In the figure shown, lines 1 and 2 are parallel. The sum of the measures of angles 4 and 5 is 150°. What is the measure of angle 1? a. 75° b. 105° c. 115° d. corresponding angles
Answers
Answer:
C. 105°
Step-by-step explanation:
The measure of <1 is 105.
What is parallel line?Two lines in a plane are said to be parallel if they do not intersect when extended infinitely in both directions. Two straight lines are said to be parallel if their slopes are equal and they have different y-intercepts. Given below are a few important properties of parallel lines that actually reflect the characteristics of parallel lines.
For the parallel lines cut by a transversal, the following properties hold true:
Two lines cut by a transversal line are parallel if the corresponding angles so formed are equal. In general, the corresponding angles are in relative positions and lie along the same side of the transversal.Two lines cut by a transversal line are parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.Two lines cut by a transversal line are parallel if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.Given:
<4 + <5 = 150 (given)
As, from the figure
<4 = <5 (alternate exterior angle)
Then,
<4 + <4 = 150
2<4 = 150
<4 = 75
and <5 = <4 = 75
Now, <1 + <5 = 180 (linear pair)
<1 + 75 = 180
< = 180 -75
<1 = 105
Hence, the measure of <1 is 105
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Related Questions
write two numbers that multiply to the value on top and add to the value on bottom.
top number : 56
bottom number:-15
Answers
Answer:
7 x 8 = 56
-3 x -5 or -5 + -5 + -5 = -15
Step-by-step explanation:
The numbers that result in the top and bottom numbers are: -7 and -8
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
You should convert the given text into linear equations.
x*y=56 (1)
x+y=-15 (2)
For equation 2, you have x=-15-y. Thus, you can replace this variable into equation 1.
(-15-y)*y=56
-15y-y²=56
-y²-15y-56=0
You find a quadratic equation. Solving this equation:
[tex]y_{1,\:2}=\frac{-\left(-15\right)\pm \sqrt{\left(-15\right)^2-4\left(-1\right)\left(-56\right)}}{2\left(-1\right)}\\ \\ y_{1,\:2}=\frac{-\left(-15\right)\pm \:1}{2\left(-1\right)}\\[/tex]
[tex]y_1=\frac{-\left(-15\right)+1}{2\left(-1\right)}=-8\\ \\ y_2=\frac{-\left(-15\right)-1}{2\left(-1\right)}=-7[/tex]
For equation 2,
For y=-8x+y=-15
x+(-8)=-15
x=-15+8=-7
For y=-7 x+y=-15 x+(-7)=-15x=-15+7=-8Read more about the quadratic function here:
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Dan's school is selling tickets to a play. On the first day of ticket sales the school sold 1 adult ticket and 6 student tickets for a total of $69. The school took in $150 on the second day by selling 7 adult tickets and student tickets How much is a student ticket?
Answers
Answer:
Let's define the variables:
A = price of one adult ticket.
S = price of one student ticket.
We know that:
"On the first day of ticket sales the school sold 1 adult ticket and 6 student tickets for a total of $69."
1*A + 6*S = $69
"The school took in $150 on the second day by selling 7 adult tickets and student tickets"
7*A + 7*S = $150
Then we have a system of equations:
A + 6*S = $69
7*A + 7*S = $150.
To solve this, we should start by isolating one variable in one of the equations, let's isolate A in the first equation:
A = $69 - 6*S
Now let's replace this in the other equation:
7*($69 - 6*S) + 7*S = $150
Now we can solve this for S.
$483 - 42*S + 7*S = $150
$483 - 35*S = $150
$483 - $150 = 35*S
$333 = 35*S
$333/35 = S
$9.51 = S
That we could round to $9.50
That is the price of one student ticket.
Help please! I’ll give brainliest!
Answers
Answer:the last one
Step-by-step explanation:
Juan got grades of 68 and 73 on his first two math tests. What grade must he get on the third test if all were weighted equally and he wants to raise his grade to a 75 average?
Answers
Answer: 84
Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.
polly the carrot has learned to say "polly wants a cracker." if she says it every five minutes for two hours and gets a cracker to eat each time, how many crackers will polly eat?
Answers
Answer:
24
Step-by-step explanation:
(60 × 2 ) ÷ 5 = 24.
60 because hour is 60 minutes
× 2 because she says it for 2 hours
÷ 5 because she says it every 5 minutes
-16/128 simplified + (3/2 + 43/23) = ?
Answers
Answer:
3.245
Step-by-step explanation:
Answer:
YES I ANSWERED IT
Step-by-step explanation:
THX I GOT 100 POINTS :)
The temperature in Allenville fell from 25°F to -23°F in 8 minutes. What's the average change in temperature per minute?
Answers
Answer:
6 Degrees per minute
Step-by-step explanation:
25 + 23 = 48
48 divided by 8 = 6
please draw a graph thank you!!!
Answers
Answer:
x is greater than or equal to 3. A closed circle dot on 3, with the arrow and closed dot going left from 3, towards the negative region.
a qUICK ALGEBRA QUESTION FOR Y'ALL FOR A POSSIBLE QUIZ CORRECTION OF MINE. i got 6,,, wish y'all got 6 too so i'm not alone :"DDD
IF X = -2
-x2 + 2
Answers
-2x2 = -4 + 2 = -2
Find the % of increase or decrease 92 lb to 200 lb
Answers
Answer:117.391304347826%
Step-by-step explanation:
In March it rained 8.23 inches. It rained 5.96 inches less in April than in March.
How much did it rain in April?
Answers
What is the x-intercept of
3x – 4y = 242
Answers
Answer:
x=242/3
alternative form= 80 2/3, x=80.6
Step-by-step explanation:
3x-4y=242
substitute y = 0
3x-4x0=242
calculate the product
3x-0=242
remove 0
3x=242
divide both sides (by 3 in order to leave x by itself)
done
simplify
y = -1x - 1
pls hurryyyyyyy
Answers
this is the answer because -1x can just be written as -x
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Use digits to write the value of the 9 in this number.
139,648
Answers
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem.
−9.5 − (−8)− 6.5
He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
Answers
Answer:
When subtracting a negative number, the two subtractions signs cancel out to be a positive.
Step-by-step explanation:
When subtracting a negative number, the two subtractions signs cancel out to be a positive.So, -9.5 - (-8) - 6.5 = -9.5 + 8 - 6.5I hope this helps!
Gina wants to make
hamburgers for 12 people.
Her recipe serves 8 people
and calls for 4.5 pounds of
ground beef. How much
ground beef should
Gia purchase?
h
Answers
Answer:
6.75 pounds
Step-by-step explanation:
This question is of direct variation. We will use x as our answer. 8 is 2/3 of 12, so 4.5 should be 2/3 of x. We can now make an equation.
[tex]4.5=\frac{2}{3} x\\4.5*\frac{3}{2} =\frac{2}{3} x*\frac{3}{2} \\6.75=x[/tex]
In order to solve the equation, we multiply both sides by the reciprocal of 2/3, which is 3/2.
* stands for multiplication
From solving our equation, we get 6.75. We can't forget the units, so the answer is 6.75 pounds.
The area of a rectangle is 72 square metres. The length of the rectangle is twice the width. Find the width of the rectangle.
Answers
Working:
Find common factors of 72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Work out which ones multiply together to make 72 and as the question states that the length is twice the width, we need to find two numbers that multiply to make 72 and one of the numbers is double the other number.
These numbers would be 6 and 12. (6 x 12 = 72)
Therefore:
Area = 72m²
Width = 6m
Length = 12m
How much of an alloy that is 30% copper should be mixed with 50 ounces of an alloy that is 60% copper in order to get an alloy that is 40% copper?
Answers
Answer: 180 i think
Step-by-step explanation: .5*200+.2X=.3(200+X)
100+.2X=60+.3X
.2X-.3X=60-100
-.1X=-40
X=-40/-.1
X=400 OUNCES OF 20% COPPER.
PROOF
.5*200+.2*400=.3(200+400)
100+80=.3*600
100+80=180
180=180
Answer: 100 ounces of the alloy.
Step-by-step explanation: To solve, we create an equation:
First, though, let's define some variables and values -
x = amount of the alloy we are trying to find
0.3 = 30% copper
0.6 = 60% copper
50 = 50 ounces of the alloy
0.3(x) + 0.6(50) = 0.4(x+50) - original equation
0.3x + 0.6*50 = 0.4x + 0.4*50 - expanded
subtract 0.3x and 0.4*50 on both sides to get...
0.2*50 = 0.1x - simplified
calculate...
10 = 0.1x - simplified
divide both sides by 0.1 to get...
100 = x --> x = 100
A farmer finds that if she plants 50 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?
Answers
Answer:
28
Step-by-step explanation:
From the given information:
Let x be the number of trees.
F(x) = (50 +x) (20 - 3x)
F(x) = 1000 - 150x + 20x - 3x²)
F(x) = -3x² - 130x + 1000
Differentiating F(x) with respect to x;
[tex]F'(x) = \dfrac{d}{dx}( -3x^2- 130x + 1000)[/tex]
[tex]F'(x) = ( -3(2x)- 130(1) +0)[/tex]
F'(x) = -6x -130
Now; we set F'(x) to be equal to zero to determine the critical value;
-6x - 130 = 0
x = - 130/6
Differentiating F''(x) with respect to x
[tex]F''(x) = \dfrac{d}{dx}( -6x- 130)[/tex]
[tex]F''(x) = ( -6(1))[/tex]
F''(x) = -6 (<0)
Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6
Therefore, the number of trees she should plant per acre to maximize her harvest is:
50 + x = 50 - 130/6
= 85/3
[tex]\simeq[/tex] 28
Therefore, the number of trees per acre to maximize the harvest is 28
Mary keeps track of how much time she goes running each week for 10 weeks. the frequency table with the data she collected. How many hours did mary spend running?
Answers
Answer:
One bad b, and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
One bad b, and she do what I say so (yeah, gang)
Two big .40s and a big a Draco (two)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s
I'm with my n*yeah, we some rockstars
And I'm with my n yeah, KK Wokhardt (KK Wokhardt)
This not my d, lil' b, my Glock hard (lil' b)
Straight to the cash, I'm a trapstar (cash)
Straight to the bag, I'm that n, huh (bag, oh)
Got me some gas, rollin' up some
Fft, fft, cash, yeah, I got me some
I ain't f her yesterday (yeah)
I'ma f some
One bad b , and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
3-0 clip in my Nina (oh, oh)
On my toes, Gucci, Valentino (yeah, b)
She on go, your b f the team, uh (lil' b )
'Cause you know your b want a winner (winner)
I just went back to my city (to my city)
And you know they all f with me (big hands)
But it ain't safe, h with me (h)
I'ma chase bands 'til they end me
One bad b, and she do what I say so
Two big .40s and a big a Draco (two, boom, boom)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s (that's how it goes)
One bad b, and she do what I say so (yeah, gang)
Two big .40s and a big a Draco (two)
Three more millions when you ask how my day go
Poured up a 4, now that's blueberry Faygo
One false move, and we straight to shooting s
Two small bands just to take you out real quick (bands)
Three more h, pull up, I'm f s
That's how it go, big bands, I'm thumbin' s
Step-by-step explanation:
PLEASEE HELP IM BEGGING YOU
Answers
Answer: god it's hard, but i will try
Clare ran 4 miles on Monday. Then for the next six days, she ran the same distance each day. She ran a total of 22 miles during the week. Which tape diagram represents this situation?
Answers
Answer:
In a week we have 7 days.
On the first day, Clare runs 4 miles.
On the other six days, she runs the same distance, let's call it D.
In total, she runs 22 miles.
Then:
4mi + 6*D = 22 mi
6*D = 22mi - 4mi = 18mi
D = 18mi/6 = 3mi.
Then the other 6 days, Clare runs 3 miles, then the tape diagram would look something like:
[tex]\left[\begin{array}{cccccc}Monday&-&-&-&-\\Tuesday&-&-&-\\Wednesday&-&-&-\\Thursday&-&-&-\\Friday&-&-&-\\Saturday&-&-&-\\Sunday&-&-&-\end{array}\right][/tex]
Where each "-" represents one mile.
Answer:
3 miles
Step-by-step explanation:
simplify 3(12 - 8) + 5
Answers
Answer:
17
Step-by-step explanation:
The value of the given linear expression 3(12 - 8) + 5 is 17.
What is a linear equation?
A linear expression is an expression in which the highest power of the variable is always 1. If there is no variable, we can assume the power of the variable as 0.
Therefore, the variable x⁰ = 1.
Given linear expression:
3(12 - 8) + 5
= 3 × 4 + 5
= 12 + 5
= 17
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you finance a $12,000 condo renovation completely on credit and you will just pay the minimum payment each month for the next few months. The APR is 18.99% and the minimum payment each month is 5% of the balance. Determine the finance charge, carry-over balance, and minimum payment required for each of the next two months, and the starting balance for month 2 in the table below.
Answers
Answer:
For Month 1, we have:
Carry-over balance = $12,000.00
Finance charge = $189.90
New balance = $12,189.90
Minimum payment = $609.50
For Month 2, we have:
Carry-over balance = $11,580.41
Finance charge = $183.26
New balance = $11,763.66
Minimum payment $588.18
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.
The explanation to the answer is now given as follows:
Note: See the attached excel file for calculations of the finance charge, carry-over balance, and minimum payment required for each of the next two months.
In the attached excel file, the following formulas are used:
r = Monthly percentage rate = APR / 12 = 18.99% / 12 = 1.5825%
Carry-over balance of the current month = New balance of the previous month - Minimum payment of the previous month
If Kishan wanted to average a 90% for the term and on his first four tests he got an 83, 94, 88, and 85, what would he have to get on the fifth test in order to meet his goal?
Answers
Answer:100%
Step-by-step explanation:
83+94+88+85+100=450
450/5=90% average
A coconut tree has 12 coconuts on it if 25% of them fell to the ground how many fell
Answers
Answer:
3
Step-by-step explanation:
25% of 12 is 3
hope it helps
Answer:
3
Step-by-step explanation:
25% of anything is also 1/4 of the whole number. Its easier (atleast for me) to make percentages into fractions to make it easier to find the answer. if you were to make 12 a fraction it would look like 12/1 and when we subtract the 1/4 of coconuts it would be 3.
Which Statement about 4(x-3) is True? Giving Brainliest
Answers
Answer:
A I think that is the ans
A jogger is running home. His distance from home, as a function of time, is modeled by y=-7x +8.
Which statement best describes the function?
A. The function is nonlinear.
B. Not enough information is given.
C. The function is linear at some points and nonlinear at other points.
D. The function is linear.
Answers
Answer: the function is a liner
Step-by-step explanation: trust
Help??
Anyone??
Need it in 3 min
7th grade math
Answers
explanation:
use proportions
What is 8 divide 1/5?
What is 8 divide by 1/5
Answers
Answer:
40
Step-by-step explanation:
