Factor like terms..
(ax + ay) + (3bx + 3by)
= a(x + y) + 3b(x + y)
Finally, group the common factors of x + y and collect the terms to get:
(x + y )(a + 3b)
The factors of the given expression are (x + y ) and (a + 3b).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been given that expression as :
ax + ay + 3bx + 3by
We have to factorize the given expression.
⇒ ax + ay + 3bx + 3by
Factor like terms.
⇒ (ax + ay) + (3bx + 3by)
⇒ a(x + y) + 3b(x + y)
Take out the common factors of x + y and combine the terms to get:
⇒ (x + y )(a + 3b)
Therefore, the factors of the given expression are (x + y ) and (a + 3b).
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The manufacturer's suggested retail price (MSRP) for a particular car is $25,425, and it is expected to be
worth $11,730 in 5 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 7 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
(Simplify your answer. Do not include the $ symbol in your answer.)
Answer:
(a) The linear depreciation function of the car which gives the worth of the car y after a number of years, t is given as follows;
y = 25,425 - 2,739 × t
(b) The value of the car 7 years from now is $6,252
(c) $2,739 per year
Step-by-step explanation:
The manufacture's suggested retail price (MSRP) for the car = $25,425
The amount the car is expected to be worth in 5 years = $11,730
(a) The linear depreciation is given as follows;
[tex]Depreciation \ Per \ Year \ = \dfrac{Cost \ of \, Asset - Salvage \ Value}{Life \ of \, Asset \ in \ use}[/tex]
Where;
Cost of Asset = $25,425
Salvage Value = $11,730
Life of Asset in use = 5 years
We get;
[tex]Depreciation \ Per \ Year \ = \dfrac{\$ 25,425 - \$11,730}{5} = \$2,739/year[/tex]
Therefore, the linear depreciation function, can be written as follows;
y - 25,425 = -2,739×(t - 0)
y = -2,739·t + 0 + 25,425 = 25,425 -2,739·t
y = 25,425 - 2,739 × t
Where;
y = The expected worth of the car after a given number of years
t = The number of years used for the calculation of the depreciation
(b) The value of the car 7 years from now is given by substitution as follows;
Whet t = 7, we have;
y = 25,425 -2,739·t = y = 25,425 -2,739 × 7 = $6,252
The value of the car 7 years from now = $6,252
(c) [tex]Depreciation \ Per \ Year \ = \dfrac{\$ 25,425 - \$11,730}{5} = \$2,739/year[/tex]
The car is depreciating at a rate of $2,739 per year.
A giraffe can run 32 miles per hour. What is this speed in feet per second?
Answer:
46.9333 feet per second
Step-by-step explanation:
WILL MARK YOU BRAINLIEST
Answer:
26. QOR = 59 - 24
= 25
27. POS = 19+31+15
=65
28. ROS = 46 - (61-28)
= 13
A diver is 19 meters below the surface of the water. Use an integer to represent how far the diver will need to travel to reach the surface.
Since the diver is 19 metres below the surface of the water, then he will need to travel 19 metres to reach the surface.
so nobody is smart enough to answer my question?
That is ver very sad
yes,
abcdefghijklmnopqrstuvwxyz
What is the distance between points F(2, 11) and G(5, 16)? Round off to the nearest whole number
Answer:
d = 5Step-by-step explanation:
[tex]d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}\\\\d_{FG}=\sqrt{(5-2)^2+(16-11)^2}=\sqrt{3^2+4^2}=\sqrt{25}=5[/tex]
y+6x=11; x = -2,0, 4
Solve the equation for y.
Match the equation with its slope and y intercept.
Answer:
1.c
2.e
3.d
3.a
5.b
best of luck!
Answer: Answer is in the steps read carefully
Step-by-step explanation:
1. y = -3x It has a slope of -3 and y intercept of 0 so it goes with C
2. y =2x+ 5 It has a slope of 2 and y intercept of 5 so it goes with E
3. y = 1/2x - 3 It has a slope of 1/2 and y intercept of -3 so it goes with D
4. y= -1x + 2 It has a slope of -1 and y intercept of 2 so it also goes with A
5. y = 1x It has a slope of 1 and y intercept of 0 so it goes with B
(4 root 6 - 2root7) (4root6 +2root7)
Martha tiene un negocio en el cual vende huevos empacados por docena. Uno de sus clientes le pide solamente 5/6 de docena, ¿cuántos huevos debe venderle Martha?
Answer:
María solamente debe venderle al cliente 10 unidades
Step-by-step explanation:
Explicación paso a paso:
Una docena representa un total de doce (12) unidades. Los huevos se empacan por docena, por lo tanto si nos piden solo 5/6 de la docena, multiplicamos dicha fracción por 12 unidades:
5/6 · 12 = (12 · 5)/6 = 60/6 = 10 unidades
Por lo tanto, María solamente debe venderle al cliente 10 unidades, es decir 5/6 representa 10 unidades de los huevos
Usando conceptos de proporción, se encuentra que Martha debe vender 10 huevos al cliente.
---------------------------
Esta pregunta se resuelve por proporciones, usando una regla de tres.Una docena está compuesta por 12 huevos. ¿cuántos huevos en 5/6 de docena?1 docena - 12 huevos
5/6 de docena - x huevos
Aplicando multiplicación cruzada:
[tex]x = 12 \times \frac{5}{6} = \frac{12 \times 5}{6} = 2 \times 5 = 10[/tex]
Martha debe vender 10 huevos.
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Carla withdrew $320 every month for four years to help pay for college how much total money did she withdraw
Answer:
1280
Step-by-step explanation:
32x4=128
320x4=1280
please explain the steps in order to solve the equation 2x+5y=28 when x=4
Answer:
Step-by-step explanation:
Plug in 4 for x
2(4) + 5y = 28
8 + 5y = 28 (subtract both sides by 8)
5y = 20 (divide both sides by 5)
y = 4
What correct equation to find the length of DF in the following diagram
Answer:
Where is the diagram... I don't see it
help me pleaseee i dont understand it.
Write an inequality that models a real world situation. Describe your situation and what a variable X represents
Answer:
The variable X represents:
X = the number of books
The real world situation can be:
1.) Jennie reads books. She reads each books for
2.) Jennie wants to read book at least 5 books today.
Write an inequality that models the minimum number of books that Jennie needs to read.
The inequality for this situation is:
[tex]2x \: \geqslant \: 5[/tex]
Solve equation.
-3x + 1 + 10x = x + 4
Answer: x=1/2
(for anyone who needs the answer)
Answer:
[tex]x=1/2[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-3x+1=10x=x+4[/tex]
First, combine like terms on the left:
[tex]7x+1=x+4[/tex]
Subtract 1 from both sides. The left cancels:
[tex](7x+1)-1=(x+4)-1\\7x=x+3[/tex]
Subtract x from both sides. The right cancels:
[tex](7x)-x=(x+3)-x\\6x=3[/tex]
Divide both sides by 6:
[tex](6x)/6=(3)/6\\x=1/2[/tex]
So, our answer is 1/2
Answer:
x = 1/2
Step-by-step explanation:
-3x + 1 + 10x = x + 4 ⇒ simplify left side7x + 1 = x + 4 ⇒ subtract x + 1 from both sides7x - x = 4 - 1 ⇒ simplify6x = 3 ⇒ divide both sides by 6x = 3/6 ⇒ simplifyx = 1/2 ⇒ answerwhich graph represents the solution to the inequality y<1/2x-4
The graph shown in option (B) represents the solution to the inequality y<1/2x-4
InequalityA relation between two mathematical expressions which are not equal is known as inequality.
Graphing inequalitiesFirst, solve the given inequality so that y is on the left side and everything else is on the right side.Then, plot the graph for the equation.Finally, we will shade above the line for the ">" and below the line for the "<".Which graph represents y < 1/2x-4?The inequality symbol is "<" (less than).
So, the line of the graph should be dashed and shaded below the line.
Comparing the graphs given in the question, we can conclude that option (B) is correct.
Hence, the graph in option (B) represents the solution to inequality y<1/2x-4.
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Answer:
B aka y<1/2x-4
Step-by-step explanation:
I did this before
Ms. Smith has 28 sixth graders and 35 seventh graders for Math. If she wants to break the two grades into identical groups without any students left over, how many students will be in each group? *
Answer:
58
Step-by-step explanation:
The length of a football field is 120m. what is the length on drawing, if the scale is 1:5m?
what are the solutions of x^2 - 4 = 0
It is a difference of squares, so we can factor this to
[tex](x+2)(x-2)=0[/tex]
Then, we can solve for [tex]x[/tex].
[tex]x=-2,2[/tex]
Hope this helps.
頑張って!
Given: B = 7 −3 5 −1 C = 1 −1 13 −5 Solve the equation: 2X + B = C X =
Answer:
Actually, this is referring to matrix equations, so it's -3 1 4 2-
Step-by-step explanation:
Hey, so I got this from the comments and wanted it to be a real answer, so please give them lot's of thanks if you can. They are keatonmorehouse0727.
Alex and his friends are studying for a geometry test and one of the main topics covered is parallel lines in a plane. They each write down what they think it means for two distinct lines in a plane to be parallel
Answer:
i rthink i understand your question but im not sure- I think you forgot to add a little bit of the question but im pretty sure your question is what is a parrllel line. IM going to answer that sorry if its wrong but im trying to be helpfull.
Step-by-step explanation:
Parallel lines are two lines that never intersect they start off beside each other and they stay where you can conect them with one line but they will never intercet.
---------
and
----------
Answer:
Literally, parallel lines are lines that extend in both directions without meeting.
The three definitions of parallel lines are correct, but Rachel's and Briana's definitions have flaws
Step-by-step explanation:
Rachel
The definition implies that two lines are said to be parallel if they are both perpendicular to another line.
This definition is correct, but the definition brings a new concept; it introduces the concept of line transversal.
Because the parallel lines can be defined without introducing the concept of line transversal (which was not part of the required definition), then we can conclude that the definition has a drawback.
Alex
Alex's definition is correct, and it has no drawback because the definition can be applied to concepts where parallel lines are used.
Briana
Here, Brianna introduced the concept of slopes.
Ideally, parallel lines have the same slope; but the concept is limited to slopes only; and cannot be applied to other concepts such as transversal of lines.
(-4, 6) and (3.-7)
Find the distance between each pair of points
Answer:
[tex]d=\sqrt{218}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug our coordinates into the distance formula to find the distance between the points:
[tex]d=\sqrt{(3 - (-4))^2+(-7 - 6)^2}[/tex]
[tex]d=\sqrt{(3 +4)^2+(-13)^2}[/tex]
[tex]d=\sqrt{(7)^2+169}[/tex]
[tex]d=\sqrt{49+169}[/tex]
[tex]d=\sqrt{218}[/tex]
Is 9.45 bigger than 0.945
Step-by-step explanation:
Yes it is
20 Characters needed but thank me later. Wouldnt mind if you marked me as brainliest
Use the diagram to the right a. What algebraic expression represents GK? b. If GK = 24. what are GH and JK? G H J K a What algebraic expression represents GK? GK (Simplify your answer Do not factor)
Answer:
Step-by-step explanation:
The question lacks appropriate diagram. Find the diagram attached below;
From the diagram GK = GH+HJ+JK
Given GH = GJ-HJ
GH = 2x+2-x
GH = x+2
HJ = x
JK = HK - HJ
JK = 6x-1-x
JK = 5x-1
GK = x+2+x+5x-1
collect like terms
GK = x+x+5x+2-1
GK = 7x+1
Given GK = 24, then;
7x+1 = 24
7x = 24-1
7x= 23
x = 23/7
Since GH = x+2
GH = 23/7 + 2
GH 23+14/7
GH = 37/7
Also JK = 5x-1
JK = 5(23/7)-1
JK = 115/7 - 1
JK = 115-7/7
JK = 108/7
Yon buys tickets to a concert for himself and a friend. There is a tax of 8% on the price of the tickets and an additional booking fee of $20 for the transaction. Enter an algebraic expression to represent the price per person. Simplify the expression if possible. Use variable t for the price of the 2 tickets in dollars. The algebraic expression is
Answer:
5.4
Step-by-step explanation:
vhtx
are f(x)=1/8x^3 and g(x)=2x^1/3 inverses of each other? Check all that apply.
PLEASE SHOW WORK!
The simplified expression for f(g(x)) is x.
The simplified expression for f(g(x)) is One-fourth x.
The simplified expression for g(f(x)) is 2x.
The simplified expression for g(f(x)) is x.
The functions are inverses of each other.
The functions are not inverses of each other.
Answer: 1,4,5
Step-by-step explanation:
The correct options are, The simplified expression for g(f(x)) is x.
The functions are not inverses of each other.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, f(x) = 1/(8x³).
f(x) = 1/(2x)³.
y = 1/(2x)³.
(2x)³ = 1/y.
[tex]2x = \frac{1}{y^\frac{1}{3}}[/tex].
[tex]x = \frac{1}{2y^\frac{1}{3}}[/tex].
[tex]f^{-1}(x) = \frac{1}{2x^\frac{1}{3}}[/tex] and g(x) = [tex]2x^\frac{1}{3}[/tex] so, they are not inverses of each other.
Now, f(g(x)) = [tex]\frac{1}{8((2x)^\frac{1}{3})^3}[/tex].
f(g(x)) = 1/16x.
g(f(x)) = [tex]2(1/8x^3)^\frac{1}{3}[/tex].
g(f(x)) = x
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Distribute 6x (5 – 7x).
Answer:
30-42x
Step-by-step explanation:
Use the distributive property to multiply 6 by 5-7x.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{30 - 42x}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{6(5 - 7x)}[/tex]
Distribute 6 through the parentheses
[tex] \dashrightarrow{\sf{6 \times 5 - 6 \times 7x}}[/tex]
[tex] \dashrightarrow{ \sf{30 - 42x}}[/tex]
Hope I helped!
Best regards! :D
You want to paint a piece of pottery at an art studio. the total cost is the cost of the piece plus an hourly studio fee.the price for the studio A is shown at the right you spend a total of $46 on the project how many hours did you spend at the studio?
A) define the variable: x=
B) write an equation
C) answer the question include the units
Answer:
5 and 3/5
Step-by-step explanation:
sorry if it is wrong
3(20 + 4) =
Help me pleases
Answer:
72 is your answer mate...