The system of equations that could be used to solve the problem are;
400a + 1000p = 8800
a + p = 13
Where a is associate and p is partner
How to write a system of equations?Let the variables be defined as:
Associate is denoted by a
Partner is denoted by p
We are told that the daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. Thus, the equations are:
400a + 1000p = 8800 -----(1)
a + p = 13 ------(2)
Make a the subject in eq 2 to get;
a = 13 - p -----(3)
Put 13 - p for a in eq 1 to get;
400(13 - p) + 1000p = 8800
5200 - 400p + 1000p = 8800
5200 + 600p = 8800
5200 + 600p = 8800
600p = 3600
p = 6 partners
a = 13 - p
a = 13 - 6
a = 7 associates
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find the slope of the line through (1,-1) and (6,2
Answer:3/5
Step-by-step explanation:
(y2-y1)/(x2-x1)
(2-(-1))/(6-1)=3/5
a paper company needs to ship paper to a large printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 7 cubic feet and the volume of each large box is 14 cubic feet. a total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. define the variables that you use to write the system.
The required system of equations is x+y = 21 and 7x +14y = 252.
Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.
Let the number of small boxes be x.
Let the number of large boxes be y.
The volume of each small box is 7 cubic feet.
The volume of each large box is 14 cubic feet.
The total number of boxes is 21.
Total volume of all boxes is 252 cubic feet.
So, x+y = 21.
This is the first equation.
Also, the total volume is equal to the sum of the volumes of all individual boxes.
So, 7x + 14y = 252
Thus, the required system of equations is x+y = 21 and 7x +14y = 252.
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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.
What are system of equations?A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.
Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.
Given total number of boxes shipped is 21. Therefore using the concept of equation,
x + y = 21 --- (1)
Total volume of small box is given by:
Total volume of small box = (Volume of a small box) * (Number of small box)
Total volume of small box = 7x
Similarly the total volume of large box is,
Total volume of small box = 14y
Given the total volume of carried box is 252 cubic feet. Using the concept of equations,
7x + 14y = 252 ---(2)
The equations (1) and (2) gives the required system of equations.
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James earned a total of $68 last week. He earned $48 washing cars and won x dollars in an art contest. Which equation can be used to find the number of dollars James won in the art contest?
Answer:
Step-by-step explanation:
since $68 is your total, let's use the example z=y+x
z is our total, and we know that he made a total of $68, therefore z is the number 68.
We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.
So 68-48= 20. therefore James made $20 at the art contest.
In Michael’s closet he can choose from a yellow, green, or orange shirt, navy or gray shorts, and tennis shoes or sandals. Create a table to represent the various clothing options.
The table is attached below.
What are table entries?
Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.
From the information given, we can make a table to display all the options available for Michael to choose clothing options.
The table is attached as follows:
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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.
What is the fundamental principle of counting?The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.
Calculation:It is given that,
Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.
So, we can write
the number of shirts = 3
the number of shorts = 2
the number of footwear = 2
Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.
I.e., 3 × 2 × 2 = 12
Therefore, there are 12 combinations for him to choose one among these.
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What is the radius of 6 inches
Answer:
28.27 sq. units or 9π sq.
Step-by-step explanation:
A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the give
polygon 4 units to the right and 5 units down?
Answer:
(-1, 3), (3, 3), (5, 3), (1, 0)
Step-by-step explanation:
A translation of 4 units to the right means adding 4 to every x-coordinate.
The new coordinates are:
(-1, 3), (3, 3), (5, 3), (1, 0)
function rule to find f(11).
the next question is more point go check it out after you answer this question!!!!!
The solution for f(11) in the function when the function f(x) = 12|x + 8| is 228
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 12|x + 8|
The above equation is an absolute value equation
An absolute value equation has the following representation
f(x) = a|x - h| + k
So, we have the following representation
f(x) = 12|x + 8|
Also from the question, we have
f(11)
This means that the value of x is 11, and we calculate f(x) when x = 11
Substitute the known values in the above equation, so, we have the following representation
f(11) = 12|x + 8|
So, we have the following equation
f(11) = 12|11 + 8|
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(11) = 12|19|
Solving further, we have
f(11) = 12 * 19
Evaluate the products
f(11) = 228
Hence, the solution is 228
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Arrange the steps in the correct order to solve the equation,
3(22-5) - 4 = 10
Add 4 to each side of the
equation:
3/22 - 5) = 14
Use the Exponential Property and
write in decimal form:
(2 - 5)log2 = log4. 67
log4. 67
Find the value of Toga
and substitute
2-5 = 2. 23
Simplify
23. 625
Take the log of each side:
log(22+ - 5) = log('9).
2 - 5 - 1034. 87
Divide each side by log 2
Tog?
Add 5 to each side of the
equation
2+ = 2. 23 +5
Divide both sides of the equation
The correct order to solve the equation is given below .
In the question ,
it is given that ,
the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 ,
Step(1) , adding 4 to each side of the equation ,
3*([tex]2^{2 t - 5}[/tex]) = 14
Step(2) , dividing both sides of the equation by 3 ,
we get , ([tex]2^{2 t - 5}[/tex]) = 14/3 .
Step(3) , taking log on each side ,
log([tex]2^{2 t - 5}[/tex]) = log(14/3)
Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,
we get ,
(2t - 5)*log(2) = log(4.67)
Step(5) , Dividing each side by log(2) ,
we get , 2t-5 = log(4.67)/log(2) .
Step(6) , Add 5 to each side of equation
we get , 2t = 2.23 + 5 ;
Step(7) , Simplifying we get ,
we get , t = 3.625 .
Therefore , the the solution of the given equation is t = 3.625 .
The given question is incomplete , the complete question is
Arrange the steps in the correct order to solve the equation,
3*([tex]2^{2 t - 5}[/tex]) - 4 = 10 .
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J53)
a) what i the x-coordinate of every point along thi line?
b) ue your anwer to ue part a) to write the equation of the line
The abscissa or x-coordinate of any point on Y-axis is zero.
Which line is the x-coordinate?
Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis.
The ordinate and abscissa are other names for the x-axis and y-axis, respectively. These two axes can be used to find or represent any point on the coordinate plane as an ordered pair of the form (x,y).
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
In order to represent the equation in y-intercept (y=mx+b) form, the slope and y-intercept must be included. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
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Write an equation in slope-intercept form of the line that is parallel to the one given and passes through the given point
(1,3); y=7x+5
Which equation models the relationship between the two variables in the table below?
2343H
5
-7
-10
-13
y=-2z
y=-3z+2
1=-3z
IN
y=-2z-3
Answer:
2nd equation
Step-by-step explaination:
1st. -7≠-2(3)
2nd. Sastifies all
3rd. -10≠-3(4)
4th. -4≠-2(2)-3
please help me i’ve got midterms and i’ve been stuck on this for like 45 minutes Dx
Answer:
f(x) = ³√(x–1) + 4
f-¹(x) = (x + 1)³ + 4
Step-by-step explanation:
i hope this helped
Sam tries to draw lines of reflection through a rectangle so that the rectangle can be reflected onto itself. How many lines of reflection can sam draw? enter the answer in the box.
Therefore the solution of this question is Sam can draw 2 lines of reflection.
What is line of reflection?If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.
To determine the quantity of lines that will reflect a rectangle back onto itself.
Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.
A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.
Therefore Sam can draw 2 lines of reflection.
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Two fair number cubes have faces labeled with the numbers 1 through 6. The two cubes will be rolled simultaneously. What is the probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 ?.
The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.
What is the probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.
Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.
When two cubes are rolled, the total sample space is 36.
The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5
The probability = 5/36
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Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.
solve: x²-3x+7=0
step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2
Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)
Answer:
Step-by-step explanation:
He made a mistake in step one turning the 7 into a -7
[tex]x^{2}[/tex] - 3x + 7 = 0
Solving:
[tex]1x^{2}[/tex] - 3x + 7 = 0 ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.
[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.
a = 1, b = -3, c = 7
x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7
2 x 1
x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7
2
x = 3 ± √9 - 4 x 7
2
x = 3 ±√9 - 28
2
x = 3 ± √-19
2
The square root of a negative number does not exist in the set of real numbers.
x = ∉ R
Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach $181,000 in 19 years?
Based on the given parameters, the value of the money to invest initially is $99341.383
How to determine the amount of investment?The given parameters about the compound interest are
Amount, A = $181000
Interest Rate, R = 5%
Time, t = 19 years
Number of times, n = 365 i.e. continuously
To calculate the amount, we have:
A = P + CI
Where
C = P(1 + R)^t
So, we have
A = P(1 + R)^t
This can be rewritten as
A = P(1 + R/n)^nt
Substitute the known values in the above equation
181000 = A * (1 + 5%/365)^(12*365)
So, we have
A = 181000 /[(1 + 5%/365)^(12*365)]
Evaluate the expression
A = 99341.383
Hence, the amount of the investment is $99341.383
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in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card?
Answer: 19120 Toaster
Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!
What is the equation of the blue line
Answer:
[tex]y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
Using the points [tex](0,2)[/tex] and [tex](2,3)[/tex], the gradient is [tex]\frac{3-2}{2-0}=\frac{1}{2}[/tex].
The [tex]y[/tex]-intercept is [tex](0,2)[/tex], so the equation is [tex]y=\frac{1}{2}x+2[/tex].
a. Prove ABD is congruent to CBD.
b. Determine whether all four triangles in the diagram are congruent.
c. Explain your reasoning.
Answer:
a. The proof is in your picture
b. Yes
c. All four triangles are congruent by the HL theorem
Step-by-step explanation:
Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.
a. Left trianglesYour picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.
b. Right trianglesSides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.
c. All trianglesThe same HL theorem reasoning applies to all of the triangles.
__
Additional comment
The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.
suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8?
The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
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Answer the question and help a brother out
Answer:
25
Step-by-step explanation:
first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25
(im not sure completely im only in 7th grade)
i’m so lost and i really need help :’). this is 9th grade algebra
Answer:
1 and 2 are functions, 3 is not a function.
Step-by-step explanation:
One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.
If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
Mr. Reynolds, the gym teacher, divided a class of 16 students into 2 equal teams. How many students were on the team?
Answer:
8
Step-by-step explanation:
16 divided by 2 is 8.
Answer: 8 students
Step-by-step explanation: 16/2=8
I need help with this geometry please i don’t understand. Just #1 please
Answer:
a) CE=PR
b) TR=FE
c) <F=<T
d) <P=<C
e) RPT=ECF
Step-by-step explanation:
A roller-coaster goes over a 12 m tall hill then approaches a 30 m hill. What is the minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill?
254.8 m/s
15.96 m/s
Not enough information to answer
18.78 m/s
Not enough information to answer
Option C is the correct answer.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.
The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.
To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.
The value of the acceleration is not given.
So,
We can not find the minimum velocity.
Thus,
Not enough information to answer
Option C is the correct answer.
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
_______
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y = _____
By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.
Given two equations are;
5x+3y=30..........(1)
−5x−2y=−25.........(2)
Now , from (2)
−5x−2y=−25
⇒ 5x +2y = 25 (multiply both sides with '-' sign)
⇒ y = [tex]\frac{(25 -5x)}{2}[/tex]
Solving the system;
substitute the above vale of y in eq (1)
5x + 3y = 30
⇒ 5x + 3 ( [tex]\frac{(25 -5x)}{2}[/tex]) = 30
⇒ 5x + ([tex]\frac{(75 - 15x)}{2}[/tex]) = 30
⇒ [tex]\frac{10x+75-15x}{2}[/tex] = 30
⇒ -5x + 75 = 60
⇒ -5x = -5
⇒ x = 1
∴ x = 1
Now substitute the value of x in (1)
5x + 3y = 30
⇒ 5 × 1 + 3y = 30
⇒ 3y = 25
⇒ y = 25/3
∴ y = 25/3
Now using the value of x and y , we can find the value of x - y
x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3
∴ x - y = -22/3
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help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer: omg never seen somthing dat complex :O
Step-by-step explanation:
is 0.04x=y proportional
Rotate triangle P 90° clockwise about the point (2, -1).
54
3
2
1
-5 -4 -3 -2 -1 0
-1
2345
-4
1 2 3 4 5
P
Answer:
p=12345
Step-by-step explanation:
Answer:
see attached
Step-by-step explanation:
You want the graphed triangle rotated 90° CW about the point (2, -1).
RotationAfter rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.
The points L(5,0) , M(-4,0) and N(5,-4) form a triangle find the perimeter of the triangle . Round your answer to the nearest tenth if necessary .
Answer:
9.1 units
Step-by-step explanation:
See diagram below ....using pythagorean theorem