Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.
Answers
Answer:
Step-by-step explanation:
11). 6x + 7 = 8x - 17 [Since vertical angles are equal in measure]
8x - 6x = 17 + 7
2x = 24
x = 12
12). (11x - 15) + (5x - 13) = 180°
16x - 28 = 180°
16x = 180 + 28
16x = 208
x = 13
13). Since DB⊥AC,
m∠CBD = 90°
m∠CBE + m∠DBE = 90°
(5x - 42) + (2x - 1) = 90°
7x - 43 = 90
7x = 133
x = 19
14). Since QS bisects angle PQR,
m∠PQS = m∠RQS
10x + 1 = [tex]\frac{82}{2}[/tex]
10x + 1 = 41
10x = 40
x = 4
15). 10x - 61 = 18y + 5 [Vertical angles]
10x - 18y = 61 + 5
10x - 18y = 66
5x - 9y = 33 ------(1)
(18y + 5) + (x + 10) = 180 [linear pair of angles are supplementary]
18y + x + 15 = 180
x + 18y = 165 ------(2)
By adding equation (1)×2 and equation (2)
(10x - 18y) + (x + 18y) = 66 + 165
11x = 231
x = 21
16). (5x - 17) + (3x - 11) = 180 [[linear pair of angles are supplementary]
8x - 28 = 180
8x = 180 + 28
8x = 208
x = 26
(3x - 11)° = 78 - 11
= 67°
67° + 90° + (2y + 5)°= 180° [Sum of angles on a line]
162 + 2y = 180
2y = 180 - 162
2y = 18
y = 9
17). NP bisects ∠MNQ.
Therefore, m∠MNQ = 2(m∠PNQ)
8x + 12 = 2×78
8x + 12 = 156
8x = 156 - 12
8x = 144
x = 18
m∠MNQ = (8x + 12)° = 156°
m∠RNM = m∠ONQ [Vertical angles]
(3y - 9)° = 180° - m∠MNQ
3y - 9 = 180 - 156
3y - 9 = 24
3y = 33
y = 11
Using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
Applying the knowledge of angle relationships, we can solve each given problem by first, creating a an equation from the relationship between angles, then solve for the variables.
11. [tex]6x + 7 $ and $ 8x - 17[/tex] are vertical angles.
Since vertical angles are congruent, therefore:[tex]6x + 7 = 8x - 17[/tex]
Solve for x[tex]6x - 8x = -7 - 17\\\\-2x = -24\\\\x = 12[/tex]
12. [tex]11x - 15 $ and $ 5x - 13[/tex] are linear pair angles.
Since, the sum of linear pair angles equals 180 degrees, therefore:[tex](11x - 15) + (5x - 13) = 180[/tex]
Solve for x[tex]11x - 15 + 5x - 13 = 180\\\\16x - 28 = 180\\\\16x - 28 + 28 = 180 + 28\\\\16x = 208\\\\x = 13[/tex]
13. <DBE and <CBE are complementary angles.
Since the some of complementary angles equals 90 degrees, therefore,[tex]m \angle DBE + m \angle CBE = 90[/tex]
Substitute[tex](2x - 1) + (5x - 42) = 90[/tex]
Solve for x[tex]2x - 1 + 5x - 42 = 90\\\\7x - 43 = 90\\\\7x = 90 + 43\\\\7x = 133\\\\x = 19[/tex]
14. Since QS bisects <PQR, therefore,
m<PQS = 1/2(PQR)
Substitute[tex]10x + 1 = \frac{1}{2} (82)[/tex]
Solve for x[tex]10x + 1 = 41\\\\10x = 41 - 1\\\\10x = 40\\\\x = 4[/tex]
15. [tex](x + 10) $ and $ (10x - 16)[/tex] are linear pair angles.
Since the sum of linear pair angles equals 180 degrees, therefore,[tex](x + 10) + (10x - 16) = 180\\[/tex]
Solve for x[tex]x + 10 + 10x - 61 = 180\\\\11x - 51 = 180\\\\11x = 180 + 51\\\\11x = 231\\\\x = 21[/tex]
Find y:Since [tex](10x - 61) $ and $ (10y + 5)[/tex] are vertical angles, they are congruent. Therefore,
[tex](10x - 61) = (10y + 5)[/tex]
Plug in the value of x and solve for y[tex]10(21) - 61 = 18y + 5\\\\149 = 18y + 5\\\\149 - 5 = 10y\\\\144 = 18y\\\\8 = y\\\\\mathbf{y = 8}[/tex]
16. Since [tex](5x - 17) $ and $ (3x - 11)[/tex] are linear pair, their sum equals 180 degrees. Therefore,
[tex](5x - 17) + (3x - 11) = 180[/tex]
Solve for x[tex]5x - 17 + 3x - 11 = 180\\\\8x - 28 = 180\\\\8x = 180 + 28\\\\8x = 208\\\\x = 26[/tex]
Find y:[tex](2y + 5) + 90 + (3x - 11) = 180[/tex] (angles on a straight line = 180 degrees)
Plug in the value of x and solve for y[tex]2y + 5 + 90 + 3(26) - 11 = 180\\\\2y + 5 + 90 + 78 - 11 = 180\\\\2y + 162 = 180\\\\2y = 180 - 162\\\\2y =18\\\\y = 9[/tex]
17. Since NP bisects <MNQ, therefore,
[tex]m \angle PNQ = \frac{1}{2}(m \angle MNQ)[/tex]
Substitute[tex]78 = \frac{1}{2}(8x + 12)[/tex]
Solve for x[tex]78 \times 2 = 8x + 12\\\\156 = 8x + 12\\\\156 - 12 = 8x \\\\144 = 8x\\\\18 = x\\\\x = 18[/tex]
[tex]m \angle RNM + m \angle MNQ = 180^{\circ}[/tex] (linear pair)
Substitute[tex](3y - 9) + (8x + 12) = 180[/tex]
Plug in the value of x and solve for y[tex]3y - 9 + 8(18) + 12 = 180\\\\3y - 9 + 144 + 12 = 180\\\\3y + 147 = 180\\\\3y = 180 - 147\\\\3y = 33\\\\y = 11[/tex]
Therefore, using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
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Related Questions
15y - 10 + y - 8 simplifies to
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Answer:
Combine Like Terms:
= 15y + −10 + y + −8
= (15y+y) + (−10+−8)
= 16y + −18
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Answer:
because it doesn't pass the verticle line test
Step-by-step explanation:
-16 = -5x + x
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Answer:
x = 4
Step-by-step explanation:
-16 = -5x + x --> Collect like terms --> -16 = -4x -->
swap the sides of the equation 4x = -16 -->
Divide both sides of the equation by -4 --> x =4
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Answer:
81
Step-by-step explanation:
Pam and her brother both open savings accounts. Each begin with a balance of zero dollars. For every two dollars that Pam save in her account, her brother save five dollars in his.
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Answer:
Ratio [Pam to her brother] = 2:5
Step-by-step explanation:
Given:
Pam saves every two dollar
Her brother saves fives dollar (For every two dollar)
Find:
Ratio [Pam saving and his brothers saving]
Computation:
It is given that if Pam saves $2 her brother saves $5
So,
Ratio [Pam to her brother] = 2/5
Ratio [Pam to her brother] = 2:5
Translate the sentence into an inequality.
Twice the difference of a number and 3 is at least -20.
Answers
Answer: 2n-3>=-20
Step-by-step explanation: instead of the equal sign put a line under the sign <
After translating the given statement, the inequality will be 2x - 3 ≥ -20.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values.
Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the information in the question,
The statement for the inequality in the question,
Twice, the difference between a number and 3 is at least -20.
Let the number be x.
Twice the number is 2x.
So,
2x - 3 ≥ -20
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what is 660 increased by 1 followed by a further one
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660+1+1= 662
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Answer:
$16
Step-by-step explanation:
2x5=10+6=16
Answer:
So if the pizza is just 6$
and every topping is 2$ each (expensive!)
2$ x 5$ = 10$
So 6$ + 10$ = 16$
Solution: In total, the pizza (with toppings) would be 16$
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True or False: The graph below is the correct graph of the function y= -7x+14 and the intercepts
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Answer:
It'ssssss Trueeeeeee
the l.c.m of 5ab and 3ab
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Answer:
The answer is 15ab. You can just simply multiply the two given number
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Answer:
Step-by-step explanation:
(x^2 - x)(2x - 2)
2x^3 - 2x^2 - 2x^2 + 2x
2x^3 - 4x^2 + 2x
It costs $14.40 for 4.5 pounds of beef. How much is the beef per pound?
A - $2.30
B - $3.20
C- .32
Can anyone help me ???
Answers
The cost of one pound beef is $3.2
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Cost 4.5 pound of beef = $14.40
So, the unit rate for beef
= 14.40 / 4.5
= $3.2
Hence, the cost of one pound beef is $3.2
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convert 4.5m to kilometers
Answers
Answer:
0.0045 km or 4.5×10^-3 km
Step-by-step explanation:
This table represents a proportional relationship. Use the table to identify the constant of proportionality between the ratio of the number of laps to the number of swimmers. A 2-column table with 4 rows. Column 1 is labeled Number of Swimmers with entries 20, 18, 14, 9. Column 2 is labeled Number of Laps with entries 240, 216, 168, 108.
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Answer:
12
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
what is the answer to this question im having trouble 3 x 2 - x?
Answers
Answer and Step-by-step explanation:
3 x 2 - x = ? Well, if you simplify it's just 5x. But, if you are trying to solve this then you have to know what x is or what your answer is. But, if you're trying to solve 3 x 2 = x then x would equal 6. Of course, if you know the answer or what x equals then plug it in as such, let's say x = 2 then you would plug 2 in for x and solve, 3 x 2 = 6 - 2 = 4. But, if you are trying to solve for x then look at the answer, let's say it is 24 so, 3 x 2 - x = 24, x would equal -18.
Hope this helped you out! Have a wonderful day!
**Note, I didn't understand what you were asking, that's why I went into so much detail to help you out. Please, be clearer with your questions. Make sure you got all the whole question in there! Thank you!**
100000000000 to the 10th power
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Answer:
The answer for this question is 1e+110
This is what I need help with.
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plant D
Plant B
Plant C
Plant A
Someone help FAST ! It’s talking about integers.
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Answer:
#1. 9
#2. -50
#3. -53
#4. 7
What are the reasons?
Given: 3x + 1 = -14; Prove: x = -5
Statements
Answers
Answer:
x=-5
Step-by-step explanation:
Statement Reason
3x+1 =-14 Given
3x=-15 Subtraction Property of Equality
x=-5 Division Property of Equality
In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of a?
Answers
Answer:
a=18
Step-by-step explanation:
The value of a or m is 18 in the linear equation, y = 5x - 2.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
The table represents a linear function.
The data is given in the attached image.
The general equation of the linear function is,
y = ax+b.
Where a is the slope and b is constant.
By using the first and the third points from the table to find the equation of the linear function,
When x = 3 and y = 13,
13 = 3a+b {equation 1}
When x = 5 and y = 23
23 = 5a+b {equation 2}
Solving the system of equation,
we get,
a = 5 and b = -2
So, the equation is,
y = 5x - 2
Now, x = 4
Then y = m = 20 - 2 = 18
Therefore, the value of m is 18.
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Evaluate: -0.7 - (-2.6 + -0.8) + 7.1
Answers
Answer:
8.36
Step-by-step explanation:
[tex]-0.7-(-2.6+ -0.8) +7.1\\ (add inside the parenthesis)\\\\-0.7 - 3.4 + 7.1\\\\=8.36[/tex]
if a is a rational number and b is a rational why could c be an irrational number
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Answer:
Let a be a rational number and b be an irrational number. b = c - a, which means that b is rational. ... Since an irrational number cannot equal a rational number.
Step-by-step explanation:
PLZ MARK BRAINLIEST
The answer is that an irrational number cannot equal a rational number.
What is an irrational number?Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, on the other hand, cannot be stated as the ratio of two integers.
Let a be a rational number and b be an irrational number. b = c - a, which means that b is rational. Since an irrational number cannot equal a rational number.
Therefore an answer is that an irrational number cannot equal a rational number.
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An aquarium is shaped like a right rectangular prism. The aquarium has a height of 14 inches, a width of 8 inches, and a length of 24 inches.
What is the volume of the aquarium?
Answers
Length x width x height is your formula
2(4x - 3)=3(x+8)
The equation above is the problem I’m stuck on, I’m in algebra two and it’s been awhile since we’ve gone over this type of equation.
Answers
Answer:
x = 6
Step-by-step explanation:
2(4x - 3) = 3(x + 8)
1. Distribute the 2 and 3 into the parentheses.
2(4x) + 2(-3) = 3(x) + 3(8)
= 8x - 6 = 3x + 24
2. Subtract 3x from both sides.
8x - 3x - 6 = 3x - 3x + 24
= 5x - 6 = 24
3. Add 6 on both sides.
5x - 6 + 6 = 24 + 6
5x = 30
4. Divide by 5.
5x ÷ 5 = 30 ÷ 5
x = 6
Hope that helps.
Convert the following values into scientific notation. Which one has the negative exponent.
Answers
Answer:
B has a negative exponent: 8 x 10^-7
A doesn't: 4.267 x 10^7
Can I get all the right answers only
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Answer:
yes, you can get all right answers.
Answer:
yes i believe that you can get all the answers right
Step-by-step explanation:
What is the solution of 2x(x+7)=0 if you are factoring
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Answer:
x= {0, 7}
Step-by-step explanation:
Repeating Decimals
to Fractions
1)0.6
2)0.45
3)0.2
4)0.90
Answers
Answer:
1. 3/5
2. 9/20
3. 1/5
4. 9/10
Step-by-step explanation:
What is the missing coefficient?
x2 + 4x
+
2x
x2 + x
please help me
Answers
x^2 + 6x since 4x + 2x = 6x