Shown below are parallel lines n and p which are cut by transversals r and s which are perpendicular to each
other. Which of the following is the measure of 21?
(1) 51
(2) 64
(3) 72
(4) 102
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Answers
Given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: [tex]\mathbf{1) 51^{\circ}}[/tex]
The angle measure where two perpendicular lines intersect each other equals 90 degrees.
Therefore, the angle formed as shown in the figure attached, where transversals r and s meet = 90 degrees.
Since lines n and p are parallel lines, therefore:
[tex]m \angle 1 + 90 = 141[/tex] (alternate interior angles are equal)
Subtract 90 from each side[tex]m \angle 1 = 141 - 90\\\\\mathbf{m \angle 1 = 51^{\circ}}[/tex]
Therefore, given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: [tex]\mathbf{1) 51^{\circ}}[/tex]
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Related Questions
Solve the system below:
10x + y = 22
2x + x = -2
Answers
Answer:
x=negative 2/3,y= positive 86/3
Step-by-step explanation:
Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5
Answers
Given:
Zero: 2, multiplicity: 3
Zero: 0, multiplicity: 2
Degree: 5
Leading coefficient = 1
To find:
The polynomial function.
Solution:
The general form of a polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeroes with multiplicity [tex]m_1,m_2,...,m_n[/tex].
Using the given information and the general form of a polynomial, we get
[tex]P(x)=a(x-2)^{3}(x-0)^{2}[/tex]
[tex]P(x)=ax^2(x^3-6x^2+12x-8)[/tex]
[tex]P(x)=a(x^5-6x^4+12x^3-8x^2)[/tex]
Leading coefficient is 1, so the value of a is also 1.
[tex]P(x)=1(x^5-6x^4+12x^3-8x^2)[/tex]
[tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex]
Therefore, the required polynomial is [tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex].
The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
According to the given condition
The given conditions to write the polynomial equations are as follows
Zero 2 and Multiplicity 3
Zero 0 and Multiplicity 2
Degree of polynomial expression = 5
Leading coefficient of polynomial expression = 1
Let us consider the polynomial equation has only one variable and hence in general form we can write the equation of polynomial as follows
[tex]\rm y (x) = a(x-\alpha)^m (x-\beta)^n........(1)\\Where \\a = Leading \; coefficient\; of\; polynomial\; expression \\\alpha ,\beta = Roots \; of \; the\; polynomial\; expression\\m\; and \; n \; are \; multiplicities \; of \; the \; roots \; \alpha,\beta \; respectively\\Degree = m+n[/tex]
From the general form of polynomial expression as shown in equation (1) we can write
Polynomial expression for the given conditions is formulated in equation (2)
[tex]\rm y(x) = 1\times (x-2)^3(x-0)^2 .......(2)[/tex]
So the polynomial for the conditions given in question is expressed as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
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What is the prime factorization of 144? Be sure to show your strategy.
Answers
Answer:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written 144 = (2^4) x (3^2)
Step-by-step explanation:
The gas tank holds a total of 15 gallons of gas.how many miles can the car travel with a full tank of gas
Answers
Answer:
....
Step-by-step explanation:
Answer:
If the car gets 30 in city miles per gallon it (MPG) would be 30×15 which would be 450 miles. If its a sportier car like the Chevrolet Camaro ZL1 which gets close to 18 miles per gallon (MPG) it would be 18×15 which would be 270 miles. There is also highway miles where a standard car would get about 40 or more miles per gallon (MPG) 40×15 which would be 600 Miles. For a car like the Toyota Prius which gets 50-58 miles per gallon (MPG) in a city but 48-53 miles per gallon 58×15=870 miles and 53×15=795 miles. It depends on the car's engine, tuning, transmission, aerodynamics, etc.
Step-by-step explanation:
Different cars get different miles per gallon (MPG).
Help me due in 5 minutes HELP ASAP
Answers
Answer:
J.
Step-by-step explanation:
It crosses through (0,0) and has a slope of 2.5 or rather 5/2 because when the x value is at 4 the y value is at 10 that simplifies to 5/2 or 2.5.
Which line below is parallel to the line that y = 1/2x - 2?
A) y = 1/2x + 2
B) y = -1/2x + 2
C) y = 1/2 - 2x
D) y= 1/2 + 2x
Answers
Answer:
The answer is b
Step-by-step explanation:
Bc it is just basicly the x and y axis
PLEASE HELP WITH THE PIC
Answers
Ricky bought a jacket for $52.00. If the sales tax is 9.5%, how much did he pay in total?
A.$4.94
B.$61.50
C.$49.40
D.$56.94
Answers
Answer:
D. $56.94
Step-by-step explanation:
52 * 0.095 = 4.94
Add $52 + $4.94
Please help
Please help please
Answers
dbhzhxgushshebnxjxjkxdhxhdh bdbdhxjdnbdbdb
What is 3/4 raised to the power of 3
Answers
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[tex] ( { \frac{3}{4} })^{3} = \frac{ {3}^{3} }{ {4}^{3} } = \frac{27}{64} \\ [/tex]
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Sushil was thinking of a number. Sushil divides by 7, then adds 12 to get an answer of 10. What was the original number?
Answers
Answer:
x=-14
Step-by-step explanation:
think the number is x
According to the question
x/7+12=10
=>x+84=70 (multiply both side by 7)
=>x=70-84
x=-14
what is a domain in math?
Answers
Answer:
"In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall."
Step-by-step explanation:
Please help!! I'll give brainlist!
Answers
Answer:
-3/5
Step-by-step explanation:
-2/5+-1/5= -3/5
I used a calculator to ensure this answer was correct
This is because -2 pulse -1 is -3. And you can’t add the denominator if it’s the same. In this case the denominators are the same so u keep it as 5. So the answer would be A
Can someone help me please
Answers
The point to the left will be -2,6
The point at the bottom will be 2,2
The point to the right will be 1,5
Math question plz help me
Answers
Answer:
The required equation of the line is:
[tex]y=\frac{1}{4}x-1[/tex]
Step-by-step explanation:
Given the equation
[tex]y=-4x+3[/tex]
comparing the equation with the slope-intercept form
[tex]y=mx+b[/tex]
Here,
m is the slope y is the interceptso the slope of the line is -4.
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: 1/4
Therefore, the point-slope form of the equation of the perpendicular line that also intersects the point (8, 1) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-1=\frac{1}{4}\left(x-8\right)[/tex]
add 1 to both sides
[tex]y-1+1=\frac{1}{4}\left(x-8\right)+1[/tex]
[tex]y=\frac{1}{4}x-1[/tex]
please find the value of x!
Answers
Answer:
the equation would be 9x+1=30
i need the answers asap :) please actually answer! i give lots of points :)
Answers
Answer:
I say 65 hours hope it helps
Step-by-step explanation:
A tv costs £800 plus VAT at 20%.
What is the total cost of the TV?
Answers
Answer:
Step-by-step explanation:
800+20%
20%= (20/100)
800/100=8*20=160
add to original price= 800+160=960
8. Given: GI +JL, GH = KL
Prove: HI~=JK
Answers
Answer: the length of GH is half the length of KL
Step-by-step explanation: edge 2021
Marissa knits caps that she supplies to several baby stores. She purchases five bundles of yarn for $62.50. Select the
quantities that would best help determine how many bundles of yarn she will need per month to knit caps.
ОА. .
amount of yarn needed for each cap and number of caps knitted in a month
OB. cost to produce each cap and price per bundle of yarn
OC. number of caps knitted in a month and cost to ship the caps to each store
OD. price per bundle of yarn and amount of yarn needed for each cap
Answers
Answer:
I think OA because you would need to know how much yarn for each cap and how many caps she will make
Work out the size of x
Answers
Answer:
They are supplementary angles so they add up to make 180°
So you do the reverse
180°-100°=x
80°=x
Step-by-step explanation:
Please give me brainliest
This is the problem ......
Answers
Answer:
4/18
Step-by-step explanation:
tell whether this sequence is arithmatic. If it is, what is the common difference. 10, 15, 21, 28
Answers
Answer:
No this is not arithmetic this is geometric
Step-by-step explanation:
10 to 15 is a increase of 5
15 to 21 is a increase of 6
21 to 28 is a increase of 7 arithmetic have to have steady increases
Answer:
Hola!
Step-by-step explanation:
three more than the quotient of a number and 7 is at most 92. Find the number
Answers
Answer:
The number is 623.
Step-by-step explanation:
[tex]\frac{x}{7}+3 =92\\\frac{x}{7} =89\\x=623[/tex]
Solve for 3a:
a + 4 = 4a + 2
3a
Answers
Answer:
x = 2/3
2/3*3 = 2
Step-by-step explanation:
Why are they parallel?
Answers
Answer:
a and d are parallel
Step-by-step explanation:
Find the value y from the given figure
Answers
Answer:y=28
Step-by-step explanation:
40+3y+2y=180
Subtract 40
3y+2y=140
Combine like terms
5y=140
Divide
y=28
What is the percent of change from 70 to 14?
Answers
Answer:
80%
Step-by-step explanation:
70-14=56
56/70=80%
HELP PLZZ ITS DUE TODAY I WILL MARK BRAINEST
Answers
I need help pls !!!!!