Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.
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:
x = 133
y = 43
Step-by-step explanation:
x + 47 = 180
so x is 133
47 + y = 90
so y is 43
What is the 50th term of Arithmetic sequence 9,2,-5
Answer:
- 334
Step-by-step explanation:
There is a common difference between consecutive terms in the given sequence, that is
d = 2 - 9 = - 5 - 2 = - 7
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 7 , thus
[tex]a_{50}[/tex] = 9 + (49 × - 7) = 9 - 343 = - 334
Please help lol
Answer options:
A. (2.5,4)
B. (2,3)
C. (1.5,3)
D. (2,3.5)
When ax3 +x2 -2x +b is divided by x+1, the remainder is 10. When it is divided by x-3, the remainder is -46. What is the value of a and b?
Step-by-step explanation:
Given
X+ 2 = 0
X = -2
on putting in polynomial
-8a +2b= 0
- 8a = 2b
b = -4a
Now
when divided by x - 1 give remainder -15
so
x - 1 = -15
x = -14
on putting in polynomial
-2744a + 198 + 14b - 4 = -14
-2744a + 56a = - 208
-2688a = -208
a = 168/13
Now
b = 672/13
Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother I’m order to earn $54
Answer:
Felipe work for 6 hours to earn $54
Step-by-step explanation:
I guess I was help full for u
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what is 1 1/3 divided by 3/5
Answer:
6.11
Step-by-step explanation:
First divide 11by 3 and 3by 5.And divide the answer of 11by 3 by 3by5
Is the equation x9 – 5x3 + 6 = 0 quadratic in form? Explain why or why not.
Answer:
NOO
Step-by-step explanation:
In order for an equation to be quadratic, the highest degree that is needed is two. The highest exponent provided is 3 therefore no it is not a quadratic function
A. Without computing each sum, find which is greater, O or E, AND by how much.
O = 1 + 3 + 5 + 7 + ... + 101
E = 2 + 4 + 6 + 8 + ... + 102
and need to explain it
Answer:
Www
Step-by-step explanation:
What is the common multiplier in the proportion? 6 over 8 = 9 over 12
Answer:
The common multiplier is 24
Step-by-step explanation:
6/8 9/12
8,16,24
12,24
6/8 × 3/3= 18/24
9/12× 2/2= 18/24
The next two numbers in the series 1 , 4 , 9 , 16 , 25 ,....................are
Answer:
36, 49
explanation:
The pattern in this series is going by perfect squares:
(1)² = 1(2)²= 4(3)² = 9(4)² =16(5)² = 25From this, we can tell the next 2 numbers in the series will be:
(6)²=36(7)²=49PLEASE HELP!!!Choose the name of the angle notated by the arc(SHOW WORK) A.MPO B.NPO C.LPM D.PLO
B. NPO
Explanation:Because P is the middle letter in the arc.
Answer: B. NPO
Step-by-step explanation: the angle has to be in middle
Raleigh went to a gaming arcade for his birthday. His parents gave him $55 to spend. He purchased $14.25 in
food and drinks, and put the rest of the money on a gaming card to spend at the arcade. Each game cost
$1.25.
How Many games can Raleigh play in the arcade?
Answer:
23 games
Step-by-step explanation:
40.75 divide by 1.25 comes out 23.28
Answer:
g<32.6
Step-by-step explanation:
1.25g+14.25<55
1.25g+14.25-14.25<55-14.25
1.25g<40.75
1.25g/1.25<40.75/1.25
g<32.6
If g(x-1) = (2-g(x))/8 and g(1) = 3, find the value of g(2).
Answer:
-22
Step-by-step explanation:
g(2-1)=g(1)=(2-g(2))/8=3
2-g(2)=24
-g(2)=22
g(2)=-22
What is the base of the triangle? A=36mm(2) H= 6mm B=?
Answer:
Area formula=b*h÷2
b=a÷h*2
b=12
Step-by-step explanation:
So if you multiply the base and height to find a triangle, you'd get the area of a rectangle instead so if you divide by 2, you'd get the area of a triangle
To find the base, you'd reverse the process. You'd divide the area by the height and multiply by 2.
36÷6=6
6*2=12
Hope that helps!
6+(-3)=
answer question plz
Answer:
-3
Step-by-step explanation: Because it is just like saying 6-3
Answer:
3
Step-by-step explanation:
6+(-3)
A addition symbol and subtraction symbol both make a negative symbol.
6-3
6-3= 3
Hope this helps!
Evaluate the expression when a=3.
a^2+12
[tex]3^{2} + 12 = 9 + 12 = 21[/tex]
The answer is 21.
Answer:
The correct answer is 21.
Step-by-step explanation:
To solve this problem, we simply substitute 3 for a in the expression.
Given the expression,
a^2 + 12
we should replace "a" with 3, as denoted by the problem, giving us:
(3)^2 + 12
Now, we simplify using the order of operations. PEMDAS tells us that we should simplify what is in the parentheses first because it has an exponent.
9 + 12
Now, we can just add the two remaining terms together, giving us:
21
Therefore, the answer is 21.
Hope this helps!
Point D best represents which of the following numbers?
tot
14
14.5
15
15.5
16
Answer:
yea your correct and 16.5
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
???
What is the same value as the expression 7/5+2 1/4+1.6
What value of x is in the solution set of 2(3x - 1) = 4x - 6?
EO
-10
Answer:
D) -1
Step-by-step explanation:
6x-2≥4x-6
6x-4x≥-6+2
2x≥-4
x≥-4÷2
x≥-2
Only -1 is greater than -2 in the list.
Answer:
x = - 1
Step-by-step explanation:
Given
2(3x - 1) ≥ 4x - 6 ← distribute parenthesis on left side
6x - 2 ≥ 4x - 6 ( subtract 4x from both sides )
2x - 2 ≥ - 6 ( add 2 to both sides )
2x ≥ - 4 ( divide both sides by 2 )
x ≥ - 2
The only value in the list greater than - 2 is - 1
x = - 1 is in the solution set
11. Your class is taking a trip to a museum that is 190 miles away. The bus can travel at 55
miles per hour. At least how many hours should your class plan for the trip to the museum?
What property is (6+2)+4=4+(6+2)
Answer: commutative property of addition
Step-by-step explanation:
(a+b)+c=a+(b+c) -- Commutative property of addition
Commutative property of addition is when the numbers are added, the sum are the same, regardless of the order of numbers.
Thus, (6+2)+4=4+(6+2) is commutative property of addition.Hope this helps!! :)
Please let me know if you need further explanation with properties of addition.
Question 14(Multiple Choice Worth 4 points)
(01.04 LC)
Solve the inequality 4x - 6 > 6x - 20.
x> 7
x<7
x<2
x>2
Step-by-step explanation:
4(7)-6,6(7)-20
28-6,42-20
22,22
22/22
=1
4(2)-6,6(2)-20
8-6,12-20
2,-8
-8/2
=-4
Answer:
Its B
Step-by-step explanation:
What kind of transformation is illustrated in this figure?
O translation
.
O reflection
dilation
Orotation
Answer:
translation
Step-by-step explanation:
shape, size, measurement all stayed the same. they just moved locations :)
a patio has an area of 120 square feet. the length of the patio is 12 feet. what is its width
w = 10 feet
Step-by-step explanation:Area formula
A = l×w
120ft² = 12ft×w
w = 120ft²/12ft
w = 10 feet
-
=\80
2.4
()
14 15
0
L: 2
4
А) . 1
( - ) 90
| —
Answer:
....
Step-by-step explanation:
Really need help with #20! I'll give brainliest!
Answer: 1 year (year 15)
Step-by-step explanation:
109.5-86.0=23.5
128.4-109.5=18.90
140.8-128.4=12.4
158.7-140.8=17.9
182.1-158.7=23.4
23.5+18.9+12.4+17.9+23.4=96.10
96.10÷5=19.22
200-182.1=17.9
182.1+19.22=201.32 subs
Find the value of the remaining variable in the formula. Use 3.14 as an approximation for a (pi).
P=2L+2W (perimeter of a rectangle); L = 4, W= 2
P =
Enter your answer in the answer box.
Answer:
P = 12
Step-by-step explanation:
Given formula for the perimeter 'P' of a rectangle is,
P = 2L + 2W
If the values of L and W are,
L = 4 and W = 2
Perimeter of the rectangle = 2(L + W)
= 2(4 + 2)
= 2 × 6
= 12 units
Therefore, value of remaining variable 'Perimeter' = 12 units
(There is no use of 'pi' in calculating the perimeter of a rectangle).
Help needed ASAP will give BRAINLIEST
Answer:
177.2 i think
Step-by-step explanation:
Evaluate the expression for d = 43.4.
Write your answer as a decimal or whole number.
4.4(d − 35) =
Answer:
36.96
Step-by-step explanation:
given
d = 43.4
equation
4.4(d - 35) =
plug d in
4.4(43.4 - 35) =
solve within parentheses
4.4(8.4) =
multiply
36.96