This is the correct answer, this is because it only function that the inverse is correctly represented
[tex]\begin{gathered} y\text{ = }\sqrt[3]{x+3} \\ y^3=\text{ x+3} \\ x=y^3-3 \\ f^{-1}(x)=x^3-3 \end{gathered}[/tex]To estimate the height of a stone figure Anya holds a small square up to her eyes and walks backwards from the figure she stops when the bottom of the figure aligns with the bottom edge of the square and the top of the figure aligns with the top edge of the square her eye level is 1.84m from the ground she is 3.50m from the figure what is the height of the figure to the nearest hundredth of a meter
SOLUTION
Let us make a sketch that will help us solve the question
From the image I provided, let the Height of the figure be H.
Then this means that the height of the figure H is
[tex]H=x+1.84[/tex]Note that I have splitted the triangle into two.
Now, we need to find the two acute angles
[tex]\begin{gathered} \alpha\text{ and }\theta\text{ in the bigger triangle.} \\ \text{Note that }\alpha+\theta+90^o=180^o\text{ (sum of angles in the big triangle)} \end{gathered}[/tex]Now, from the triangles splitted in the right side, both are right-angles just like the first (biggest) triangle.
So we will use the trig-ratio, SOHCAHTOA to find the acute angles.
From the smallest triangle in the image,
[tex]\begin{gathered} \tan \alpha=\frac{opposite}{\text{adjacent }} \\ \tan \alpha=\frac{3.5}{\text{1.84 }} \\ \alpha=\tan ^{-1}\frac{3.5}{\text{1.84 }} \\ \alpha=62.27^o \end{gathered}[/tex]Now, the second acute angle becomes
[tex]\begin{gathered} \text{ }\alpha+\theta+90^o=180^o \\ 62.27+\theta+90=180 \\ \theta+152.27=180 \\ \theta=180-152.27 \\ \theta=27.73^o \end{gathered}[/tex]The other triangle that is the bigger one which was splitted has opposite side of 3.5m and adjacent side x, hence
[tex]\begin{gathered} \tan \theta=\frac{opposite}{\text{adjacent}} \\ \tan 27.73=\frac{3.5}{x} \\ x\times\tan 27.73=3.5 \\ x=\frac{3.5}{\tan 27.73} \\ x=6.65804m \end{gathered}[/tex]Now H becomes
[tex]\begin{gathered} H=x+1.84 \\ H=6.65804+1.84 \\ H=8.49804 \end{gathered}[/tex]Hence, the height of the figure is 8.50 m to the nearest hundreth
A basket holds m apples you pick 2n-3 apples and your friends picks n+4 how many baskets do you need to carry all the apples.
Answer: The number of baskets = (3n+1)/m
Step-by-step explanation:
The total number of apples picked:
yours (2n-3) + your friend (n+4)
Divide the combined total by the number in one basket (m):
((2n-3)+(n+4))/m
Simplify:
(3n+1)/m
I need questions 10 , 13 , 15 , and 16 solved with steps and graph
The graphic solutions for the expressions are given as follows:
10. x = 2.667 and x = 8.
13. x = 8.
15. x < -1 or x > 8.
16. x > 3.
Item 10In item 10, we are going to solve an equation graphically, hence we have to find the points of intersection of the two curves given by:
y = |x - 4|.y = 0.5x.From the first graph given at the end of the answer, the x-coordinates of these points are given as follows:
x = 2.667 and x = 8.
Item 13Now we have to find the point of intersection of these two equations:
y = 0.75x.y = 2x - 10.They have only one intersection point, at x = 8, which is the solution to the system.
Item 15The inequality is:
x² - 7x- 8 > 0.
Hence we have to find the intervals for which the function x² - 7x - 8 is above the x-axis, and from the third graph, these intervals are described as follows:
x < -1 or x > 8.
Item 16The inequality is:
x - 5 > -2x + 4.
Combining the like terms, it can be written as;
3x > 9
x > 3.
The interval for which the increasing line is above the decreasing line is x > 3, and is shown in the fourth graph.
More can be learned about the graphic solutions of expressions at https://brainly.com/question/28708772
#SPJ1
The table lists several points that form a line on a coordinate plane. x y 4 6 12 8 16 9 28 12 Based on the information in the table, what are the y-intercept and slope of the line described by these points?
A.y-intercept: = 2; slope: m = 4
B.y-intercept: = –20; slope: m =14
C.y-intercept: = 5; slope: m = 4
D.y-intercept: = 5; slope: m =14
Slope is 1/4 (0.25) while y-intercept is 5.
Here, we are interested in getting the y intercept and slope of the line joining the given points.
We can get the slope by using any two points
Let’s say (4,6) and (12,8)
Mathematically; slope
= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25
To get the y-intercept, we proceed
kindly recall that the equation of a straight line is;
y = mx + c
where m is the slope and c is the y-intercept
Let’s take any of the points (28,12)
Thus:
12 = 0.25(28) + c
12 = 7 + c
c = 12-7
c = 5
To learn more about slope visit:https://brainly.com/question/3605446
#SPJ1
QUESTION 9 1 POINTSimplify: ( 12 + 1/2 m)÷ 0, where + #0.4 2If the given expression is undefined enter Ø as your answer.Provide your answer below:Content attribution
Given
[tex](\frac{1}{4}+\frac{1}{2}m)\div0[/tex]Find
Simplify
Explanation
[tex]\begin{gathered} (\frac{1}{4}+\frac{1}{2}m)\div0 \\ \\ (\frac{1+2m}{4})\div0 \end{gathered}[/tex]as we know , any number divided by zero is infinity because division by zero is undefined and infinity does not really exist.
so , the solution is undefined.
Final Answer
Hence , the solution is undefined. so , the answer is
[tex]\emptyset[/tex]What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
Write a function rule to model each situation.
1 You are starting a yard-care business. You
decide to charge a flat fee of $15 plus a rate
of $8 per hour. Write a function rule in which
x is the number of hours and y is the total
amount you charge.
The function rule of the scenario is f(x) = 15 + 8x
How to determine the function rule?From the question, the given parameters are:
Flat fee = $15
Rate = $8
To determine the function rule of the scenario, we make use of the following template equation
f(x) = Flat fee + Rate * Number of hours
Where
f(x) = total and x = number of hours
So, we have
f(x) = Flat fee + Rate * x
This gives
f(x) = 15 + 8x
Hence, the function rule is f(x) = 15 + 8x
Read more about linear equations at
https://brainly.com/question/13738662
#SPJ1
please help asap !!!!
What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?
x=4
How is the given equation solved?
[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics.Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.To learn more about equation solving, refer:
https://brainly.com/question/25678139
#SPJ13
A scuba diver is swimming at -30 feet the divers depth then changes to 5 feet where could the diver be explain
The scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
What is depth of a river?
The depth of a river is the vertical distance measured in straight line towards the center of earth from the surface of earth indicating to what level below the lithosphere does the sea beds exist.
Given is a scuba diver who is swimming at - 30 feet. The divers depth then changes to 5 feet.
The initial depth of the scuba driver = [D] = - 30 ft
Now, as the depth of the scuba driver changes by +5 feet, then the scuba driver will be at -
- 30 + 5
- 25 ft
Hence, the scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
Therefore, the scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
To solve more questions on river depth, visit the link below-
https://brainly.com/question/14212071
#SPJ1
PLEASE HURRY ASAP
What is the product of (−4)(23)(−7)?
Answer:
644
Step-by-step explanation:
-4x23=-92
-92x-7=644
hope this helped :)
Answer:
644
Step-by-step explanation:
if you multiply -4 by 23 it equals -92 and then if you multiply -92 by -7 it comes out to a positive 644 because if multiplying a negative by a negative it becomes a positive.
thank you for your question and let me know if it is right or wrong
blessings!
simplify for 4^n
4^11/4^-8
Answer: 4^3
Step-by-step explanation:
Answer: 4^3.
Step-by-step explanation:
For each calculation choose the correct answer written in standard form.
a) (7 × 10⁵ ) × (3× 10²)
A 21 × 10¹⁰
B 21 ×10⁷
C 2.1 × 10¹¹
D 2.1 × 10⁸
b) ( 2 × 10⁵) ÷ ( 4 × 10² )
A 2 × 10 ³
B 5 × 10²
C 0.5 × 10³
D 2 × 10²
Answer:
A car travels at average speed of 4m/s and covers a distance of 2.4km calculate the time take help me
5/6x+1/12= 15 1/3+1/3xsolve for x
Answer:
x = 61/2 = 30.5 = 60 1/2
Step-by-step explanation:
We have:
[tex]\frac{5}{6}x+\frac{1}{12}=15+\frac{1}{3}+\frac{1}{3}x[/tex]We have to find the Least Common Multiple to solve this question:
[tex]\begin{gathered} \frac{2\cdot5x+1=12\cdot15+4+4x}{12} \\ \frac{10x+1=180+4+4x}{12} \\ 10x+1=180+4+4x \\ 10x-4x=180+4-1 \\ 6x=183 \\ x=\frac{183}{6} \\ x=\frac{61}{2}=30.5=30\frac{1}{2} \end{gathered}[/tex]Multiple choice math pls help urgent
The correct option R avg(x) = 100 - 5x, shows the average revenue function.
What is termed as the revenue function?The average revenue demonstrates how much money is made per unit of output. In other words, it computes how much revenue a company earns on average from each unit of product sold. To find the average revenue, multiply the total revenue by the number of output units.Total revenue income is the money earned by a company from the sale of a specific amount of output. Total revenue is calculated by multiplying the price by the number of units sold.For the given question;
The revenue function is given by the equation,
R(x) = 100x - 5x²
Let the
Let the total revenue be 'x'.
Then,
Average revenue function = revenue function/ total revenue
Average revenue function = (100x -5x²)/x
Average revenue function = 100 - 5x
Thus, the average revenue function is given by the equation 100 - 5x.
To know more about the revenue function, here
https://brainly.com/question/25638609
#SPJ13
I have a calculus question about limit functions. Pic included.
Answer:
Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.
Explanation:
P(25, 10) lies on the curve:
[tex]y=\sqrt{x}+5[/tex]Q is the point (x, √x+5).
For any value of x, the slope of the secant line PQ is determined using the formula:
[tex]\text{ Slope of secant PQ}=\frac{(\sqrt{x}+5)-10}{x-25}[/tex](a)When x=25.1
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{25.1}+5)-10}{25.1-25}=0.0999[/tex](b)When x=25.01
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{25.01}+5)-10}{25.01-25}=0.09999[/tex](c)When x=24.9
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{24.9}+5)-10}{24.9-25}=0.1001[/tex](d)When x=24.99
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{24.99}+5)-10}{24.99-25}=0.10001[/tex]Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.
factored form of y=x2-x-12
The factored form of y = x² - x + 12 will be (x + 3)(x - 4).
What is factor?It should be noted that a factor simply means the number than can be multiplied by another number to get the original number. The factored form is when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form can be restated in standard form.
This will be illustrated as:
x² - x - 12
x² - 4x + 3x - 12.
x(x - 4) + 3(x - 4)
(x + 3)(x - 4)
The factored form is (x + 3)(x - 4).
Learn more about factor on:
brainly.com/question/25829061
#SPJ1
(2, y) for all real y
[if solved and correct give 30 points+ brainliest]
Answer:
You actually cannot find Y using this knowledge!
Step-by-step explanation:
( 2, y ) It only shows how X is 2, you need more information to find y. If you can respond, try to give me more information, I am willing to help!
Convert the following angle from degrees to radians. Express your answer in simplestform.285°
Answer:
19π/12
Explanation:
We know that
180 degrees = π radians
and we are asked
285 degrees = ? radians?
This can be treated as a ratio problem by saying that
[tex]\frac{180}{\pi}=\frac{285}{x}[/tex]where x is the angle in radians.
Cross multpication gives
[tex]180x=285\pi[/tex]dividing both sides by 180 gives
[tex]x=\frac{285\pi}{180}[/tex][tex]x=\frac{19}{12}\pi[/tex]where we have used the fact that 285/12 = 19/12.
Select the correct answer.What is the solution to this equation?loge + + log 3 = log (+ + 1)OA1 =IO HICOB.1 =O C.सेNICOOD. r = 1
Given the equation:
[tex]\log _6x+\log _63=\log _6(x+1)[/tex]Let's solve for x.
To find the solution, take the following steps:
Step 1:
Apply the product property of logarithm to the left side of the equation:
[tex]\begin{gathered} \log _6(x\ast3)=\log _6(x+1) \\ \\ \log _6(3x)=\log _6(x+1) \end{gathered}[/tex]Step 2:
Eliminate the log on both sides
[tex]\begin{gathered} 3x=(x+1) \\ \\ 3x=x+1 \end{gathered}[/tex]Step 3:
Subtract x from both sides
[tex]\begin{gathered} 3x-x=x-x+1 \\ \\ 2x=1 \end{gathered}[/tex]Step 4:
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{1}{2} \\ \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the solution to the given equation is:
[tex]x=\frac{1}{2}[/tex]ANSWER:
[tex]\text{ B. x = }\frac{1}{2}[/tex]One of the legs of a right triangle measures 13 cm and the other leg measures 11 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.03 cm
Step-by-step explanation:
Use the Pythagorean theorem, which states a^2+b^2=c^2. 13^2+11^2=290, sqrt290 cannot be simplified down into a whole number, therefore the next closes rounded to the nearest tenth is 17.03.
If the interest rate changed from 10%
to 2%, what would happen to
borrowing?
A. Debtors would less likely want to borrow.
B. There would be a government law against rising
interest rates.
C. There would be no impact on borrowing.
D. There would be an increase in borrowing.
Consequently, borrowing would increase with the change in interest rate from 10 % to 2 %. The correct answer is Option D.
What happens to interest rates when borrowing becomes more expensive?The greater the ability of banks to lend, the greater the amount of credit available to the economy. And as the supply of credit expands, so does the cost of borrowing (interest). The amount of credit available to the economy decreases as lenders decide to postpone loan repayment.What effect does a change in interest rates have on business borrowing?Higher interest rates make it more expensive for businesses to borrow money through loans and lines of credit, and they also affect how much interest you pay on credit card or home purchase purchases.
Given that the interest rate has risen from 10% to 2%.
Borrowers can easily borrow by paying less interest now that the interest rate has dropped from 10% to 2%.
As a result, borrowing would increase with the decrease in interest rates. Option D is thus correct.
Learn more about interest rates here:
https://brainly.com/question/25793394
#SPJ9
Answer this for me please Number 2 have 3 more answer choices Which are 16:57D - the number of centimeters in x inches E- the height of a swinging pendulum as a function of timeF- the height of a ball tossed in the air as a function of time
1)
Consider P to be at the same vertical distance between the maximum and minimum height the blades can reach. Therefore, at t=0, P has to be at h=0 (the maximum height is 1 and the minimum one is -1).
Then, since the fan blades rotate counterclockwise, after t=0, h has to increase until it reaches a value of 1.
Finally, a revolution is completed after 1 second; therefore, at t=1, the h has to be equal to 0 (the same height as at t=0).
Thus, the graph that models the function is option D.2)
Approximately, every year the Earth reaches its maximum distance from the sun and its minimum distance once a year, and that is a cycle that repeats almost without alteration. Furthermore, since the position of the Earth around the sun is given by an ellipse, the position of the Earth around the Sun can be expressed using trigonometric functions (because of polar coordinates).
Similarly, a rotating wheel will reach its maximum and minimum height eventually; therefore, it can be modeled using trigonometric functions which are periodic.
Finally, as for the area of a sheet of paper. Notice that the more we fold it, the less its area becomes, it does not reach its maximum anymore.
Given x inches, the number of centimeters is 2.54x, this is not a periodic function.
Due to the effects of gravity, the height of a pendulum can be expressed using a periodic function given that no energy is lost.
The trajectory of a tossed ball is given by a parabola, unless one tosses the ball again at the same initial height, option F cannot be modeled using a periodic function.
The answers to part 2 are A, B, and E.Let F(x) = f(x ^ 5) * ndG(x) = (f(x)) ^ 5 You also know that a ^ 4 = 3 , f(a) = 2 , f^ prime (a)=13 , f^ prime (a^ 5 )=2
Given the functions:
[tex]\begin{gathered} F(x)=f(x^5) \\ \\ G(x)=(f(x))^5 \end{gathered}[/tex]Additionally, we know that:
[tex]\begin{gathered} a^4=3 \\ f(a)=2 \\ f^{\prime}(a)=13 \\ f^{\prime}(a^5)=2 \end{gathered}[/tex]We use the chain rule to find the derivatives of F(x) and G(x):
[tex]\begin{gathered} F^{\prime}(x)=f^{\prime}(x^5)\cdot(x^5)^{\prime}=5x^4\cdot f^{\prime}(x^5) \\ \\ G^{\prime}(x)=5(f(x))^4\cdot f^{\prime}(x) \end{gathered}[/tex]Finally, evaluating for x = a and using the results stated before:
[tex]\begin{gathered} F^{\prime}(a)=5\cdot a^4\cdot f^{\prime}(a^5)=5\cdot3\cdot2 \\ \\ \therefore F^{\prime}(a)=30 \end{gathered}[/tex][tex]\begin{gathered} G^{\prime}(a)=5\cdot(f(a))^4\cdot f^{\prime}(a)=5\cdot2^4\cdot13 \\ \\ \therefore G^{\prime}(a)=1040 \end{gathered}[/tex]what is the scale factor form polygon ABCD to the polygon PQRS
The scale factor in this polygon comparison can easily be found as 1.5 because when we divide the length of for example side PS (3 units) by the size of side AD (its pre-image which measures 2 units) we get:
3/2 = 1.5
We could try also the same with any other of the sides in image and pre-image, like PQ comared to AB. PQ has a length of 1.5 units, while AB has a length of 1 unit. Then:
PQ/AB = 1.5/1 = 1.5
How many degrees mustFigure A be rotatedcounterclockwise aroundthe origin in order to lineup with Figure B?АBA. 90B. 180C. 270D. 360
The answer is A 90 degrees
PLS HELP ASAP WILL GIVE BRAINLIST
The values a = 10 and b = -6 will make the quadrilateral QRST a parallelogram
What values of a and b will make QRST a parallelogram?For the quadrilateral QRST to be a parallelogram, the diagonal lines TR and QS divide each other into two equal parts at P. Therefore, we can say:
For diagonal line QS, QP = PS:
-a + 27 = -6a + 77
-a + 6a = 77 -27
5a = 50
a = 50/5
a = 10
For diagonal line TR, TP = PR:
2b + 24 = -8b - 36
2b + 8b = -36 - 24
10b = -60
b = -6
Therefore, the value of a and b that will make the quadrilateral QRST a parallelogram is a = 10 and b = -6.
Learn more about parallelogram on:
https://brainly.com/question/24587399
#SPJ1
I need help again……..
Answer:
me again. hope it can help.lol
Answer:
See below
Step-by-step explanation:
For this equation to have non-real roots, the discriminant (b^2 - 4ac) of the Quadratic Formula must be < zero
b^2 - 4ac < 0 b = 5 a = (n-2) c = -2
5^2 - 4 ( n-2)(-2) <0
25 + 8n - 16 <0
8n + 9 < 0
8n < -9
n < - 9/ 8
Wha What is 12 tens in standard form
the freshman class is selling popcorn and candles as a fundraiser popcorn and sell them for $5 a bag and candle sell $15 each a total of 824 items were sold and 5555 was raised how many of each item was sold
Step 1. Define our variables.
[tex]undefined[/tex]I need help with number two please and thank you
Given:
Karla has a garden that is 14 feet long.
To convert feet into yards:
We know that,
[tex]\begin{gathered} \text{3 fe}et=1\text{ yard } \\ \text{1 fe}et=\frac{1}{3}\text{yard} \end{gathered}[/tex]So, for the 14 feet,
[tex]\begin{gathered} \text{14 fe}et=\frac{1\times14}{3}\text{yard} \\ =4\frac{2}{3}yards \end{gathered}[/tex]Hence, the answer is,
[tex]4\frac{2}{3}\text{ yards (or) 4.67 yards}[/tex]