The compositions of the given functions are as follows:
hf(x) = 3/(x² - 1)
fh(x) = (9 - x²)/x²
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable).
So, we have:
h(x) =3/x, x and f(x) = x^2 - 1
Now, solve as follows:
h(x) = 3/x
f(x) = x² - 1
h(f(x)) = 3/f(x)
hf(x) = 3/(x² - 1)
f(h(x)) = (h(x))² - 1
= (3/x)² - 1
= 9/x² - 1
fh(x) = (9 - x²)/x²
Therefore, the compositions of the given functions are as follows:
hf(x) = 3/(x² - 1)
fh(x) = (9 - x²)/x²
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Correct question:
Suppose that the functions h and f are defined as follows. h(x) =3/x, x notequalto 0 f(x) = x^2 - 1 Find the compositions h composite function h and f composite function f Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)
What steps should be taken to calculate the volume of the right triangular prism? Select three options. A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. The area of the base, A, is One-half (7) (8) = 28 meters squared. The area of the base, A, is One-half (8) (14) = 56 meters squared. The volume of the prism, V is (56) (7) = 392 meters cubed.
The steps that should be taken to calculate the volume of the right triangular prism are;
Use the formula A = one-half b h to find the area of the baseThe area of the base, A, is One-half (8) (14) = 56 meters squaredvolume of the prism, V is (56) (7) = 392 meters cubed.What steps should be taken to calculate the area of a triangular prism?Base = 8 meters
Height = 14 meters
Length of the prism = 7 meters
Area = ½ × base × height
= ½ × 8 × 14
= 56 square meters
Volume of the rectangular prism = Area × length of the prism
= 56 square meters × 7 meters
= 392 cubic meters
Ultimately, the volume of the right triangular prism is 392 cubic meters
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solve the ratio 2.4:3/4:1 2/3
The simplified ratio of [tex]2.4:3/4:1 2/3[/tex] is [tex]28.8:9:20[/tex].
What does a ratio means?A ratio refers to the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
To solve this ratio, we need to convert all the fractions to a common denominator:
2.4 : 3/4 : 1 2/3 = 2.4 : (3/4) : (5/3)
To eliminate the fractions, we can multiply all terms by the LCD of 12:
2.4 * 12 : (3/4) * 12 : (5/3) * 12
= 28.8 : 9 : 20
So the simplified ratio for the given ratio is: 28.8 : 9 : 20
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5. Use the conversion formula to write the equation for the new function, F(t).
(4 points: 2 points for setting up the equation, 2 points for the answer)
Hint: Substitute the equation for C(t) into F(t) = 9/5C(t) + 32
The equation for the new function F(t) is F(t) = 9t - 256/9.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
The conversion formula for converting temperature from Celsius to Fahrenheit is:
F = 9/5C + 32
Substituting the equation for C(t) into F(t) = 9/5C(t) + 32, we get:
F(t) = 9/5(5t - 160/9) + 32
Simplifying this equation, we get:
F(t) = 9t - 320/9 + 32
F(t) = 9t - 256/9
Therefore, the equation for the new function F(t) is F(t) = 9t - 256/9.
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what is the volume of this right rectangular prism
anter your answer in the box
ft3
The volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.
What is volume ?
Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape.
It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.
the length of the prism is 7 feet, the width is 2 feet, and the height is 3.5 feet.
Volume = Length x Width x Height
Volume = 7 ft x 2 ft x 3.5 ft
Volume = 49 cubic feet
So, the volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.
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Help me please. Today I have to turn this in.
distance between (1,5) and (-6,-2)
[tex]\:\: \:\: \:\star[/tex] We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -
[tex] \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]
As per question, points are -
A (1,5)B(-6,-2)Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -
[tex]\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]
[tex] \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\[/tex]
[tex]\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\[/tex]
[tex]\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\[/tex]
[tex]\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\[/tex]
[tex]\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\[/tex]
[tex]\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\[/tex]
[tex]\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\[/tex]
[tex]\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\[/tex]
Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).
Find the height given a volume of 145.14 in and a radius of 6 in.
volume of a cone
Answer:
Step-by-step explanation:
23cm givinExpand and simplify y(2y+5) +4(2y+3)
Step-by-step explanation:
y ( 2y + 5 ) + 4 ( 2y+3)
2y^2 + 5y + 8y + 12
2y^2 + 13 y + 12
please please help me rn
Answer: it is one of the last two
Step-by-step explanation:
Help me out please, thanks !! <3
Answer:
A
Step-by-step explanation:
because I took the test
Answer: I think it's a. 84 cubic units
Hope it helped : D
A van travels at a constant speed. The distance y in miles tat the van has traveled after x hours is shown in the table below.
The van would have traveled approximately 8 miles of distance after 12 minutes.
To calculate the distance traveled by the van after 12 minutes, we can use the formula:
y = mx
Where m is the rate of travel, and x is the time in minutes.
To find the value of m, we can use the first two data points:
m = (y2 - y1) ÷ (x2 - x1)
m = (8 - 0) ÷ (10 - 0)
m = 8 ÷ 10
m = 4 ÷ 5
Therefore, the formula becomes:
y = (4 ÷ 5) x
Now, we can substitute x = 12 to find the distance traveled after 12 minutes:
y = (4 ÷ 5) × 12
y = 0.8 × 12
y = 9.6
y ≈ 8 miles
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The complete question is:
A van travels at a constant speed. The table shows the distance y (in miles) that the van travels after x minutes. How far does the van travel after 12 minutes?
Time (minutes), x 0 10 20 30
Distance (miles), y 0 8 16 24
Which expressions are completely factored? Select each correct answer.
Responses
12a^3+8a=4(3a^3+2a)
24a^4+18=6(4a^4+3)
16a^5−20a^3=4a^3(4a^2−5)
30a^6−24a^2=3a^2(10a^4−8)
According to the given expression some are shortlisted factored expressions are [tex]4(3a^3 + 2a) for 12a^3 + 8a , 6(4a^4 + 3) for 24a^4 + 18, 4a^3(4a^2 - 5) for 16a^5 - 20a^3.[/tex]
Explain expressions?Expressions in mathematics are numerical, variable, and operation combinations that are used to indicate a quantity or a relationship between values.
One or more variables or numbers are combined with one additional operation to form an expression. An illustration of an expression is X + 1.
The completely factored expressions are:
[tex]4(3a^3 + 2a) for 12a^3 + 8a\\\6(4a^4 + 3) for 24a^4 + 184a^3(4a^2 - 5) for 16a^5 - 20a^3[/tex]
So the correct answers are:
[tex]12a^3+8a=4(3a^3+2a)24a^4+18=6(4a^4+3)16a^5−20a^3=4a^3(4a^2−5)[/tex]
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$8, 100 is invested in an account earning 3.7% interest (APR), compounded daily.
Write a function showing the value of the account after t years, where the annual
growth rate can be found from a constant in the function. Round all coefficients in
the function to four decimal places. Also, determine the percentage of growth per
year (APY), to the nearest hundredth of a percent.
The function is [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Here the principal p = $8100
Rate of interest r = 3.7% = 3.7/100 =0.037
Compounded daily then n= 365
Now using compound interest formula then,
=> CI = [tex]P(1+\frac{r}{n})^{nt}[/tex]
=> CI = [tex]8100(1+\frac{0.037}{365})^{365t}[/tex]
=> CI = [tex]8100(1+0.000101369)^{365t}[/tex]
=> CI = [tex]8100(1.000101369)^{365t}[/tex]
Then the function is f(t) = [tex]8100(1.000101369)^{365t}[/tex] .
Now percentage of growth per year is ,
=> [tex]8100(1.000101369)^{365t}[/tex][tex]\times\frac{1}{100}\%[/tex]
Put t=1 then
=> 8,405.30[tex]\times\frac{1}{100}\%[/tex]
=> 84%
Hence the function is [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.
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Calculate the values of x and y.
Answer:
Step-by-step explanation:
answer this with complete solution thanks
Answer:
balls
Step-by-step explanation:
Solve the following: 5x + 3x = 2(4x - 5) - 2
This statement is false. Therefore, the original equation has no solution.
How to solve an equation?
To solve the equation 5x + 3x = 2(4x - 5) - 2, we need to simplify each side of the equation using the order of operations (PEMDAS).
First, we simplify the left side of the equation by combining like terms. 5x + 3x equals 8x, so we have:
8x = 2(4x - 5) - 2
Next, we simplify the right side of the equation using the distributive property of multiplication. We multiply the 2 by each term inside the parentheses:
8x = 8x - 10 - 2
We can simplify further by combining like terms on the right side of the equation:
8x = 8x - 12
Now we have an equation with variables on both sides. To solve for x, we want to isolate the variable on one side of the equation. We can do this by subtracting 8x from both sides:
0 = -12
This statement is false. Therefore, the original equation has no solution.
The equation 5x + 3x = 2(4x - 5) - 2 is an example of a contradiction. It means that there is no value of x that makes both sides of the equation equal. In this case, we can see that the left side of the equation is always greater than or equal to the right side, no matter what value of x we choose. Therefore, the equation has no solution.
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Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.
The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."
To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:
Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:
[tex]4x^2 - 20x + 25 = 0[/tex]
This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:
[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]
Substituting the values of a, b, and c, we get:
x = (-(-20) ± - 4(4)(25))) / 2(4)
x = (20 ± sqrt(400 - 400)) / 8
x = 5/2
Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.
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Find the surface area of a rectangular pi with dimensions of 6 m by 4 m by 15
The surface area of the rectangular prism is 348 square meters.
Hello! I'd be happy to help you find the surface area of a rectangular prism with dimensions 6 m by 4 m by 15 m. The surface area can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
where l = length, w = width, and h = height.
Given the dimensions 6 m (length), 4 m (width), and 15 m (height), we can plug in the values
The surface area can be calculated using the formula:
Surface Area = 2(6)(4) + 2(6)(15) + 2(4)(15)
Surface Area = 48 + 180 + 120
Surface Area = 348 m²
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Any help with this ???
Answer:
a) 2 new printers
b) 11 min
Step-by-step explanation:
Given:
5 old printers take 30 min to produce a batch of comic books
4 new printers take 18 min to produce a batch of comic books
.
a) First, we need to find how long does one old and new printer take to produce a batch of comic books:
.
Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):
.
1 old printer does the job in:
5 × 30 = 150 min
1 new printer does the job in:
4 × 18 = 72 min
.
Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):
6 old printers would take:
150 / 6 = 25 min
2 new printers would take:
72 / 2 = 36 min
.
25 < 36
That means, 2 new printers would do this job faster
.
b) In order to find how much less time would this take, we have to subtract:
.
36 - 25 = 11 min
Chang is building a circular sandbox with a circumference of 31.4 meters. She uses a string tied to a metal stake to trace out a circle in her backyard.
Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter
What exactly is pi?
The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.
We must first determine the circle's radius in order to determine the length of Mr. Chang's string.
C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.
Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:
C = 2r 31.4
=2x3.14xr
= 31.4/(2x3.14)r
= 3.14/6.28r
r = 5
Thus, the circle's radius is roughly 5 meters.
The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.
Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter
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HELP ASAP PLEASE
Question 5(Multiple Choice Worth 2 points)
(Line of Fit MC)
A donut shop wanted to determine the best price to sell its donuts. The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x. He created the following scatter plot with a line of fit.
scatter plot titled donut pricing with the x axis labeled number of donuts and the y axis labeled total cost in dollars, with points at 1 comma 1, 2 comma 2 and a half, 5 comma 3, 6 comma 5 and a half, 3 comma 2, 7 comma 5, 4 comma 4, 8 comma 4 and a half, 12 comma 7, 10 comma 7, 9 comma 7, and 8 comma 5 and a half, with a line passing through the coordinates 2 comma 2 and 7 comma 5
Find the slope of the line of fit and explain its meaning for the real-world situation.
The slope is 3 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.60.
The slope is 4 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.80.
The slope is 3 over 5, which means for each additional donut sold, the shop is predicted to earn $0.60.
The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80
The correct answer is "The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80."
The slope of the line of fit represents the rate of change in the dependent variable (total cost, y) with respect to the independent variable (number of donuts, x). In other words, it represents the amount by which the total cost increases or decreases for each unit increase in the number of donuts sold.
In this case, the slope of the line of fit is 4/5, which means that for each additional donut sold, the total cost is predicted to increase by $0.80. This indicates that the donut shop should expect to make a profit of $0.80 for each donut sold, assuming that all other factors remain constant. This information can be used by the donut shop to determine the optimal price to sell its donuts and maximize its profits.
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A bag contains 6 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.
To find the probability of drawing three green marbles from the bag, we need to use the formula for calculating the probability of multiple independent events. The probability of multiple independent events occurring together is the product of the individual probabilities of each event.
Let's first calculate the probability of drawing a green marble on the first draw. We have a total of 6 + 4 + 7 = 17 marbles in the bag, and 7 of them are green. So the probability of drawing a green marble on the first draw is:
P(green on first draw) = 7/17
After we draw a green marble on the first draw, we have 16 marbles left in the bag, including 6 red marbles and 4 blue marbles. Since we don't replace the marble after we draw it, the probability of drawing a green marble on the second draw is:
P(green on second draw) = 6/16
Finally, after we draw a green marble on the second draw, we have 15 marbles left in the bag, including 5 green marbles. So the probability of drawing a green marble on the third draw is:
P(green on third draw) = 5/15
To find the probability of drawing three green marbles in a row, we need to multiply these probabilities:
P(three green marbles) = P(green on first draw) x P(green on second draw) x P(green on third draw)
P(three green marbles) = (7/17) x (6/16) x (5/15)
Simplifying this expression, we get:
P(three green marbles) = (7 x 6 x 5) / (17 x 16 x 15)
P(three green marbles) = 0.0735
Therefore, the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.
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Pls Answer Fast!!!! Whoever gets it correct first I will give a brainly.
Answer:
Step-by-step explanation:
use a calculator it's free
7 + 4x - 9 = 6
Solve for X
Ans:-
[tex] \purple{ \large \sf \: 2}[/tex][tex] \: [/tex]
Solution:-
[tex] \mathfrak{7 + 4x - 9 = 6}[/tex][tex] \: [/tex]
[tex] \mathfrak{7 + 4x = 6 + 9}[/tex][tex] \: [/tex]
[tex] \mathfrak{7 + 4x = 15}[/tex][tex] \: [/tex]
[tex] \mathfrak{4x = 15 - 7}[/tex][tex] \: [/tex]
[tex] \mathfrak{4x = 8}[/tex][tex] \: [/tex]
[tex] \mathfrak{x = \cancel\frac{8}{4} }[/tex][tex] \: [/tex]
[tex] \boxed{ \mathfrak{ \color{hotpink} \: x = 2\: }}[/tex][tex] \: [/tex]
The value of x is 2 !
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps:)
The value of solution of expression is,
⇒ x = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 7 + 4x - 9 = 6
Now, We can simplify as;
⇒ 4x - 2 = 6
⇒ 4x = 4 + 2
⇒ 4x = 8
⇒ x = 2
Thus, The value of solution of expression is,
⇒ x = 2
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A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players. Each hoodie costs $60 and each long sleeve performance shirt costs $45. The entire order totaled $2,400.
For a total of $2,400, the coach purchased 30 hoodies and 15 long sleeve shirts. A hoodie costs $60 and a long sleeve shirt is $45.
Let x represent the number of hoodies ordered and y represent the number of long sleeve shirts ordered. To describe the provided data, we may construct the following system of two equations:
x + y = 45 (because there are 45 players) (since there are 45 players)
60x + 45y = 2400 (the total cost of the order) (the total cost of the order)
We may determine that x = 30 and y = 15 by solving for x and y. As a result, the coach placed orders for 15 long sleeve jerseys and 30 hoodies. We can confirm that the total price is $2400: (30 x $60) + (15 x $45) = $1800 + $675 = $2400
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What do i do for a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side. Help me please
The area of the rectangle is 40 square inches.
For a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side, there are a few things you can do.
The perimeter of a rectangle is the sum of the lengths of all four sides.
To calculate the perimeter, add the lengths of the top and bottom sides (8 + 3 = 11) and the lengths of the two side lengths (5 + 5 = 10).
To find the area of a rectangle with an 8-inch long side, a 3-inch bottom side, and a 5-inch side, follow these steps:
Identify the dimensions of the rectangle.
The dimensions are given as 8 inches long, 3 inches on the bottom, and 5 inches on the side.
However, a rectangle only has two different side lengths, so we can assume that the 3-inch measurement is irrelevant.
Confirm the side lengths.
In this case, the side lengths are 8 inches and 5 inches. The 8-inch side is the length, and the 5-inch side is the width.
Calculate the area of the rectangle.
To find the area, multiply the length by the width. In this case, that is 8 inches (length) multiplied by 5 inches (width).
Area = Length × Width
Area = 8 inches × 5 inches
Area = 40 square inches
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PLesea help with this yall i need to finish
The missing property is the distributive property of multiplication.
What is the distributive property of multiplication?
The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.
For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:
1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.
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A family wants to send supplies to a hospital via a suitcase they want to fill it up with as many supplies as possible. Their suitcase height is 5 ft and length 4 ft and width 4 f. Each supply has a base area of 9. And they can put 5120 supplies in the trunk. what is the height of each supply?
Answer:
approximately 0.0018 feet, or about 0.0216 inches.
Step-by-step explanation:
The volume of the suitcase is:
V_suitcase = height x length x width
V_suitcase = 5 ft x 4 ft x 4 ft
V_suitcase = 80 cubic feet
The volume of each supply is:
V_supply = base area x height
We know that the base area of each supply is 9 square feet. Let's assume that the height of each supply is h.
So, the total volume of all the supplies that can be put in the suitcase is:
V_total_supplies = V_supply x number of supplies
V_total_supplies = (9 ft^2 x h) x 5120
We want to find the height of each supply, so we can rearrange the equation above to solve for h:
h = V_total_supplies / (9 ft^2 x 5120)
Substituting the values we know:
h = (80 ft^3) / (9 ft^2 x 5120)
Simplifying, we get:
h = 0.0018 ft
So the height of each supply is approximately 0.0018 feet, or about 0.0216 inches.
In ΔLMN, the measure of ∠N=90°, NM = 28, LN = 45, and ML = 53. What is the value of the sine of ∠M to the nearest hundredth?
There are two are parallel vertical lines l and m intersected by another line t making angles 1 and 3 with l and 5 and 7 with m. 1 and 4 and 2 and 3 are opposite angles at the point of intersection of l and t. 5 and 8 and 6 and 7 are opposite angles at the point of intersection of m and t. If m∠2 = 120°, what is m∠7?
Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.
We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.
Thus, we can set up the following equation:
m∠7 = m∠8 - m∠5 = m∠4 - m∠5
We are given that m∠2 = 120°, so we can use this to find m∠1:
m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)
m∠1 + 120° = 180°
m∠1 = 60°
Since angles 1 and 5 are congruent, we know that m∠5 = 60°.
We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:
m∠1 + m∠3 = 90°
60° + m∠3 = 90°
m∠3 = 30°
Now we can find m∠4:
m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)
60° + m∠4 = 180°
m∠4 = 120°
Finally, we can use these values to find m∠7:
m∠7 = m∠4 - m∠5
m∠7 = 120° - 60°
m∠7 = 60°
Therefore, m∠7 is 60°.