In the figure below, what is the value of x if angles m and n are congruent?
Answers
We want to find the measure of x given that we know that m and n are congruent.
The measure of x is 116°.
Two angles are congruent if they have the same measure.
Then we have ∠n = ∠m
We also know that the sum of all interior angles of a triangle is equal to 180°, then if we look at the smaller triangle we have that:
114° + ∠n + ∠m = 180°
∠n + ∠m = 180° - 114° = 66°
Knowing that these measures are equal we can write:
2*∠m = 66°
∠m = 66°/2 = 33°
Now that we know the measure of m, we can do the same thing for the larger triangle:
∠x + ∠m + 31° = 180°
∠x + 33° + 31° = 180°
∠x = 180° - 64° = 116°
The measure of x is 116°.
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Applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]
Recall:
Sum of triangles = 180 degrees
Exterior angle = sum of two interior opposite angles
Since we know that angles m and n are congruent, therefore:
[tex]m = \frac{1}{2} (180 - m \angle RTU)[/tex]
Substitute[tex]m = \frac{1}{2} (180 - 114)\\\\\mathbf{m = 33^{\circ}}[/tex]
Find x (exterior angle of triangle SUV):
[tex]x = 31 + m[/tex] (exterior angle of a triangle theorem)
Substitute[tex]x = 31 + 33\\\\\mathbf{x = 64^{\circ}}[/tex]
Therefore, applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]
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Related Questions
TRUE/FALSE: The slope of the line that is PEREPNDICULAR to this line is -3/2.
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Answer:
True
Step-by Step Explanation:
Find the measure of the indicated arc.
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Hope this helps :D
Look at the picture I need help
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Answer:its 7 because half of 14 cp=14 so pd =7
Step-by-step explanation:
In a sandwich shop, 22% of the sandwiches they sell are ham. What is 22% written
as a decimal?
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Answer:
0.22
Step-by-step explanation:
It is 0.22 written as a decimal instead as a percent%.
What's the square root of 17 rounded to the nearest tenth
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Answer:
4.0
Step-by-step explanation:
Answer:
4.1
Step-by-step explanation:
4.1231056 is [tex]\sqrt{17}[/tex]
When rounding to the nearest tenth, we get
4.1
Hope I helped,
PumpkinSpice1
Giving 15 points plz plz help me
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Mark and his 3 friends are out at Applebee's. Their bill totaled $52.35. If they left the server a 20% tip, how much would each person pay splitting the bill evenly
Answers
i'll mark you as brainliest
Answers
Answer:
y=x+30
Step-by-step explanation:
use y2-y1/x2-x1 to find the slope
the y-int is 30 since looking at the answer choices
Answer:
y=x+30
Step-by-step explanation:
What’s the value of c ? Just type in the answer!!!
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Answer:
43
Step-by-step explanation:
Aretha Foster, single, is marketing director for
The Canterbury Community, a senior living center. She is paid
a weekly salary of $735.00. If her weekly federal income tax
withholding is $66.84, find the number of withholding allowances
she claims if the tax is computed using the percentage method.
Answers
Answer:
11.14 brailiest please
Step-by-step explanation:
Find the factors of function f, and use them to complete this statement.
f(x)= 2x^4 - x^3 -18x^2 + 9x
Answers
Answer:
-3, 0, 1/2, 3
The factors of function f is -3, 0, 1/2, 3
We have given that,
the factors of function f, and use them to complete this statement.
f(x)= 2x^4 - x^3 -18x^2 + 9x
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
We have to determine the factor of the given function
[tex]2x^4 - x^3 -18x^2 + 9x =0[/tex]
[tex]x(2x^3-x^2-18x+9)=0[/tex]
[tex]x=0 \ and \ 2x^3-x^2-18x+9=0[/tex]
[tex]2x^3-x^2-18x+9=0[/tex]
[tex]2x-1=0\quad \mathrm{or}\quad \:x+3=0\quad \mathrm{or}\quad \:x-3=0[/tex]
Therefore the factors [tex]2x^3-x^2-18x+9=0[/tex] are
[tex]x=\frac{1}{2},\:x=-3,\:x=3[/tex]
-3, 0, 1/2, 3
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−x + y = 2 2x + 4y = 32 What action was completed to create this new equivalent system of equations? −x + y = 2 x + 2y = 16
A. Divide the second equation, 2x + 4y = 32, by 2.
B. Divide the first equation, −x + y = 2, by 2.
C. Multiply the second equation, 2x + 4y = 32, by −1.
D.Multiply the first equation, −x + y = 2, by −1.
Answers
Answer:The answer is A
Step-by-step explanation:
Six girls of differing heights are arranged in 2 rows of 3 each. Each girl is taller than the girl in front of her and also taller than the girl to her right. How many arrangements of the six girls are possible?
Answers
Answer:
5 possible ways
Step-by-step explanation:
Questions like this are a bit technical. Therefore, there are no perfect formula, all you have to do is picture the scene and count. Having said that. Let us use name the positions the girls are standing according to the question:
D E F
A B C
I have arranged this according to how the question has specified, meaning F is the tallest and A is the shortest if I take F to be at the back right and A to be at the front left.
In reality, A and F can never change their positions if we maintain the arrangement specified.
What we have left is to look for how to rearrange, D, E, B and C that will still make it fit the arrangement. Take note that E cannot be in front of B because she is taller than B.
Since positions for shortest and tallest are fixed, you are left with 4 people and you need two of them for the front position. This can be gotten using 4C2 = 6, but the two tall persons can't be in the front else it will disrupt the arrangement, so we have to eliminate that case which will occur once, therefore we have 5 possible ways we can make the arrangements as required.
Plz quick can some one help me with these two questions also plz show working out
Answers
total salary = £3600 x 4 = £14400
total amount of salary spent
= (£14400x20%) + (2/5 x £14400) + £3600
= £2880 + £5760 + £3600
= £12240
total amount saved
= £14400 - £12240
= £2160
23a. amount anwar saves = 12%
= 0.12 of his salary
amount bethany saves = 1 - 7/8
= 1/8 = 0.125 of her salary
hence, bethany saves more money each week.
The absolute value of ______ is the same number
Fill in the blank
Answers
Answer: I dont know what the fill in the blank would be, but simply make any number not negative
Step-by-step explanation: Example |-3| = 3
there are always positive
4 fl oz for $8.36 unit rate
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Answer:
I'm pretty sure it's $2.09 for 1 fl oz.
Three more than the product of a number and 5 is equal to 6.
Answers
5x + 3 = 6
5x = 3
x = 3/5 or .60
5x = 3
x = 3/5
What is the slope of the line that passes through the points (2, 6) and (-1, -9).
Answers
Hey again.. Please answer!!
Answers
Answer:
I can't see the question
its too small can you type it out?
Step-by-step explanation:
Answer:
32 cups and 24 cups
Step-by-step explanation:
4x + 3x = 56
7x = 56
x = 8
4(8) = 32 cups of pretzels
3(8) = 24 cups of candy corn
SOMEONE HELP I DONT KNOW WHAT THE HECK IM DOING (7th grade)
Answers
Answer:
Step-by-step explanation:
I'm 8th grade, G
For this problem, you can start by taking the 35 and dividing it by 5 to get 7. Then you need to take 300 and divide that by 5 to get the right proportions. Then you can take your new number from 300 and divide that by 7, and you should not be on the right path because I'm probably an idiot.
Sorry bout it
Answer:
hi
Step-by-step explanation:
The sum of four times a number and negative three is twelve. What is the number?
2 1/4
3 3/4
-2 1/4
6
Answers
Answer:
Dgfyb
Step-by-step explanation:
After 3 hours of of driving, Paul had gone 183 miles. What was his average rate of speed? Explain your answer.
Answers
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[tex]s(av) = \frac{∆x}{∆t} \\ [/tex]
[tex]s(av) = average \: \: speed[/tex]
[tex]∆x = covered \: \: distance[/tex]
[tex]∆t = time \: \: of \: \: the \: \: covered \: \: distance \\ [/tex]
_________________________________
[tex]s(av) = \frac{183}{3} \\ [/tex]
[tex]s(av) = 61 \: \: \frac{mile}{hour} [/tex]
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Solve for AB
a: 3.6
b: 15
c: 4
d: 10
Answers
On the set of axes below, triangle ABC is graphed. Triangles A'B'C'
and A"B"C", the images of triangle ABC, are graphed after a
sequence of rigid motions.
Answers
Answer:
Step-by-step explanation:
a reflection followed by a rotation
The sequence of rigid motions of the triangle is a reflection followed by a rotation, option (D) is the correct answer.
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. Graphs are used to map out functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis and a vertical y-axis.
For the given situation,
The graph shows the triangle ABC plotted in the fourth quadrant.
The triangle A'B'C' are graphed in the third quadrant as its reflection.
The triangle A''B''C'' are graphed in the second quadrant by reflecting the triangle A'B'C' and then rotating it.
Hence we can conclude that the sequence of rigid motions of the triangle is a reflection followed by a rotation, option (D) is the correct answer.
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A spinner with 9 equal sections is numbered 1 through 9. The probability of spinning a 3 is
What is the probability of not spinning a 3?
Enter your answer as a fraction, in simplest form, in the box.
Answers
Answer:
8/9
Step-by-step explanation:
the probability of spinning 3 is 1/9 so just subtract with 1 or 9/9
#11
write the equation of a line in point slope-form
Answers
Answer:
y - 5 = 1/4 (x+1)
Step-by-step explanation:
y - 5 = 1/4 (x - (-1))
to simplify the problem you can change (x - (-1)) to (x+1) because subtracting a negative is the same as adding a positive
y - 5 = 1/4 (x+1)
and that is your final answer if you want to keep it in point slope formula
Jerilyn made 40 treats for her birthday. She gave away 14 to her family before taking the rest to school. What percent did she give away to her family?
Answers
This is because Jerilyn gave away 14 of her sweets.
100/40 = 2.5
2.5 x 14 = 35%
What’s the answers? ,,
Answers
3. Multiply and simplify: (4x + 3)(x - 1)
Answer =
Answers
Answer: = 4x² - x - 3
(4x+3)(x -1 ) = 4x² + 3x - 4x - 3 = 4x² - x - 3
Step-by-step explanation:
A circular rug has a circumference of 314 inches. What is the approximate area? Round to the nearest whole inch. Use 3.14 for pie 
Answers
Answer:
The area is 7850 square inches
Step-by-step explanation:
Given the circumference, we want to calculate the area
mathematically, the circumference is;
C = 2 pi r
So r is C/2 pi
Area = pi * r^2
Substitute value for r from circumference;
Area = Pi * c^2/4pi^2
Area = C^2/4pi
Area = 314^2/4 * 3.14
Area = 7850 Inches square
Answer:
7,850
Step-by-step explanation: