The table below shows the average annual salary of the workers at the Pearson
Corporation over the course of time since 1980. Let x represent the number of years
since 1980 with x = 0
representing the year 1980. Let y represent the average annual
salary of the workers. Complete the slope-intercept form of the equation for the line of
best fit below with the appropriate value for the slope.
Answer:
[tex]y = 1164x + 14242[/tex]
Step-by-step explanation:
From the question, we understand that
x = 0, when year = 1980
First, we need to determine the slope of the table.
Pick any two corresponding values of year and average salary
year = 1982, average salary = 16570
year = 2002, average salary = 39850
Convert years to x values
year = 1982 implies that x = 2 i.e. 1982 - 1980
year = 2002 implies that x = 22 i.e. 2002 - 198-
So, we have:
[tex](x_1,y_1) = (2,16570)[/tex]
[tex](x_2,y_2) = (22,39850)[/tex]
Determine the slope.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{39850 -16570}{22 - 2}[/tex]
[tex]m = \frac{23280}{20}[/tex]
[tex]m = 1164[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 1164[/tex]
[tex](x_1,y_1) = (2,16570)[/tex]
So,
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 16570 = 1164(x - 2)[/tex]
[tex]y - 16570 = 1164x - 1164*2[/tex]
[tex]y - 16570 = 1164x - 2328[/tex]
Add 16570 to both sides
[tex]y - 16570 + 16570 = 1164x - 2328 + 16570[/tex]
[tex]y = 1164x - 2328 + 16570[/tex]
[tex]y = 1164x + 14242[/tex]
Answer:
y = 1164x + 14,242
Step-by-step explanation:
In triangle ABC show find BC..
Need help ASAP!!!
Answer: BC=22cm
Step-by-step explanation:
5d-3=3d+7
2d=10
d=5
plug 5 into the equation for BC, and you get 22
Answer:
Segment BC is (3d + 7)cm, where d=5. So, BC= 22cm.
Step-by-step explanation:
Segment BC is (3d + 7)cm, where d=5. You find this through these steps:
(5d-3)=(3d+7) Subtract 3d from 5d, which equals 2d.
2d-3=7 Now, add 3 to 7.
2d=10 Divide 10 by 2.
d=5 The solution is 5.
Plug 5 into the equation of Segment BC:
3(5) + 7
BC= 22
Andre and Diego were each trying to solve `2x+6=3x-8`. Describe the first step they each make to the equation.
The result of Andre's first step was `-x+6=-8`.
A biker cycles 9 miles in 2/3 of an hour.
a
Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours, 3 hours, 3.5 hours
Answer:
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
He rides 27 miles in two hours, 81/2 miles in 3 hours, and 189/4 in 3.5 hours.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A biker cycles 9 miles in 2/3 of an hour.
∴ He rides (9×3/2) is (2/3)×(3/2) hours.
He rides 27/2 miles in 1 hour.
So, He rides (27/2)×2 in 2 hours.
27 miles in 2 hours.
He rides (27/2)×3 miles in 3 hours.
81/2 miles in 3 hours.
He rides (27/2)×(7/2) miles in 7/2 hours.
189/4 miles in 7/2 hours.
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What is the difference of 4 cubed and 25????
Answer:
39
Step-by-step explanation:
4 cubed is 64 and 64-25 is 39
Which table represents a linear function?
ху
х
y
1
7
2
2
11
4
3
12
6
12
4
13
8
15
ху
х
у
N X
7
1
7
4
9
2.
9
6
11
3
12
8
13
4
15
The second table at the bottom represents a function because the slope for consecutive pairs of values is the same as 2, all through. The answer is: {(2, 7), (4, 9), (6, 11), (8, 13)}.
How to Identify a Table that Represents a Linear FunctionA table that represents a linear function will have the same slope across all pairs of values.Change in y / change in x will remain the same between consecutive pairs of values.Thus, the second table at the bottom represents a function because the slope for consecutive pairs of values is the same as 2, all through. The answer is: {(2, 7), (4, 9), (6, 11), (8, 13)}.
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Mark and some of his friends had eaten pizzas. What is this written as a decimal?
Answer:
We don't really have the whole question, but to convert to a decimal, you should divide the numerator by the denominator.
Example:
Convert 5/8 to a decimal.
5 divided by 8 = 0.625
please help, my time is running out
Answer: 40 ?
Step-by-step explanation:
$64 for four video games
What is the ratio and unit rate
Answer:
16 for each video game
Step-by-step explanation:
The unit rate is 16x
the ratio is 16:1
The slope is y=16x
Answer:
The ratio: $65:4
The unit rate: 16.25:1
Step-by-step explanation:
The ratio is money to video games.
The unit rate is how much money each video games cost.
What is the perimeter of this shape
Answer:
40.9
Step-by-step explanation:
8+10+8.9+10+4=40.9
hope this helps :3
if it did pls mark brainliest
Answer:
40.9 ft
Step-by-step explanation:
Perimeter is the sum of lengths of all outer sides of the shape. Since the rectangle has two pairs of parallel lines of the same length... It is safe to assume that the unmarked side length is 10 ft (just like it's parallel counterpart)
Now it is a simple matter of adding all of the outer sides.
8ft + 10 ft + 10 ft + 8.9 ft + 4 ft = 40.9 ft
Which statement about rigid transformations is true?
A.
A rigid transformation preserves only the side lengths of a polygon.
B.
A rigid transformation preserves only the angle measures of a polygon.
C.
A rigid transformation preserves both the side lengths and the angle measures of a polygon.
D.
A rigid transformation preserves neither the side l
Answer:
The answer is B because it is only the measure of the polygon
Describe the transformation of f(x) = x2 represented by g(x)=(x-1)2 + 3, then graph the function
shift right ?______
Shift left ?______
Stretch factor?_____
The transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
What do you mean by transformation of a graph ?
The modification of an existing graph or graphed equation to create a different version of the following graph is known as transformation.
The functions given are :
f(x) = x²
and
g(x) = (x - 1)² + 3
Now , we know that , the horizontal shift depends on the value of h. The horizontal shift is described as:
g(x) = f (x + h)
Then , the graph is shifted to left by h units.
and
g(x) = f (x - h)
Then , the graph is shifted to right by h units.
If we compare f(x) with g(x) , their is a difference of -1 , it meant shift is right by 1 units.
Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:
g(x) = f(x) + k
Then , the graph is shifted up by k units.
and
g(x) = f(x) - k
Then , the graph is shifted down by k units.
Here , if we compare f(x) with g(x) there is addition of 3 in g(x) , this meant the graph is shifted upward by 3 units.
The graph of the function is attached below. Here , both of the functions are graphed.
Therefore , the transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
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Is y=(x/3) an inverse or direct variation
Answer: y=x3 is a direct variation.
Step-by-step explanation:
Ms. Sakai rode her bike 7.25 miles on Friday. She then rode 12.3 miles on Saturday and then 7.3 miles on Sunday. How many total miles did she ride over those three days?
Answer:26.85 miles
Step-by-step explanation: 7.25+12.3+7.3=26.85
figure out the slope of the line that passed through each pair of points (4,-11) and (7,-8)
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[tex]slope = \frac{ - 8 - ( - 11)}{7 - 4} \\ [/tex]
[tex]slope = \frac{ - 8 + 11}{7 - 4} \\ [/tex]
[tex]slope = \frac{3}{3} \\ [/tex]
[tex]slope = 1[/tex]
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PLZZZZ HURRY ILL GIVE BRAINLEST POINTS PLZZZZ I NEED A 100% ON THIS TEST
determine the equation of the line given by the graph y=2/3x-1 y=3/2x-1 y=-2/3x-1 y=-3/2x-1
Answer:
y=2/3-1
Step-by-step explanation:
Two coordinate points are (-3,-3) and (3,1). If you use Y2-Y1/X2-X1, you will find the slope. Then use y=mx+b to find the equation.
More detailed:
1+3/3+3 ** It is + because when there are minus signs it turns to a plus
4/6 Then simplify it
2/3
Now that the slope is found, we need to use y=mx+b
(I used the point (3,1)) 1=2/3(3)+b
1=2+b
-1=b
I hope this is helpful gl on the test! :)
In the diagram, AB= DC and AC= DB. Why does DBC = ACB?
Answer:
AB = DC Given
AC = DB Given
BC = BC Reflexive property
△ACB = △DBC SSS
m∠DBC = m∠ACB CPCTC
Step-by-step explanation:
Reflexive property basically means that something is congruent to itself
SSS means that if all 3 sides of 2 triangles are congruent, the triangles are congruent
CPCTC means C.orresponding P.arts of C.ongruent T.riangles are C.ongruent
meaning because the triangles are congruent, all the corresponding sides and angles are also congruent
HELP ASPCA PLZ
How long is the flight from Baltimore to Miami?
2 hours 25 minutes
O 2 hours 35 minutes
O 3 hours 25 minutes
o 3 hours 35 minutes
71 3/7% Express the percent as a fraction in simplest form.
please help.
Answer:
5/3
Step-by-step explanation:
We want to express the percentage as a fraction
We have;
500/3/100 = 500/300 = 5/3
NEED HELP FO THE ONE TIME ASAP NO ROCKY
Answer: X=32
Step-by-step explanation: 85+63=148. The tree angles of a triangle equals 180 degrees, so 180-148=32
The sum of two integers is 5. Their difference is 11. What are
the two integers?
A 3 and 14
B
-3 and 8
C 2 and 3
D -14 and -3
The probability of getting 3 is the half of getting 6. Is Victoria correct?
yes because 6÷2 is 3 and that gets you the answer
*15 Points* need help quickly plz
Answer:
Both of these statements are correct.
Step-by-step explanation:
Adjacent means next to each other, vertical angles are like angles 2 and 5, where they are right across from each other.
I hope this helps/ makes sense!!!
Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-
response question. There are 15 questions on the test and the students have been given 55 minutes to complete it.
Test Time
Number of Time per Item
Questions (minutes)
m
3
15-m
8
15
Multiple Choice
Free Response
Total
Which value could replace x in the table?
Total Time
(minutes)
3m
х
55
7-m
23-m
8(15 - m)
O 8(15) -
Answer:
See below :)
Step-by-step explanation:
The solution is, 12 multiple-choice questions are on the test.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
The right answer for the question that is being asked and shown above is that:
m + f = 15 ---> 3m + 3f = 45
3m + 5f = 51
now, we have.
3m + 3f = 45
3m + 5f = 51
-------------------
-2f = -6
f = 3
so, we get,
m + f = 15
m = 15 - 3
m = 12
So the correct answer is 12.
Hence, The solution is, 12 multiple-choice questions are on the test.
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Complete question:
Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.
The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.
m + f = 15
3m + 5f = 51
How many multiple-choice questions are on the test?
3
5
12
14
1. If f(x) = 4x + 5, what is the value of f(-3)? *
Answer:
-7
Step-by-step explanation:
Plug the value in.
4(-3)+5=-12+5=-7
Hope I helped!
What are some good insults
Also so this don't get deleted: What is an exponent?
Answer:
a person who believes in and promotes the truth or benefits of an idea or theory.
Step-by-step explanation:
you are pretty
smart
kind
beautiful
"My daddy said your a stranger"
Gina uses 1 1/5 teaspoons of salt for every kilogram of ground beef. How many teaspoons of salt are needed for 12 1/2 kilograms of beef?
answer with solution pls hehe
Answer:
The possible answer should be 15 teaspoons
Write the equation in standard form. x + 7 = 6y *
x + 6y = -7
x - 6y = -7
x + 6y = 7
x - 6y = 7
Answer:
x−6y=−7
____________
HURRY I NEED HELP SOON
Zola and her friends are going bowling. The bowling alley charges each person a $14 fee to rent shoes, plus $4.50 per game.
Which equation represents the cost, y, for each friend to go bowling in terms of the number of games played, x?
a. y=4.50x +14
b. y= -14x - 4.50
c. y= -4.50x - 14
d. y= 14x + 4.50
Answer:
i think a
Step-by-step explanation:
becuade 4.50 per game(x) and the additional fee would be 14
The admission fee to an amusement park is $27. It costs an additional d dollars to rend a locker to hold your belongings. The total cost for 10 people to enter the amusement park and each rent a locker is $330. How much does it cost for one person to rent a locker?
Answer:
$33
Step-by-step explanation:
If each locker costs $6, 33x6=330 (the 33 is from 27+6)
