Answers
1) We can find the inverse function, by following some steps. So let's start with swapping the variables this way:
[tex]\begin{gathered} f(x)=\sqrt[3]{x-1}+4 \\ y=\sqrt[3]{x-1}+4 \end{gathered}[/tex]2) Now let's isolate that x variable getting rid of that cubic root:
[tex]\begin{gathered} x=\sqrt[3]{y-1}+4 \\ x-4=\sqrt[3]{y-1} \\ (x-4)^3=(\sqrt[3]{y-1})^3 \\ (x-4)^3=y-1 \\ y=(x-4)^3+1 \end{gathered}[/tex]Note that when we isolate the y on the left we had to adjust the sign dividing it by -1, to get y, not -y.
Related Questions
7 in.Rounded to the nearest tenth, find:Surface Area =square inchesVolume =cubic inchesBlank 1:Blank 2:
Answers
The Solution.
By formula, the surface area of the given figure is
[tex]S.A=4\pi r^2[/tex][tex]\begin{gathered} SA=\text{surface area}=\text{?} \\ r=7\text{ inches} \\ \pi=3.14 \end{gathered}[/tex][tex]S\mathrm{}A=4\times3.14\times7^2=4\times3.14\times49=615.44\approx615.4inches^2[/tex]b. By formula, the volume of the given figure is
[tex]V=\frac{4\pi r^3}{3}[/tex]Where,
[tex]r=7\text{ inches,}\pi=3.14,V=volume=?[/tex]Substituting the values in the formula, we have
[tex]V=\frac{4\times3.14\times7^3}{3}=\frac{4\times3.14\times343}{3}=\frac{4308.08}{3}[/tex][tex]V=1436.0267\approx1436.0inches^3[/tex]Hence, the correct answers are:
a. Surface area = 615.4 square inches
b. Volume = 1436.0 cubic squ
The rectangle has side length r and s for each expression determine whether it gives the perimeter of the rectangle the area of the rectangle or neither select the correct choice in each row r+s r times s 2r+2a r2+s2
Answers
we have the following:
[tex]\begin{gathered} P=2r+2s \\ A=r\cdot s \end{gathered}[/tex]there P is perimeter and A is area
therefore, r + s and r^2 + s^2 are neither
Find the distance between the points ( 3,1 ) and (9,9). Write answers as a whole number or a fully simplified radical expression. Do not round
Answers
The distance between two points (x1, y1) and (x2, y2) can be calculated as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The points are given: (3, 1) and (9, 9), thus:
[tex]d=\sqrt[]{(9-3)^2+(9-1)^2}[/tex]Operating:
[tex]\begin{gathered} d=\sqrt[]{6^2+8^2} \\ d=\sqrt[]{36+64} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]The distance is 10
Rewrite in simplest terms: -0.3(8b – 2c)+7c - 0.9(9c – 2b)
Answers
The given expression is
-0.3(8b – 2c) +7c - 0.9(9c – 2b)
We would apply the distributive property as shown below
a(b + c) = a * b + a * c
The term outside the bracket is used to multiply the terms inside the bracket. Thus, we have
- 0.3 * 8b + - 0.3 * - 2c + 7c - 0.9 * 9c + - 0.9 * - 2b
= - 2.4b + 0.6c + 7c - 8.1c + 1.8b
The next step is to collect like terms. Thus, we have
- 2.4b + 1.8b + 0.6c + 7c - 8.1c
= - 0.6b - 0.5c
The simplified expression is
- 0.6b - 0.5c
I need help with 1.76 only. Thanks.1-75Your seam will be given a bag containing a set of coloredblocks or counters, Bach seam will receive a bag that isidentical to yours2. Taka the blocks in your buy. If you were toreach into the bag and select one block withoutkuking, what is the likelihood that it would beRed?ii. Green?fil, Blue?iv. Orange?b. Do your answers for pant (a) represent theoretical or experimentalprobabilities? Judify your response1.76If you were to select one back from the bag 12 times, replacing the block youdrew baween each selection, how many of those times would you expect tohave selected a blue block? What if you drew 24 times? Discuss bothsituations with your team and explain your answers,
Answers
The number of possiblities is given by the combinations of 5 blue block taken at 1
[tex]5C1[/tex]where 5C1 denotes the combinations of 5 blue block taken at 1 time. Then, we have
[tex]5C1=5[/tex]then, we will expect 5 times form the total of 12.
Similarly, for the other case (number of times = 24), we will get
[tex]2\times5C1=2\times5=10\text{ times}[/tex]that is, we will double the number of times.
For the function, f(x) = 38 • 0.24%, what is the decay factor? A) 38 B) 0.24 C) 0.14 D) 0.76
Answers
The decay factor is equal to 24%. In decimal form its equal to 0.24. Hence, the answer is B) 0.24
In which quadrant is the coordinate pair (-11, 1) located?a IVb Ic IId III
Answers
Step 1: Using the cartesian plane, let's locate the coordinate par (-11, 1)
The following data represents the weight of goods in a truck in tons. Find the lower limit of the outlier.1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
Answers
0.5
Explanations:The given dataset is:
1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
Step 1: Rearrange the dataset in ascending order
1.2, 1.4, 1.5, 1.7, 1.8, 2, 2.5
Step 2: Find the lower quartile, Q₁
The lower quartile is the median of the first half of the data set
That is Q₁ is the median of 1.2, 1.4, 1.5
Q₁ = 1.4
Step 3: Find the upper quartile, Q₃
The upper quartile is the median of the second half of the data set
That is Q₃ is the median of 1.8, 2, 2.5
Q₃ = 2
Step 4: Find the interquartile range (IQR)
IQR = Q₃ - Q₁
IQR = 2 - 1.4
IQR = 0.6
Step 5: Find the lower limit of the outlier using the formula below
Lower limit = Q₁ - 1.5(IQR)
Lower limit = 1.4 - 1.5(0.6)
Lower limit = 1.4 - 0.9
Lower limit = 0.5
1. Nasir had 2.45 inches of tape thatwill be divided into 3 pieces. What is the length of each piece round-ed to the nearest hundredth?a. .81b. .82c. 7.35d. 7.36
Answers
Answer:
b. 0.82
Explanation:
Nasir had 2.45 inches of tape
The tape will be divided into 3 pieces.
Therefore:
[tex]\text{Length of each piece}=2.45\div3[/tex]Now, we know that:
[tex]\begin{gathered} \frac{245}{3}=81\frac{2}{3} \\ \frac{2}{3}=0.667 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2.45\div3=0.81667 \\ \approx0.82\text{ }(to\text{ the nearest 100th}) \end{gathered}[/tex]The correct choice is B.
jared has 12 coin 4th 75 cents. 3 of the coins are worth twice as much as tge rest. construct a math argument to justify the conjecture thqt jared has 9 nickels and 3 dimes
Answers
To solve this question, we proceed as follows:
Step 1: Let x be the worth of one of the type of coins Jared has, and let y be the worth of the other type of coin
Thus:
Since 3 of the coins are of a different type, we have that:
[tex]\begin{gathered} 3x+(12-3)y=75 \\ \Rightarrow3x+9y=75 \end{gathered}[/tex]Also, since 3 of the coins are worth twice as much as the rest, we have that:
[tex]x=2y[/tex]Now, substitute for x in the first equation:
[tex]\begin{gathered} 3x+9y=75 \\ \Rightarrow3(2y)+9y=75 \\ \Rightarrow6y+9y=75 \\ \Rightarrow15y=75 \\ \Rightarrow y=\frac{75}{15} \\ \Rightarrow y=5cents \end{gathered}[/tex]Since y = 5 cents, we have that:
[tex]\begin{gathered} x=2y \\ \Rightarrow x=2(5) \\ \Rightarrow x=10cents \end{gathered}[/tex]Now, since x = 10 cents (the equivalent worth of a dime), and y = 5 cents (the equivalent worth of a nickel), we have from the first equation that:
[tex]3x+9y=75\text{cents}[/tex]From the above equation, therefore, we can conclude that Jared has nine 10 cents coins (dimes), and three 5 cents coins (nickels)
Rewrite 3^x = 243 as a logarithmic equation. log3(243) = x logx(243) = 3 log3(x) = 243 log243(x) = 3
Answers
In general, the logarithmic function definition states that
[tex]y=log_b(x)\Leftrightarrow x=b^y[/tex]Therefore, in our case,
[tex]3^x=243\Leftrightarrow x=log_3(243)[/tex]Thus, the answer is log3(243)=x, the first option.Which statements are best supported by the graph K?I. The X-intercept is located at (-3,0)II. The coordinates of the y-intercept are(0,9)III. The axis of symmetry is x=-3
Answers
Answer
All of the statements (I, II and III) given are supported by the graph K.
Step-by-step Explanation
The question asks us to check which statements are best supported by the graph K? The statements include
I. The X-intercept is located at (-3,0)
II. The coordinates of the y-intercept are (0,9)
III. The axis of symmetry is x=-3
We will take each of the statements one at a time.
I. The X-intercept is located at (-3,0)
Note that the x intercept is the point where the graph meets the x-axis, that is, the value of x on the graph when y=0.
From the graph, we can see the point where the graph meets the x-axis is x = -3, hence, the x-intercept is truly located at (-3, 0).
II. The coordinates of the y-intercept are (0,9)
The y intercept is the point where the graph meets the y-axis, that is, the value of y on the graph when x=0.
From the graph, we can see that the point where the graph meets the y-axis is y = 9, hence, the coordinates of the y-intercept is (0, 9)
III. The axis of symmetry is x = -3
The axis of symmetry is the central axis of the graph, which signifies the middle point of the graph. It is evident that this graph is centered on x = -3.
Hence, this statement too, is correct.
Hope this Helps!!!
only need help finding the length please and thank you
Answers
Solution:
Let the length of the chocolate bar is L and the width be W.
The area of the chocolate bar is expressed as
[tex]\begin{gathered} \text{Area = length}\times width \\ =L\times W \end{gathered}[/tex]Given that the area of the chocolate bar is 47.94 square feet, we have
[tex]\begin{gathered} A=L\times W \\ \Rightarrow47.94=LW\text{ ---- equation 1} \end{gathered}[/tex]linear equations in deletion method2x + 2y − z = 04y − z = 1−x − 2y + z = 2
Answers
The given system is:
[tex]\begin{gathered} 2x+2y-z=0\ldots(i) \\ 4y-z=1\ldots(ii) \\ -x-2y+z=2\ldots(iii) \end{gathered}[/tex]Multipliy (iii) by 2 to get:
[tex]-2x-4y+2z=4\ldots.(iv)[/tex]Add (i) and (iv)
[tex]\begin{gathered} 2x+2y-z=0 \\ + \\ -2x-4y+2z=4 \\ -2y+z=4\ldots(v) \end{gathered}[/tex]Add (ii) and (v) to get:
[tex]\begin{gathered} 4y-z=1 \\ + \\ -2y+z=4 \\ 2y=5 \\ y=\frac{5}{2} \end{gathered}[/tex]Put y=5/2 in (ii) to get:
[tex]\begin{gathered} 4(\frac{5}{2})-z=1 \\ 10-z=1 \\ -z=-9 \\ z=9 \end{gathered}[/tex]Put y=5/2 and z=9 in (i) to get:
[tex]\begin{gathered} 2x+2(\frac{5}{2})-9=0 \\ 2x+5-9=0 \\ 2x=4 \\ x=2 \end{gathered}[/tex]Hence x=2, y=5/2 and z=9.
solve each variable first
Michael recently started a new hourly wage job. The equation y=18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked.A. What is Miguel's hourly rate of pay?B. Does it appear the Miguel received a signing bonus? If so, how much was the bonus?How many hours must Miguel worked to receive $10,000 in total pay?
Answers
Given
y = 18.75x + 2500
Part A:
Based on the given equation where x is the number of hours worked. Since the coefficient of this term is 18.75, then we can conclude that Miguel's hourly rate is $18.75.
Part B:
The given equation has a constant of 2500, at x = 0, where the number of hours worked is zero, then the value of the equation is 2500. This appears that Miguel has a signing bonus, and the amount of bonus is $2500.
Part C:
Substitute y = 10000, to the equation and solve for x
[tex]\begin{gathered} y=18.75x+2500 \\ 10000=18.75x+2500 \\ 10000-2500=18.75x \\ 7500=18.75x \\ 18.75x=7500 \\ \frac{18.75x}{18.75}=\frac{7500}{18.75} \\ x=400 \end{gathered}[/tex]Therefore, Miguel must work 400 hours to receive $10,000 in total.
I’m not sure if I’m suppose to include “x=___” in my answer or just put the answer in alone without including the variable. Please let me know which way is correct. I’m not sure if I’m writing out the problem wrong.
Answers
SOLUTION
Given the question in the inage on the question tab;
[tex](x-9)^2=2[/tex][tex]\begin{gathered} \sqrt{(x-9)^2}=\pm\sqrt{2} \\ x-9=\pm\sqrt{2} \\ x=\pm\sqrt{2}+9 \\ \therefore x=\sqrt{2}+9,\text{ -}\sqrt{2}+9 \\ \end{gathered}[/tex]Final answer:
[tex]x=\sqrt{2}+9,\text{ -}\sqrt{2}+9[/tex]Claire has 11/12pound of butter. She will use 5 /12 pound of butter to make cookies She estimates she will have 1 /2 pound of butter when she is finished. Is Claire correct?
Answers
Explanation:
We have to substract 5/12 from 11/12:
[tex]\frac{11}{12}-\frac{5}{12}=\frac{11-5}{12}=\frac{6}{12}[/tex]And simplify the fraction:
[tex]\frac{6}{12}=\frac{1}{2}[/tex]Answer:
Claire is correct, she'll have 1/2 pound of butter.
A 7m long ladder leans against a wall such that the foot of the ladder is 4.5m away from the wall. What is the angle of elevation of the ladder?
Answers
Given:
• Height of ladder = 7 m
,• DIstance of foot of ladder to the wall = 4.5 m
Let's find the angle of elevation of the ladder.
First sketch the figure representing this situation.
Where x is the angle of elevation of the ladder.
Let's solve for x.
To solve for x, apply the Trigonometric ratio formula for cosine.
[tex]\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]Where:
• Adjacent side is the side adjacent to the angle x = 4.5
,• Hypotenuse is the longest side = 7
,• θ is the angle = x
Hence, we have:
[tex]\cos x=\frac{4.5}{7}[/tex]Take the cos inverse of both sides:
[tex]\begin{gathered} x=\cos ^{-1}(\frac{4.5}{7}) \\ \\ x=49.9\approx50^o \end{gathered}[/tex]Therefore, the angle of elevation of the ladder is 50 degrees.
ANSWER:
c. 50 degrees
Hannah bought 3.8 pounds of tomatoes at a farmer's market for $1.45 per pound. How much did Hannah pay for the tomatoes?
Answers
Answer:
Hanna would pay $5.51 for the tomatoes.
Step-by-step explanation:
You can multiply 3.8 by 1.45 and that will get you 5.51.
Making 5.51 your total cost.
The amount for 3.8 pounds of tomato is given by the equation A = $ 5.51
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for the tomatoes be represented as A
Now , the equation will be
The cost of 1 pound of tomatoes = $ 1.45
Now , Hannah bought 3.8 pounds of tomatoes
So , the amount for 3.8 pounds of tomatoes A = 3.8 x cost of 1 pound of tomatoes
Substituting the values in the equation , we get
The amount for 3.8 pounds of tomatoes A = 3.8 x 1.45
On simplifying the equation , we get
The amount for 3.8 pounds of tomatoes A = $ 5.51
Therefore , the value of A is $ 5.51
Hence , the amount is $ 5.51
To learn more about equations click :
https://brainly.com/question/19297665
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can you tell me which one is the answer just that I don't need anything else.
Answers
Thus the answer is Option (D) 7/15.
Alice traveled 30 miles in 3 hours. What graph shows the relationship between time traveled in hours and total miles traveled?The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Answers
Given that Alice traveled 30 miles in 3 hours. Initially, the distance traveled is 0 miles.
Take distance on the x-axis and time on the y-axis.
From the given information, the two points on the graph are (0,0) and (30,3).
Mark the points on the graph.
The distance-time graph of a body is a straight line. Join the points by a straight line to get the required graph.
The 'range' of numbers is the greatest number minus the smallestnumber.OFalseTrue
Answers
If a set of numbers is given, then the range is largest number minus the smallest number in the given data set.
So, the given statement is true.
L
Ost< and cost is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find sin t.18) cos i =316I need help with #18
Answers
sin^2t + cos^2t = 1
sint = 1/4
(1/4)^2 + cos^2 t = 1
1/16 + cos^2 t = 1
cos^2 t = 1 - 1/16
cos^2 t = (16 - 1)/16
cos^2 t = 15/16
take root both side,
[tex]\begin{gathered} cost=\sqrt[]{\frac{15}{16}} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]so the answer is option D
Item 26Which relation is a function?{(1, 2), (2, 3), (3, 2), (2, 1)}{(1, −1), (−2, 2), (−1, 2), (1, −2)} {(4, 2), (3, 3), (2, 4), (3, 2)}{(1, 4), (2, 3), (3, 2), (4, 1)}
Answers
Using the given relations, let's determine the relation which represents a function.
A relation represents a function if for each value of x there is only one possible y-value.
This means that in the relation no value of the x-coordinate must appear twice or be repeated.
Using the relations given, the relation which is a function is:
{(1, 4), (2, 3), (3, 2), (4, 1)}
This is because, in this relation, there is only one value y for each value of x.
In this relation, no x value appears more than once.
Therefore, the relation which is a function is:
{(1, 4), (2, 3), (3, 2), (4, 1)}
ANSWER:
{(1, 4), (2, 3), (3, 2), (4, 1)}
In the year 2010, Xavier's car had a value of $22,000. When he bought the car in 2006 he paid $28,000. If the value of the cardepreciated linearly, what was the annual rate of change of the car's value? Round your answer to the nearest hundredth if necessary.
Answers
The annual rate of change is given by:
[tex]A\mathrm{}R\mathrm{}C=\frac{f(b)-f(a)}{b-a}[/tex][tex]\begin{gathered} A\mathrm{}R\mathrm{}C=\frac{22000-28000}{2010-2006} \\ A\mathrm{}R\mathrm{}C=\frac{-6000}{4}=-1500 \end{gathered}[/tex]Hence, the annual rate of change is -1500 dollars/year, meaning the car depreciates/loses value by an amount of 1500 dollars
In the figure, segment RS bisects segment DE at S. Given that DS=4x+12 andSE=8x-8, find the value of x.
Answers
Step 1: Let's recall that a segment bisector is a ray or segment which cuts another line segment into two equal parts.
Step 2: Upon saying that, we have:
DS = SE
Step 3: Replacing with the equation we have to solve for x:
4x + 12 = 8x - 8
4x - 8x = - 8 - 12
-4x = -20
Dividing by - 4
-4x/-4 = -20/-4
x = 5
Step 4: If x = 5, let's find the length of DS and SE:
4 * 5 + 12 = 8 * 5 - 8
20 + 12 = 40 - 8
32 = 32
Step 5: x = 5 and DS/SE = 32
А
B
The scale factor that takes A onto B is
The scale factor that takes B onto A is
Answers
Let,
x₁, y₁ = 2, 2
x₂, y₂ = 6, 10
a.) The slope of the line.
[tex]\text{ Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{\text{ 10 - 2}}{\text{ 6 - 2}}\text{ = }\frac{\text{ 8}}{\text{ 4}}[/tex][tex]\text{ Slope = 2}[/tex]Therefore, the slope of the line is 2.
b.) The y-intercept of the line.
Substitute slope = m = 2 and x, y = 2, 2 in y = mx + b
[tex]\text{ y = mx + b}[/tex][tex]\text{ 2 = 2(2) + b}[/tex][tex]\text{ 2 = 4 + b }\rightarrow\text{ b = 2 - 4}[/tex][tex]\text{ b = y-intercept = -2}[/tex]Therefore, the y-intercept is -2.
For us to answer the other 2 questions, let's first complete the equation of the graph.
Substitute slope = 2 and y-intercept = -2 in the y = mx + b
y = mx + b
y = (2)x + (-2)
y = 2x - 2
The equation of the line is y = 2x - 2
c.) Finding the value of a.
x = a
y = 8
We get,
[tex]\text{ y = 2x - 2}[/tex][tex]\text{8 = 2a - 2}[/tex][tex]\text{ 2a = 8 + 2 = 10}[/tex][tex]\text{ }\frac{\text{2a}}{\text{ 2}}\text{ = }\frac{\text{10}}{\text{ 2}}[/tex][tex]\text{ a = 5}[/tex]Therefore a = 5
d.) Finding the value of b.
x = 4
y = b
[tex]\text{ y = 2x - 2}[/tex][tex]\text{ b = 2(4) - 2}[/tex][tex]\text{ b = 8 - 2 = 6}[/tex]Therefore, b = 6
The wholesale price for a pair of shoes is $7.50. A certain department store marks up the wholesale price by 60%. Find the price of the pair of shoes in the department store. Round your answer to the nearest cent, as necessary.
Answers
Given:
Wholesale price for a pair of shoes is $7.50
[tex]\text{The price of pair of shoes in the departmental store=7.50}+(7.50\times\frac{60}{100})[/tex][tex]\text{The price of pair of shoes in the departmental store=7.50}+4.50[/tex][tex]\text{The price of pair of shoes in the departmental store= \$12}[/tex]D In the diagram, ABDE, ZA ZD, andCAFD What theorem can be used to prove the triangles are congruent? E HL SSA AAS SAS
Answers
there are two triangles and
it is given that two sides of both the triangle is equal or congruent
and there is also given that so by side - angle - side the given triangles are congruent
so the answer is SAS.
What is the equation of the line that is perpendicular to the line 5x – 3y = 2 and passes through the point (-1,3)?
Answers
Answer:
3x+5y=12.
Explanation:
Given the line: 5x-3y=2
First, we determine the slope by making y the subject of the equation.
[tex]\begin{gathered} 3y=5x-2 \\ y=\frac{5}{3}x-\frac{2}{3} \end{gathered}[/tex]Comparing with the slope-intercept form: y=mx+b
• Slope = 5/3
Let the slope of the perpendicular line = n
By definition. two lines are perpendicular if the product of their slopes is -1.
Therefore:
[tex]\begin{gathered} \frac{5}{3}\times n=-1 \\ n=-\frac{3}{5} \end{gathered}[/tex]Next, we use the point-slope form to find the perpendicular to the given line that is passing through (-1, 3).
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{3}{5}(x-(-1)) \\ y-3=-\frac{3}{5}(x+1)\text{ Multiply both sides by 5} \\ 5(y-3)=-3(x+1) \\ 5y-15=-3x-3 \\ 5y+3x=-3+15 \\ 3x+5y=12 \end{gathered}[/tex]The required equation is 3x+5y=12.