Answers
Answer:
1) x = 55°
2) x = 30°
3) x = 68°
Step-by-step explanation:
In the given set of questions where it requires to find the unknown value of x to prove that v ||w:
Definition of Consecutive Interior Angles Theorem:The Consecutive Interior Angles Theorem states that for any given two parallel lines cut by a transversal, the measures of a pair of consecutive interior angles have a sum of 180°. Hence, the pair of consecutive interior angles are supplementary.
Question 11.) In the given diagram, the two consective interior angles are m ∠70° and m ∠ 2x°. As defined by the Consecutive Interior Angles Theorem:
m ∠70° + m ∠ 2x° = 180°
Solve for x algebraically:
70° + 2x° = 180°
Subtract 70° from both sides:
70° - 70° + 2x° = 180° - 70°
2x° = 110°
Divide both sides by 2 to solve for x:
[tex]\LARGE\mathsf{\frac {2x^{\circ}}{2}\:=\:\frac{110^{\circ}}{2}}[/tex]
x = 55°
Verify whether the value for x is valid:
70° + 2x° = 180°
70° + 2(55)° = 180°
70° + 110° = 180°
180° = 180° (True statement).
Question 2:2) In the given diagram, the two consective interior angles are m ∠2x° and m ∠ 4x°. As defined by the Consecutive Interior Angles Theorem:
m ∠2x° + m ∠ 4x° = 180°
Solve for x algebraically:
2x° + 4x° = 180°
Add like terms:
6x° = 180°
Divide both sides by 6 to solve for x:
[tex]\LARGE\mathsf{\frac {6x^{\circ}}{6}\:=\:\frac{180^{\circ}}{6}}[/tex]
x = 30°
Question 3:The Consecutive Interior Angles Theorem still applies in this question. The two consective interior angles are m ∠90° and m ∠ (x + 22)°. As defined by the Consecutive Interior Angles Theorem:
m ∠90° + m ∠ (x + 22)° = 180°
Solve for x algebraically:
90° + x° + 22 = 180°
Combine like terms:
112° + x° = 180°
Subtract 112° from both sides to isolate x:
112° - 112° + x° = 180° - 112°
x = 68°
Verify whether the value for x is valid:
90° + x° + 22 = 180°
90° + 68° + 22 = 180°
180° = 180° (True statement).
Related Questions
Jeriel decides to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches, then throws back into the water. After plotting all his data, he draws a line of best fit. Based on the line of best fit, how much would you predict a catfish with a length of 33 inches would weigh?
Answers
A catfish with a length of 33 inches would weigh 30 pounds.
Linear equationA linear equation is in the form of:
y = mx + b
where y,x are variables, m is the rate of change and b is the y intercept.
Let y represent the catfish weight with x inches length
From the line of best, it passes through (20, 4) and (23, 10), hence:
y - 4 = [(10 - 4)/(23 - 20)](x - 20)
y = 2x - 36
For a length of 33 inches:
y = 2(33) - 36 = 30 pounds
A catfish with a length of 33 inches would weigh 30 pounds.
Find out more on Linear equation at: https://brainly.com/question/14323743
Decide if the following situation is a unit rate or not why or why not?
You score 12 points in one basketball game.
Answers
Answer:
Yes, because in 1 game you scored 12 points you didn't score multiple points in multiple games.
What is the area of a rectangle with a width of x^2+x+1 and a length of 3x^2-2x-1?
Please help!
Answers
Answer: width= 2x-1 and length= 3x+2
Step-by-step explanation: SOLUTION: Choose a possible dimensions of a rectangle with a width= 2x-1 and length= 3x+2 so that its area is greater than 153cm² a. W= 13 L= 15 b. W= 11 L= 20
which answer is correct
Answers
Answer:
see below for answer
Step-by-step explanation:
(4p^2+32p)/(p-2)=(4p(p+8))/p-2
(p^2+p-6)/(2p^3+16p^2)=(p+3)(p-2)/(2p^2)(p+8)
(4p(p+8)/(p-2))*((p+3)(p-2)/((2p^2)(p+8)))=2(p+3)/p
Makayla’s test grades increased from 80 to 95. What is the percent of increase? Write the number only, no percent sign.
Answers
Answer:
18.75
Step-by-step explanation:
80 = 100%
1% = 100%/100 = 80/100 = 0.8
the grades changed by 95 - 80 = 15.
how many % is that ?
we find the answer by checking how often 1% fits into 15. and we do this kind of check by division :
15 / 0.8 = 18.75
so, the grades changed by 18.75%.
Can someone plz help with this
Answers
Answer:
hexagonal prism
sami is making necklaces for a craft show. each necklace is 33.4 cenimeters long. if she has 233.8 centimeters of cord, how many necklaces can sami make
Answers
Answer:
Sami can make 7 necklaces.
233.8cm ÷ 33.4 = 7
An equation is shown below:
4(x − 3) − 5(x + 1) = 3
Which statement shows a correct next step in solving the equation? (1 point)
Group of answer choices
The equation can become 4x − 12 − 5x − 5 = 3 by applying the associative property of multiplication.
The equation can become 4x − 3 − 5x + 1 = 3 by applying the associative property of multiplication.
The equation can become 4x − 3 − 5x + 1 = 3 by applying the distributive property.
The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.
Answers
Answer:
The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.
Step-by-step explanation:
4(x − 3) − 5(x + 1) = 3
The first thing would be distribute the 4 and the 5 respectively
4x-12 -5x-5 =3
Write a mathematical question that explains the following sentence:
two more than triple a number is fourteen
Answers
two more than triple a number is fourteen might be 2×7=14
Twice the difference of a number 8 equals 5
Answers
Answer:
2(n-8) = 5
Step-by-step explanation:
I'm assuming that its supposed to say "a number and 8"
Answer:
x=10.5
Step-by-step explanation:
x will be a number
2(x-8)=5 --> I'm assuming your question is " twice the difference of a number and 8 equals 5.
Solving
2(x-8)=5
2x-16=5 --> distrubute the 2--> 2*x = 2x and 2*-8 = 16
2x=16+5--> add 16 to other side of x
2x=21--> add like terms
2x / 2 =21 / 2--> single out x
x=10.5 --> 21/2 --> just divide
Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
Which statements are true based on the diagram? Select three options.
Plane S contains points B and E.
The line containing points A and B lies entirely in plane T.
Line v intersects lines x and y at the same point.
Line z intersects plane S at point C.
Planes R and T intersect at line y
Answers
Answer:
B,D,E
Step-by-step explanation:
Which is NOT a function?
A. y = x + 3^2
B. x + y = 3^2
C. x + 3 = y^2
D. y = x^2 - 3
Answers
Answer:
All are functions
Step-by-step explanation:
A. y = x + 9 A graph of a line. There are no x-values that are the same on the graph. The graph passes the vertical line test.
B. x + y = 9
y = -x + 9 A graph of a line. There are no x values that are the same number on the graph. The graph passes the vertical line test
C. x + 3 = y²
[tex]\sqrt{x + 3} = y[/tex] The graph passes the vertical line test. On the graph, there are no x-values that are the same number.
D. y = x² - 3 The graph is a parabola. The graph passes the vertical line test (there are no x- values are the same number on the graph).
Hallar el área lateral de un cilindro que tiene de radio de la base 10 cm y de altura 5 cm.
Answers
Answer:
942.48
Step-by-step explanation:
f(x)=3/5x-4/3 What x value makes f(x)=0
(will give brainliest to whoever answers first)
Answers
Answer:
3
Step-by-step explanation:
I need this really quick!!
Answers
Answer:
400 ft
Step-by-step explanation:
H = 160t - 16t^2 = 16t(10 - t)
The minimum/maximum of a quadratic function is always exactly in between the 0 points (or any other points with equal value, as a parabole is symmetrical).
Let's solve for H = 0
16t(10-t) = 0
t = 0 or 10 - t = 0
t1 = 0, t2 = 10
the maximum is at (t1+t2)/2 = 5
H(5) = 16*5(10-5) = 80*5 = 400
Kenny has 576 baseball cards. He would like
to put them in a blnder. Each binder page
holds 12 cards. 'How many pages does he
need for his baseball card binder?
Answers
Answer:
Divide 576 by 12 and you'll get your answer.
Answer:
Kenny will need 48 pages
Step-by-step explanation:
576 into 12 = 48 therefore Kenny will need 48 pages for his baseball card binder.
Amount of baseball cards into How among pages a binder can hold equal Amount if pages needed.
Question 3
Find the Slope.
(2,8) and (4, -3)
Answers
Answer:
5.5
Step-by-step explanation:
slope formula is y2-y1 over x2-x1
plugging your values in, you get 8-(-3)/ 4-2
which is 11/2
11 divided by 2 is 5.5, so that is your slope
Answer:
5.5
Step-by-step explanation:
because the explanation above
What is y x y x y simplified
Answers
Answer:
y x y x y is simplified as y³
Step-by-step explanation:
Hoped this helped.
Y x Y x Y is simplified as y^3
Hope this helps!!!
Norachai was going to sell all of his stamp
collection to buy a video game. After
selling half of them he changed his mind.
He then bought seven more. How many did
he start with if he now has 25?
Answers
find slope and y intercept
x + y = -2
Answers
Answer:
slope =1 and y intercept = -2
Step-by-step explanation:
Find Slope and Y intercept
Slope and Y intercept
x+y=-2<-- subtract x to get y alone
y=-x-2
Thus slope is 1/1 or 1
and y intercept is -2
Answer:
-1
Step-by-step explanation:
y=mx+c m=slope
c=y intercept
y=-x+2
so the slope is -1 and intercept of 2
What is the solution to -4(8 - 3x) >_6x -8?
O x >_-4/3
O x<_-4/3
O x>_4
Ox<_4
Answers
First I distributed the -4
Then I isolated all of the x on one side
Then I divided everything by 6 to get the value (greater than or equal to) of one x
Savannah decides to download some new music. she downloaded 5 albums and 7 singles, and his total was $71. The next day she purchased more music from the same retailer and downloaded 3 more albums and 6 singles for a total of $48.
Assuming that all albums and singles are the same prices, how much did she spend on each album and each single? Write a system of equations to represent this situation. Then solve for the solution using the elimination method.
Answers
Answer:
Step-by-step explanation:
downloaded= 5 albums and 7 singles and total price is $71
Know,
album + singles = 5+7= 12
∴ price÷ from total of albums and singles
$71÷12=$5.92
per album = $5.92
per single = $5.92
Next day;
3+6=9
total price =$48
⇒ =$48÷9 = $5.3
per album= $5.3
per album= $5.3
""""" I just try to Solve """"""
Answer: Singles are $3/each and albums are $10 each.
Step-by-step explanation:
Let A and S represent the number of Albums and Singles, respectively.
We are told that:
5A + 7S = $71
and also that:
3A + 6S = $48
We have two equations and 2 unknowns. Use elimination to find the price of one and then that will tell us the price of the other. I'll choose to eliminate the A:
5A + 7S = $71
3A + 6S = $48
We can do the elimination in one of 2 ways:
1) Solve one of the equations for A or S, and substitute it in the other:
3A + 6S = $48
3A = $48 - 6S
A = ($48 - 6S)/3
Now use this definition of A in the first equation:
5A + 7S = $71
5(($48 - 6S)/3) + 7S = $71
5(($48 - 6S)/3) + 7S = $71
$80 - 10S + 7S = $71
-3S = - 9
S = $3
Now we can find A:
5A + 7S = $71
5A + 7(3) = $71
5A + 21 = $71
A = $10
======
2) We could also modify one of the equations and then subtract to eliminate a variable:
5A + 7S = $71
3A + 6S = $48
Let's multiply the second equation by -(5/3):
-(5/3)*(3A + 6S = $48)
-5A - 10S = -90
Now add this to the first equation:
5A + 7S = $71
-5A - 10S = -80
- 3S = - 9
S = $3 and therefore A = $10
A pool is being filled at the rate of 66 gallons per hour. ?hours = 22gallons 1.5hours = ?gallons
Answers
Answer:
1/3 hours : 22 gallons
1.5 hours : 99 gallons
Step-by-step explanation:
set a proportion fo all of them
x hours : 22 gallons:
66 22
--- = ---
60 x
22/66 = 0.3333333333333 x 60
= 20 and convert to fraction
20/60 simplified is 1/3
1.5 hours : x gallons
66 x
-- = ---
1 1.5
1.5 / 1 = 1.5
1.5 x 66 = 99
x = 99
What is 216/162 written as an improper fraction in simplest form?
6/4
4/3
3/2
Answers
Answer:
4/3
Step-by-step explanation:
216/162 216 is divisible by 54 and so is 162 so if you divide both by 54 you get 4/3
Answer:
4/3
Step-by-step explanation:
lowest terms is 4/3 e e e. e
PLEASE HELP!!!!!!!!! URGENT!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
the answer is
A. True
that is correct
Someone help me pls!
You can buy 3 apples at Quick Mart for $1.17. You can buy five of the same apples at Shop & Save for $2.40
How much will you save per apple if you buy them at the cheaper store?
Answers
Answer:
You save $0.09 at Quick Mart for price per apple
Step-by-step explanation:
Quick mart = 1.17/3 = $0.39 per apple
Shop & Save = $0.48
$0.39 - $0.48 = $0.09
You save $0.09 per apple at Quick Mart
-Chetan K
Does this table represent a function or not? Why or why not?
Answers
Answer:
D. No, because two of the y-values are the same
Step-by-step explanation:
The y values cannot be the same
Answer:C
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
1) YES
2)NO
3)YES
4)YES
5)YES
Step-by-step explanation:
HOPE IT CAN HELP YOU LOVELOTS
Determine whether each function is even, odd, or neither.
f(x) = x²_9
g(x) = |x-3
f(x) = 22-1
g(x) = x + x2
Answers
Rule for even
[tex]\\ \sf\longmapsto \boxed{\sf f(-x)=f(x),x\in D_f}[/tex]
Rule for odd
[tex]\\ \sf\longmapsto \boxed{\sf f(-x)=-f(x),D_f}[/tex]
Here D_f means domain of function.#1
[tex]\\ \sf\longmapsto f(x)=\sqrt{x^2}-9[/tex]
Take x=4[tex]\\ \sf\longmapsto f(4)=\sqrt{4^2}-9=4-9=-5[/tex]
[tex]\\ \sf\longmapsto f(-4)=\sqrt{(-4)^2}=4-9=-5[/tex]
Even function✓#2
[tex]\\ \sf\longmapsto g(x)=|x-3|[/tex]
Take x=2[tex]\\ \sf\longmapsto g(2)=|2-3|=|-1|=1[/tex]
[tex]\\ \sf\longmapsto g(-2)=|-2-3|=|-5|=5[/tex]
[tex]\\ \sf\longmapsto -g(2)=-1[/tex]
Odd function✓#3
[tex]\\ \sf\longmapsto f(x)=\dfrac{x}{x^2-1}[/tex]
Take x=3[tex]\\ \sf\longmapsto f(3)=\dfrac{3}{3^2-1}=\dfrac{3}{9-1}=\dfrac{3}{8}[/tex]
[tex]\\ \sf\longmapsto f(-3)=\dfrac{-3}{(-3)^2-1}=\dfrac{-3}{8}[/tex]
[tex]\\ \sf\longmapsto -f(3)=\dfrac{-3}{8}[/tex]
Odd function ✓#4
[tex]\\ \sf\longmapsto g(x)=x+x^2[/tex]
Take x=1[tex]\\ \sf\longmapsto g(1)=1+(1)^2=2[/tex]
[tex]\\ \sf\longmapsto g(-1)=-1+(-1)^2=0[/tex]
[tex]\\ \sf\longmapsto -g(1)=-2[/tex]
Neither✓i need to find what is 18 divided by 8
Answers
Answer:
2.25
Step-by-step explanation: