Answer:
x≈12.6
Step-by-step explanation:
We have the equation:
19(1.12^x) = 8(1.18^x)
Divide both sides by 8:
19/8 (1.12^x) = (1.18^x)
Take the natural logarithm of both sides:
ln[19/8 (1.12^x)] = ln[1.18^x]
Using the properties of logarithms, we can simplify the left side:
ln(19/8) + ln(1.12^x) = x ln(1.18)
Substituting y = 1.12^x, we get:
ln(19/8) + ln(y) = ln(1.18) y
Now we can solve for y:
ln(y) = ln(1.18) y - ln(19/8)
Using a numerical method or a graphing calculator, we can find that y ≈ 10.584.
Substituting back to solve for x:
1.12^x ≈ 10.584
Taking the logarithm base 1.12 of both sides:
x ≈ ln(10.584)/ln(1.12)
x ≈ 12.6
Therefore, the solution to the equation is x ≈ 12.6.
United Airlines' flights from Chicago to Seattle are on time 60 % of the time. Suppose 6 flights are randomly selected, and the number on-time flights is recorded.
Round answers to 3 significant figures.
The probability that exactly 3 flights are on time is =
The probability that at most 4 flights are on time is =
The probability that at least 3 flights are on time is =
Therefore , the solution of the given problem of probability comes out to be 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672,
What is probability?Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .
Here,
=> P(X = k) = (n choose k) * p * k * (1-p) (n-k)
where p is the chance of success and (1-p) is the probability of failure, (n choose k) is the binomial coefficient, and P(X = k) is the probability of k successes in n trials.
The likelihood that precisely 3 planes will depart on time is:
P(X = 3)
=> (6 choose 3) * 0.60 * 0.40 * 0.311
The likelihood that up to 4 planes depart on time is:
=> P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= > (6 choose 0) * 0.60^0 * 0.40^6 + (6 choose 1) * 0.60^1 * 0.40^5 + (6 choose 2) * 0.60^2 * 0.40^4 + (6 choose 3) * 0.60^3 * 0.40^3 + (6 choose 4) * 0.60^4 * 0.40^2
≈> 0.672
The likelihood that at least three planes will depart on time is:
P(X >= 3) = 1 - P(X < 3)
= 1 - P(X = 0) - P(X = 1) - P(X = 2)
= 1 - (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) * 0.60^1 * 0.40^5 - (6 choose 2) * 0.60^2 * 0.40^4
≈ 0.695
=> P(X>=3) = 1 - P(X3) = 1 - P(X0) - P(X = 1) - P(X = 2)
=> 1 - (6 choose 0) (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) (6 choose 1) * 0.60 * 0.40 * 6 (select 2) * 0.60 * 0.40 * 4
≈> 0.695
Therefore, the likelihood that precisely 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672, and the likelihood that at least 3 flights will depart on time is roughly 0.695.
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Find the area of the region bounded by the x-axis, line x=2, line x=6, and lines y=x+3, and y=10-x.
Answer:
A=∫
1
3
x
2
dx
A=[
3
x
3
]
1
3
A=(
3
27
−
3
1
)
A=
3
26
Write out the sample space for the given experiment. Use the following letters to indicate each choice: Y for yellow, W for white, R for red, U for unfinished, T for teak, and C for cherry.
While renovating your house, you have a choice of paint colors for your game room: yellow, white, or red. You also have the following options for the finish on your entertainment center: unfinished, teak, or cherry.
The sample space can then be written as: S = {(Y,U), (Y,T), (Y,C), (W,U), (W,T), (W,C), (R,U), (R,T), (R,C)}Thus, the sample space consists of nine possible outcomes or options.
The sample space for this experiment is composed of all the possible combinations of the two variables (paint color and finish). The possible combinations are:
Therefore, the sample space is {Y + U, Y + T, Y + C, W + U, W + T, W + C, R + U, R + T, R + C}.
Here, the experiment involves choosing a paint color and a finish for a game room and entertainment center respectively. We are given that there are three paint color options and three finish options. Therefore, the sample space can be written as follows:
Let Y, W, and R represent the paint colors yellow, white, and red respectively. Let U, T, and C represent the finish options unfinished, teak, and cherry respectively.
Each outcome is an ordered pair, where the first element represents the paint color option and the second element represents the finish option.
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nick hiked up 10 miles up a hill. he is 8 miles east from his starting point. to the nearest degree, at what angle was the incline of the hill?
The required angle of the incline of the hill, to the nearest degree, is 37 degrees.
How to find the inclined angle?We can use trigonometry to find the angle of the incline of the hill.
we can see that Nick has hiked 10 miles up the hill, and is now at point A. His starting point is at point O, which is 8 miles east of A. Let's call the angle at A, between the incline of the hill and the horizontal ground, theta.
We can use the tangent function to find theta:
[tex]$$\tan(\theta) = \frac{h}{8}$$[/tex]
where h is the height of the hill (the distance from A to the horizontal ground at O).
We know that Nick hiked 10 miles up the hill, so we can use the Pythagorean theorem to find h:
[tex]$$h^2 = 10^2 - 8^2 = 36$$[/tex]
Therefore,
[tex]$$h = \sqrt{36} = 6$$[/tex]
Substituting into the equation for tangent, we get:
[tex]$\tan(\theta) = \frac{6}{8} = 0.75$$[/tex]
To find the angle whose tangent is 0.75, we can use the arctangent function:
[tex]$$\theta = \arctan(0.75)$$[/tex]
Using a calculator, we find that
[tex]$$\theta \approx 36.87^{\circ}$$[/tex]
Therefore, the angle of the incline of the hill, to the nearest degree, is 37 degrees.
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A new cylindrical can with a diameter of 7 cm is being designed by a local company. The surface area of the can is 130 square centimeters. What is the height of the can? Estimate using 3 14 for x, and
round to the nearest hundredth. Apply the formula for surface area of a cylinder SA= 2B+ Ph.
Answer:
see below
Step-by-step explanation:
[tex]SA = 2\pi r \ \ (h+r)[/tex]
[tex]130=2(3.14)(7\div2)(h+(7\div2))[/tex]
[tex]130\div(2(3.14)(7\div2)) = h+(7\div2)[/tex]
[tex]5.91=h+(7\div2)[/tex]
[tex]h = 5.91-3.5[/tex]
Answer Below:
[tex]\bold{x=2.41}[/tex]can yall help me with this I have been up since 7 in the morning and I need some help with this do you think you can help me
Answer: (3/6) then (2/6)
Step-by-step explanation:
FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.
Which of the following expressions are equivalent to a - b? A a Choose all answers that apply: B a + b b a = b None of the above + 0 look at picture giving 80 points
Answer:
None of the above
Step-by-step explanation:
The absolute value of a-b is equal to none of the above. say A was -4, and b was -1. -4 minus -1 is -3. absolute value of -3 is 3. so lets see if any problems equal 3. |a+b| = 5 (absolute value of -4+-1). a-b is -3. ((-4)-(-1))
Janelle wants to enlarge a square photograph that she has made so that each side of the new graph will be 1 inch more than twice the original side g. What trinomial represents the area of the enlarged graph? Make sure to explain your answer.
Answer:
Let's start by assigning a variable to the original side length of the square photograph. We'll use g to represent this length.
According to the problem, each side of the new photograph will be 1 inch more than twice the original side length g. This means that the new side length will be:
2g + 1
Since this is a square photograph, all four sides are equal in length. Therefore, the area of the new photograph can be represented by the square of the new side length:
(2g + 1)^2
To simplify this expression, we can use FOIL (First, Outer, Inner, Last) to expand the squared binomial:
(2g + 1)^2 = (2g + 1)(2g + 1)
= 4g^2 + 2g + 2g + 1
= 4g^2 + 4g + 1
So the trinomial that represents the area of the enlarged photograph is:
4g^2 + 4g + 1
To check our work, we can plug in a value for g and compare the areas of the original and enlarged photographs. For example, if g = 2 (meaning the original side length is 2 inches), then the area of the original photograph is:
2^2 = 4 square inches
And the area of the enlarged photograph is:
4(2)^2 + 4(2) + 1 = 25 square inches
This makes sense, since the new photograph has sides of length 2(2) + 1 = 5 inches, and therefore an area of 5^2 = 25 square inches, which is indeed 1 inch more than twice the original area of 4 square inches.
The ratio of the measures of two angles that form a linear pair are 1:17. What is the measure of the larger of the two angles
The measure of the smaller angle is 10 degrees. We find the measure of the larger angle, we can substitute x = 10 into the expression, the measure of the larger angle is 170 degrees.
When two angles form a linear pair, they are adjacent angles that share a common side and form a straight line. The sum of the measures of these two angles is always 180 degrees.
Let x be the measure of the smaller angle in this problem. Since the ratio of the measures of the two angles is 1:17, we can express the measure of the larger angle in terms of x by multiplying 17 to x. Thus, the measure of the larger angle is 17x.
To find the value of x, we can use the fact that the sum of the measures of the two angles is 180 degrees. So we have:
x + 17x = 180
Simplifying the equation, we get:
18x = 180
Dividing both sides by 18, we obtain:
x = 10
Therefore, the measure of the smaller angle is 10 degrees. To find the measure of the larger angle, we can substitute x = 10 into the expression we derived earlier for the measure of the larger angle:
17x = 17(10) = 170 degrees
Hence, the measure of the larger angle is 170 degrees.
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Jean drove 66 miles per hour for a total of 396 miles on a trip. She used the equation below to calculate the time, t, it would take her to complete the trip. What is the constant of proportionality in the equation?
396 = 66t
A. t
B. 396
C. 66
D. 6
The equation given is:
396 = 66t
This equation relates the distance traveled (396 miles) to the rate of travel (66 miles per hour) and the time it takes to travel that distance (t hours).
We can rearrange this equation to solve for the constant of proportionality, which is the rate of travel:
66t = 396
Dividing both sides by 66, we get:
t = 6
Therefore, the constant of proportionality in the equation is 66. The correct answer is C.
There are 8 finalists in a science fair competition. How many ways can they stand on the stage?
In total, there are 8! (8 factorial) ways that the 8 finalists can stand on the stage. 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320. This means that there are 40,320 possible combinations in which the 8 finalists can stand on the stage.
To calculate this, we can use the formula n!, which stands for n factorial. n! is the product of all the numbers from n down to 1, so 8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This formula can be used to find the total number of combinations that 8 people can stand in on the stage.
It's important to remember that the order matters in this case, so a configuration where the finalists are standing in a line is different from a configuration where they are standing in a circle.
In conclusion, there are 40,320 ways in which the 8 finalists can stand on the stage. This can be determined by using the formula n!, which stands for n factorial.
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Hot dogs at a carnival cost $2. 99 each plus 7% tax what is the total cost for one hot dog?
Graph the numbers that are solutions to x−3≤8 and 6x<72 .
can u send a visual picture of the graph?? (94 points)
The graph fοr the sοlutiοns οf the inequalities have been plοtted and attached belοw.
What is an inequality?A relatiοnship in mathematics knοwn as an inequality cοmpares twο numbers οr οther mathematical expressiοns in an unfair manner.
Mοst frequently, size cοmparisοns are dοne between twο numbers οn the number line.
We are given twο inequalities as x - 3 ≤ 8 and 6x < 72.
Nοw, οn sοlving the first inequality, we get⇒ x - 3 ≤ 8⇒ x ≤ 11Similarly, οn sοlving the secοnd inequality, we get⇒ 6x < 72⇒ x < 12
Nοw, οn the graph the sοlutiοns are plοtted and attached belοw. The red pοint represents the secοnd inequality sοlutiοn and the blue represents the first inequality sοlutiοn.
Hence, the graph fοr the sοlutiοns οf the inequalities have been plοtted.
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Which correctly describes a cross section of the cube below? Check all that apply.
A cube with 4 centimeter sides.
A cross section parallel to the base is a square measuring 4 cm by 4 cm.
A cross section parallel to the base is a rectangle measuring 4 cm by greater than 4 cm.
A cross section perpendicular to the base through the midpoints of opposite sides is a rectangle measuring 2 cm by 4 cm.
A cross section perpendicular to the base through the midpoints of opposite sides is a square measuring 4 cm by 4 cm.
A cross section that passes through the entire bottom front edge and the entire top back edge is a rectangle measuring 4 cm by greater than 4 cm.
Point A (-3,-3) to A' is a glide reflection where the translation is (x+2, y) and the
line of reflection is y=1? What are the new coordinates?
O(-3,8)
O(-2,-2)
O (5,-1)
O (-1,5)
The new coordinates is A'(-1,5) which is glide reflection of point A(-3,-3) where the translation is (x+2,y) and the line of reflection is y = 1.
What is Glide Reflection?Glide Reflection, it is known as composition of transformations.
In glide reflection, before reflected over a line it translation is first performed on the figure.
The coordinate of A are given as (-3,-3).
The rule of translation is (x, y) → (x+2,1) and the line of reflection is y=1.
Now,
Applying the rule of translation, we get;
A = (-3, -3) → (-3+2, -3) = (-1, -3)
Since, -3 which is 4 unit below line of reflection,
then,
after reflection, over the line y=1 we get, the reflected point A' would be 4 units above line of reflection
so, A' (-1, 1+4) =(-1, 5)
Therefore, the coordinate of A' (-1, 5).
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When a car goes around a curve at twice the speed, the centripetal force on the car doubles. (True or False)
Answer:
True
Step-by-step explanation:
A book sold 42800 copies in its first month of release. Suppose this represents 7. 3 of the number of copies sold to date. How many copies have been sold to date?
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets. So far, 312440 copies have been sold.
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means.
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets.
We are given that the copies sold on first release date= 42800 copies.
And this is the 7.3 of the number of copies sold on date.
So, let the number of copies sold out on date is x.
Therefore, x= 7.3*42800 OR [tex]x= \frac{73}{10} * 42800= 73*4280= 312440[/tex]
Hence, the number of copies sold out on the date are 312440.
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through: (-4,-3), parallel to y=2x+4
Whts this in slope int form
Answer:
y=2(x+4)-3
Step-by-step explanation:
To make it parallel to y=2x+4, the slope needs to be the same
Point-slope form is: y=m(x-x1)+y1
In this case,
m = 2
x1 = -4
y1 = -3
So when put into point-slope form, it is y=2(x+4)-3
(anyone who answers gets brainliest) Pick the correct trig tool to solve for the variables. There’s a solve for x problem I was struggling with. You don’t have to do them all, thank you
Answer:
(anyone who answers gets brainliest) Pick the correct trig tool to solve for the variables. There’s a solve for x problem I was struggling with. You don’t have to do them all, thank you
Step-by-step explanation:
2 screenshots!!
giving brai. to whoever can solve both of them correct
What is the equation of the line that passes through the point (-9,6) and is perpendicular
to the line 3x-5?
M
Oy--x-3
О У - 3x + 21
Oy - 3x +33
Answer:
y = (-1/3)x + 3.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.
The slope of the given line Y=3x-5 is 3. Therefore, the slope of a line perpendicular to this line would be -1/3.
Now, using the point-slope form of a line, we can write the equation of the line passing through (-9,6) and having a slope of -1/3:
y - 6 = (-1/3)(x - (-9))
Simplifying:
y - 6 = (-1/3)x - 3
y = (-1/3)x + 3
Therefore, the equation of the line that passes through (-9,6) and is perpendicular to the line Y=3x-5 is y = (-1/3)x + 3.
I dont know how to do this
pls answer if u know with simple working
Answer:
21. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Find the function value.
csc330° =
2
-2√3/3
2√3/3
-2
The function value is csc 330° = -2.
A function formula: what is it?Function establishes the relationship between input and output. The x-intercept, y-intercept, and slope of any function are calculated using function formulas. You could also figure out the vertex of a quadratic function. Moreover, a graph of the function can be created for a range of x values.
Since the sine of 360 degrees (which has a sine of 0) is similar to 30 degrees being subtracted from it, we can determine using the unit circle that the sine of 330 degrees is equal to -1/2 and thus the sine function is negative in the fourth quadrant. The reciprocal of sine 330 degrees, which is -2/1 or -2, is the cosecant of 330 degrees.
Thus, csc 330° = -2.
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The following table specifies the joint distribution of Age group (3 levels) and Education level (4
levels) for U.S. adults.
Education Level
Age group Not HS grad HS only Some college College grad
25–44 77 101 99 123
45–64 123 171 46 60
65+ 101 59 20 20
(a) Summarize the association between these variables by reporting the 2 ×3 table of local odds
ratios
θij = πij πi+1,j+1
πi,j+1πi+1,j
for i = 1,2 and j = 1,2,3 .
Identify the odds ratio corresponding to the strongest of these pairwise associations, and
carefully interpret that odds ratio.
(b) Summarize the association between these variables by reporting the 2×3 table of odds ratios
θij = πij π14
πi4π1j
for i = 2,3 and j = 1,2,3 ;
that is, treating the youngest age group and highest education level as baseline categories
for comparison. Identify the odds ratio corresponding to the strongest of these pairwise
associations, and carefully interpret that odds ratio.
(a) 25-44
(b) 45-64
(a) The 2×3 table of local odds ratios for the association between age group and education level is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.78, which indicates that adults aged 45-64 are 78% more likely to have a high school diploma than adults who are 25-44.
(b) The 2×3 table of odds ratios for the association between age group and education level when treating the youngest age group and highest education level as the baseline categories for comparison is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.48, which indicates that adults aged 25-44 are 48% more likely to have a high school diploma than adults aged 45-64.
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Kylie invested $2,800 in an account paying an interest rate of 5. 5 % compounded annually. Ariana invested $2,800 in an account paying an interest rate of 5. 75% compounded continuously. After 12 years, how much more money would Ariana have in her account than Kylie, to the nearest dollar?
After 12 years, Ariana would have 366.65 more in her account than Kylie, to the nearest dollar.
The formula used to calculate the amount of money Ariana would have in her account after 12 years is [tex]A = Pe^rt[/tex], where A is the amount of money, P is the principal amount (initial investment), e is the mathematical constant (2.71828), r is the rate at which interest is compounded, and t is the time (in years).
Kylie's total amount after 12 years would be calculated using [tex]A = 2800(1.055)^12[/tex], while Ariana's total amount would be calculated using [tex]A = 2800(2.71828)^(0.0575*12)[/tex].
After substituting the values into the formulas, Kylie would have 4,841.22 in her account and Ariana would have 5,207.87 in her account. This means that Ariana would have 366.65 more than Kylie in her account, to the nearest dollar.
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Using transformations, create a design for fabric that represents you as a person to be used on project runway. How will you combine transformations to move your design around the fabric? what combination of transformations was used to create your design?
Combined translation, rotation, reflection, and enlargement to create a vibrant average pattern on fabric that represents me.
My design would consist of a colorful pattern with a variety of forms, including circles, triangles, squares, and stars. I would mix several transformations, such as translation, rotation, reflection, and enlargement, to get this design. I would first create the shapes and then move them across the cloth using translation and transformation. The forms would then be rotated using the rotation transformation. I would also apply the reflection transformation to the same forms to produce a mirror appearance. Ultimately, I would enhance certain forms while reducing others using the transformation. The cloth would have a distinctive and dynamic appearance that symbolizes me as a person thanks to this mix of alterations.
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4. A submarine is traveling a 375 feet below sea leven
rises183 feet and then dives 228 feet if the subm
come safely to the surface at 30 feet per second how many seconds will it take to reach the surface?
97
The submarine will take 14 seconds to safely reach the surface.
What is Speed?Speed is a measure of how quickly an object is moving, calculated as the distance traveled per unit time.
The submarine rises 183 feet, which means its depth decreases by 183 feet. Therefore, its depth is now 375 - 183 = 192 feet below sea level.
The submarine then dives 228 feet, which means its depth increases by 228 feet. Therefore, its depth is now 192 + 228 = 420 feet below sea level.
To reach the surface, the submarine needs to ascend a distance of 420 feet.
The speed of the submarine is given as 30 feet per second. Therefore, the time it will take for the submarine to reach the surface can be calculated as:
[tex]Time = \frac{Distance}{Speed} = \frac{420}{30}[/tex]
= 14 seconds
Therefore, it will take the submarine 14 seconds to safely reach the surface.
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What is
4y+6x=18
3y-2x=33
Answer:
x = -3 and y = 9
Step-by-step explanation:
Solving system of linear equations by elimination method:4y + 6x = 18 -----------------(I)
3y - 2x = 33 -----------------(II)
Multiply equation (II) by 3.
(I) 4y + 6x = 18
(II)*3 9y - 6x = 99 {Now add the equations}
13y = 117
Divide both sides by 13,
y = 117 ÷ 13
[tex]\boxed{\bf y = 9}[/tex]
Substitute y = 9 in equation (I) and obtain the value of 'x',
4*9 + 6x = 18
36 + 6x = 18
Subtract 36 from both sides,
6x = 18 - 36
6x = -18
Divide both sides by 6
x = -18 ÷ 6
[tex]\boxed{\bf x = -3}[/tex]
[tex] \\ 4y + 6x = 18 \\ \\ 6x= 18 - 4y \\ = x = 3 - \frac{2}{3 }y \\ x = - \frac{2}{3} y+ 3[/tex]
In triangle FGH, what is m∠F + m∠G + m∠H
?
°
Since, the triangle FGH is a right angle triangle, The angles of the ∠F = 62°, ∠G = 90° and ∠H = 28°.
Right Angle Triangle:
A right triangle (American English) or right triangle (UK), or more formally an orthogonal triangle, formerly known as a right triangle, is a triangle in which one angle is a right angle (i.e. say an angle of 90 degrees), i.e. two of its sides are perpendicular. The relationship between the sides of a right triangle and the other angles is the basis of trigonometry.
According to the Question:
Interior angles of a triangle add up to 90 degrees
∠F + ∠ G + ∠H = 180
⇒ 9x - 1 + 90 + 3x + 7 = 180
⇒ 12x + 96 = 180
⇒ 12x = 180 - 96
⇒ 12x = 84
⇒ x = 84/12
⇒ x = 7
Therefore,
∠F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62
And, ∠G = 90
And, ∠ H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28
If we add the angles :
62 + 90 + 28 = 180°
Complete Question:
Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?
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HElp pleaseeeeeeeeeeeee
what are the answer choices?
Answer:
3/4
Step-by-step explanation: