All of 4x+8 is under a cube root sign.
=====================================================
Work Shown:
To find the inverse, we swap x and y, then solve for y.
[tex]y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\[/tex]
------------
Side note:
If [tex]f(x) = \frac{1}{4}x^3 - 2[/tex] and [tex]g(x) = \sqrt[3]{4x+8}[/tex], then [tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.
A) Ali travelled 40 kilometers in his car and it took him 50 minutes to complete the journey. How long will it take if he had to travel 100 kilometers in the same car?
Answer:
2 hours and 5 minutes
Step-by-step explanation:
50/40=1.25 km/m
100*1.25=125 minutes
125 minutes= 2.08 hours= 2 hours and 5 minutes
Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
What is the tangent ratio of KJL? (Question and answers provided in picture.)
Answer:
Option (1)
Step-by-step explanation:
The given triangle JKL is an equilateral triangle.
Therefore, all three sides of this triangle will be equal in measure.
Side JK = JL = KL = 48 units
Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.
By applying tangent rule in ΔJML,
tan(∠KJL) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{LM}}{\text{JM}}[/tex]
= [tex]\frac{\text{LM}}{24}[/tex]
Since, Sin(K) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{LM}}{48}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{LM}}{48}[/tex]
LM = 24√3
Now, tan(∠KJL) = [tex]\frac{\text{LM}}{24}[/tex]
= [tex]\frac{24\sqrt{3} }{24}[/tex]
Therefore, Option (1) will be the answer.
Which section of the function is decreasing? (4 points) A graph is shown. Segment A is a horizontal line beginning at the y-axis. Segment B moves upward. Segment C is a horizontal line. Segment D moves downward Select one: a. A b. B c. C d. D
Answer: D
Step-by-step explanation:
If segment D moves downward it means its function has a negative slope so the line will be decreasing.
Answer:
D
Step-by-step explanation:
Obviously just because the slope is going down hence decreasing. \
Hope this helps! :)
Estimate the solution to the following system of equations by graphing 3x +7y=10 2x-3y=-6
please mark me brain list
Answer:
(- 1/2,5/3)
Step-by-step explanation:
There are five red balls, three yellow balls, and four green balls in a bin. In each event, you pick one ball from the bin and observe the color of the ball. The balls are only distinguishable by their colors. After observation, you put the ball back into the bin.
What is the probability of choosing a red ball in an event?
Answer:
5/12Step-by-step explanation:
step one:
Given the sample space, which is the value of individual number of colored balls in the bin
Red balls=5
Yellow balls=3 and
Green balls= 4
And the sample size is the sum of all the colored balls in the bin
The sample size S= {5+3+4}= 12
step two:
The probability of choosing a red ball in an event can be expressed as, the total number of the red balls over the total number of balls in the bin
P(r)= 5/12
Hence the probability of selecting a red ball in one event 5/12
Complete the equation of the line through (-8, 8) and (1, -10).
Use exact numbers.
y =
Answer:
y = -2x - 8
Step-by-step explanation:
Find the slope using rise/run (y2 - y1) / (x2 - x1)
(-10 - 8) / (1 + 8)
-18/9
= -2
Next, plug in the slope and a point into the equation to find b:
y = mx + b
-10 = -2(1) + b
-10 = -2 + b
-8 = b
Now, plug this and the slope into the equation:
y = -2x - 8
What is the ratio of the length of to the length of?
Answer:
1/4
Step-by-step explanation:
What is the ratio of the length of to DE the length of BC
The perimeter of a sector is given by:
P = [tex]\frac{\theta}{360}**2\pi r[/tex]
Where [tex]\theta[/tex] is the angle it subtends from the center and r is the radius of the circle.
For Sector ADE, the radius (r) = r/2 and the angle [tex]\theta[/tex] = β. Therefore:
Perimeter of DE = [tex]\frac{\beta}{360}**2\pi (\frac{r}{2} )=\frac{\beta}{360}(\pi r)[/tex]
For Sector ABC, the radius (r) = r and the angle [tex]\theta[/tex] = 2β. Therefore:
Perimeter of BC = [tex]\frac{2\beta}{360}**2\pi r=\frac{2\beta}{360}(2\pi r)=\frac{\beta}{360}*(4\pi r)[/tex]
The ratio of the length of to DE the length of BC =
Answer:
1/4
Step-by-step explanation:
9x) = 27^y and X-Y = -3/2
find the value of y
Answer:
− y ln (27) + ln (9x) = 0
The weight of a small starbucks coffee is a normally distributed random variable with a mean of 325 grams and a standard deviation of 10 grams. Find the weight that corresponds to each event (round your final answers to 2 decimal places)
The weight of a small starbucks coffee is a normally distributed random variable with a mean of 325 grams and a standard deviation of 10 grams. Find the weight that corresponds to each event (round your final answers to 2 decimal places)
a. Highest 10 percent
b. Middle 50 percent
Answer:
the weight that corresponds to Highest 10% = 337.8
the weight that corresponds to Middle 50 % lies between 318.26 and 331.74
Step-by-step explanation:
From the information provided for us:
we have the mean = 325
the standard deviation = 10
The objective is to find the weight that corresponds to each event i.e for event (a) , highest 10%
So;
The probability of P (Z > z) = 10%
Same as:
0.1 = 1 - P( Z < z)
P( Z < z) = 1 - 0.1
P( Z < z) = 0.9
From the standard normal tables for z;
P( Z < 1.28) = 0.9
z = 1.28
Similarly. from the z formula; we have:
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z \times \sigma = X - \mu[/tex]
[tex]z \times \sigma + \mu= X[/tex]
[tex]X= z \times \sigma + \mu[/tex]
X = (1.28 × 10) + 325
X = 12.8 + 325
X = 337.8
Therefore, the weight that corresponds to Highest 10% = 337.8
b. the weight that corresponds to Middle 50 % can be computed as follows:
the region of z values at 0.50 lies between -0.674 and +0.674
from the z formula; we have:
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z \times \sigma = X - \mu[/tex]
[tex]z \times \sigma + \mu= X[/tex]
[tex]X= z \times \sigma + \mu[/tex]
X = -0.674 × 10 + 325 and X = 0.674 × 10 + 325
X = - 6.74 + 325 and X = 6.74 + 325
X = 318.26 and X = 331.74
the weight that corresponds to Middle 50 % lies between 318.26 and 331.74
I need help on both answers. They’re different from my other problems so I’m kinda confused
Jessica recently purchased her dream car a Porsche 911. for $55,000. the value of this car will depreciate by 8% each year. Find the value of the car after 5 years.
55,000(0,92)^5= $36,249.
Answer:
The future value of the car after 5 years is $36,249.5
Step-by-step explanation:
Given the value at which a car depreciates, we are interested in finding the value of the car after a period of 5 years.
To find the value, we make use of an exponential equation;
The exponential equation to use is;
FV = PV(1 - r)^n
where FV is the future value of the car which is what we want to calculate
PV is the present value of the car which is $55,000
r is the depreciation percentage = 8% = 8/100 = 0.08
n is the number of years.
So now, we input these values into the formula;
FV = 55,000(1 -0.08)^5
FV = 55,000(0.92)^5
FV = $36,249.5
What is the value of x in the equation 3x-4y =65, when y = 4? i will gift brainliest
Answer:
3x-4y=65
3x=65+4y
x=(65+4y)/3, when y=4
x=(65+4*4)/3
x=(65+16)/3
x=81/3
x=27
Answer:
x = 27
Step-by-step explanation:
3x - 4y = 65
Let y= 4
3x - 4(4) = 65
3x -16 = 65
Add 16 to each side
3x-16+16 = 65+16
3x = 81
Divide by 3
3x/3 =81/3
x=27
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
When Mr. Gree bought a used car he made a
down payment of $825. This was 30% of the
total cost. The total cost was:
PLEASE HELP! QUICKLY PLEASE!
Answer:
2750
Step-by-step explanation:
825/30=27.5
27.5X100=2750
The total cost of the car will be $2,750.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.
The percentage is given as,
Percentage (P) = [Initial value - Final value] / Initial value x 100
When Mr. Gree bought a used car he made a down payment of $825.
This was 30% of the total cost.
Let x be the total cost of the car.
Then the total cost of the car will be
30% of x = $825
0.30x = $825
x = $2,750
Then the total cost of the car will be $2,750.
More about the percentage link is given below.
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What is the solution to:
[tex] \frac{5}{8} = \frac{m}{12} [/tex]
HELP! answer if you can.
Answer:
[tex]\boxed{m=7.5}[/tex]
Step-by-step explanation:
Hey there!
Cross multiply the given info
60 = 8m
Divide both sides by 8
m = 7.5
Hope this helps :)
Stephanie is helping her band collect money to fund a field trip. The band
decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each
box contains 20 bars. Which equation represents the profit they will earn
for each box sold? *
O p = 20 - $1.50
O p= 20 + $1.50
O p = 20 ($1.50)
O p = 20/$1.50
5.How much profit will be made if they sell 100 boxes?
Answer:
O P=20($1.50)
They will make $3,000 if they sell 100 boxes of chocolates
Step-by-step explanation:
It is multiplication because it is $1.50 per each chocolate bar, and since there is 20 per box, we need to find the profit for the entire box
using that info, we find that each box of chocolates is 30 dollars
multiplied by 100 boxes is $3000.
In the expression 2^3 the 2 is known as the
base
exponent
rational number
irrational number
Answer:
Hey there!
In this problem, 2 is known as the base.
Let me know if this helped :)
Answer:
The Base
Step-by-step explanation:
The base in a power is the number being raised to the exponent's power. It is the bigger number in the power.
2 is being raised to the third power. This means that 2 is the base of the power.
3 would be the exponent in the power.
Brainilest Appreciated.
4.
Aliyah, Brenda and Candy share a sum of money in the ratio of 3:5:6. After
Candy gives $100 to Aliyah and $50 to Brenda, the ratio becomes 2 : 3:3.
(a) Suppose Aliyah has $3x at the start, express Candy's initial sum of money in
terms of x.
(b) Find the value of x.
(c) Hence, how much money does Brenda have in the end?
Answer:
(a) Candy's initial sum as a terms of x is $6x
(b) x = $60
(c) $350
Step-by-step explanation:
The given parameters are;
The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6
The amount Candy later gives Aliyah = $100
The amount Candy later gives Brenda = $50
The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3
(a) Whereby Aliyah has $3x at the start, we have;
Total sum of mony = Y
Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14
Therefore, Y×3/14 = $3x
x = Y×3/14 ÷ 3 = Y/14
Amount of Candy's initial share = Y × 6/14
Therefore Candy's initial sum as a terms of x = $6x
(b) Given that Aliyah's and Candy's initial sum as a function of x are $3x and $6x, therefore, in the ratio 3:5:6, Brenda's initial sum as a function of x = $5x
Which gives;
Total amount of money = $14x
With
6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3
Therefore, we have;
14·x × 2/(2 + 3 + 3) = (6·x - 150)
14·x × 2/(8) = (6·x - 150)
14·x × 1/4 = (6·x - 150)
7·x/2 = (6·x - 150)
12·x - 300 = 7·x
12·x - 7·x = 300
5·x = 300
x = $60
(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350
The final amount of money with Brenda = $350.
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer: D) right 9 units
Step-by-step explanation:
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
a is the vertical stretch or shrink(x, h) is the vertex→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
The graph of y = f(x) will shift right 9 units.
Step-by-step explanation:
If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.
Factor as the product of two binomials. 81+18x+x^2
Answer:
(x+9)(x+9)
Step-by-step explanation:
To factor this expression, we first need to put into standard form, that is, [tex]ax^2 + bx + c[/tex].
So it becomes [tex]x^2 + 18x + 81[/tex]
Now we need to find two numbers that:
A. When multiplied get us c (81)
B. When added get us b (18)
9 and 9 match those requirements, so out product of two binomials for this becomes (x+9)(x+9).
Hope this helped!
Which property can you use to show that 6x – 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5)?
Answer:
Distributive property
Step-by-step explanation:
6x – 3x + 9y + 4 + 11 =
First, we combine like terms.
= 3x + 9y + 15
Now we use the distributive property to factor out a common factor.
= 3(x + 3y + 5)
The property can you use to show that 6x – 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5) is Distributive property
What is Distributive property
To show that 6x - 3x + 9y + 4 + 11 is equivalent to 3(x + 3y + 5), we can use the distributive property of multiplication over addition.
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
6x – 3x + 9y + 4 + 11 =
First, we combine like terms.
= 3x + 9y + 15
Now we use the distributive property to factor out a common factor.
= 3(x + 3y + 5)
Read more about Distributive property here:
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Can integers be written as fractions?
Answer:
Step-by-step explanation:
Yes you can just write them with denominator 1,
So 3 = 3/1 and -6 = -6/1.
Answer:
Yes.
Step-by-step explanation:
ALL real numbers can be written as fractions, and since integers fall under the category of real numbers, it is official that they can be written as fractions.
I am joyous to assist you at any time.
Please help me!! I'll give brainliest btw
Answer:
e. cannot be determined
Step-by-step explanation:
m = 1/2( x + x + 10) = 1/2(2x + 10) = x + 5
n = 1/2(x² + x + 10) =
m/n = (x+5)/(1/2(x² + x + 10))
Not enough information
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 24.2 σ=24.2. You would like to be 98% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?
Answer:
use a z* value accurate to TWO places for this problem. (Not z = 2)
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
;)
What is the set of x-intercepts of this graphed function ? A.{-3,-1} B. {-3,-1,3} C. {-3,3} D.{-3}
Answer:
second option
Step-by-step explanation:
The x- intercepts are the values on the x- axis where the graph crosses.
These are
x = - 3, x = - 1 and x = 3
if AD is the altitude to BC what is the slope of AD
Answer:
The answer is most likely 1/3
The correct option D. 3. The slope of AD, where A is (-2, 4), B is (-6, 2), and C is (3, -1), is 1/3 using the slope formula.
Given points :
[tex]A(-2, 4)\\B(-6, 2)\\C(3, -1)[/tex]
To find the slope of AD, to determine the slope of the line passing through points A and D.
Calculate the slope of the line passing through points A and D using the formula:
slope [tex]= (y_2 - y_1) / (x_2 - x_1).[/tex]
First, let's find the slope of BC using the coordinates of points B and C:
Slope of BC [tex]= (y_2- y_1 / (x_2- x_1)\\[/tex]
Plugging the coordinates of points B and C gives:
[tex]= (-1 - 2) / (3 - (-6))[/tex]
On adding gives:
[tex]= (-3) / (9)[/tex]
On dividing both numerator and denominator by 3
[tex]= -1/3[/tex]
Since A is the altitude to BC, it is perpendicular to BC.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of that line.
Therefore, the slope of AD will be the negative reciprocal of -1/3.
Negative reciprocal of -1/3 = -1 / (-1/3) = 3
Hence, the slope of AD is 3. The option is D. 3
Learn more about slopes here:
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Find the common ratio of the geometric sequence: 12.5,−62.5,312.5,−1562.5,… A. 5 B. -5 C. −15 D. 15
Answer:
B
Step-by-step explanation:
The common ratio r exists between consecutive terms in the sequence, that is
r = - 62.5 ÷ 12.5 = 312.5 ÷ - 62.5 = - 1562.5 ÷ 312.5 = - 5
Using the Distributive Property to factorize the equation 3x2 + 24x = 0, you get
Answer:
3x(x+8)=0
x=0,-8
This is how to solve for x.
A coin is tossed 7 times. What is the probability that the number of heads obtained will be between 2 and 7 inclusive? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.9375
Step-by-step explanation:
Given the following :
Number of coin tosses = 7
Probability that number of heads obtained will be between 2 and 7 inclusive?
x = 2,3,4,5,6,7
Probability (P) = number of required outcomes / total possible outcomes
For a coin toss = 1 Head (H), 1 tail (T)
P(H) = 1 / 2
P(X) = C(7,x) * (1/2)^7
P(X) = C(7, x) / 0.5^-7
P(X) = [C(7,2) + C(7, 3)+ C(7,4) +C(7,5) + C(7,6) +C(7,7)] / 128
P(X) = (21 + 35 + 35 + 21 + 7 + 1) / 128
P(X) = 120 / 128
P(X) = 0.9375
