Answer:
Since BD bisects angle ABC, the resultant angles, angles ABD and CBD will be equal in magnitude. Since we are not given either the value of ABC nor are we given the figure, the answer we can get to from the given question is
angle ABD = angle CBD
Johnson's Household Products has a division that produces two sizes of bar soap. The demand equations that relate the prices p and q (in dollars per hundred bars), to the quantities demanded, x and y (in units of a hundred), of the 3.5-oz size bar soap and the 5-oz bath size bar soap are given by p = 80 - 0.01x - 0.005y and q = 50 - 0.005x - 0.015y. The fixed cost attributed to the division is exist10,000/week, and the cost for producing 100 3.5-oz size bars and 100 5-oz bath size bars is exist8 and exist12, respectively.
(a) What is the weekly profit function P(x, y)? P(x, y) =
(b) How many of the 3.5-oz size bars and how many of the 5-oz bath size bars should the division produce per week to maximize its profit? 3.5-oz bars 5-oz bars What is the maximum weekly profit?
Answer:
The weekly profit function P(x,y) = 72x - 0.01x² -0.005xy + 38y - 0.005xy -0.015y² - 10000
3.5 oz bars = 3560
5 oz bars = 80
The maximum weekly profit = 119680
Step-by-step explanation:
Given that:
the demand functions are p and q
the variable cost of x = 8x and the variable cost of y = 12y
Since the fixed cost attributed to the division is exist 10,000/week
∴ the total cost C = 8x + 12y + 10000
R(x,y) = p(x) + q(y)
where ;
xp(x) = 80x -0.01x² -0.005y
yqz(y) = 50 -0.005x -0.015y²
R(x,y) = 80x -0.01x² -0.005xy + 50y -0.005xy -0.015y²
The weekly profit function P(x,y) = R(x,y) - C
P(x,y) = 80x -0.01x² -0.005xy + 50 -0.005xy -0.015y² - ( 8x + 12y + 10000)
P(x,y) = 80x -0.01x² -0.005xy + 50 - 0.005xy -0.015y² - 8x -12y - 10000
P(x,y) = 72x - 0.01x² -0.005xy + 38y - 0.005xy -0.015y² - 10000
(b) How many of the 3.5-oz size bars and how many of the 5-oz bath size bars should the division produce per week to maximize its profit?
profit will be maximized if:
[tex]\dfrac{\partial P}{\partial x} =0 \ and \ \dfrac{\partial P}{\partial y} =0[/tex]
given that:
[tex]\dfrac{\partial^2 P}{\partial x^2} < 0 \ and \ D >0[/tex]
where;
D = Px Py -Pxy²
Now;
[tex]\dfrac{\partial P}{\partial x} =(-0.02 x -0.01 y +72)[/tex]
[tex]\dfrac{\partial P}{\partial y} =(-0.03 x -0.01 y +38)[/tex]
[tex]\dfrac{\partial P}{\partial x} =0 \to 2x+y = 7200[/tex]
[tex]\dfrac{\partial P}{\partial y} =0 \to x+3y = 3800[/tex]
2x + y = 7200
2x + 6y = 7600
5y = 400
y = 400/5
y = 80
From
x + 3y = 3800
x + 3(80) = 3800
x = 3800 - 240
x = 3560
∴ 3.5 oz bars = 3560
5 oz bars = 80
What is the maximum weekly profit?
The maximum weekly profit = 72x - 0.01x² -0.005xy + 38y - 0.005xy -0.015y² - 10000
The maximum weekly profit = 72(3560) - 0.01(3560)² -0.005(3560)(80) + 38(80) - 0.005(3560)(80) -0.015(80)² - 10000
The maximum weekly profit = 256320 - 126736 - 1424 + 3040 - 1424 -96 - 10000
The maximum weekly profit = 119680
Terrence is selling tulip bulbs for $0.35 per bulb and daffodil bulbs for $0.64 per bulb. He makes a 40% profit on the sales of tulip bulbs and a 45% profit on the sales of daffodil bulbs. He is trying to determine the number of tulip bulbs, x, and the number of daffodil bulbs, y, he will need to sell m a week to earn a profit of $1,200 for the week. Which of the following equations can Terrence use to make this determination?
a) 0.35x +0.64y=1200(0.40+0.45)
b) (0.40+0.45)(0.35x+0.64y)=1200
c) (0.40)(0.35)x + (0.45)(0.64)y = 1200
d) (0.35+0.64)(x+y) = 1200(0.40+0.45)
Answer:
c) (0.40)(0.35)x + (0.45)(0.64)y = 1200
Step-by-step explanation:
Profit on each tulip bulb is:
$0.35 + 40% = $0.35*0.40Profit on x amount of tulip bulbs:
(0.35)*(0.40)xSimilarly, profit on y amount of daffodil bulbs is:
(0.45)(0.64)ySince the target is $1200, the required equation is:
(0.40)(0.35)x + (0.45)(0.64)y = 1200Correct answer option is C)
Leila's father used six-tenths of a full tank of gasoline on their trip. Nine gallons were used.
About how many gallons does the tank hold?
Answer:
15
Step-by-step explanation:
if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten
Answer:
D): 15
Step-by-step explanation:
if 6/10 = 9 gal. then we can divide 9 by 6 and then multiply that answer by ten
Use the numerals 1,7,7,7, and 7 to create the number 100
Answer:
[tex]77\div.77\cdot1[/tex]
Step-by-step explanation:
What we're basically looking for here are ways to get 100 using these numbers.
My immediate first thought was "can we divide the 7's by some 7's to get 100?"
I know that [tex]7 \div .7=10[/tex], so I had the idea to make it [tex]77 \div .77 = 100[/tex]. This means that we can use the number 7 four times in the equation [tex]77 \div .77=100[/tex].
However, we're still missing a 1 that we need to include. This is easy, we can just multiply [tex]77 \div .77[/tex] by 1.
So in conclusion, we get [tex]77 \div .77\cdot1[/tex]
Hope this helped!
Answer:
177 - 77 = 100
Step-by-step explanation:
there are basically 4 7s
77-77 = 00
177 - 77 = 100
hope this helps （＾▽＾）
Simplify (3a) (a^-3) =
Answer:
3 a^(-2)
3 / a^2
Step-by-step explanation:
(3a) (a^-3)
Multiply
3 a^1 * a^-3
Since we are multiplying, we add the exponents
3 a^ ( 1-3)
3 a^(-2)
If you are not supposed to leave a negative exponent
x^-b = 1 / x^b
3 / a^2
Find the axis of symmetry and vertex for the parabola y=-4x^2-32x-10
Answer:
Axis of Symmetry: x = -4
Vertex: (-4, 54)
Step-by-step explanation:
We use a graphing calc.
Answer:
the equation of the axis of symmetry is [tex]x=-4[/tex]
Step-by-step explanation:
Recall that the x-value of the vertex of a parabola of the form:
[tex]y=ax^2+bx +c[/tex]
is given by the expression:
[tex]x_{vertex}=-\frac{b}{2\,a}[/tex]
therefore, in our case the x-position of the vertex becomes;[tex]x_{vertex}=-\frac{b}{2\,a}=\frac{32}{-8} =-4[/tex]
and since the equation of the axis of symmetry is [tex]x=x_{vertex}[/tex]
Then, the equation of the axis of symmetry is [tex]x=-4[/tex]
seven times the sum of a number and three
Answer: The answer is 7 ( x + 3 ).
Step-by-step explanation:
So we are given in word-form this equation:
seven times the sum of a number and three
We can rewrite this as:
7 times ( number + 3)
This number can be rewritten as a variable. Take any variable of your pick. I'll use x because that's one of the most used variables.
7 ( x + 3 )
There you go! Finished.
AY
Which best describes the association of this
scatterplot?
linear, weak
O linear, strong
O nonlinear, weak
O nonlinear, strong
A.) linear,weak
just got it right on edge 2020
The best describes the association of this scatterplot will be linear, and weak. Then the correct option is A.
What is a scatter plot?Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.
In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are created to plot data points on both horizontal and vertical axis.
A set of dots plotted on an azimuth and elevation axis is known as a scatter plot. Given that they can demonstrate the degree of connection, if any, in between values of measured quantities or events, scatter plots are crucial in statisticians (called variables).
The best describes the association of this scatterplot will be linear, and weak. Then the correct option is A.
More about the scatter plot link is given below.
https://brainly.com/question/13984412
#SPJ2
K=C+273 What is C in terms of K?
Answer:
K-273=C
Step-by-step explanation:
K=C+273
Subtract 273 from each side
K-273=C+273-273
K-273=C
I need all the help I can get! Please!
Answer:
See below.
Step-by-step explanation:
Triangle:
The area for a triangle is given by the formula:
[tex]A=\frac{1}{2}bh[/tex]
Where b is the length of the base and h is the vertical height.
We can see that the base length is (2x+4) and the height is (x+3). So, the expression for the area would be:
[tex]\frac{1}{2}(2x+4)(x+3)[/tex]
Rectangle:
The perimeter of a rectangle is given by the formula:
[tex]P=2l+2w[/tex]
Where l is the length and w is the width.
We can see that the length is 2x-1 and the width is 3x+2. Thus, the perimeter is:
[tex]2(2x-1)+2(3x+2)[/tex]
For the area, the formula is:
[tex]A=lw[/tex]
So, the expression for area would be:
[tex](2x-1)(3x+2)[/tex]
Rectangular Prism:
The volume for a rectangular prism is given by the formula:
[tex]V=lwh[/tex]
The length is (x+2), the width is (x), and the height is (2x+1). Thus:
[tex]x(x+2)(2x+1)[/tex]
Y=2x+2 graph the equation using the slope and y-intercept
Answer:
See graph attached
Step-by-step explanation:
Our life is simple because the equation [tex]y=2x+2[/tex] is already put in slope-intercept form.
This form is called slope-intercept because it states exactly what it's called: The number multiplied by [tex]x[/tex] (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)
With this info, we can start graphing.
We know that the y-intercept is 2, meaning one point will be (0,2).
We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.
Hope this helped!
The graph of the function y = 2x + 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 2
The above function is a linear function that has been transformed as follows
Slope = 2y-intercept = 2Next, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
Read more about functions at
brainly.com/question/2456547
#SPJ6
28 1/2% covert the percent to a decimal
Answer:
0.285
Step-by-step explanation:
To do this, divide 28 1/2% by 100%, obtaining:
28.5%
---------- = 0.285
100%
Write a word problem about adding integers with the same sign. *
Peter weighs 156 pounds, but he would like to wrestle in a lower weight class.He loses 4 pounds one week, gains back 2 pounds the next, loses 5 pounds the third week and loses 3 pounds the fourth week.How much does
Peter weigh now?
Consider the tables that represent a continuous function and its inverse. Which is an accurate comparison of the functions? -9 0 0 27 3 36 12 63 f(x) 9 х – 12 f-1(x) -13 -3 -10 0 -9 6 -7 9 -6 ✓ The reciprocal of the slope of f(x) is the same as the slope of f1(x). The negative reciprocal of the slope of f(x) is the same as the slope of f'(x). The y-coordinate of the y-intercept of f(x) is the same as the y-coordinate of the y-intercept of f'(x). The opposite of the y-coordinate of the y-intercept of f(x) is the same as the x-coordinate of the x-intercept of f'(x). Submitted
Answer:
the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x)
Step-by-step explanation:
To find the equation of a line given two points, we use the formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
The standard equation of a line is given by:
y = mx + c; where m is the slope of the line and c is the intercept on the y axis
For the function f(x), we have to select two points, let us select (-6, 9) and (0, 27)
Hence the equation of the line f(x) is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-9=\frac{27-9}{0-(-6)}(x-(-6))\\ \\y-9=\frac{18}{6} (x+6)\\\\y-9=3(x+6)\\\\y-9=3x+18\\\\y=3x+18+9\\\\y=3x+27\\[/tex]
Comparing y = 3x + 27 with y = mx + c, we can see that the slope (m) = 3 and the y intercept is 27
For the inverse function f⁻¹(x), let us use the points (-3, -10) and (0, 9)
Hence the equation of the line f⁻¹((x) is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-10)=\frac{-9-(-10)}{0-(-3)}(x-(-3))\\ \\y+10=\frac{1}{3} (x+3)\\\\y+10=\frac{1}{3}x+1\\\\y=\frac{1}{3}x+1-10\\\\y=\frac{1}{3}x-9\\[/tex]
To find the x intercept put y = 0
0 = (1/3)x - 9
(1/3)x = 9
x = 27
Comparing y = (1/3)x - 9 with y = mx + c, we can see that the slope (m) = 1/3 and the y intercept is -9
Hence, the reciprocal of the slope of f(x) is the same as the slope of f⁻¹(x) (i.e reciprocal of 3 = 1/3)
Answer: A
The reciprocal of the slope of f(x) is the same as the slope of f–1(x).
Step-by-step explanation:
Can someone help me please I’m confused!!!
Answer:
10) -1
11) 1/2 or 0.5
12) -1/5 or -0.2
13) -13/6 or -2.166666666
14) -1/8 or -0.125
15) 1/2 or 0.5
hope it helps;)
good luck!
10x-7x+3
simply plssss
Answer:
3x+3
plz mark brainliest
Answer:
3x + 3
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables.
10x - 7x + 3
(10x - 7x) + 3
Subtract:
10x - 7x = 3x
Remember to bring the constant down.
3x + 3 is your answer.
~
help will give brainliest
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So the "back" of the arrow is on/above -20.
The arrow points to -12.
You added something to -20 to get to -12.
So the first number is -20. You added ? to get -12. -12 is the last number / the answer to the equation.
So the equation from what you have so far is -20 + ? = -12
You need to isolate the ? so that you know what it is.
So to get rid of the -20 (make it 0), you have to add 20. -20 plus 20 equals 0, which basically means it is gone. You also have to add 20 to -12. 20 plus -12 equals 8.
Now the equation is ? = 8.
So you know that the second number is 8.
The equation makes sense; -20 + 8 = -12.
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Help ASAP please!!!!!!
Answer:
22.4cm
Step-by-step explanation:
Opposite side of the triangle is x
Adjacent side of the triangle is 10
Tangent 20° = x/10
2.237 = x/10
x = 2.237 × 10
x = 22.37cm
x = 22.4cm to the nearest tenth
It’s 11:50 am showtimeonclock
Answer: LOL
Step-by-step explanation:
Explain the difference between dry friction and drag due to fluid friction
Answer: Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other
Hope it helps:) I got it right on my test btw
Step-by-step explanation:
If mountains rose by 1 mm/yr, how high would they be (in meters) after 1,000 years? 10 million years? 50 million years?
Answer:
a)after 1,000 years?
1 meter
b) 10 million years?
10,000 meters
c) 50 million years?
50,000 meters
Step-by-step explanation:
We are told in the question that mountains rise 1 mm per year.
a) After 1000 years
1 year = 1 mm
1000 years =
Cross Multiply
1000 × 1 mm
= 1000mm
Converting to meters
1 mm = 0.001 m
1000 mm =
1000 × 0.001m
= 1 meter
b) After 10 million (10,000,000) years
1 year = 1 mm
10000000years =
Cross Multiply
10000000 × 1 mm
= 10,000,000mm
Converting to meters
1 mm = 0.001 m
10,000,000mm =
10,000,000 × 0.001m
= 10,000 meters
c) After 50 million years(50,000,000)
After 50,000,000 years
1 year = 1 mm
50,000,000years =
Cross Multiply
50,000,000 × 1 mm
= 50,000,000mm
Converting to meters
1 mm = 0.001 m
50,000,000mm =
50,000,000 × 0.001m
= 50,000 meters
Will mark brainliest
Answer:
A
Step-by-step explanation:
12x-8/4 divide
12x/4 = 3x
-8/4 = -2
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3x - 2}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ \frac{12x - 8}{4} }[/tex]
Factor out 4 from the expression
⇒[tex] \sf{ \frac{4(3x - 2)}{4} }[/tex]
Reduce the fraction with 4
⇒[tex] \sf{3x - 2}[/tex]
Hope I helped!
Best regards! :D
PLS HELP BEST ANSWER GETS BRAINLIEST
If 1 cake can be made with 1/6 lb. sugar, how many cakes can be made with 2/3 lb. of sugar?
Thomas has 19 playing cards. He gives 6 playing cards to his brother.
How many playing cards does Thomas have now?
Answer:
13 playing cards
Step-by-step explanation:
Thomas = 19 playing cards
Brother = 6 playing cards (which give Thomas)
Thomas = 19 playing cards - 6 playing cards = 13 playing cards
Answer:
[tex]\huge\boxed{\sf 13\ cards}[/tex]
Step-by-step explanation:
Thomas has total = 19 playing cards
He gave away = 6 cards
Thomas have now:
=> 19-6
=> 13 cards
Two canoes travel down a river, starting at 10:00. One canoe travels twice as fast as the other. After 3.5 hr, the canoes are 5.25 mi apart. Find the average
rate of each canoe.
Answer:
Step-by-step explanation:
The time for each canoe is 3.5 hours
The total distance traveled by the first canoe is not known. Nor is the distance for the second canoe. We do know that the difference is 5.25 miles.
So let the rate of the slower canoe = x
Let the rate for the second canoe = 2x
The first canoe goes a distance of 2*x * 3.5 = 7x
The second canoe goes a distance of 3.5x
The difference = 7x - 3.5x = 5.25
3.5x = 5.25 divide by 3.5
x = 5.25/3.5
x = 1.5 which is the rate of the slower canoe
2x = 3 which is the rate of the faster canoe
Annie is running a trail that is 4 1/2 miles long. She ran the first 2/3 of the distance. Then the trail became very steep, so she slowed down to a walk. Annie walked for 1/2 of the remaining distance and then ran again for the rest of the way. How far did Annie walk? Write the answer as a simplified fraction.
Answer:
[tex]\frac{3}{4}[/tex] miles
Step-by-step explanation:
Total length of the trail = [tex]4\frac{1}{2}[/tex] miles = [tex]\frac{9}{2}[/tex] miles
She ran the first [tex]\frac{2}{3}[/tex] of the distance i.e.
The distance for which she ran = [tex]\frac{2}{3} \times \frac{9}{2} = 3\ miles[/tex]
Remaining distance = Total length of trail minus the distance for which she has already run = [tex]\frac{9}{2} - 3 = \frac{3}{2}[/tex] miles
Given that: After running, Annie has to walk due to steep nature of the trail, So, Annie walked for [tex]\frac{1}{2}[/tex] of the remaining distance.
The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] Remaining distance
The distance for which Annie walked = [tex]\frac{1}{2} \times[/tex] [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] miles
So, the answer is: [tex]\frac{3}{4}[/tex] miles
- 1/2 (-5/6 + 1/3) simplified
Take 4a-3b+2c from 2a-3b+4c
Answer:
2a-6b+6c
Step-by-step explanation:
Combine like terms
Answer: -2a + 2c
Step-by-step explanation:
The situation is saying that subtract 4a-3b+2c from 2a-3b+4c.
(2a-3b+4c) - (4a - 3b +2c) Subtract by terms
-2a + 2c
Marian buys a dress that costs $32.00 She pays 10%
sales tax
Answer:
$35.2
Step-by-step explanation:
I’m assuming you meant the total of the dress after tax.
1. 32 * 1.1 = 35.2
OR
1. 32 * 0.1 = 3.2
2. 32 + 3.2 = 35.2
You could do it either way.
Find an equation of the line passing through the point (−6,−5) that is parallel to the line y=4/3x−5
Answer:
The answer is
[tex]y = \frac{4}{3} x + 3[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
y = 4/3x - 5
Comparing with the general equation above
Slope/ m = 4/3
Since the lines are parallel their slope are also the same
So we have
Slope of parallel line = 4/3
Equation of the line using point (−6,−5) and slope 4/3 is
[tex]y + 5 = \frac{4}{3} (x + 6) \\ y + 5 = \frac{4}{3} x + 8 \\ y = \frac{4}{3} x + 8 - 5[/tex]We have the final answer as
[tex]y = \frac{4}{3} x + 3[/tex]Hope this helps you.