Answer: False
The correct expression is -4(x-1)^3+2
====================================================
Work Shown:
[tex]f(x) = x^3\\\\f(x-1) = (x-1)^3\\\\-4f(x-1) = -4(x-1)^3\\\\-4f(x-1)+2 = \boldsymbol{-4(x-1)^3+2}\\\\[/tex]
So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3
Side note: (x-1)^3 expands to x^3-3x^2+3x-1
B. locate and plot (square root of)15 on a number line. find a better approximation using decimals.
The number line for √15 is shown in the figure and the value of √15 is approximately 3.87298.
Number line:
Number line used for visual representation of numbers on a straight line.
Given:
Here we need to locate and plot √15 on a number line.
Steps for the construction:
Step 1) Draw a line AB that is 15 in length, and then add 1 to C so that the distance from A to C is 16.
Step 2) From the midpoint of A C on the line, use your compass and make a half circle from A to C.
Step 3) Draw a vertical line up from B until it touches the red half circle you made in Step 2.
Step 4) From B on the number line, use your compass and make a quarter circle from D to E.
The square root of 15 is the distance from B to E. To make things clearer, we have also created the illustration below showing where B, E, and the square root of 15 are located on the number line, labeled with numbers instead of the half circle, quarter circle and vertical line.
Based on the steps the number line is looks like,
Therefore, The square root of 15 (√15) is approximately 3.87298.
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Your revenue (in dollars) for selling x bracelets is given by f(x) = 5x and your profit is $50 less than 80% of the revenue. What is your profit for 77 sales?
From the calculation carried out below, it can be observed that the profit for 77 sales is $258.
How do we calculate profit for sales?Given revenue as:
f(x) = 5x ............................ (1)
Where:
x = Number of bracelets sold or sales = 77
Total obtain the revenue, substitute x = 77 into equation (1), we have:
Revenue = f(77) = 5 * 77
Revenue = $385
Since profit is $50 less than 80% of the revenue, we have:
Profit = (Revenue * 80%) - 50
Profit = (385 * 80%) - 50
Profit = 308 - 50
Profit = $258
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A truck enters a highway driving 60 mph. A car enter the highway at the same place 14 minutes later and drives 67 mph in the same direction . From the time the car enters the highway, how long will it take the car to pass the truck
Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.
As given in the question,
Speed of a truck=60mph
⇒60 minutes = 60miles
⇒14 minutes = (60/60)×14
= 14 miles
Car speed =67mph
67 miles=60minutes
⇒1miles = (60/67) minutes
⇒14miles = (60/67)×14
≈12.54 minutes (approximately)
Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.
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The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The area of the resulting rectangle is 90 ft2. Find the original area of the square.
Answer:
64 ft^2
Step-by-step explanation:
It is a square to start, so each side = x
then (x+7 ) * ( x -2) = 90
x^2 + 5x -14 = 90
x^2 + 5x - 104 = 0 factor or use Quadratic Formula to fin x = 8 ft
Original area is then 8 x 8 = 64 ft^2
Miguel tracks four stocks during the day. The changes for the stocks are shown in the table. A 2-column table with 4 rows. Column 1 is labeled Stock with entries A, B, C, D. Column 2 is labeled Change with entries negative three-fourths, 0.7, negative 1, 0.2. Which list shows the values of the changes in order, from least to greatest?
Stock A, Stock B, Stock C, Stock D
Stock B, Stock D, Stock A, Stock C
Stock C, Stock A, Stock D, Stock B
Stock D, Stock C, Stock B, Stock A
The list shows the values of the changes in order, from least to greatest as Stock C, Stock A, Stock D, and Stock B which is the correct option (C).
What is descending order?Descending order is defined as when numbers (or other items) are arranged from the largest numbers to the least numbers, it is said to be in descending order.
What is ascending order?Ascending order is defined as when numbers (or other items) are arranged from the least numbers to the largest numbers, it is said to be in ascending order.
We have been given four stocks during the day. The changes for the stocks are shown in the table.
-3/4, 0.7, -1, 0.2
Here the least numbers to the largest numbers, it is said to be in ascending order.
⇒ -1 < -3/4 < 0.2 < 0.7
Arrange the stock in increasing order.
Stock C, Stock A, Stock D, Stock B
Therefore, the list shows the values of the changes in order, from least to greatest as Stock C, Stock A, Stock D, and Stock B.
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Your question is incomplete, probably the missing part is:
find the value of x ?
The value of x from the given diagram is 64 degrees
Lines and anglesA line is defined as the shortest distance between two points. From the given diagram, we have that the line AB bisects FAB, hence;
<FAB = <CAB = 58 degrees
Also since the sum of angles on a straight line is 180 degrees, hence;
58 + 58 + x = 180
116 + x = 180
x = 180 - 116
x = 64 degrees
Hence the value of x from the given diagram is 64 degrees
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Julie had $237 to spend. She returned a calculator and received a $128 refund. She then bought a chair for $62. How much money in dollars and cents did Julie have to spend after buying the chair?
Answer:
$303 0cents
Step-by-step explanation:
237 + 128 -62 = 303
The amount Julie has to spend after buying the chair is $303.
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.
As per the given data:
We are given the details of the transactions that Julie did.
We have to find out the remaining amount of money that is left with Julie after the transactions.
Initial amount that Julie had to spend (A) = $237
Amount received as a refund after returning that calculator (B) = $128
Price that had to be paid to buy a chair (C) = $62
For finding out money in dollars and cents did Julie have to spend after buying the chair:
= A + B - C
= 237 + 128 - 62
= 365 - 62
= 303
The amount Julie has to spend after buying the chair is $303.
Hence, The amount Julie has to spend after buying the chair is $303.
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Solve the inequality.
-2.5w<6.8
W>?
Answer:
-2.5w<6.8
-2.5w/-2.5<6.8/-2.5
w>-2.72
Triangle ABC has coordinates (-1, 3), (4, 2), and (0, -5). Its image is a dilation of ABC with a scale factor of 3. Identify the coordinates of its image.
The coordinates of ABC are respectively (-1/3,1), (4/3,2/3), and (0/3,5/3) .
Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).
If we are given the dilated point, then we can find the original point by dividing by the scale factor.
Triangle ABC was dilated by a scale factor of 3 about the origin mapping it to triangle A'B'C' with vertices A'(-1/3), B'(4/,2), and C(0/-5).
The coordinates of triangle ABC are:
A=(-1/3,3/3) = (-1/3)
B=(4/3,2/3) = (4/3,2/3)
C=(0/3,-5/3) = (0/3,-5/3)
coordinates are formed by two components that are a latitude , giving the north-south position, and a longitude, giving the east-west position.
Therefore the coordinates of ABC are respectively (-1/3,1), (4/3,2/3), and (0/3,5/3)
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Using your ruler to measure, draw segment EF so that it bisects RS shown below. Mark their intersection
as point A. Mark all relevant measures to justify your answer.
Using the segment addition postulate and the bisection concept, the segment EF bisecting RS is given at the end of the answer.
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
From this, the bisection concept is derived, which is when a line crosses a segment exactly at the segment's midpoint, meaning that point A is the midpoint of RS.
The illustration of this situation is given at the end of the answer.
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a rectangele has and area of 48 in every dimension
Graph The Lines (Algebra 1)
Answer:
See the picture below
Step-by-step explanation:
Your equations are in the slope-intercept form of a line. The equations are make up of a slope and a y-intercept.
y = mx + b The m is the slope (the steepness of the line) and b is the y-intercept. This is where the line crosses the y axis.
I would start with the y intercept. Look at the first equation
y = x -8 The -8 tells us that this graph crosses the y axis at (0,-8) From that point, we will use the slope. The slope is the number before the x. If we do not see a number than it is 1. We want to make this a fraction. What is 1 as a fraction? 1/1 This means that from -8 where the graph crosses the y axis we will follow the pattern of up one, one to the right.
Let's look at the second graph
y = -x + 5. This tells us that we cross the y axis at (0,5). Our slope is -1. What is -1 as a fraction? -1/1. This means that we will move down 1 and right one. We will follow that pattern.
Let's look at the third graph
y = 3/4x - 1 We cross the y axis at (0,-1) From that point we move up 3 and right 4.
y = 3 means that no matter what x is, y will be -3. This creates a horizontal line.
x = -4 means that not matter what y is, x will be -4. This creates a vertical line.
please help me as soon as possible with this
Part A: The student was supposed to divide before subtracting
Part B: The student was supposed to simplify the parentheses before finding the exponents
Part C: The simplification of the expression gives -16.
From the question, we are to simplify the given expression
The given expression is
(∛64 - 16 ÷ 2)(2 - 4)²
Part A:
The mistake the student made was not applying the PEMDAS rule
P - Parentheses
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
Since division comes before subtraction, the student was supposed to divide before subtracting
Part B:
The student mistake was trying to simplify the exponent before simplifying the parentheses. The student was supposed to simplify the parentheses before finding the exponents.
Part C:
Simplifying the expression
(∛64 - 16 ÷ 2)(2 - 4)²
Simplify the cube root
(4 - 16 ÷ 2)(2 - 4)²
Divide
(4 - 8)(2 - 4)²
Simplify the parenthesis
(-4)(-2)²
Simplify the exponent
(-4)(4)
Evaluating
-16
Hence, the simplification of the expression gives -16.
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Liza earned some money by taking care of her neighbors pet. she bought a drink for $1.95 and a concert ticket for $30. she bought a ring for $7.20 and then two-thirds of the remaining money on a wireless speaker. if liza has 38.50 left, write and solve an equation to find the amount of money m liza earned by taking care of her neighbors pet.
The equation is 1.95+30+7.20+2/3(m-1.95-30-7.20)+38.50=m
The amount of money Liza earned is $154.65
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
let the money she earn be m.
the remaining money = m-1.95-30-7.20
So, her total earning is,
1.95+30+7.20+2/3(m-1.95-30-7.20)+38.50=m
39.15+38.50+2/3(m-39.15)=m
77.65+2m/3-26.10=m
77.65-26.10=m-2m/3
51.55=(3m-2m)/3
51.55*3=m
m=$154.65
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using ratios.
1. The ratio of male employees to
female employees is 1:3. If
there are 144 female
employees in total, how many
males are there?
Answer:
48
Step-by-step explanation:
set up a proportion of 1/3 and x/144 and then divide 144 by 3 which is 48
[tex]\stackrel{\textit{ratio of 1~:~3}}{\cfrac{males}{females}~~ = ~~\cfrac{1}{3}}\implies \cfrac{males}{144}~~ = ~~\cfrac{1}{3}\implies 3males=144 \\\\\\ males=\cfrac{144}{3}\implies males=48[/tex]
Pls help I’m gonna fail
Answer:
3. w = 4
4 . g = 8
5. q = 1
6. m = -3
7. z = -32
8. a = 6
9. h = 4
10. d = -16
11. y = 4
12. n = 4
13. v = 3
14. c = -2
Step-by-step explanation:
3). 3w + 7 = 19
3w = 12
w = 4
4). 2g - 13 = 3
2g = 16
g = 8
5). 11 = 12 - q
q + 11 = 12
q = 1
6). 10 = 7 - m
m + 10 = 7
m = -3
7). -4 * (5) = (z/-4 - 3) * -4
-20 = z + 12
z = -32
8). 3 * (a/3 + 4) = (6) * 3
a + 12 = 18
a = 6
9). 5 * ((h + 6)/5) = (2) * 5
h + 6 = 10
h = 4
10). -2 * ((d - 8)/-2) = (12) * -2
d - 8 = -24
d = -16
11). 8y + 3y = 44
11y = 44
y = 4
12). 36 = 13n - 4n
36 = 9n
n = 4
13). 12v + 10v + 14 = 80
22v + 14 = 80
22v = 66
v = 3
14). 6c - 8 - 2c = -16
4c - 8 = -16
4c = -8
c = -2
You're welcome47.
48.
3m-4+2
m+5
j³-64
j-4
49.
-5p+4p² +4
p-2
50. (4p + 3p²-1) ÷ (p + 4)
51. (20x² 13x + 2) = (5x - 2)
52. (12x² - 6x³ - 3-9x) ÷ (3x − 3)
53. (8x² - 2x - 3) + (2x + 1)
54.(-3x² + 6x³ - 4 - x) ÷ (2x + 1)
-
Please solve this
Answer:
29282829939999999 and yea
Please answer!!!! Spending 100 points on this, so you get 50 points for solving. 1st person to tell me ALL 3 of the answers gets Brainliest!
Answer:
6
Step-by-step explanation:
Hans spent $38 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?
A cylindrical can has a radius of 4 centimeters. Write the volume V of the can as a function of the height h.
The volume of cylinder V as a function of the height h is: V = 50.24h
In this question, we have been given the radius of the cylinder which is 4 centimeters.
We need to write the volume V of the can as a function of the height h.
We know that, the formula of volume of the cylinder of radius r and height h is, V = π × r² × h
In this question, r = 4 centimeters
Substitute r = 4 in above formula of volume of cylinder.
⇒ V = π × r² × h
⇒ V = π × 4² × h
⇒ V = 3.14 × 16 × h
⇒ V = 50.24 × h
⇒ V = 50.24h
Therefore, the volume of cylinder V as a function of the height h is:
V = 50.24h
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Aunt Anne has a container of 24 cookies. The container has 2 oatmeal raisin cookies, and the rest are chocolate chip cookies. If Cyrus reaches in and takes a cookie without looking, is the probability of choosing a chocolate chip cookie impossible, unlikely, likely, or certain? Express the probability as a number between 0 and 1.
Answer:
Likely
11/12 aka 0.916666666667 aka 91.67%
Step-by-step explanation:
24 - 2 = 22
22/24
11/12
Likely means more than 50% but not 100% in this case.
Which of the following is equivalent to (3a + 5b) + 7c?
3a + (5b + 7c)
3a(5b + 7c)
7c(5b + 3a)
8ab + 7c
Answer:
3a + (5b + 7c)
Step-by-step explanation:
The answer cannot be 3a(5b +7c) because when the number is immediately before the brackets, it signifies multiplication. therefore the 3a(5b+7c) would be equivalent to 15ab+21ac
the answer cant be 7c(5b+3a) because of the same explanation as the one above, therefore 7c(5b+3a) would be equivalent to 35cb+21ca
the answer finally cant be 8ab+7c because it means that one added 3a and 5b giving you 8 but it cannot be ab because ab is equivalent to a×b, hence, one cant put a multiplied algebraic expression with an added number
The equation equivalent to the the expression (3a + 5b) + 7c is 3a + (5b+7c). Hence, the first option is the correct one.
What is an expression?In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.
For instance, the equation x + y has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.
The first option is correct because it does not affect the main equation rest are not the same as the equation.
For example, let's take the second equation :
3a (5b + 7C)
After solving this option we get 15ab + 21 ac so it is incorrect because it changed the main expression.
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find the product of 12 0.6 and 6 1/4
Find the value of each variable.
2(5x − 5)°
20yº
(5y + 5)
(3x - 5)°
Answer:
The answer is 10 for your math equation
Step-by-step explanation:
The values of each variable are x = 15° and y = 7°.
Given are two lines, intersecting each other at a point to make angles,
2(5x − 5)°, 20y°, (5y + 5)° and (3x - 5)°.
We need to find the values of the variables.
The lines are intersected in such a way that the angles 2(5x − 5)°, (3x - 5)°and (5y + 5)°, 20y° are making linear pairs.
We know that the linear pair angles sum up to make 180°.
So,
2(5x − 5)° + (3x - 5)° = 180°
10x - 10 + 3x - 5 = 180°
13x - 15 = 180°
13x = 195°
x = 15°
Similarly,
(5y + 5)° + 20y° = 180°
5y + 5 + 20y = 180°
25y = 175°
y = 7°
Hence the values of each variable are x = 15° and y = 7°.
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1.) Raisins and nuts were mixed in a
bowl. If 34 of the mixture was
made up of nuts, what was the
ratio of raisins to nuts?
Answer:
8−5=3
Step-by-step explanation:
Jolene works at Food Lion and she makes $13.25. She works 4 hours a day Monday through Friday and 8 hours a day on the weekend. How much would she make during a 7-day week?
She would make $477 during a 7-day week
How much would she make during a 7-day week?The given parameters are
Hourly rate = $13.25Weekdays = 4 hours dailyWeekends = 8 hours dailyThere are 5 days in a weekday and 2 in a weekend
So, the total earning is
Total = Rate * [Weekday hours * 5 + Weekend hours * 2]
This gives
Total = $13.25 * [4 * 5 + 8 * 2]
Evaluate
Total = $477
Hence, she would make $477 during a 7-day week
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What is the range for the set of scores: 7, 8, 11, 15, 17, 20?
a. 20
b. 1
c. 13
d. 7
The range of the set of scores is 13.
Here,
The set of scores:
7, 8, 11, 15, 17, 20
We have to find the range of the set of scores.
What is Range of set?
The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.
Now,
The highest number = 20
The lowest number = 7
Hence, Range of the data set = 20 - 7 = 13
So, The range of the set of scores is 13.
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Which of the following numbers can be expressed as decimals that terminate? (1 point) 5 over 2 , 4 over 5 , 2 over 7 , 4 over 3 5 over 2 and 2 over 7 4 over 5 and 4 over 3 5 over 2 and 4 over 5 2 over 7 and 4 over 3
Answer:
all of them are terminating decimals
Step-by-step explanation:
5/2=2.5
4/5=1.25
2/7=3.5
4/5=1.25
4/3=0.75
5/2=2.5
4/5=1.25
2/7=3.5
4/3=0.75
they are terminating decimals because they have a finite end
George is comparing two different phones. The screen of phone A has a width of 5.3 cm. The width of the screen on phone B is 5 and one-third cm. Which statement explains which phone has the wider screen?
Answer:
Step-by-step explanation:
Screen B is wider
Jake ran 121.3 miles a week. if jake ran an equal number of miles each day, then what distance did he run in a day? (write the answer up to two decimal places)
Distance ran by Jake in a day is 17.33 miles.
It is given in the question that Jake ran 121.3 miles in a week. Also, Jake ran an equal number of miles each day.
We have to find the distance ran by him in a day.
Let the distance ran by him in a day be x miles.
We know that there are 7 days in a week.
Hence, according to the data given in the question, we can write,
Number of days in a week * distance ran in a day = total distance
Hence,
7*x = 121.3 miles
Solving the linear equation, we get,
x = 121.3/7 miles
x = 17.3285 ≈ 17.33 miles
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