Average student loan debt after a bachelors degree increases from 18,108 in 2004 to 28,522 2014. Find the absolute change
Answer:
The absolute change is 10,414
Step-by-step explanation:
To get the absolute change, we simply use the mathematical formula below
Absolute change = New value - Original value
From the question, the new value is 18,108 while the original value is 28,522
So the absolute change will be;
28,522-18,108 = 10,414
Please help with this math question...
When using Interval Notation, explain how the grouping symbols are used and how to determine the order of the numbers used in the interval. Use words such as: brackets, smallest, non-included, included, largest, interval, and parentheses.
Answer:
Step I: Simplify the operations inside grouping symbols. Step II: Simplify the powers. Step III: Solve multiplication and division from left to right. Step IV: Solve addition and subtraction from left to right.
1. Find the slope between (-1, -3) and (4, 0)
a. 5/3
b. -3
c. - 3/5
d. 3/5
2. Given the equation: 3y = 15x + 9, find slope.
a. 5
b. 2/3
d. -2/3
c. Undefined
3. Given a point and a slope, write the equation in slope-intercept form; (1, 2) and m= -3
a. y = -3x + 1
b. y = -3x – 5
c. y = -3x + 5
d. y = -3x – 1
4. Write the equation of the line in slope-intercept form: y-int = (0,3) , m = 2
a. y = 2x + 3
b. y = -2x + 3
c. y = 2x
d. y = 3x +2
5. Given two points, write the equation in point-slope form: (1, 3) and (-2, 12)
a. y – 1 = -3(x – 3)
b. y – 3 = 5(x – 1)
c. y – 3 = -3(x – 1)
d. y + 12 = -3(x – 1)
6. Write the equation of the function graphed below.
a. y= x - 1
b. y= -x - 4
c. y = x - 4
d. y = x +1
7. The table below represents a linear function. What is the slope of this function?
a. 1/3
b. -1/3
c. 3
d. -3
Answer:
Step-by-step explanation:
1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)
2.
Compare to the equation y= mx+b, where m is the slope
3y = 15x+9 divide by 3 each term
y = 15x/3 +9/3
y= 5x + 3 so slope is 5 ( a)
3.
use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b
y-y1 =m (x-x1)
y-2 = -3( x-1)
y = 2-3x+3
y= -3x +5 ( c)
4.
if the point y- intercept is at (0, 3) then the y-intercept is b=3
y= mx+b
y = 2x +3 (a)
5.
the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)
m= 3-12/ 1+2 = -9/3 = -3
y-1 = -3(x-3) is (a)
6.
y-intercept is at -4 ( yet the graph is off a bit -tell your teacher)
slope m = 1
so the equation is y=mx+b and here is y=x -4 (c)
7.
the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope
for example (0, 3) and (1, 0)
m = (3-0)/ (0-1) = 3/-1 = -3 (d)
1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)
2.
Compare to the equation y= mx+b, where m is the slope
3y = 15x+9 divide by 3 each term
y = 15x/3 +9/3
y= 5x + 3 so slope is 5 ( a)
3.
use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b
y-y1 =m (x-x1)
y-2 = -3( x-1)
y = 2-3x+3
y= -3x +5 ( c)
4.
if the point y- intercept is at (0, 3) then the y-intercept is b=3
y= mx+b
y = 2x +3 (a)
5.
the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)
m= 3-12/ 1+2 = -9/3 = -3
y-1 = -3(x-3) is (a)
6.
y-intercept is at -4 ( yet the graph is off a bit -tell your teacher)
slope m = 1
so the equation is y=mx+b and here is y=x -4 (c)
7.
the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope
for example (0, 3) and (1, 0)
m = (3-0)/ (0-1) = 3/-1 = -3 (d)
What is the y-intercept of the graph of the line whose equation is y=3/4x+1
0
1
3/4
4/3
Answer:
The correct answer is "1".
Step-by-step explanation:
You need only set x to zero, and solve for y:
[tex]y = \frac{3}{4} x + 1\\y = \frac{3}{4}0 + 1\\y = 1[/tex]
Adriana went to school for 6 2/5 hours on Tuesday. What is 6 2/5 expressed as a decimal?
Answer:
6.4 .
Step-by-step explanation:
this was on my test
6. A stack of paper is 4.875 cm tall.
How many pieces of paper are in
the stack if each piece is 0.0075 cm
thick?
Answer:
650 pieces of paper
Step-by-step explanation:
each piece is 0.0075 so all you need to do is divide 4.875 by 0.0075
answer the question plz
The Question’s above
Answer:
B
Step-by-step explanation:
How would you factor a^3 - b^3? Please leave detailed instructions. Thanks so much!
a³ - b³ = (a - b) (a² + ab + b²)
You can see why this works if you expand the right side as
a (a² + ab + b²) - b (a² + ab + b²)
(a³ + a²b + ab²) - (a²b + ab² + b³)
Both the a²b and ab² terms cancel, leaving you with a³ - b³.
Help plz
Btw it's NOT A and B
Answer:
C
Step-by-step explanation:
I'd like to remember that the signs are pointing at the direction
Answer:
its c
Step-by-step explanation:
please help me. will give brainlist
Answer:
x= 2.2
Step-by-step explanation:
10/11 = 2/x
cross multiply to get
10x=22
x=2.2
Answer:
x = 2.2 (Verified Answer) ✅Step-by-step explanation:
We need to set up a proportion where the triangle with side x is proportional to the triangle with a side measure of 2.
So, 10/2 = 11/x
We cross multiply to get 10x = 22
Dividing gives us x = 2.2
We can check our answer by substituting our answer in for x.
10/2 = 11/2.2
22 = 22 ✅
Suppose you just deposited $500 into a bank account that has earned 5% interest on the amount you initially
invested. If the new balance is $1,760, what was your initial investment?
Answer:
$1200
Step-by-step explanation:
Let the initial amount that you invested be $ x.
We are told that the new balance after investing $500 is $1760.
Thus, the balance you had before the deposit $500 us;
$1760 - $500 = $1260
So, when the amount invested was $x, the balance was $1260.
Since this money earned 5% interest on the amount you initially
Thus;
$1260 = initial deposit + (5% of inital deposit)
Thus;
x + (5% * x) = 1260
x + (0.05x) = 1260
1.05x = 1260
x = 1260/1.05
x = $1200
Write the ratio
2/3 /5
in simplest form
Answer:
A) 2/15
Step-by-step explanation:
So just divide it normally, do keep change flip
2/3*1/5
2/3 keep
divison change
Denomeinator, flip it, 5 to 1/5
now multiply
2/15
function f gives the distance of a dog from a post, in feet, as a function of time in seconds, since its owner left. Find the value of f(20) and of f(140)
The value of f(20) is 3 feet , and the value of f(140) is 3.5 feet .
In the question ,
the graph represents a function which gives the distance of a dog from a post (in feet ) ,
to find, f(20) which means the distance of the dog from the post after 20sec .
As we can see from the graph that at t=20 sec the distance from post (in feet ) is 3feet .
which means f(20) = 3feet .
Also from the graph we see that at t=140 sec the distance from post (in feet ) is 3.5 feet .
which means f(140) = 3.5 feet .
Therefore , the value of f(20) is 3 feet , and the value of f(140) is 3.5 feet .
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Your cell phone company charges $20 per month for 500 minutes plus an additional
10 cents per minute for additional usage. If you use 510 minutes this month how
much should you expect to pay?
$1000
$21
$20
$20.10
Answer:
$21
Step-by-step explanation:
$20 for the 500 minutes
We still have to pay for 10 minutes.
10 cents per minute.
10centsx10 minutes.
100 cents, also known as 1 dollar.
$20 plus $1 means the answer is $21.
Hope this helps!
-AxekickNebulite
What is the equation of the line that passes through the points (5, 3) and (-3,-1)?
Answer:
y=1/2x+1/2
m=1/2
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(5,3) and (-3,-1).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (5,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=5 and y1=3.
Also, let's call the second point you gave, (-3,-1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=-1.
Now, just plug the numbers into the formula for m above, like this:
m=
-1 - 3 over
-3 - 5
or...
m=
-4 over
-8
or...
m=1/2
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=1/2x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(5,3). When x of the line is 5, y of the line must be 3.
(-3,-1). When x of the line is -3, y of the line must be -1.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (5,3) and (-3,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(5,3). y=mx+b or 3=1/2 × 5+b, or solving for b: b=3-(1/2)(5). b=1/2.
(-3,-1). y=mx+b or -1=1/2 × -3+b, or solving for b: b=-1-(1/2)(-3). b=1/2.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(5,3) and (-3,-1)
is
y=1/2x+1/2
what is a linear equation that contains these points?
The area of a rectangle is 24 square centimeters and its side lengths are x centimeters and x+ 2 centimeters,
a. Find the side lengths of the rectangle. Justify your answer.
b. Find the perimeter of the rectangle.
Step-by-step explanation:
area of rectangle= x ( x +2 ) = 24
X2 + 2X = 24
X 2 +2X _24 = 0
(X +6 ) ( X _4 ) = 0
X= 4
X= - 6.......refused
side length of rectangle is 4 , 6
perimeter= 2( 4+6) = 20 Cm
The side lengths are 4cm , 6cm and perimeter of rectangle is 20cm.
What is perimeter of rectangle?The perimeter of a rectangle is the sum of its four sides. Hence,
Perimeter of Rectangle = 2 (Length + Width) units.
What is area of rectangle?The area of the space occupied within the perimeter of a rectangle is called the area of a rectangle. It is calculated by finding the product of the length and breadth of the rectangle.
Area of rectangle = Length * Breath
According to the question
Area of a rectangle = 24 square centimeters
Side length = x+ 2
Side Breath = x
Now,
a> using Formula of Area of rectangle
Area of rectangle = Length * Breath
substituting the value
24 = x * (x+2 )
24 = [tex]x^{2} +2x[/tex]
[tex]x^{2} +2x[/tex] - 24 = 0
[tex]x^{2} + (6-4)x -24 =0[/tex]
(x +6 ) (x-4) = 0
x = -6 , +4
side cannot be negative
Therefore
Breath of rectangle (x) = 4 cm
Length of rectangle (x+2) = 6 cm
b> Perimeter of the rectangle = 2 (Length + Breath) units.
substituting the value
Perimeter of the rectangle = 2 ( 4 + 6 )
= 20 cm
Hence, The side lengths are 4cm , 6cm and perimeter of rectangle is 20cm.
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Can anybody help me with this plzzz‼️
(If answer is correct i will cashapp you $6)
Step-by-step explanation:
h(x) = 3. g(x) + 5
x= -1 h(x) = 3×8 + 5= 29
x= 0h(x) = 3×5 + 5= 20
x= 2 h(x) = 3×1 + 5= 8
x= 5 h(x) = 3×-5 + 5= -10
[tex]h(x) = 3*g(x)+5[/tex]
When x = -1.
Substitute x = -1 in both h(x) and g(x). | As shown in the table, when x = -1, g(x) = 8 |
h(-1) = 3*8+5 = 24+5 = 29
h(0) = 3*5+5 = 15+5 = 20
h(2) = 3*1+5 = 3+5 = 8
h(5) = 3*(-5)+5 = -15+5 = -10
If 3 sodas cost $6 then what is the cost per soda??
Answer:
$2 per soda
Step-by-step explanation:
6/3= 2
Which matrix represents the system of equations?
3x + y = -9
x + 5y = 16
A. [3 0 ]
[0 5 ]
B. [3 1]
[1 5]
C. [3 0| -9]
[0 5| 16]
D. [3 1| -9]
[ 1 5| 16]
9514 1404 393
Answer:
D. [3 1 | -9]
[ 1 5 | 16]
Step-by-step explanation:
The matrix of B represents the coefficients of the variables. It would generally be part of a matrix equation:
[tex]\left[\begin{array}{cc}3&1\\1&5\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}-9\\16\end{array}\right][/tex]
However, the entire system of equations can be represented by the augmented matrix ...
[tex]\left[\begin{array}{cc|c}3&1&-9\\1&5&16\end{array}\right] \qquad\textbf{matches D.}[/tex]
If the coordinates of point a are (-2 3) what is the image of a under y-axis d3
Answer:
The coordinates of the image under the y-axis will be:
a'(2, 5)Step-by-step explanation:
Given the point
(2,3)We know that when we reflect a point across the y-axis, the y-coordinate remains the same, but the x-axis reverses its sign.
Thus,
Rule of reflection under y-axis:
P(x, y) → P'(-x, y)
Here, P'(x, y) is the image of the P(x, y)
Given that the point
a(-2, 5)Thus, the coordinates of the image under the y-axis will be:
(x, y) → (-x, y)
a(-2, 5) → a'(-(-2), 5) = a'(2, 5)
Therefore, the coordinates of the image under the y-axis will be:
a'(2, 5)I will mark brainlist and 5 stars, please help.
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
since the rectangles are similar their sides are in proportion
h/210 = 60/84
h= 60*210/84 = 150 cm
PLZ HELP ME ON THIS QUICK
Answer:
the answer will be x=6 because 6×3=18 hope this helps
Andre poured 27 ounces of rice into 6 containers. If all containers have the same amount of rice, how many ounces are in each container?
Find the quotient of -72÷-9
Answer: 8
Step-by-step explanation:
hope this helped :)
Answer:
8
Step-by-step explanation:
I need help with this
Answer:
I WAS BORN TO FLEX DIMONDS ON MY NECK I LIKE MORNING CHECKS I LIKE MORING S**
Step-by-step explanation:
Please I need your help quickly guys,
Substitute -6 for x.
(-6+3)/(-6-1).
-3/-7.
--=+
Answer: 3/7.
Need help with this one
Please and thank you
Answer: -2 is a no. -9 is a yes. 2 is a no. -8 is a no.
Step-by-step explanation:
Find the quotient 17÷3,145
Answer:
0.0054054054
Also simplify to 0.005
Answer:
17÷3,145=0.00540