We will need to use the substitution method to solve the question. The difference between the two numbers is 11.5
Substitution method is used to solve a system of equations. First the equation is solved for one variable and then the value is used in the other equation to solve for the other unknown variable. In this question we have been told the sum of two numbers is 32. Let us take the two numbers as x and y. Then we can say that
x+y=32 ...(i)
Next we know that when 5 is subtracted from 4 times one number the result is 8 times the other number, we can write it as
4x-5=8y
4x-8y=5....(ii)
So we have two equations
x+y=32
4x-8y=5
We will multiply equation (i) by 4 to cancel out x and solve for y
4x+4y=128
4x-8y=5
(-) (+) (-)
-----------------
12y=123
y=10.25
We substitute the value of y in equation (i)
x+y=32
x+10.25=32
x=32-10.25=21.75
We need to find the difference between two number which is x-y=21.75-10.25=11.5
Therefore we found out by substitution method that the difference between the two numbers is 11.5
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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)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]
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
what is a linear equation that contains these points?
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
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
answer the question plz
What is the first term of an AP whose common difference is 2 and 31st term begin -88
Answer:
a₁ = - 148
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given d = 2 and a₃₁ = - 88 , then
a₁ + (30 × 2) = - 88
a₁ + 60 = - 88 ( subtract 60 from both sides )
a₁ = - 148
a₁ = - 148
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given d = 2 and a₃₁ = - 88 , then
a₁ + (30 × 2) = - 88
a₁ + 60 = - 88 ( subtract 60 from both sides )
a₁ = - 148
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.
Please I need your help quickly guys,
Substitute -6 for x.
(-6+3)/(-6-1).
-3/-7.
--=+
Answer: 3/7.
What decimal is equal to 6/20
O 0.2
O 0.3
O 0.6
O 0.8
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:
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 ✅
What is perpendicular to 1/6
Note: Your question is a little ambiguous and incomplete. I am assuming you are talking about the slope of lines here.
Answer:
the slope of the perpendicular line will be:
[tex]\frac{-1}{\frac{1}{6}}=-6[/tex]
Step-by-step explanation:
Note: I am assuming you are talking about the slope of lines here.
Given
The slope of line = 1/6
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.Thus, the slope of the perpendicular line will be:
[tex]\frac{-1}{\frac{1}{6}}=-6[/tex]
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.
Please help me in this Im failing.
Answer:
B and C
Step-by-step explanation:
3)
Which two ratios form a proportion?
A)
4
and
2
B)
IN
4
and
1 8
8
and
D)
IN
16
and
8
Answer:
D is the correct answer
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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(6x + 5)
°
(3x + 4)º
A)16
B)10
C) 6
D) 9
E) 14
Answer:
9
Step-by-step explanation:
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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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:
The Question’s above
Answer:
B
Step-by-step explanation:
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
e^2 x e^3=? jbdbiuevdeqdkjufwdufhdkfbskdjbfwjrbfkuwvkusnaer
Answer:
e^5
Step-by-step explanation:
When you multiply with exponents you add ONLY the exponents and multiply the variables
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
2. Find f(x)*g(x) *
f (x) = -2x + 4 and g(x) = 2x2 – 3x + 4
Answer:
i believe your answer is ..... f(2x^2-3x+4)= -4x^2+6x-4
Step-by-step explanation:
hope that helps
PLS ANSWER ASAP
Subtract.
−13−(−27)
Enter your answer in the box.
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
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:
I’ll love you forever if you help me with this ASAP PLEASE
Answer:
A: -0.33
Step-by-step explanation:
If you convert it to slope-intercept form, you get y = -1/3x + 4 so the slope is -1/3 or -0.33