Answer:
x^3-x^2-17x+12
Step-by-step explanation:
(x+4)(x^2-5x+3)
x^3-5x^2+3x+4x^2-20x+12
x^3-5x^2+4x^2+3x-20x+12
x^3-x^2-17x+12
Linda's start up cost for her online jewelery store was $250, as she has to pay an additional $60per month to keep it running. Write an expression or equation modeling the real world
Total Cost = 250 + 60x is the equation that models the given situation
Solution:
Given that, Linda's start up cost for her online jewelery store was $250
She has to pay an additional $60 per month to keep it running
To find: Equation that models this situation
From given,
Start up cost = $ 250
Let "x" be the number of months she keeps the store running
Additional pay per month = $ 60
Thus, the total cost Linda spend to keep the store running is given as:
Total Cost = Startup cost + (Additional pay per month)(number of months)
[tex]Total\ Cost = 250 + 60x[/tex]
Thus the equation that models the given situation is found
What is the equation of the line that has a slope of -4 and goes through (-1,6)
Answer:
y = - 4x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 6) into the partial equation
6 = 4 + c ⇒ c = 6 - 4 = 2
y = - 4x + 2 ← equation of line
Michelle sets up a lemonade stand to make some extra money.She spends $4.75 purchasing supplies.She earns $16.50 selling lemonade.How much money does she make after she subtracts her expenses?
How can I use fractions tiles to help divide a whole number by a unit fraction
Final answer:
To divide a whole number by a unit fraction using fraction tiles, treat the division as multiplication by the reciprocal of the unit fraction and then split the whole number tiles accordingly.
Explanation:
To use fraction tiles to help divide a whole number by a unit fraction, you can follow these steps:
Understand that dividing by a unit fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as multiplying by 2, since 2 is the reciprocal of 1/2.Start with fraction tiles that represent the whole number you want to divide. For instance, if the whole number is 6 and you're dividing by 1/2, use 6 whole tiles.Since you're multiplying by the reciprocal of the unit fraction, convert the action of dividing into multiplication. Each whole tile would be split into the number of pieces that are equivalent to the denominator of the unit fraction. If dividing by 1/2, split each whole into 2 pieces.Count all the new pieces. The result is the number of pieces you have after dividing by the unit fraction. In our example with 6 whole tiles and dividing by 1/2, you'd end up with 12 pieces since each whole tile is split into 2 pieces.what should be added to both sides of the equation to solve for the variables? 45=30+m
Answer: m = 15
Step-by-step explanation:
45 = 30 + m
subtract 30 , from both sides , that is , -30 should be added to both sides to find the variable
45 - 30 = 30 + m - 30
15 = m
Therefore : m = 15
elizabeth can run 5 mils in 24 1/2 minutes Dez can run 8 miles in 32 1/3 minutes. who can run faster?
Equivalent ratio 1:
Equivalent ratio 2:
Answer:
Des can run faster than Elizabeth.
Des can run 1 mile in 4.037 minutes while Elizabeth can run 1 Mile in 4.9 minutes
Step-by-step explanation:
If Elizabeth can run 5 miles in 24.5 minutes. Elizabeth will run 1 mile in 24.5/5=4.9 minutes.
If Dez can run 8 miles in 32 1/3 minutes. Then Dez will run 1 mile in 32.3/8=4.037 minutes
Therefore if Dez can run 1 mile in 4.037 minutes and Elizabeth can run 1 mile in 4.9 minutes then Dez can run faster than Elizabeth.
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
A: y=-1/4x +33
B: y=-1/4x + 36
C: y = 4x - 16
D: y = 4x + 16
Answer:
Option D: y = 4x + 16
Step-by-step explanation:
Given the line: y - 1 = 4(x + 3) ⇒ y = 4x + 13
The slope of the given line = m = 4
The required line is parallel to the given line
So, the slope of the required line = m = 4
So, the general equation of the required line: y = 4x + c
Where c is constant represents y-intercept
To find the value of c, substitute with the point (4,32)
At x = 4 y = 32
∴ 32 = 4 * 4 + c
∴ c = 32 - 16 = 16
∴ y = 4x + 16
The answer is option D: y = 4x + 16
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is 12 more than the second.
Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
x = first angle
y = second angle
z = third angle
x + y + z = 180
The sum of the measures of the second and third angles is twice the measure of the first angle. ----> y + z = 2x
The third angle is 12 more than the second. ----> z = y + 12
Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation
y + z = 2x Plug in (y + 12) for z
y + (y + 12) = 2x Simplify
2y + 12 = 2x Divide 2 on both sides
y + 6 = x Isolate "y"
y = x - 6 Next you could plug this into z = y + 12, so that z has the x variable
z = y + 12
z = x - 6 + 12
z = x + 6
Now that you have y and z, you can do this:
x + y + z = 180
x + (x - 6) + (x + 6) = 180 Simplify
3x = 180 Divide 3 on both sides
x = 60 Now that you found x, plug it into the other equations to find y and z
y = x - 6
y = 60 - 6
y = 54
z = x + 6
z = 60 + 6
z = 66
x = 60°
y = 54°
z = 66° [sorry if this is confusing]
PROOF
x + y + z = 180
60 + 54 + 66 = 180
180 = 180
The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.
Explanation:To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:
The sum of the angles of a triangle is 180 degrees, so x + y + z = 180.The sum of the measures of the second and third angles is twice the measure of the first, so y + z = 2x.The third angle is 12 more than the second, so z = y + 12.First, let's substitute z = y + 12 into the other two equations:
In x + y + z = 180, replace z with y + 12 to get x + y + y + 12 = 180; or, simplifying further, x + 2y = 168.In y + z = 2x, replace z with y + 12 to get y + y + 12 = 2x or, simplifying further, 2x = 2y + 12 or x = y + 6.We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.
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find the value of m<1 m<2 and m<3
Answer:
i don't know
Step-by-step explanation:
Perform the indicated operation.(7 - 11/) + (-3 + 5/)
Answer:
The correct answer is C. 4 -6
Step-by-step explanation:
Let's solve the operation given, this way:
(7 - 11/) + (-3 + 5/)
7 - 11 - 3 + 5=
12 - 14 = - 2
After resolving the parenthesis, adding and subtracting the result of thhe operation is - 2
The correct answer is C. 4 -6
rectangle ABCD is graphed in the cordinate plane. The following are the verticies of the rectangle; A(-6,-4),B(-4,-4),C(-4,-2), and D (-6,-2). what is the perimiter
Answer:
Therefore Perimeter of Rectangle ABCD is 4 units
Step-by-step explanation:
Given:
ABCD is a Rectangle.
A(-6,-4),
B(-4,-4),
C(-4,-2), and
D (-6,-2).
To Find :
Perimeter of Rectangle = ?
Solution:
Perimeter of Rectangle is given as
[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]
Length = AB
Width = BC
Now By Distance Formula we have'
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]
[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]
Similarly
[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]
[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]
Therefore now
Length = AB = 2 unit
Width = BC = 2 unit
Substituting the values in Perimeter we get
[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]
Therefore Perimeter of Rectangle ABCD is 4 units
Answer:
Therefore Perimeter of Rectangle ABCD is 4 units
Step-by-step explanation:
Given:
ABCD is a Rectangle.
A(-6,-4),
B(-4,-4),
C(-4,-2), and
D (-6,-2).
To Find :
Perimeter of Rectangle = ?
Solution:
Brian has reduced his cholesterol level by 20% after his last check up. If his original level was 240, what is his cholesterol level now?
Answer:
192
Step-by-step explanation:
20% of 240 is 48
240-48 = 192
Answer:
192
Step-by-step explanation:
20%/100% x 240 =48
His cholesterol level now will be 240 - 48 = 192
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
Answer:
20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
in general, f−1(f(x)) = f(f−1(x)) =
Answer:
f−1(f(x)) = f(f−1(x)) = x
Step-by-step explanation:
Follow this simple example using the function f(x) = x + 2
f(x) = x + 2
NOw we find the inverse function f^(1)(x).
y = x + 2
x = y + 2
y = x - 2
f^(-1)(x) = x - 2
The inverse function is f^(-1)(x) = x - 2
Now we do the two compositions of functions:
f^(-1)(f(x)) = x + 2 - 2 = x
f(f^(-1)(x)) = x - 2 + 2 = x
Both are equal to x.
Answer: f−1(f(x)) = f(f−1(x)) = x
The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
We are to prove the relationship;
[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]
To get the unknown, let f(x) = x - 2
Find its inverse:
Let y = x - 2
Replace y with x;
x = y - 2
y = x+2
Hence [tex]f^{-1}x = x+2[/tex]
Next is to get [tex]f(f^{-1}(x))[/tex]
[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]
We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]
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If 5/8 = x/16 , then x is equal to
Answer:
10/16
Step-by-step explanation:
What is the inverse of f(x)=-x-1
Answer:
f^-1 (x)=-x-1
Step-by-step explanation:
y=-x-1
x=-y-1
-y=x+1
y=-x-1
Find fifth roots of z⁵ + 32 = 0 and draw its graph?
Answer:
Step-by-step explanation:
Draw a model for a fraction1/6
Answer:
Step-by-step explanation:
picture to help
Answer: I can't draw it but i answered
Step-by-step explanation:
To draw a model for 1/6 you would have draw six shapes of any kind. Then you would only fill one of them.
jacob qnd jordan are training for track season. jacob did 39 sit-ups in 30 secs. jordan did 59 sit-ups in 50 secs. who will likely do more sit-ups in 2 1/2 mins
Jordan it a bigger number
Mark as Brainliest3,562,185 What is the value of 3?
Answer: 3 millions
Explanation: To determine what the digit "3" means in 3,562,185, if we put 3,562,185 into the place value chart, we can see that the 3 appears in the units column of the millions period so in this problem 3 refers to 3 millions.
1. Justin divided 403 by a number and got a quotient of 26 with a remainder of 13. What was the
number Justin divided by?
a. 13
b. 14
c. 15
d. 16
Answer:
15
Step-by-step explanation:
First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.
The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.
What number was used to divide 403?
Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.
In order to detemine the number used to divide 403, take the following steps:
Subtract 13 from 403 = 403 - 13 = 390
Now divide 390 by 26: 390 / 26 = 15
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Select True or False.
The expression 5x − 3(2x − 4) is equivalent to the expression 12 − x.
True
False
Answer:true
Step-by-step explanation:
5x-3(2x-4)=
1) solve the parentheses
5x-6x-12=0
2) we just can rest the X
5x-6x=X
3) X-12=0
4) The order of factors does not alter the product
12-X=0
Answer:
True
Step-by-step explanation:
5x − 3(2x − 4)
Expand
5x - 6x + 12
-x + 12
12 - x
( ) are called "parentheses" or "brackets "
Whatever is inside the ( ) needs to be treated as a "package".
So when multiplying: multiply by everything inside the "package".
Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:
In that case −3 · -5 = +15 (a positive answer)
ASAP
Of 450 lunches sold at school on Thursday, 40% were hamburgers
and the rest were pizza. How many more pizza lunches were sold than
hamburgers? Explain how you found your answer.
Answer: 90
Step-by-step explanation:
Total number of lunches sold = 450
Number of hamburgers = 40% of the total , that is
number of hamburgers = 40/100 x 450 = 180
number of pizza = 450 - 180 = 270
Therefore , the number of pizza lunches sold more than hamburgers will be
270 - 180 = 90
Therefore : 90 more pizza lunches were sold than hamburgers.
why do banks pay interest on saving accounts
Answer: irs
Step-by-step explanation:
Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank
The reason why banks pay interest
Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank.
Banks can attract and maintain consumer cash by providing interest, which they can then use to lend to other people or invest in various financial operations.
Paying interest on savings accounts assists banks in maintaining liquidity, generating money, and developing a mutually beneficial relationship.
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The friends now To go on the loop D loop and the roller coaster. Explain why only 1 of the friends can go on both of these rides
Are there any more instructions or information?
Due to requirements such as height and ride capacity, only one friend can go on both the loop and the roller coaster at the same time.
Explanation:In order to go on the loop and the roller coaster, the friends need to meet certain requirements. For example, they need to be tall enough to ride the roller coaster and meet any age restrictions. Additionally, the roller coaster may have a limited number of seats or ride capacity. Due to these factors, it's possible that only one friend can go on both of these rides at the same time.
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Solve by using substitution. Express your answer as an ordered pair.
3x+y=10
Y=x+2
A.) 8,10
B.) 8/3,2
C.) 2,4
D.) 4,2
Answer:
c. 2,4
Step-by-step explanation:
The line passing through (11,y) and (2,0)is parallel to the line joining (7,5) and (-2,2). Find y.
Answer: y = 3
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
For the first line
[tex]x_{1}[/tex] = 11
[tex]x_{2}[/tex] = 2
[tex]y_{1}[/tex] = y
[tex]y_{2}[/tex] = 0
substituting into the formula , we have
m = [tex]\frac{0 - y}{2 - 11}[/tex]
m = [tex]\frac{-y}{-9}[/tex]
m = [tex]\frac{y}{9}[/tex]
Also Finding the slope of the second line we have
[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]
Since the two lines are parallel , we will equate their slope , that is
[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]
3y = 9
y = 3
Which of the following points is a solution of the inequality y < -|x|?
a) (1, -2)
b) (1, -1)
c) (1, 0)
Answer:
a) (1, -2)
Step-by-step explanation:
The given inequality is y < -|x|
We substitute the point to see which points satisfy the inequality.
For a) (1, -2), we substitute x=1 and y=-2 to get:
-2 < -|1|---------->-2<-1--------->True
For b) (1, -1), we substitute x=1 and y=-1 to get:
-1 < -|1|---------->-1<-1--------->False
For a) (1, 0), we substitute x=1 and y=0 to get:
0 < -|1|---------->0<-1--------->False
The first choice is correct.
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
–8
–5
0
6
Answer: 0 on edge
Step-by-step explanation:
got it correct
Answer: C
Step-by-step explanation:
took quiz
Which equation represents the line shown
on the graph?
x = y + 2
y = x + 2
y = 2x
x = 2y
Answer: Third option:
Step-by-step explanation:
The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The equation in Slope Intercept form of a line that passes through the Origin, is:
[tex]y=mx[/tex]
Where "m" is the slope of the line.
In this case you can observe in the picture attached that the line passes through the point (0,0).
You can also notice that "y" would be the Dependent variable and "x" the Independent variable.
Therefore, the equation of this must have this form:
[tex]y=mx[/tex]
The only equation that matches with that form, is the one given in the Third option. This is:
[tex]y=2x[/tex]
The linear equation shown in the graph can be written as.
y = 2x
Which equation represents the line shown on the graph?A general linear equation is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
In this graph, we can see that the line intercepts the y-axis at y = 0, so we have:
y = ax
We also can see that the line passes through the point (1, 2), replacing these values in the equation we will get:
2 = a*1
2 = a
Then the linear equation is:
y = 2x
The third option.
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