Step-by-step explanation:
a general line equation is
y = ax + b
the slope of a line is always the factor of x (a).
it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.
so, here it is -5/4.
it says, when x changes by +4, then y changes by -5.
a parallel line must have the same slope. it just crosses the y-axis at a different point. and that is what b specifies in the equation. it tells us the y value when x = 0.
and we get it by using the point coordinates in the equation and then solve for b :
1 = -5/4 × -4 + b = (-5 × -4)/4 + b = 20/4 + b = 5 + b
b = -4
so, the full equation of the parallel line is
y = -5/4x - 4
4) A company manufactures widgets. The expense function E=8q+12,000 and the
demand function q= -10p +20,000, where p is the price.
a. Express the variable expense V in terms of q, where q is the quantity of widgets
produced
b. Express the total expenso E in terms of p.
c. Determine the Revenue R in terms of p. (Hint: R=p•q).
d. Determine the profit P in terms of p. (Hint: P=R-E).
e. Determine the price that will yield the maximum profit. (Hint: x = -b/2a).
f. Determine the maximum profit.
Revenue, profit and expenses are all integral parts of a company's balance sheet
The expense in terms of q is [tex]\mathbf{E = 8q + 12000}[/tex]The expense in terms of p is [tex]\mathbf{E = -80p + 172000}[/tex]The revenue in terms of p is [tex]\mathbf{R = -10p^2 + 20000p}[/tex]The profit in terms of p [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]The price that yields the maximum profit is $1004The maximum profit is $9908160The expense function is given as:
[tex]\mathbf{E = 8q + 12000}[/tex]
The demand function is given as:
[tex]\mathbf{p = -10p + 20000}[/tex]
(a) The expense in terms of q
This is already given as: [tex]\mathbf{E = 8q + 12000}[/tex]
(b) The expense in terms of p
Substitute -10p + 20000 for p in [tex]\mathbf{E = 8q + 12000}[/tex]
[tex]\mathbf{E = 8(-10p + 20000) + 12000}[/tex]
Expand
[tex]\mathbf{E = -80p + 160000 + 12000}[/tex]
[tex]\mathbf{E = -80p + 172000}[/tex]
(c) The revenue in terms of P
This is calculated as:
[tex]\mathbf{R = p \times q}[/tex]
So, we have:
[tex]\mathbf{R = p \times (-10p + 20000)}[/tex]
Expand
[tex]\mathbf{R = -10p^2 + 20000p}[/tex]
(d) The profit in terms of p
We have:
[tex]\mathbf{R = -10p^2 + 20000p}[/tex] and [tex]\mathbf{E = -80p + 172000}[/tex]
So, the profit P is calculated as:
[tex]\mathbf{P =R - E}[/tex]
This gives
[tex]\mathbf{P =-10p^2 + 20000p +80p - 172000}[/tex]
[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
(e) The price that yields maximum profit
In (d), we have:
[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
The maximum price is calculated using:
[tex]\mathbf{p = -\frac{b}{2a}}[/tex]
Where:
[tex]\mathbf{b =20080}[/tex]
[tex]\mathbf{a = -10}[/tex]
So, the equation becomes
[tex]\mathbf{p = -\frac{20080}{2 \times -10}}[/tex]
[tex]\mathbf{p = 1004}[/tex]
Hence, the price that yields the maximum profit is $1004
(f) The maximum profit
In (e), we have: [tex]\mathbf{p = 1004}[/tex]
Substitute 1004 for p in [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]
[tex]\mathbf{P =-10(1004)^2 + 20080(1004) - 172000}[/tex]
[tex]\mathbf{P =9908160}[/tex]
Hence, the maximum profit is $9908160
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On the way to her babysitting job, Mary rode her bike for the first mile. She stopped at a traffic light and waited a few minutes for the traffic light to turn green. She then walked her bike across the street and up a short steep hill. Finally, she rode the bike at a constant speed for one more mile. If Mary created a graph of her time and distance, which statement describes the part of her graph that would show no change in distance?
A.Mary used her bike to ride the first mile.
B.Mary stopped and waited for the traffic light to turn green.
C.ary walked her bike across the avenue and up a short hill.
D.Mary rode her bike at a constant speed for one mile.
Answer:mile.
B.Mary stopped and waited for the traffic light to turn green.
Step-by-step explanation:
edge 2020 its simp3l
I need help ASAP no links and no tricks the one who answers correctly I will mark brainiest. If I got #5 wrong let me know and tell me the right answer and show your work. Ty for ur help ❤️❤️❤️
Answer:
[tex]y=-\frac{4}{3} x+4[/tex]
Step-by-step explanation:
Slope-intercept form is written in [tex]y=mx+b[/tex]
So, to solve, we must separate y onto one side and make its coefficient one.
[tex]4x+3y=12[/tex]
Subtract 4x on both sides.
[tex]3y=12-4x[/tex]
Divide both sides by the coefficient of [tex]y[/tex], which is 3.
[tex]\frac{3y}{3} =\frac{12-4x}{3}[/tex]
Simplify.
[tex]y=4-\frac{4}{3} x[/tex]
Rewrite this equation into standard form by changing the order of [tex]mx[/tex] and [tex]b[/tex]
[tex]y=-\frac{4}{3} x+4[/tex]
Answer
y=4/5 times 2/3
Step-by-step explanation:
Wanda is a nurse at a busy city hospital. What qualities might help Wanda in her career?
Answer:
b.
This may be the complete question:
Wanda is a nurse at a busy city hospital. What qualities might help Wanda in her career?
a. Wanda is task oriented and likes to be alone.
b. Wanda has a lot of energy and is a good multitasker.
c. Wanda has remarkable typing skills and does well with computers.
d. Wanda has very good concentration skills and likes to create things with her hands.
Answer: b.
help me plssssssssssssssss
Answer:
1/2= 5/10
this is answer
I really need help asap please!
Answer:
49
Step-by-step explanation:
the line joined by midpoints of sides is called midsection
which is parallel to the third side and is half its length
so (5x - 26) * 2 = 9x - 37
10x - 52 = 9x - 37
x = 52 - 37
x = 15
so PQ is 5x - 26
= 5*15 - 26
= 75 - 26
= 49
The equation y=−15x+12 is the slope-intercept form of which equation?
5x+13y−4=05 x plus 1 third y minus 4 is equal to 0
−y15+12=xnegative y over 15 plus 12 is equal to x
y−5x=−4y minus 5 x is equal to negative 4
y−15x=−12
I honestly don't know but I think it would come out to be 4/5
does the graph represent a function? yea or no
Answer:
no
Step-by-step explanation:
It is not because it does not pass the vertical line test.
****************************************************************
This is the vertical line test:
Imagine a vertical line that starts at the left side of the graph, at x = -8, and is moving right to x = 8. If at any time in the vertical line's movement from left to right, it intersects more than 1 point of the relation simultaneously, then the relation is not a function.
******************************************************************
Here, when the vertical line is x = -7, the vertical line intersects points (-7, 4) and (-7, 6) simultaneously. That means this relation does not pass the vertical line test, and it is not a function.
100 POINTS IF U GET THIS RIGHT!
Answer:
y-intercept: 5/3
Step-by-step explanation:
Our equation: y = mx + b
Given equation: y = -8/3 + 5/3
=> Now, let's compare.
=> y = mx + b = y = -8/3 + 5/3
=> we can tell that the y-intercept is b, which is 5/3.
Hoped this helped.
[tex]y = - \dfrac 83 x + \dfrac 53 \\\\\\\text{The above equation is in a form of y = mx +b where b is the y-intercept}\\\\\text{Hence}~ \dfrac 53~ \text{is the y-intercept}[/tex]
PLZ HELP AND ANSWER QUICK Find the gradient of the line segment between the points (2,-3) and (-3,-8).
Answer:
1
Step-by-step explanation:
I assume you mean slope
(-3-(-8))/(2-(-3))=5/5=1
Rashid solves the following system of equations using the elimination method.
6x−5y=−315x+3y=10
What value does he correctly determine for x?
Enter you answer in the box.
X=6 and 6=K so x=
Use the transitive property of equality to finish the equation
Answer:
X=6
Step-by-step explanation:
Hope this helps.
Answer:
x = K
Step-by-step explanation:
If,
x = 6
and 6 = k
=> x = 6 = k
=> x = k
The Transitive Property of Equality states the same fact as:
"If two units are equal to each other and the second unit is equal to a third unit, then the first unit is also equal to the third unit."
What is the equation in point-slope for the linear function whose graph contains points (1, -2) and (-3, 6)?
A. y - 6 = 2(x + 3)
B. y - 6 = -2(x + 3)
C. y - 2 = -2(x - 1)
Answer:y+2 = 2(x-1)
Step-by-step explanation:
First we find the slope
(1,-2) (-3,6)
rise/run
change of y/change of x
8/-4
-2
The slope is -2
point slope form is y-y1 = m(x-x1)
m is the slope, y1 is y coordinate of a point and x1 is x coordinate of same point as the y1 point.
lets use (1,-2)
y-(-2) = 2(x-1)
point slope form
y+2 = 2x-2
y = 2x-4
slope intercept form
A taxi service charges an initial fee plus $1.80
per mile. How far can you travel for $12
?
What information do you need in order to be able to solve the problem?
Answer:
You would need the intial fee in dollars/cents
Expression:
c=initial fee
x=amount of miles
[tex]1.80x+c=12[/tex]
Step-by-step explanation:
You would need the intial fee in dollars/cents
Expression:
c=initial fee
x=amount of miles
[tex]1.80x+c=12[/tex]
Fifty-four percent of the students in your class have moved at least one
time. Write this percent as a decimal.
Answer:
0.54
Step-by-step explanation:
54 space 2 times is 0.54
will give brainliest
Answer:
Steeper: y=-3/2x+1/2 AND y=-2x+7/3 AND y=-7/4x+3/2
Less Steep: y=-4/3x+2/3 AND y=-8/7x+4/7
Step-by-step explanation:
Hope this helps :)
Ten less than the product of a number and 45.
Answer:
45*x-10
Step-by-step explanation:
10 less than a number would give you
x - 10
and the product of a number means your multiplying and your multiplying 45 so you would get
45*x
add them together and you get
45*x-10
A particular variety of bamboo grows for
4
months out of the year at a rate of
3
inches per day. The rest of the year, the bamboo is dormant and does not grow.
A graph of the growth for a
12
-month period is shown.
What is the domain of the function that models this phenomenon?
Using function concepts, it is found that the domain of the function that model this phenomenon is [0, 12].
The domain of a function is the set that contains all possible input values.
In this problem, the function is the height of the bamboo according to the month of the year, hence, the input is the month of the year, which has values between 0 and 12, and thus, the domain of the function that model this phenomenon is [0, 12].
A similar problem is given at https://brainly.com/question/10891721
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y=2x+1
y=x-2
one solution; (–3, –5)
infinitely many
no solution
one solution; (–5, –3)
Answer:
y=11-2x x + y =15
4x − y=7 and 2x − y=15 all have one solution
x=12 − 3y 2x + y=7
3x + 9y=24 and -4x=2y + 14 have no solution
you can just put the rest in infinite solutions
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!
The answer is P and R
Answer:
Q and R
Step-by-step explanation:
to be similar all sides must have the same scaling factor :
the factor from 2 to 8 is 4.
and the factor from 3 to 12 is also 4.
therefore, these 2 parallelograms are similar.
pls give ans for the following image
Answer:
7 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
The reciprocal of a number n is [tex]\frac{1}{n}[/tex]
The reciprocal of 8 is [tex]\frac{1}{8}[/tex]
The reciprocal of [tex]\frac{1}{7}[/tex] is [tex]\frac{1}{\frac{1}{7} }[/tex] = 7
sum = 7 + [tex]\frac{1}{8}[/tex] = 7 [tex]\frac{1}{8}[/tex]
pleaseeeee helpppppppppppppp
A math class has 3 girls and 7 boys in the seventh grade and 3 girls and 3 boys in the eight grade. The teacher randomly selects a seventh grader and an eight grader from her class for a competition. What is the probability that the students she selects are both boys?
Answer: 3/5
solve pls brainliest
Answer:
1/4
Step-by-step explanation:
The constant of proportionality is 1/4.
Answer:
b
Step-by-step explanation:
The form of an equation representing proportion is
y = kx ← k is the constant of proportionality
y = [tex]\frac{1}{4}[/tex] x ← is in standard form
with k = [tex]\frac{1}{4}[/tex]
Solve for x.
4/5(x−3/10)=−2 1/4
Enter your answer as a mixed number in simplest form in the box.
Answer:
x = -201/80
Mixed form: x = -2 41/80
Step-by-step explanation:
Value of x = [tex]-2\frac{1}{4}[/tex]
What is algebraic equation?Algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Examples: (y²x² + 2xy – y)/(x – 1) = 12.
Given, equation
[tex]\frac{4}{5}(x- \frac{3}{10} )[/tex] = [tex]-2\frac{1}{4}[/tex]
⇒4/5[(10x-3)/10] = -9/4
⇒2/5[(10x-3)/5] = -9/4
⇒(20x-6)/25 = -9/4
⇒80x - 24 = -225
⇒80x = -225 + 24
⇒x = -201/80
⇒x = -2.5125
⇒x = [tex]-2\frac{1}{4}[/tex]
Hence, the value of x in simplest mixed number is [tex]-2\frac{1}{4}[/tex]
Learn more about algebraic equation here:
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Find the value of the variable(s) in each figure explain your reasoning.
Answer:
...............................
x^2 + y^2 = z^2
A) The square of the sum of the first number and second number is the square of the third number
B) The sum of the square of the first number and the square of the second number is the square of the third number
pls need help with this..
Find the area of the parallelogram. b = 90 ft h = 2 yd The area of the parallelogram is __ft² or __yd².
I ain’t giving n9 answer
What is the equation of the line that passes through points (10,6) and (2,2) ?
Answer:
y = (1/2)x + 1
Step-by-step explanation:
y = mx + b
m = slope = (y2 - y1)/(x2 - x1) = (6 - 2)/(10 - 2) = 4/8 = 1/2
y = (1/2)x + b
Use point (2, 2) to find b.
2 = (1/2)(2) + b
2 = 1 + b
b = 1
Equation: y = (1/2)x + 1
The cost of a blue balloon is 4 times the cost of a yellow balloon. Rashmi spent₹ 910 in buying both blue and yellow balloons, find the cost of a blue balloon?
The cost of the blue balloon is ₹728.
let
the price of the yellow balloon = x
cost of the blue balloon = 4x
Total amount spent = ₹ 910
Therefore,
4x + x = 910
5x = 910
divide both sides by 5
5x / 5 = 910 / 5
x = 182
cost of the blue balloon = 4x = 4(182) = ₹728
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The angle measurements in the diagram are represented by the following expressions
Answer:
∠ B = 126°
Step-by-step explanation:
∠ A and ∠ B are alternate angles and are congruent , then
8x + 78 = 2x + 114 ( subtract 2x from both sides )
6x + 78 = 114 ( subtract 78 from both sides )
6x = 36 ( divide both sides by 6 )
x = 6
Then
∠ B = 2x + 114 = 2(6) + 114 = 12 + 114 = 126°