The angles shown above form a linear pair. Show all of your work for full credit.
A. What is the angle relationship between these two angles?
B. Set up an equation and solve for n.
C. Substitute your values into the equation and find the measurements of both angles.
Answers
Answer:
A. [tex] (4n + 22) + (8n - 10) = 180 [/tex]
B. [tex] n = 14 [/tex]
C. 78° and 102°
Step-by-step explanation:
A. The relationship between the two angles that are a linear pair is: their sum gives us 180°. That is:
[tex] (4n + 22) + (8n - 10) = 180 [/tex]
B. [tex] (4n + 22) + (8n - 10) = 180 [/tex]
Solve for n.
[tex] 4n + 22 + 8n - 10 = 180 [/tex]
Collect like terms
[tex] 12n + 12 = 180 [/tex]
Subtract 12 from both sides
[tex] 12n + 12 - 12 = 180 - 12 [/tex]
[tex] 12n = 168 [/tex]
Divide both sides by 12
[tex] \frac{12n}{12} = \frac{168}{12} [/tex]
[tex] n = 14 [/tex]
C. Plug in the value of 14 to get the measurement of both angles
[tex] (4n + 22) = 4(14) + 22 = 56 + 22 = 78 [/tex]
[tex] (8n - 10) = 8(14) - 10 = 112 - 10 = 102 [/tex]
Related Questions
Determine the density in g/cm3 of a mineral that has a volume of 3.8 cm3 and a mass of 22.4 g.
Answers
Answer:
5.89 g/cm³
Step-by-step explanation:
givens,
Mass = 22.4 g
volume = 3.8 cm³
Density = mass / volume
= 22.4 / 3.8
= 5.89 g/cm³
The density with a volume of 3.8 cm³ and a mass of 22.4 g is 5.89 g / cm³.
Given,
The volume of a mineral = 3.8 cm3
And the mass of the mineral = 22.4 g
We need to find the density.
What is density?It is the ratio of mass and volume.
Density = mass / volume
Find the density.
Volume = 3.8 cm³
Mass = 22.4 g
Density
= Mass / Volume
= 22.4 / 3.8
= 5.89 g / cm³
Thus the density with a volume of 3.8 cm³ and a mass of 22.4 g is
5.89 g / cm³.
Learn more about how to find density in the cgs system here:
https://brainly.com/question/9989733
#SPJ6
The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra CO2. The response variable is the mean increase in base area for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. Here are one year's data.
Pair Control plot Treated plot
1 9.728 10.748
2 7.276 8.332
3 5.612 6.632
Required:
a. State the null and alternative hypotheses.
b. Explain clearly why the investigators used a one-sided alternative.
1. The researchers have no preconceived idea what extra CO2 will do to the growth rate.
2. The researchers have reason to believe that CO2 will decrease growth rate.
3. The researchers have reason to believe that CO2 will increase growth rate.
c. Carry out a test and report your conclusion in simple language.
Answers
Answer:
this is math go to siecne noob
Step-by-step explanation:
I need help on math
Answers
Can you guys help me with this angle problem for Geometry tysm
Answers
Answer:
You need to solve for x
Step-by-step explanation:
3x + 5 + 10x - 7 = 180
13x + 5 - 7 = 180
13x - 7 = 175
13x = 182
x = 14
Plug in x
3(14) + 5 for QRT and 10(14) - 7 for TRS
QRT = 47 and TRS = 133
Answer:
QRT = 47
TRS = 133
Step-by-step explanation:
The two angles form a straight line so they add to 180
3x+5 + 10x-7 = 180
13x-2 =180
Add 2 to each side
13x-2+2 =180+2
13x= 182
Divide by 13
13x/13 = 182/13
x =14
We want QRT = 3x+5 = 3*14+5 = 42+5 = 47
TRS = 10x-7 = 10*14-7 = 140-7 = 133
An investigation of wages paid to its employees by a large company was undertaken as a result of an allegation of discrimination. Data was collected for 1000 randomly selected employees. The data included employee ID, gender, race, annual wages in dollars (Salary), whether the employee had full-time status or part-time status (Full_Part), number of years of education (Ed), and number of years with the company (Tenure). The first two rows of data in the worksheet are displayed below.
1 Gender Race Salary Full_Part Ed Tenure
2 Female Caucasian 32196 Full 14 2
3 Male Black 62385 Full 16 10
How many cases does this data set contain?
How many variables does this data set contain? (3 p)
How many quantitative variables does this data set contain, and what are they? How many qualitative variables does this data set contain, and what are they?
Answers
Answer:
Step-by-step explanation:
First, the data set is:
Gender Race Salary WorkTimeStatus Education Tenure
1. Female Caucasian 32196 Full Time 14yrs 2 yrs
2. Male Black 62385 Full Time 16yrs 10yrs
Now to the questions:
(A) This data set contains 2 cases; 1 for the first employee (the female caucasian) and 2 for the second employee (the male black).
(B) This data set contains 6 variables;
1. Gender 2. Race 3. Salary 4. Work time status 5. Years of education
6. Number of years in/with the company
(C) Out of these 6 variables, the quantitative ones (those that can be measured or weighted numerically) are:
3. Salary 5. Years of education 6. Years with the company
Altogether, 3 in number
(D) The qualitative variables are:
1. Gender 2. Race 4. Work Time Status
Altogether that's 3 variables
Write 1/8% as a decimal number Enter your number in the box
Answers
Answer:
it is 0.125
Step-by-step explanation:
......................
PLEASE HELP! 6TH GRADE MATH please write done what number you're doing
Answers
Answer:
# 10 is 4/3 or 1 and 1/3
#11 is 4/10 or 2/5
#12 is 2 and 3/4
#13 is 36/12 or 3 and 1/12
Step-by-step explanation:
i am not 100% sure on #13 btw
hope this helped!
p.s it would be cool if you gave me brainliest.
Answer:
Hey your answers on there are correct.
Step-by-step explanation:
Help to solve x and Y
Answers
Solving steps:
1. Solve for x
Look at picture
2. Find y
(10x-6)+(9y-5)=180
(10(11)-6)+(9y-5)=180
104+(9y-5)=180
9y-5=76
9y=81
y=9
Express 610.47 in unit form.
Answers
Answer:
6 hundreds
1 tens
0 ones
4 tenths
7 hundredths
Assemble the proof by dragging tiles to the statements and reasons columns
Answers
Answer:
Here, I did the assignment. I wish you good luck!
List the numbers in order from least to greatest.
-4,8,-15,-8,4,1
The numbers in order from least to greater Are
Answers
Answer: -15, -8, -4, 1, 4, 8
A closet is 3 yards wide. What is its width in inches?
Answers
Answer:
The closet is 108 inches wide.
Step-by-step explanation:
Because 1 yard is 36 inches, and 36 times 3 is 108.
Write the equation of the line parallel to the given line and through the given
point. y=2x - 8 through (3.10)
Answers
Answer:
y-2x -8
Step-by-step explanation:
your jus gonna right it back because it's parallel which means it's the same thing.
Over the past several years, the owner of a boutique on Aspen Avenue has observed a pattern in the amount of revenue for the store. The revenue reaches a maximum of about $ 46000 in March and a minimum of about $ 28000 in September. Suppose the months are numbered 1 through 12, and write a function of the form ()=sin([−])+ f ( x ) = A sin ( B [ x − C ] ) + D that models the boutique's revenue during the year, where x corresponds to the month. If needed, you can enter π =3.1416... as 'pi' in your answer. ()= f ( x ) =
Answers
Answer:
F(x) = [tex]9000 sin (\frac{\pi }{3} (x-3) + 37000[/tex]
Step-by-step explanation:
Revenue reached in March = $46000 ( Maximum )
Revenue reached in September = $28000 ( Minimum )
f(x)=Asin(B[x−C])+D
attached below is the detailed solution of the problem
attached below is the detailed solution
F(x) = [tex]9000 sin (\frac{\pi }{3} (x-3) + 37000[/tex]
Evaluate the expresion for x=6. -2x + 1/3(x2 + 6) - 36/6
Answers
Answer:
x=6/7 hope i did it right- im so sorry if thats wrong
Step-by-step explanation:
Brandon enters bike race. He bikes 9 1/2 miles every 1/2 hour
Answers
Hope this helps:)
please answer....writing assignment for math
Answers
Answer:
This information tells me that f equals a number and 3 multiplied by the number that f equals is 16.
Could I please have Brainliest?
Need help ASAP pls !!!!!
Answers
Answer:
growth and .09% increase I believe
Step-by-step explanation:
Help me please!!!!!!!!
Answers
Answer:
y = -6x - 5
Step-by-step explanation:
To find the equation using the point-slope equation, we need the slope and the y-intercept of the line
Finding the slope of the line:
We will calculate the slope between these 2 points: (-1 , 1) and (0 , -5)
Slope = Rise / Run
Rise of the line = y1 - y2
Rise = 1 - (-5)
Rise = 1 + 5
Rise = 6
Run of the line = x1 - x2
Run = -1 - 0
Run = -1
Slope of the line:
Slope = Rise / Run
Slope = 6 / -1
Slope = -6
Finding the y-intercept:
y-intercept of a line is the y-ordinate of the point where the line intersect the y-axis
From the graph, we can see that the line intersects the y-axis at (0 , -5)
y-coordinate of the point = -5
y-intercept = -5
Equation of the line:
This is the general formula of the slope-intercept:
y = mx + b (where m is the slope of the line and b is the y-intercept )
Replacing the variables
y = (-6)x + (-5)
y = -6x - 5
Graph the line that represents the equation
Answers
Answer:
In the attachment.Step-by-step explanation:
We need only two points.
Choose any two values of x. Put them to the equation and calculate the value of y:
[tex]y=-\dfrac{2}{3}x+1\\\\\text{for}\ x=0\\\\y=-\dfrac{2}{3}\cdot0+1=0+1=1\to A(0;\ 1)\\\\\text{for}\ x=3\\\\y=-\dfrac{2}{3}\cdot3+1=-2+1=-1\to B(3;\ -1)[/tex]
If you have metamorphic rock and melt it, what does it become?
A. Magma
B. Minerals
C. Sedimentary Rock
D. Soil
Answers
Step-by-step explanation:
When metamorphic rock melts it turns into magma.
What is 5/8 of $16 restaurant bill=
What is the answer
Answers
Answer:
$10
Step-by-step explanation:
16 * 5 / 8 = 16 * 0.625 = $10
I’m not well with percentages lol. Can someone help me with solving it and answer
Answers
Answer:
1. Dracula Answer: D) 12.5%
2. Jack-O-Lantern Answer: D) 40%
Step-by-step explanation:
1. 54 - 48 = 6
6/48 = 0.125 x 100 = 12.5%
2. $20 - $12 = 8
8/20 = 0.4 x 100 = 40%
Compare and contrast xy with xy
Answers
Answer:
theres positive and negative
Step-by-step explanation:
i think that's what your talking about
One box of pencils costs rupees 28 . What is the cost of 509 boxes
Answers
One box of pencils costs rupees 28 . What is the cost of 509 boxes
Given:1 pencil costs=₹281 pencil costs=₹28No. of boxes=509We know:Costs of total no. of pencil boxes
=1 pencil box's costs×No. of boxes
=509×28
=14252✓
The variables x and y are related proportionally. When x = 8, y = 20. Find y when x = 80.
Answers
Answer:
y = 200
Step-by-step explanation:
Use the equation y = kx, where k is a constant.
Plug in the given x and y values, then solve for k:
y = kx
20 = k(8)
2.5 = k
Then, plug in k and the given x value, and find y:
y = 2.5x
y = 2.5(80)
y = 200
So, y = 200 when x = 80
The red-tailed tropic bird, Phaethon rubricauda, is an extremely rare sea bird that nests on several islands of the Queensland coast of Australia. As part of a conservation e ort to manage these endangered birds, every nesting pair was measured and weighed. Below are the body weights of these birds (in kg).
Female 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84
Required:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
b. Determine the mean, variance, and standard deviation for the male weights.
Answers
Answer:
This is a population
a) Female
Mean : 2.432857143kg
Variance: 0.05162040817kg
Standard deviation: 0.2272012504kg
b) Male
Mean : 2.641428571kg
Variance : 0.03432653062kg
Standard deviation: 0.1852742039kg
Step-by-step explanation:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
a) Female: 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Mean
The formula = Sum of term/ Number of terms
Mean = 2.45 + 2.57 + 2.81 + 2.37 + 2.01 + 2.50 + 2.32/7
17.03/7
= 2.432857143kg
Variance
This is a population
Hence: The formula for Population variance =
= (X - Mean)²/N
Where N = Number of terms = 7
= (2.45 - 2.432857143)² + (2.57 -2.432857143)² + (2.81 -2.432857143)² + (2.37- 2.432857143)²+ (2.01 - 2.432857143)²+ (2.50 - 2.432857143)² + (2.32 - 2.432857143)² /7
= 0.0002938775509 + 0.01880816325 + 0.1422367347 + 0.003951020409 + 0.1788081633 + 0.004508163265 + 0.0127367347/7
= 0.3613428572/7
= 0.05162040817kg
Standard Deviation
Formula = √Variance
= √0.05162040817
= 0.2272012504kg
b. Determine the mean, variance, and standard deviation for the male weights
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84
Mean
The formula = Sum of term/ Number of terms
= 2.86 + 2.65 + 2.75 + 2.60 + 2.30 + 2.49 + 2.84/7
= 18.49/7
= 2.641428571 kg
Variance
= ( 2.86 -2.641428571)² + (2.65 - 2.641428571)² + (2.75 -2.641428571)² + (2.60 +2.641428571)² + (2.30 - 2.641428571)² + (2.49+2.641428571)² (2.84 + 2.641428571)²/7
= 0.0477734694 + 0.00007346938775 + 0.01178775511 + 0.001716326531 + 0.1165734694 + 0.02293061224 +! 0.03943061226/7
= 0.2402857143/7
= 0.03432653062kg
Standard Deviation
= √Variance
= √0.03432653062
= 0.1852742039kg
A scale drawing of a building needs to be made using the scale 1 in = 230 ft. How tall will the building in the scale drawing be if the building is 1380 ft tall?
Answers
adult men weights mean of 190 30 3 random men mean weight
Answers
Answer:
is this the question ?
Step-by-step explanation:
pls help meeeeeeeeeeee!!
Answers
Answer:
45 with a remainder of 27.
Step-by-step explanation:
Hope this helps you! Good luck! <3