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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Answer:
Combine Like Terms:
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Translate the sentence into an inequality.
Twice the difference of a number and 3 is at least -20.
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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,
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Let the number be x.
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Statements
Answers
Answer:
x=-5
Step-by-step explanation:
Statement Reason
3x+1 =-14 Given
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x=-5 Division Property of Equality
Repeating Decimals
to Fractions
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Answer:
1. 3/5
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Step-by-step explanation:
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.
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Hope that helps.
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Answer and Step-by-step explanation:
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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!**
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Answer:
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Step-by-step explanation:
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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,
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Where a is the slope and b is constant.
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Solving the system of equation,
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Answer:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Given:
Pam saves every two dollar
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Find:
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Computation:
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Answer:
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Step-by-step explanation:
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The cost of one pound beef is $3.2
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For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
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Answer:
x= {0, 7}
Step-by-step explanation:
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Step-by-step explanation:
Answer:
a
Step-by-step explanation:
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Answer:
$16
Step-by-step explanation:
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Answer:
So if the pizza is just 6$
and every topping is 2$ each (expensive!)
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Solution: In total, the pizza (with toppings) would be 16$