The correct option is- I, IV. Fixed Annuity and Traditional IRA are the plans are not considered a defined contribution plan.
Explain about the contribution plan:In contrast, a defined contribution plan does not guarantee a certain level of benefits at retirement. Under these plans, either the employee or even the employer (or both) may make contributions to the owner's individual account under the plan.
These contributions may be made at a specified rate, such as 5% of annual earnings. Usually, the employee's money is invested with these contributions.401(k) plans, 403(b) plans, stock ownership plans for staff, and profit-sharing plans are a few types of defined contribution plans.Traditional IRA:
An individual retirement account (IRA) of this type allows your income to increase tax-free. Only when you take withdrawals in retirement do you have to pay taxes on the investment earnings.
Fixed Annuity:
A fixed annuity is a financial contract that offers a retirement income stream and guarantees a certain rate of return, such as 2%. You can predict how much your annuity will increase and how much money it will produce by using a set interest rate.
Thus, Fixed Annuity and Traditional IRA are the plans are not considered a defined contribution plan.
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look at the picture below
The surface area of the composite solid is given as follows:
194 units squared.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The prism in this problem is composed as follows:
Rectangular prism of dimensions 4, 7 and 3.Two right triangles of dimensions 4 and 3.One square of side length 5.One rectangle of dimensions 5 and 7.Hence the surface area of the prism is given as follows:
S = 2(4 x 7 + 4 x 3 + 3 x 7) + 4 x 3 + 5² + 5 x 7
S = 194 units squared.
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3. "Frank has four different credit cards, the balances and interest information of which are outlined in the table below.
He would like to consolidate his credit cards to a single credit card with an APR of 18% and pay off the balance in 24 months.
What will his monthly
credit card payment be?
Hint use the monthly payment formula where PV = (all balances combined), i=0.18/12, and n=24
A. $390.00
B. $462.91
C. $454.31
D. $52.00
Answer:
Therefore, Frank's monthly credit card payment will be $454.31.
Step-by-step explanation:
Monthly payment = (PV * r) / (1 - (1 + r)^-n)
PV = $2,500 + $1,000 + $3,000 + $1,500
= $8,000
r = 0.18 / 12
= 0.015
Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)
= $454.31
Can anybody help me on the question.
ASAP
The hanger in the illustration will have the value x = 6, and it will remain balanced.
Define equations?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.
Here's the query,
Considering the graph,
The hanger's equation is as follows:
4x= 24
There are 4 numbers here that represent the value of the hanger.
So, x+x+x+x will be 24.
The equation is thus:
4x = 24.
Now, by resolving the equation, we can determine the value of x that balances the hanger:
4x = 24.
When you divide 4 on both sides:
x = 24/4
x = 6.
As a result, the hanger will remain in equilibrium for x = 6.
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What is m∠a?
A straight angle divided by a ray into two angles. The smaller angle has a measure of 50 degrees.
40°
50°
90°
130°
When Joann and Shana were counting the amount of money they had in their wallets, the total was at least$56 and at most $85. If Shana has only in her wallet, which of the following inequalities represents all possible values for the amount of money, j, that Joann has?
The inequality that represents all possible values for the amount of money that Joann has is 21 ≤ J ≤ 50.
What inequalities represents values for the amount of money that Joann has?Let's call the amount of money that Joann has in her wallet "J" and the amount of money that Shana has in her wallet "S".
We know that the total amount of money they have is at least $56 and at most $85. Therefore, we can write two inequalities:
J + S ≥ 56 (the total is at least $56)
J + S ≤ 85 (the total is at most $85)
We also know that Shana has only $35 in her wallet. We can substitute this value for S in the inequalities to get an inequality that represents all possible values for the amount of money that Joann has:
J + $35 ≥ 56 (substituting S = $35 in the first inequality)
J + $35 ≤ 85 (substituting S = $35 in the second inequality)
Simplifying these inequalities by subtracting $35 from both sides, we get:
J ≥ 21 (the amount of money Joann has is at least $21)
J ≤ 50 (the amount of money Joann has is at most $50).
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URGENT Complete the table.
It is in the image below
Answer:
Step-by-step explanation:
Step-by-step explanation:
4=2×2
8=2×4
12=2×6
16=2×8
20=2×10
24=2×12
if 8 out of 12 marbles in a bag are green, what is the probability that a marble selected at random from the bag will NOT be green?
Answer:
The Probability that a marble selected at random from the bag will NOT be green is 1/3
Step-by-step explanation:
The probability of selecting a green bag
= Total No.of green bags/ Total number of bags
=8/12
= 2/3
Then the probability not of selecting a green bag
= 1 - The probability of selecting a green bag
= 1-(2/3)
= 1/3
. Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance. Because a clerk mistakenly discarded some labor records, however, Ellen has only partial data for April. She knows that the total direct-labor flexible-budget variance was $1,643 favorable. Moreover, a recent pay raise produced an unfavorable labor price variance for April of $1,157. The actual hours of input were 1,780 and the standard labor price was $20 per hour. 1. Find the actual labor rate per hour 2. Determine the standard hours allowed for the output achieved.
Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.
1. Actual Labor Rate per Hour:
The labor price variance formula is:
Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours
We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:
-1,157 = (Actual Labor Rate - 20) x 1,780
-1,157 = 1,780Actual Labor Rate - 35,600
1,780Actual Labor Rate = 34,443
Actual Labor Rate = 19.35
Therefore, the actual labor rate per hour for April was $19.35.
2. Standard Hours Allowed for the Output Achieved:
The flexible-budget variance formula is:
Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate
We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.
Using the formula above and plugging in the known values, we can solve for the standard hours allowed:
1,643 = (1,780 - Standard Hours) x 20
1,643 = 35,600 - 20Standard Hours
20Standard Hours = 33,957
Standard Hours = 1,697.85
Therefore, the standard hours allowed for the output achieved in April was 1,697.85.
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What is the equation in point-slope form of the line that passes through the points (7,5) and (−4,−1) ? Responses y+1=67(x+4) y plus 1 equals fraction 6 over 7 end fraction left parenthesis x plus 4 right parenthesis y+1=611(x+4) y plus 1 equals fraction 6 over 11 end fraction left parenthesis x plus 4 right parenthesis y+4=116(x+1) y plus 4 equals fraction 11 over 6 end fraction left parenthesis x plus 1 right parenthesis y−1=611(x−4)
The line that goes through the specified points has the equation into point-slope form is [tex]y+1=6/11(x+4)[/tex].
What is a straight line equation?X-axis points equal (7, -4).
Y-axis points are equal to (5, -1).
To determine the equation of the line passing through the specified points in point-slope form:
A straight line equation's direction and steepness are commonly described by its slope, which is also known as a line's gradient.
In mathematics, the following formula yields the slope of a line:
Slope(m) = [tex]y2-y1/x2-x1[/tex]
slope= [tex]\frac{-1-5}{-4-7}[/tex]
slope= 6/11
To find point slope:
[tex]y-y1=m(x-x1)\\y-(-1)=6/11(x-(-4)\\y+1=6/11(x+4)[/tex]
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b) d=22,4 mm d) d= 7 km f) r=0,5 hm h) r= ² kr km 3 C≈ C≈ C≈ C≈
The height is 230 feet after 9.125 seconds.
How do we calculate?We have the equation that describes the height of the object as a function of time as:
h(t) = -16t^2 + 145t + 2
We input the values and simplify:
-16t^2 + 145t + 2 = 230
-16t^2 + 145t - 228 = 0
we can use the quadratic formula, to solve this quadratic equation,
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -16, b = 145, and c = -228.
t = (-145 ± √(145^2 - 4(-16)(-228))) / 2(-16)
t = (-145 ± √ (21025)) / (-32)
t = (-145 ± 145) / (-32)
t = 0.625 seconds or t = 9.125 seconds
In conclusion, the height is 230 feet after 9.125 seconds.
#complete question:
An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
The diagram below not drawn to scale. Shows a triangle ABC which represent; the cross-section of a roof. BD is the perpendicular to ADC. Calculate the A) length= BD
B) measure of angle CBD
c) area of triangle ABC
d) bearings of B and C
Answer) : B measure of angle CBD
Step-by-step explanation: BD is perpendicular to ADC now we know that there is no scale so all you have to do is measure the length and we gat that answer.
Find the range of the list of values. 3, 16, 22, 25, 24, 23, 16, 16
Answer:
range = 22
Step-by-step explanation:
the range is the difference between the largest and smallest values in the data set.
largest value = 25 , smallest value = 3
range = 25 - 3 = 22
ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB?
Answer:
We can use trigonometry to find AB.
First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:
A + B + C = 180°
A + 90° + 30° = 180°
A = 60°
Now, we can use the sine function to find AB:
sin A = opposite/hypotenuse
sin 60° = AB/96
AB = 96 * sin 60°
AB = 96 * √3/2
AB = 48√3
Therefore, AB is approximately 83.14 cm (rounded to two decimal places).
A normal distribution has a mean of19 and a standard deviation of . What percent of values are from 19 to 34
what is the % of the values from 19to 34
It should be noted that 49.87% of the values fall between 19 and 34 in the original normal distribution.
How to calculate the percentageFor the lower bound of 19, the z-score is:
z = (19 - 19) / 5 = 0
For the upper bound of 34, the z-score is:
z = (34 - 19) / 5 = 3
Looking up the area under the curve for a z-score of 3 in a standard normal distribution table, we find it to be 0.9987. Looking up the area under the curve for a z-score of 0, we find it to be 0.5. Therefore, the area under the curve between z-scores of 0 and 3 is:
0.9987 - 0.5 = 0.4987 = 49.87%
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Describe a real-world problem that can be modeled by a circle.
A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.
Describe a real-world problem that can be modeled by a circle.Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.
This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.
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A checkout clerk at a department store is expected to complete 16 transactions every hour.
In the past 20 minutes, he completed 6 transactions.
Choose True or False for each statement.
Statements:
If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
At his current rate, the clerk will complete 12 transactions in 1 hour.
At his current rate, the clerk will complete 9 transactions every half hour.
If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
✓ - True If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
➜ This is true. The clerk is currently going at 6 transactions per 1/3 hours. 6 * 3 = 18, and 18 > 16.
✗ - False At his current rate, the clerk will complete 12 transactions in 1 hour.
➜ This is false. As stated above, he will complete 18.
✓ - True At his current rate, the clerk will complete 9 transactions every half hour.
➜ Let us set up a proportion to check. Then we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{30\;min}{x}[/tex]
180 = 20x
x = 9
➜ Yes, he will complete 9 every half hour.
✗ - False If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
➜ We can utilize a proportion again. 6 hours is equal to 360 minutes. Then, we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{360\;min}{x}[/tex]
20x = 2,120
x = 106
➜ He will complete 106 transactions, not 96. It depends on if they're asking for exactly 96 or at least 96.
A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 17 years with a variance of 16 . If the claim is true, in a sample of 43 wall clocks, what is the probability that the mean clock life would be less than 17.9 years? Round your answer to four decimal places.
There is a 0.9830, or 98.30%, probability that the mean clock life will exceed 12.5 years.
What is probability?Probability is a metric used to express the possibility or chance that a particular event will occur.
Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
So, the likelihood that the average clock life would exceed 12.5 years:
This is the p-value of Z when X = 12.5 subtracted by 1.
So,
Z = X - μ/σ
Z = 12.5 - 14/.07071
Z = -2.12
Z = The pvalue for -2.12 is 0.0170.
1 - 0.0170 = 0.9830
The likelihood that the mean clock life will be longer than 12.5 years is 0.9830, or 98.30%.
Therefore, there is a 0.9830, or 98.30%, probability that the mean clock life will exceed 12.5 years.
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Complete question:
A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 14 years with a variance of 25. If the claim is true, in a sample of 50 wall clocks, what is the probability that the mean clock life would be greater than 12.5 years? Round your answer to four decimal places.
At the school's holiday craft fair, Colette and her classmates get to make gingerbread houses. Their teacher divides a bag of licorice ropes evenly among the 9 students at the table. Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.
Answer: So, what are you asking?
Step-by-step explanation:
5. Jennifer solved a math problem. The answer. to her problem was in square inches. Which formula did Jennifer most likely use to solve her problem?
A P=(2xl) + (2xw)
B V=SxSxS
C P= 4xs
D A= SXS
Answer:
D. A = s × s
Step-by-step explanation:
D. A = s × s is an area formula. Area is side times side. This is an area formula for a square. The units of area are square units. Since Jennifer has square inches in her answer, she was working on an area problem.
A. and C. are perimeter formulas. Perimeter is the distance around the outside of a shape. The units of perimeter are straight up plain, one-dimensional units like inches (or feet, meters, miles, km)
B. is a volume formula. The units of volume is cubic units or units to the third power.
The answer is D.
The function = 50 − 1.6 can be used to determine the amount, in fluid ounces, of laundry detergent remaining after x loads of laundry have been done. What is the rate of change amount of laundry in fluid ounces with respect to the number of loads of laundry that have been done?
The rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.
What is linear equation?Any equation that has terms that are either constants or the product of a constant and a variable of the first degree (exponent 1) is said to be linear. In other words, the equation's greatest degree for any variable is 1. One way to express a linear equation is as follows:
ax + b = 0
If an is not equal to zero, a and b are constants, and x is the variable. This is how a linear equation is typically expressed.
The given function is f(x) = 50 - 1.6x.
Now, the rate of change is the slope of the equation.
Comparing the equation with that of the linear equation y = mx + c we see that the slope is -1.6.
Hence, the rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.
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Can you prove this trigonometric identity?
tan1/2x(2cotx+tan1/2x)=1
The trigonometric identity has been proven as 1 in the space below
How to prove the identityGiven the identity:
tan(1/2x) (2cot(x) + tan(1/2x)) = 1
To prove this identity, let's start by expressing cot(x) in terms of tan(x):
cot(x) = 1 / tan(x)
Now, replace cot(x) in the given identity:
tan(1/2x) (2(1/tan(x)) + tan(1/2x)) = 1
Now, let's use the double angle formula for tan(x):
tan(x) = 2 * tan(1/2x) / (1 - tan^2(1/2x))
Replace tan(x) in the equation:
tan(1/2x) (2(1/(2 * tan(1/2x) / (1 - tan^2(1/2x))) + tan(1/2x)) = 1
Simplify the equation:
tan(1/2x) ((1 - tan^2(1/2x)) + tan(1/2x) * tan(1/2x)) = 1
Now, notice that the expression in the parentheses is equal to 1:
(1 - tan^2(1/2x)) + tan^2(1/2x) = 1
So, we can simplify the equation further:
tan(1/2x) * 1 = 1
This directly leads us to the original identity:
tan(1/2x) = 1
Thus, the trigonometric identity is proven.
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Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
no
Yes, (3, 5) is a solution to this system of equations.
How do you calculate the equation system?
The system has a single solution if the m-values of the two equations differ. The system has no solution if the two equations have the same m-value but distinct b-values.
Substituting x = 3 and y = 5 into the equations, we get:
y = 5 (which is already given)
y = (-5/3)x + 10
y = (-5/3) * 3 + 10
y = -5 + 10
y = 5
Therefore, both equations are satisfied by the point (3, 5), making it a solution to the system of equations.
Yes, (3, 5) is a solution to this system of equations.
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
m + 2(m + 1) = 14 {4}
The equation simplifies to 14 = 14, which is a true statement.
What is the purpose of the equation?In mathematics, an equation is defined as a set of numbers that contains operations and may contain a variable. Equations are used to solve for these unknown variables using various operations such as addition, subtraction, multiplication and division.
Replacing m by 4, we get:
m + 2 (m + 1) = 14
4 + 2 (4 + 1) = 14
4 + 2(5) = 14
4 + 10 = 14
14 = 14
The equation simplifies to 14 = 14, which is a true statement. Therefore, the given value 4 is a solution to Eq.
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Use slopes and y-intercepts to determine if the lines 15x−6y=−5 and 5x−2y=5 are parallel.
The two lines are parallel because they have thesame slope and different y intercept
How do we know parallel lines?If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.
15x-6y = -5
-6y = -15x-5
y = 5x/2 +5/6
for the second equation,
5x-2y =5
-2y = -5x-5
y = 5x/2 +5/2
therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.
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The___is the sum of the lengths of the sides of a closed figure. A-apothem B-area C-total D-perimeter
Answer: D-perimeter
Step-by-step explanation: The sum of the lengths of all the sides of a closed figure is called its perimeter.
Answer:
Perimeter
Step-by-step explanation:
The sum of the lengths of all the sides of a closed figure is called its perimeter.
The frequency table represents the fraction of an hour
Rita spends writing in her journal each night. Represent
this data in the line plot.
16. What fraction of an hour did Rita spend most days
writing?
17. What is the difference between the greatest amount
of time spend writing and the least?
A line plot that represents the data is shown in the image attached below.
A fraction of an hour which Rita spend most days writing is 3/4.
The difference between the greatest amount of time spend writing and the least is 3/4.
What is a line plot?In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.
Additionally, we can logically deduce that the mode of the data set is equal to 3/4 (the fraction of an hour Rita spend most days writing) because it has the highest frequency of 5.
Difference = greatest amount of time - least amount of time
Difference = 1 - 1/4
Difference = 3/4.
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Find the measure of angle A.
A
8x + 2
10x - 4
38°
Answer:
8x + 2 + 10x - 4 + 38 = 180
18x + 36 = 180
18x = 144, so x = 8
Angle A measures 8(8) + 2 = 64 + 2 = 66°.
I really need help with this two please help to find x value and explain with reasons
In the first triangle, the angle x = 45°
In the second triangle, the angle y = 75°
In the second triangle, the angle x = 45°
How to find the angles in the triangles?To find the angles in the triangles, we proceed as folows.
a. In the first triangle, let the base angle to the left be p. We know that we have a parallelogram there.
Now, in the parallelogram,
102° + p = 180°sum of (interior angles of a parallelogram)
So, p = 180° - 102°
= 78°
Now, in the larger triangle,
x + p + 57° = 180° (sum of angles in a triangle)
Since p = 78°, we have that
x + 78° + 57° = 180°
x + 135° = 180°
x = 180° - 135°
= 45°
So, x = 45°
b. In figure 2, we have two isoceles triangles.
i. In the first triangle, both base angles are y.
So, y + y + 30° = 180° (sum of angles in atriangle)
2y + 30° = 180°
2y = 180° - 30°
2y = 150°
y = 150°/2
y = 75°
So, y = 75°
ii. In the second triangle also, both base angles are x and the other angle is a right angle which is 90°.
So, x + x + 90° = 180° (sum of angles in a triangle)
2x + 90° = 180°
2x = 180° - 90°
2x = 90°
x = 90°/2
x = 45°
So, x = 45°
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Word problem down below: Fairly easy.
Based on the word problem, the answer is not one of the given options (E. NOTA).
How to explain the word problemIn this case, we have 9 letters and we want to select all of them, so n = 9 and r = 9. Therefore:
A = 9!
A = 362,880
B) The hypotenuse of a right triangle can be found using the Pythagorean theorem:
c^2 = a^2 + b^2
In this case, we have a = 9 and b = 12. Therefore:
c^2 = 9^2 + 12^2
c = 15
So, B = 15.
y - 9 = 3(x - 6)
y - 9 = 3x - 18
y = 3x - 9
The y-intercept of this line is -9, so C = -9.
Therefore, A + B + C = 362,880 + 15 - 9 = 362,886.
So the answer is not one of the given options (E. NOTA).
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which of the following equations can be used to find the misssing angle x in triangle 42
The equation in the triangle to find x is x + 84 = 180.
Option B is the correct answer.
We have,
The sum of the angles in a triangle is 180.
And,
42 + 42 + x = 180
84 + x = 180
x = 180 - 84
x = 96
Thus,
The equation in the triangle to find x is x + 84 = 180.
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