Answers
Answer:
(0,-4)
Step-by-step explanation:
write the coordinates of the point where the two lines intercept themselves
Answer:
A. (0,-4)
x is 0 and y is -4
Related Questions
pls help mepls pls pls pls pls pls
Answers
The expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a expression with a coefficient of 10 and a constant of 5.
The expression with a coefficient of 10 and a constant of 5 is given by -
10x + 5
Therefore, the expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
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Gianna purchased 5\tfrac{1}{2}5
2
1
pints of ice cream for a party. If each guest will be served exactly \tfrac{1}{3}
3
1
pint of ice cream, what is the maximum number of guests Gianna can serve?
Answers
The maximum number of guests Gianna can serve will be 16.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers
From the information, Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream
The maximum number of guests Gianna can serve will be:
= 5 1/2 ÷ 1/3
= 11/2 ÷ 1/3
= 11/2 × 3
= 33/2
= 16.5
The maximum number will be 16.
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Complete question
Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream, what is the maximum number of guests Gianna can serve?
The question and the Triangle is in the same image. I'm on point 3
Answers
ANSWER
• Ratio: 2
,• Lengths of the sides of the new triangle: 6, 6√2
,• Circles: ,see explanation
,• Triangle: ,see explanation
EXPLANATION
• The ratio is the quotient between the length of segment DE and, for example, segment AB,
[tex]\frac{DE}{AB}=\frac{6}{3}=2[/tex]• Now, we have to multiply each side of triangle ABC by 2 to obtain the lengths of the sides of triangle DEF,
[tex]\begin{cases}DF=2BC=2\cdot3=6 \\ \\ EF=2AC=2\cdot\sqrt[]{3^2+3^2}=2\cdot\sqrt[]{2\cdot9}=6\sqrt[]{2}\end{cases}[/tex]• Next, draw the two circles mentioned,
• The intersection between the two circles is point F. The ,triangle is,
if a/ b+1 = 2, what does 2b equal?
Answers
A fish descends 4 meters per minute for 2 minutes. Then it ascends 3 meters per minute for 3 minutes. What is the total distance, in meters, the fish traveled?
Answers
Answer:
1 meter of dispalcement,
17 meters of path distance
Step-by-step explanation:
-4meters/min * 2min = -8meter
3 m/m * 3m = 9meters
-8+9 = 1 meter of displacement, it's looking for the total path's distance, then that is just |-8|+|9|=17 meters
I hope this helps
Answer:
The fish ascended a total of meter.
Step-by-step explanation:
distance= rate x time
D= -4(2)= -8m
A= 3(3)= 9m
-8m+9m= 1m
;)
find the slope of 4x + 3y equals to
Answers
find the slope of 4x + 3y equals to
I will assume a value of a
so
4x+3y=a
Isolate the variable y
3y=-4x+a
y=-(4/3)x+a/3
therefore
the slope is -4/3Note: the value of the slope not depend of the value of a
Given 3 and one-tenth times negative 6 times seven-twelfths, determine the product.
eighteen and one sixtieth
negative eighteen and 7 over 120
ten and 17 over 20
negative 10 and 17 over 20
Question 2(Multiple Choice Worth 2 points)
(One-Step Inequalities MC)
Write the statement "the sum of a number and 18.4 is at least −3.8" as an inequality.
−3.8 + b > 18.4
b + 18.4 ≥ −3.8
b + 18.4 ≤ −3.8
−3.8 + b < 18.4
Question 3(Multiple Choice Worth 2 points)
(Adding and Subtracting Rational Numbers MC)
Simplify negative 3 and two-thirds minus 6 and three-fourths.
3 and one-half
negative 10 and one-twelfth
negative 10 and five-twelfths
negative 18 and one-half
Question 4(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
Question 5(Multiple Choice Worth 2 points)
(Dividing Rational Numbers MC)
Divide negative 3 and one-sixth ÷ negative 8 and two-fifths.
252 over 95
95 over 252
51 over 30
30 over 51
Question 6(Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve one eighth times quantity x plus 32 end quantity equals negative 7.
x = 56
x = 7
x = −88
x = −24
Question 7(Multiple Choice Worth 2 points)
(Rewriting Rational Numbers LC)
Which number is equal to four and one-sixth?
four and sixteen hundredths with the six repeating
six twenty-fifths
4.2
416%
Question 8(Multiple Choice Worth 2 points)
(Laws of Exponents with Whole Number Exponents LC)
Which expression is equivalent to 2 and one tenth raised to the fifth power divided by nine tenths raised to the fourth power, all raised to the fifth power?
0.55
0.56
2 and one tenth raised to the twenty fifth power divided by nine tenths raised to the twentieth power
2 and one tenth raised to the tenth power divided by nine tenths raised to the ninth power
Question 9(Multiple Choice Worth 2 points)
(Adding and Subtracting Rational Numbers MC)
Julie wanted to match Lisa's obstacle course record of 68.2 seconds. She has already spent thirty-nine and one fourth seconds on wall climbing and 12.84 seconds on the ropes. How much time did she have left to match the record?
12.24 seconds
16.11 seconds
26.41 seconds
28.95 seconds
Question 10(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Write the math sentence as an equation: Negative nine times the sum of a number and 12.3 is 30.8
−9(r − 12.3) = 30.8
−9r + 12.3 = 30.8
−9r − 12.3 = 30.8
−9(r + 12.3) = 30.8
Question 11(Multiple Choice Worth 2 points)
(Laws of Exponents with Whole Number Exponents MC)
Evaluate two and two tenths raised to the sixth power divided by two and two tenths raised to the fifth power, all raised to the second power.
4.84
4.4
2.2
1
Question 12(Multiple Choice Worth 2 points)
(Adding and Subtracting Linear Expressions MC)
Write the expression in simplest form.
the quantity negative three fifths x minus 8 end quantity minus the quantity negative 14 plus three tenths x end quantity
negative nine tenths x plus 6
negative nine tenths x minus 6
negative three tenths x minus 6
negative three tenths x plus 6
Question 13(Multiple Choice Worth 2 points)
(Order of Operations MC)
Simplify the expression.
negative 15 plus the quantity negative 1 and six tenths plus 9 and 34 hundredths end quantity divided by 6 all times 3 squared minus 5 and 7 tenths
−4.125
−9.09
−12.96
129.09
Question 14(Multiple Choice Worth 2 points)
(Equivalent Linear Expressions LC)
Which expression is equivalent to −4(b − 5)?
−4b − 20
4b + 5
−4b + 20
−4b − 5
Question 15(Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.24x − 16.4 = 1.96
x = −60.2
x = 60.2
x = −76.5
x = 76.5
Answers
To solve the multiple questions performed, a process is being followed to get accurate results which are mentioned after the respective questions.
What are different operations in mathematics?Addition is the process of joining two or more numbers to determine their total. The result of adding the numbers 3 and 4 is 3 + 4 = 7, for instance. Any sort of number, including whole integers, fractions, decimals, and even negative values, can be added to.
The process of subtracting involves calculating the difference between two numbers. For example, subtracting 4 from 7 yields 7 - 4 = 3. Any sort of number, including whole integers, fractions, decimals, and negative values, can be subtracted.
Multiplication is the process of combining two or more numbers to determine their product. The result of multiplying the numbers 3 and 4 is 3 * 4 = 12, for instance. such as addition. Any kind of number may be used for addition, subtraction, and multiplication.
The act of dividing two integers involves determining their quotient. For example, dividing 12 by 4 yields 12 / 4 = 3. Any sort of value could be divided, although some combinations of numbers, such dividing by zero, are not described as division.
How to solve?
1) 3 * (-6) * (7/12) which is -7.5. So, the answer is -18 and 7/120 or negative 18 and 7 over 120.
2) -3.8 + b - 18.4 ≥ 0
-22.2 + b >= 0
∵sum of a number and 18.4 is at least -3.8, we can say that b is greater than or equal to -22.2.
∴b + 18.4 ≥ −3.8.
3) (-3/3) - (6/4) = (-9/3) - (6/4)
(-9/3) - (6/4) = (-9/3) * (4/4) - (6/4) * (3/3)
= (-36/12) - (18/12)
(-36/12) - (18/12) = -54/12 = -9/2 = -4 and 1/2
The correct answer is negative 18 and one-half.
4) 37.50w = $300
w = 8
37.5w + 155.95 = 455.95; w = 8.
5) (-7/6) / (-17/5) = (-7/6) * (5/17)
= (-35/102)
(-35/102) / (35/35) = (-1/3) / 1
= -1/3
6)x/8 + 32 = -7
x/8 = -39
x = -8 * -39
x = 8 * 39
x = 312
7)x = 56
x = 7
x = −88
x = −24
8)= [(2 and one tenth)^5] / [(9 tenths)^4]^5
= [2^5 * (1/10)^5] / [9^4 * (1/10)^4]^5
= [2^5 * (1/10)^5] / [9^4 * (1/10)^4]^5
= 2^5 * (1/10)^5 / (9^4 * (1/10)^4)^5
= 2^5 * (1/10)^5 / 9^4 * (1/10)^4 * 5
= 2^5 * (1/10)^5 / 9^4 * (1/10)^4 * 5
= 2^5 / 10^5 / 9^4 / 10^4 * 5
= 2^5 / (10^5 * 9^4) / 10^4 * 5
= 2^5 / (10^5 * 9^4) / 10^4 * 5
= 32 / (10^9 * 6561) * 5
= 32 / (10^9 * 6561) * 5
= 32 / 65610000 * 5
= 32 / 65610000 * 5
= 32 / 3285050000
= 32 / 3285050000
= 0.0000977077
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Determine algebraically ifthe function is even, odd, or neither. f(x)= -9
Answers
Background:
• Even ,functions are symmetric with respect to the ,y-axis,.
,• Odd ,functions are symmetric with respect to the origin.
,• Neither ,has no symmetry with respect to the origin or ,y-axis,.
Answer: Even
pls help I was taught this concept today and I can't understand or get it right!! Find the measure of the arc or angle indicatedFind the measure of mPSQa) 53°b) 248°c) 72°d) 65°
Answers
Step 1:
Find the value of x
Using secant theorem
[tex]<\text{PQR =}\frac{1}{2}\text{ }\timesStep 2:If x = 9
Then 6x+2 = 6(9) + 2 = 54+2 = 56 degrees
The measure of arc PQ = 14(9) - 14 = 126 - 14 = 112 degrees
Step 3:
The total angle in a circumference is 360 degrees
Therefore ,
mPQ + mPSQ = 360
mPSQ = 360 - mPQ
mPSQ= 360 - 112 = 248degrees
The answer is option B
find the coordinates of the ends of each latus rectum and equations of asymptotes.
Answers
For conic section of the form:
[tex](\frac{x^2}{a^2})-(\frac{y^2}{b^2})=1[/tex]The Ends of the Lactus Rectum is given as:
[tex]L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a})[/tex]The e in the equation above is the Eccentricity of the Hyperbola.
This can be obtained by the formula:
[tex]e=\frac{\sqrt[]{a^2+b^2}}{a}[/tex]Thus, comparing the standard form of the conic with the given equation, we have:
[tex]\begin{gathered} \frac{(y+8)^2}{16}-\frac{(x-3)^2}{9}=1 \\ \text{This can be further expressed in the form:} \\ \frac{(y+8)^2}{4^2}-\frac{(x-3)^2}{3^2}=1 \\ By\text{ comparing this with:} \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \\ We\text{ can deduce that:} \\ a=4;b=3 \end{gathered}[/tex]Then, we need to obtain the value of the Eccentiricity, e.
[tex]\begin{gathered} e=\frac{\sqrt[]{a^2+b^2}}{a} \\ e=\frac{\sqrt[]{4^2+3^2}}{4} \\ e=\frac{\sqrt[]{16+9}}{4} \\ e=\frac{\sqrt[]{25}}{4}=\frac{5}{4} \end{gathered}[/tex]Hence, the coordinate of the ends of the each lactus rectum is:
[tex]\begin{gathered} L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a}_{}) \\ L=(4\times\frac{5}{4},\frac{3^2}{4}),L=(4\times\frac{5}{4},\frac{-3^2}{4}) \\ L=(5,\frac{9}{4}),L=(5,\frac{9}{4}) \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Andrea labels ten cards with the numbers 1 through 10. She places the cards with prime numbers (2,3,5,7) in one box, and places the rest of the cards in another box. If Andrea draws one random card from the box of prime numbers and then one random card from the other box, how many different pairs of numbers are possible outcomes?
Answers
Box with prime numbers = 2, 3, 5, 7
Box with the other numbers = 1, 4,6,8,9, 10
Possible pairs
12 13 15 17 Four pairs
42 43 45 47 Four pairs
62 63 65 67 Four pairs
82 83 85 87 Four pairs
92 9 3 95 97 Four pairs
102 103 105 107 Four pairs
Total numbers of pairs 24 pairs
List the transformations.
Answers
The transformation of the equation [y = 4 - 1/2 √x + 3] is shown on the graph where the curve touched the x-axis on (61, 0).
What is a graph?To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph.
Bar graphs, circle graphs, and line graphs are the three most often used types of graphs.
Different types of data can be displayed using different types of graphs.
So, plotting the equation on the graph as follows:
The equation: y = 4 - 1/2 √x + 3
Plot the equation on the graph:
(Refer to the graph attached below)
The curve touches the x-axis on the coordinate (61, 0).
Therefore, the transformation of the equation [y = 4 - 1/2 √x + 3] is shown on the graph where the curve touched the x-axis on (61, 0).
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3. A car originally cost $16,000. The owner reduced the price of the car by 20%. After a few
weeks, the owner reduced the price of the car by another 20%, Belinda then purchased the
If a 3% sales tax was added, how much did Belinda pay for the car?
A. $9,600.80
B. $9,888,20
C. $10,240.00
D. $10,547.20
Answers
Answer:
the answer is D: $10547.20
start new workings.
What value of x makes the two expressions
below equal? Give your answer as a
decimal.
5x-8
First expression
3x+5
Second expression give ur answer as a decimal maths
Answers
The value of x that makes both expressions equal is 6.5.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.So, the value of x that makes both the expression equal.
So, we can write the expression as:
5x - 8 = 3x + 5
Now, solve for x as follows:
5x - 8 = 3x + 5
5x - 3x = 5 + 8
2x = 13
x = 13/2
x = 6.5
Therefore, the value of x that makes both expressions equal is 6.5.
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Find the equation of line containing given points. Write the equation in slope- intercept form (0,2)(2,-3)
Answers
Answer:
[tex]y=\frac{-5x}{2}\text{ + 2}[/tex]Explanation:
Here, we want to get the equation of the line
The general equation of a line in slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
We can get the equation through the following:
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) is (0,2) and (x2,y2) is (2,-3)
Substituting the values, we have it that:
[tex]\begin{gathered} \frac{y-2}{x-0}\text{ = }\frac{-3-2}{2-0} \\ \\ \frac{y-2}{x}\text{ = }\frac{-5}{2} \\ \\ \left(y-2\right)\text{ = }\frac{-5x}{2} \\ \\ y\text{ = }\frac{-5x}{2}\text{ + 2} \end{gathered}[/tex]Hello! Need a little help on this functions question. Thanks!
Answers
..
SOLUTION
EXPLANATION;
The range of the graph is:
[tex][-1,\infty)[/tex][tex]The\text{ range of f\lparen x\rparen=}\sqrt[\placeholder{⬚}]{x+1}-3\text{ is \lbrack-3,}\infty)[/tex]Therefore the difference is;
[tex][-3,-1)[/tex]pls help me wi this question
Answers
Answer:
1 block west and 8 blocks north
Step-by-step explanation:
One block east and two blocks north to the coffee shop. Subtract two blocks west from the one block east, and you get one block west. Add the six blocks north to the two blocks north, and you get eight blocks north.
20 POINTSSS!!! Graph the ellipse.
Name the coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse.
Answers
The coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse. is (2,-1+3√3) & (2,-1 -3√3).
Calculation:-
[tex]\sqrt{1-\frac{a^{2} }{b^{2} } } =\sqrt{1-\frac{9}{36} } =\sqrt{\frac{36-9}{36} }[/tex]
= [tex]\sqrt{\frac{27}{36} } = \frac{\sqrt{3} }{2}[/tex]
=( b,H ± be) = (2, -1 ± 6x [tex]\frac{\sqrt{3} }{2}[/tex])
(2,-1+3√3) & (2,-1 -3√3).
The long axis is called the major axis and the short axis is called the minor axis. Each major axis endpoint is an ellipse vertex, and each minor axis endpoint is an ellipse vertex. The center of the ellipse is the center of both the major and minor axes. The endpoints of the principal axis are called vertices.
The midpoint of focus is the center of the ellipse. The minor axis is a line segment perpendicular to the major axis, passing through the center, and having ellipses at both ends. Ellipse focal points are two reference points that help draw the ellipse. The foci of the ellipse are on the major axis of the ellipse, equidistant from the origin. An ellipse represents the location of a point that is a constant distance from two fixed points.
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>)How many people were surveyed about their favorite pets?A) 46B) 34C36D) 44
Answers
ANswer:
From the bar diagram,
Number of people own rabbit as pet = 4
Number of people own dog as pet = 8
Number of people own cat as pet = 11
Number of people own goldfish as pet = 6
Number of people own hamster as pet = 5
So, the number of people surveyed about their favorite pets equals the sum of number of people own rabbit, dog, cat, goldfish or hamster as pet.
Number of people surveyed about their favorite pets
[tex]\begin{gathered} =4+8+11+6+5 \\ =34 \end{gathered}[/tex]Hence 34 people surveyed about their favorite pets.
Option B is correct.
the circle graph shows how a family budgets its annual income. if the total annual income is $90,000 what amount is budgeted for clothing?
Answers
Answer:
$11700
Step-by-step explanation:
comment if u need the explanantion ;D
The sale price of women's wool coats is $ ____question attached below
Answers
By '70% off' the text means that there is a discount of 70% on the item, in other words we are only paying 30% of the original value of the item. Therefore if we multiply 30% by the value of the item, we will find the price. This is done below:
[tex]\begin{gathered} \text{price}=220\cdot30\text{ \%} \\ \text{price}=220\cdot\frac{30}{100} \\ \text{price}=220\cdot0.3 \\ \text{price}=66 \end{gathered}[/tex]The price of the with discount coat is $66
Write an equation in slope-intercept form for the line that passes through (0,4) and is parallel to the line described by y=3x-7
Answers
slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.
If two lines are parallel, that means the slope of both equations are equal.
L2: y = 3x - 7, m = 3
So, m for L1 is m = 3.
Now we just need to find y - intercept, as follows:
L1 passes through (0,4), then:
4 = 3(0) + b
4 = 0 + b
b = 4
The equation for the line is y = 3x + 4
A baker can bake 20 cupcakes in two hours, 30 cupcakes in three hours, and 40 cupcakes in four hours. What is the constant rate of change?
Answers
A baker can bake 20 cupcakes in two hours, 30 cupcakes in three hours, and 40 cupcakes in four hours.
so, the rate can be calculated as following:
number of cupcakes over the number of hours
So,
[tex]\begin{gathered} \frac{20}{2}=10 \\ or,\frac{30}{3}=10 \\ or,\frac{40}{4}=10 \end{gathered}[/tex]Please I need you to help me and show the steps please so I can understand it better
I will mark brainliest
Answers
Answer:
LM = √34
Step-by-step explanation:
L is at (-7, 4), and M is at (-2, 1).
LM
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]
determine the miss term 3:5:7:?:25:
Answers
Proof Practice
Given: ∠ PQR and ∠ XYZ are complementary
m ∠ XYZ = 10 degrees
Prove: m ∠ PQR = 80 degrees
5 statements and Reasons needed
Answers
Answer:
1. Given (angle PQR and angle XYZ are complimentary)
2. Definition of complimentary angles (Complimentary means they are added to 90 degrees)
3. Definition of Complimentary angles (Complimentary angles only include two angles)
4. Subtraction postulate (90 degrees - 10 degrees= 80 degrees which proves they are complimentary)
5. Complimentary angles theorem (angle XYZ is 80 degrees)
Sorry if that's too vague, but I really hope this helps you! I bet someone elses answer would clear it up better, so more research or finding a different answer would probably help, just to confirm. I tried to explain as much as I could, I'm not good at teaching what I know.
Kyle can was the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
Answers
No, they can not wash the car in less than 16 minutes while working together.
Given, Kyle can wash the car in 30 minutes.
Michael can wash the car in 40 minutes.
Now, we are asked that working together, can they wash the car in less than 16 minutes.
So, Kyle wash the car = 30 min
Kyle can wash (1/30)th part of the car in 1 min.
Michael wash the car = 40 min
Michael can wash (1/40)th part of the car in 1 min.
Kyle and Michael can together wash the ( 1/30 + 1/40 )th part of the car in 1 min.
Kyle and Michael = 1/30 + 1/40
Kyle and Michael = (4 + 3)/120
Kyle and Michael = 7/120
So, Kyle and Michael can together wash the 7/120th part of the car in 1 min.
and both can together wash the car in 120/7 min i.e. 17.14 min
So, working together both can wash the car in 17.14 min.
Hence, No, they can not wash the car in less than 16 minutes while working together.
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I’m not sure how to solve 3d. College calculus 1
Answers
Step 1
Given;
[tex]f(x)=(x^2+5)^3[/tex]Required; To simplify
[tex]\frac{f(x)-f(0)}{x},\text{ x}\ne0[/tex]Step 2
[tex]\frac{(x^2+5)^3-(0^2+5)^3}{x}[/tex][tex]\mleft(a+b\mright)^3=a^3+3a^2b+3ab^2+b^3---(apply\text{ p}\operatorname{erf}ect\text{ cube formula)}[/tex][tex](x^2+5)^3=(x^2)^3+3(x^2)^2(5)+3x^2(5^2)+5^3[/tex][tex](x^2+5)^3=x^6+15x^4+75x^2+125[/tex][tex]\frac{(x^6+15x^4+75x^2+125)-125}{x}[/tex][tex]\begin{gathered} \frac{x^6+15x^4+75x^2+125-125}{x} \\ \frac{x^6+15x^4+75x^2}{x} \\ \frac{f(x)-f(0)}{x}=x^5+15x^3+75x \end{gathered}[/tex]Hence if we factorize we get;
[tex]x(x^4+15x^2+75)[/tex]Therefore;
[tex]\frac{f(x)-f(0)}{x}=x(x^4+15x^2+75)[/tex]Answer:
See below
Step-by-step explanation:
f(x) = ( x^2 + 5)^3 f(0) = 5^3 = 125
(x^2+5)^3 = x^6 + 15x^4 + 75 x^2 + 125
so you have (x^6 + 15x^4 + 75x^2 + 125 - 125) /x
= x^5 + 15x^3 + 75x = x ( x^4 + 15x^2 + 75)
A firm has a monthly fixed cost of $2000, and the variable cost per unit of its product is $25. a. Determine the cost function. b. The revenue R obtained by selling x units is given by R(x) = 60x - 0.01x2. Determine the number of units that must be sold each month so as to maximize the revenue. What is the maximum revenue? c. How many units must be produced and sold each month to obtain a maximum profit? What is the maximum profit?
Answers
a) We can write the cost function (in function of the units made) as the sum of the fixed cost (2000) and the variable cost (25*x):
[tex]C(x)=2000+25x[/tex]b) The revenue R(x) is:
[tex]R(x)=60x-0.01x^2[/tex]To find the value of x that maximizes R(x) we derive R(x) and equal it to 0:
[tex]\frac{dR}{dx}=60(1)-0.01(2x)=60-0.02x[/tex][tex]\begin{gathered} \frac{dR}{dx}=0 \\ 60-0.02x=0 \\ 60=0.02x \\ x=\frac{60}{0.02} \\ x=3000 \end{gathered}[/tex]We can now calculate the maximum revenue as R(3000):
[tex]\begin{gathered} R(3000)=60\cdot3000-0.01\cdot(3000)^2 \\ R(3000)=180000-0.01\cdot9000000 \\ R(3000)=180000-90000 \\ R(3000)=90000 \end{gathered}[/tex]c) The profit function P(x) can be calculated as the difference between the revenue and the cost:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=(60x-0.01x^2)-(2000+25x) \\ P(x)=-0.01x^2+60x-25x-2000 \\ P(x)=-0.01x^2+35x-2000 \end{gathered}[/tex]In the same way as we did in b), we can calculate the number of units x that maximize the profit by deriving P(x) and making it equal to 0:
[tex]\begin{gathered} \frac{dP}{dx}=-0.01(2x)+35(1)-2000(0)=0 \\ -0.02x+35=0 \\ 35=0.02x \\ x=\frac{35}{0.02} \\ x=1750 \end{gathered}[/tex]The maximum profit can be then calculated as P(1750):
[tex]\begin{gathered} P(1750)=-0.01(1750)^2+35(1750)-2000 \\ P(1750)=-0.01\cdot3062500+61250-2000 \\ P(1750)=-30625+61250-2000 \\ P(1750)=28625 \end{gathered}[/tex]We can graph R(x) and P(x) as:
Answer:
a) C(x) = 2000 + 25x
b) x = 3000 units
R(3000) = $90000
c) x = 1750 units
P(1750) = $28625