law of cosines is used to solve a triangle when given the lengths of the three sides of a triangle, and it is expressed by the formula:
c² = a² + b² - 2ab × Cos C.
Given the following:
a = 4 b = 5 c = 7Find C by substituting the values into the law of cosines formula:
7² = 4² + 5² - 2 × 4 × 5 × Cos C
49 = 16 + 25 - 40 × Cos C
49 = 41 - 40Cos C
49 - 41 = -40Cos C
8/-40 = Cos C
-0.2 = Cos C
C = Cos^(-1)(-0.2)
C = 101.5°
Find B using the Law of Sines:
sin B/b = sin C/c
Substitute
sin B/5 = sin 101.5/7
(sin B)(7) = (sin 101.5)(5)
sin B = (sin 101.5)(5)/7
sin B = 0.69995
B = Sin^(-1)(0.69995)
B = 44.4°
Find the measure of angle A using the triangle sum theorem:
A = 180 - 101.5 - 44.4
A = 34.1°
Learn more about the law of cosines on:
https://brainly.com/question/4372174
#SPJ1
Related Questions
The population of the United States increased from 249 million in 1990 to 308 million in
2010.
The absolute change in the population was
The relative change in the population was
of a percent)
million.
% (round to the nearest tenth
Answers
The absolute change in the population was 59 million. The relative change in the population was 23.69%
The absolute population change is the magnitude of the increase or decrease in population for a defined period.
What is absolute change ?Absolute change describes the straightforward difference between the indicator over two time periods. The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage.
Small numbers can make relative changes appear more significant than they actually are. This is true because a minor change in the number's absolute value can generate a significant change in the percentage.
Big numbers may make relative changes appear less significant. This is so that any change in the number that represents a substantial relative change may be seen.
The relative change can be minor even when the absolute change is significant if it is a change on a larger number.
Absolute change = Final value – Initial value
= 308m- 249m = 59m
The absolute change in the population was 59 million
Relative change Formula = (Final value – Initial value) / Initial value * 100%
= 308m- 249m/ 249*100 = 23.69%
The relative change in the population was 23.69%
To learn more about absolute change refer :
https://brainly.com/question/28888240
#SPJ1
Suppose that 12 inches of wire costs 60 cents.
At the same rate, how many inches of wire can be bought for 25 cents?
Answers
Answer:
5 inches of wire.
Step-by-step explanation:
60/12 = 5
So at .05 an inch, you can afford 5 inches at 25 cents
Please mark brainliest!
Please help me with this (will give more credit for the best answer)
Answers
Answer:
1. 5ft
2. 2ft
3. 2ft
4. 1ft
Step-by-step explanation:
Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
Answers
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
Read more about function transformation at
https://brainly.com/question/1548871
#SPJ1
y=600(0.75)^x
growth or decay by what precent?
Answers
The function f(x) = 600(0.75)^x. is a decay function by 25%
How to graph the function?The equation of the function is given as
f(x) = 600(0.75)^x.
The above function is an exponential function
An exponential function is represented as
y = ab^x
When f(x) = 600(0.75)^x. and y = ab^x are compared, we have
b = 0.75
The value of b in this case is the factor
Also if b is less than 1, then the function is a decay function
0.75 is less than 1
So, the function represents a decay function
The decal percentage is then calculated as
Decay = 1 - b
So, we have
Decay = 1 - 0.75
Evaluate
Decay = 25%
Hence, the function is a decay function
Read more about exponential functions at
brainly.com/question/11464095
#SPJ1
If segment BD is congruent to segment BC, BD=4x-18, BC=x+3, and AC=34, find AB
Answers
If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.
What is meant by Congruent angles?Congruent angles are two or more angles that are exactly the same. As a result, the lengths of these angles are equal. Angle measurement is the same for congruent angles. A regular pentagon, for example, has five sides and five angles, each of which is 108 degrees. Angles in a regular polygon will always be congruent regardless of size or scale. Congruent angles are another name for equal angles. Angles that are congruent are those that are vertically opposite each other. Congruent angles are those formed by the intersection of two parallel lines and a transversal.Let the equation be AB + BC = AC
substitute the values in the above equation, we get
AB + x + 3 = 34
simplifying the value of x,
Subtract A B from both sides AB + x + 3 - AB = 34 - A B
x + 3 = 34 - AB
Subtract 3 from both sides,
x + 3 - 3 = 34 - AB - 3
x = -AB + 31
Plug in this value of x into the line segments to find BC and AC.
Where, BC = x + 3
substitute the value of x in the above equation, we get
BC = [-AB + 31 ] + 3
BC = -AB + 34
Then, AB + BC = AC
x = -AB + 31
AB = 31/x
Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,
BC = x + 3, and AC = 34, then AB = 31/x.
To learn more about Congruent angles, refer to:
https://brainly.com/question/28262429
#SPJ1
a top speed an object travels 3,200 millimeters in 4 seconds how many millimeters does the object travel each second
Answers
If Y Varies inversely as X. If Y=6 and X=10. FIND X when Y=18, correct to 3 significant figures.
Answers
Answer:
x ≈ 3.33
Step-by-step explanation:
given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 6 , x = 10
6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )
60 = k
y = [tex]\frac{60}{x}[/tex] ← equation of variation
when y = 18 , then
18 = [tex]\frac{60}{k}[/tex] ( multiply both sides by k to clear the fraction )
18k = 60 ( divide both sides by 18 )
k = [tex]\frac{60}{18}[/tex] ≈ 3.33 ( to 3 significant figures )
A store is having a sale in which all items
are discounted 20%. Including tax, Colin paid $21 for a picture. If the
sales tax rate is 5%, what was the original price of the picture?
Answers
In linear equation, that price of shorts before discount was $25
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Assume that the price of shorts after the discount is x
Total payment = price of shorts + taxes
We know that:
total payment = $21
taxes = 5% = 0.05 of the price
This means that:
21 = x + 0.05x
21 = 1.05x
x = $20
Therefore, the price of the shorts is $20 after the discount
Now, we will get the price of the shorts before the discount:
Assume that the price of shorts before discount is y
We know that:
The discount was 20%
This means that Jennifer paid:
100% - 20% = 80% of the price of the shorts
Therefore:
80% of the price = $20
0.8y = 20
y = $25
This means that price of shorts before discount was $25.
Learn more about linear equation
brainly.com/question/11897796
#SPJ13
A ride-all-day amusement park ticket last season was $35, and this season it is $27
.
What is the percent Markdown?
Answers
Answer:
Step-by-step explanation:
35-27=8
Answer:22.85%
Step-by-step explanation:
27 - 35
|35|
× 100% =
-8
35
× 100 = -22.8571428571% (decrease)
I need help fast with my math homework.
Answers
Answer:15 twice
Step-by-step explanation:
which fraction on the number line is equal to 3
Answers
Answer:
? can't answer if there's no number line
Justin works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 30% of his total sales for the week. How much would Justin make in a week in which he made $2425 in sales? How much would Justin make in a week if he made x dollars in
Answers
We can convert that 30% into a decimal, as: 0.3 (That's 30/100)
Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.
For example, let's take Justin's commission:
[tex]2425\cdot0.3=727.5[/tex]Adding this to his base salary,
[tex]450+727.5=1177.5[/tex]We can conclude that Justin's paycheck for the week would be $1,117.5
Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:
[tex]0.3x+450[/tex]Kirby is buying a new grill that has been reduced for an end of summer sale by 25% to $496. what was the original price of the grill?
Answers
Given:
percentage decerease = 25%
current price of the grill = $496
Let the original price of the grill be x
We can calculate percentage decrease using the formula:
[tex]\text{Percent decrease = }\frac{Orig\text{ inal value - new value}}{Orig\text{ inal value}}\text{ }\times\text{ 100}[/tex]Substituting the given values we have:
[tex]\begin{gathered} 25\text{ = }\frac{x-496}{x}\times\text{ 100} \\ 25\text{ = }\frac{(x-496)\times100}{x} \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 25x\text{ = 100x - 49600} \\ \text{Collect like terms:} \\ -75x\text{ = -49600} \\ \text{Divide both sides by -75} \\ \frac{-75x}{-75}\text{ = }\frac{-49600}{-75} \\ x\text{ }\approx\text{661.33} \end{gathered}[/tex]Hence, we can conclude that the original price of the grill is approximately $661.33
Answer:
$661.33
Write in words the meaning of P^2 - 7P.
Answers
Answer:
P squared minus 7 times P
Step-by-step explanation:
Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.
What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?
A = {KL}
A = {KJ, KL}
A = {KL, LK}
A = {KJ, KL, LJ}
Answers
Answer:
A = {KL}
Step-by-step explanation:
The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The sample space of this experiment consists of all possible ways of choosing two names from a group of three.
Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.
The three possible outcomes are: {JK, JL, KL}.
If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.
There are two such outcomes: JL and KL.
Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ5
what are the roots of the equation ?-3x = -10x^2-4
Answers
Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]2.1. AP-8 Write the integer value that point B represents, then write its opposite. B - 10 5 5 10 Point B represents the integer
Answers
In the line, the point B represents the integer -3, because it is 3 units left from 0.
Its opposite is the number 3, that is 3 units right from 0.
MTR
3 MAINTAIN ACCURACY In Exercises 27-30, determine
whether the statement uses the word function in a way
that is mathematically correct. Explain your reasoning.
27. The selling price of an item is a function of the cost of
making the item.
28. The sales tax on a purchased item in a given state is a
function of the selling price.
29. A function pairs each student in your school with a
homeroom teacher.
30. A function pairs each chaperone on a school trip
with 10 students.
Please just do 28 and 30
Answers
Answer:
28. Correctly used
30. Incorrectly used
Step-by-step explanation:
You want to know if the word "function" is correctly used in the following cases:
28. The sales tax on a purchased item in a given state is a function of the selling price.
30. A function pairs each chaperone on a school trip with 10 students.
28. Sales taxThere is exactly one value of sales tax associated with any given selling price. This means the ordered pair (selling price, sales tax) will be unique for any given selling price. Hence, the relation between selling price and sales tax is a function. The word function is used correctly in describing this relation.
29. ChaperonesThere are 10 different students associated with any given chaperone. This means there will be multiple (chaperone, student) ordered pairs for any given chaperone: (c1, s1), (c1, s2), ..., (c1, s10), (c2, s11), (c2, s12), ..., (c2, s20), .... The relation between chaperones and students is not a function. The word function is used incorrectly in describing this relation.
Write the equation in slope intercept form: -6x+4y=20
Answers
Answer:
[tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]
a³ = 125
Each edge of the cube is
feet long.
Answers
Answer:
each cube is 5 feet long because 5*5*5 = 125
Step-by-step explanation:
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist? *
Answers
The car will catch up with cyclist in 3 hours
What is time ?Time refers to the interval in seconds , minutes or hours it took for an event to take place
How to calculate How many hours it will take the car to catch up with cyclistInformation given for the question include
A cyclist has average speed of 9 miles per hour
A car leaves has average speed of 21 miles per hour
following same route when
The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already
Calculation of distance covered by the cyclist
average speed = distance / time
distance = 9 mph * (x + 4)
Calculation of distance covered by the car
average speed = distance / time
distance = 21 mph * x
equating both gives
9 mph * (x + 4) = 21 mph * x
9x + 36 = 21x
36 = 21x - 9x
12x = 36
x = 3
hence the car will meet the cyclist in 3 hours
Learn more on distance covered : https://brainly.com/question/4931057
#SPJ1
what is 11/12 ÷ 1/30 2 1/40 2 3/40 3 1/30 3 2/3
Answers
The given expression is
[tex]\frac{11}{12}\colon\frac{1}{3}[/tex]First, we change 1/3 for its reciprocal to transform the division into a product.
[tex]\frac{11}{12}\cdot\frac{3}{1}[/tex]Then, we multiply the fractions.
[tex]\frac{11\cdot3}{12\cdot1}=\frac{33}{12}=\frac{11}{4}[/tex]At last, we transform the fraction into a mixed fraction.
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Therefore, the right answer is B. 2 3/4.I need help with this practice problem solving the subject is trig I have an additional picture that is the answer options, I will send this to you
Answers
Given
[tex]f(x)=\tan x[/tex]To fill the blanks.
Now,
The grpah of f(x)=tanx is given as,
Therefore, from the graph,
[tex]\tan x=\tan (x+\pi)=\tan (x+2\pi)[/tex]Then,
[tex]\pi\text{ is the fundamental period of tanx.}[/tex]Also,
For x=0, tan(0)=0.
Therefore, the y-intercept is (0,0).
The points for the function f(x)=tanx is,
[tex]\begin{gathered} x=\frac{\pi}{3},\text{ y=tan(}\frac{\pi}{3})=\sqrt[]{3} \\ x=\frac{\pi}{4},y=\tan \frac{\pi}{4}=1 \end{gathered}[/tex]Since
[tex]\tan (-A)=-\tan A[/tex]Then, the points of the graph y=tanx is,
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]Hence, the answer should be in the order,
i)
[tex]\pi[/tex]ii)
[tex](0,0)[/tex]iii)
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]Which of the following sentences properly uses semicolons in a serial list?
There is so much you can do to cut down on waste; such as composting, which uses food waste to help plants grow, recycling, which keeps plastic, metal, and glass out of landfills, and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting; which uses food waste to help plants grow; recycling; which keeps plastic; metal; and glass out of landfills; and thrifting; which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste; such as composting; which uses food waste to help plants grow, recycling; which keeps plastic, metal, and glass, out of landfills, and thrifting; which cuts down on clothing waste from fast fashion.
Answers
The sentence that properly uses semicolons in a serial list is B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
What are semicolons?A semicolon is a punctuation mark consisting of a period put on top of a comma.
Semicolons can be used for the following purposes:
To join two independent clauses without the coordinating conjunctions (and, but, or, nor, for, so, yet)As a serial listTo introduce evidence for a preceding statement.Thus, the proper use of semicolons in a serial list is Option B.
Learn more about using semicolons at https://brainly.com/question/551059
#SPJ1
Answer:
B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
Step-by-step explanation:
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate31.4π units 10π units 31.4 units
Answers
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate
31.4π units
10π units
31.4 units
we know that
the circumference of a circle is equal to
[tex]C=2\pi r[/tex]we have
pi=3.14
r=5 units
substitute
[tex]\begin{gathered} C=2\pi(5) \\ C=10\pi\text{ units} \end{gathered}[/tex]the exact value is 10pi units
the approximate value (assume pi=3.14)
C=31.4 units
so
order from most accurate to least accurate is
10π units
31.4 units
31.4π units
order from least accurate to most accurate is31.4π units31.4 units10π units50 points if this is correct i need this asap please
Which is the best definition of a two-step equation?
In a two-step equation, you must always start by using the division property of equality.
In a two-step equation, you need to use one inverse operation to solve.
A two-step equation is one that you need to use two properties of equality to solve.
A two-step equation is one that you need to use only a single property of equality to solve.
Answers
Answer:
c
Step-by-step explanation:
A two-step equation is one that you need to use two properties of equality to solve.
Solve for x. 23r + 2 = 156 + 481 + 6 A. x = 1/12 B. x = -2/5C. x = -1/10 D. x = -12/5
Answers
C) x= -1/10
1) Evaluating the following expression
23x+2= 15x + 48x + 6 Add the like terms
23x +2 = 63x +6 Subtract 63x and 2 from both sides
23x -63x = 6 -2
-40x =4 Divide both sides by -40
x = -4/40 Simplify it by 4
x= -1/10
2) Hence, the answer is x= -1/10
12. Six hundred people will buy tickets at $4 each
for a district championship game. For each 20¢
decrease in price, 50 more people will buy
tickets. Find the best ticket price, the maximum
income, and the corresponding number of
tickets.
Answers
Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.
What is Quadratic Equation?A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.
We know that,
No. of people who will buy tickets at $4 = 600
For each 20¢ decrease, additional no. of people buying tickets = 50
Revenue = (No. of tickets sold)(Pricing)
Revenue = (600+50x)(4+x)
= 50[tex]x^{2}[/tex] + 800x + 2400
Solving the quadratic equation we got,
x = -4 or -12
Since we're dealing with real-life entities such as money, we'll take the value of x as positive.
Taking x as 12 (higher value),
No. of tickets sold = 600 + 50x = 1200
Pricing = 4 + x = 16
Revenue = 1200×16 = $19,200
To know more about Quadratic Equations, visit:
https://brainly.com/question/1863222
#SPJ13
75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?
Answers
Answer:
1/2
Step-by-step explanation:
75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:
= 100% - 75%
= 25%
The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:
= 75% - 25%
= 50%
= 1/2