[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \stackrel{\pi =3.14}{\cfrac{6430.71}{4(3.14) }}=r^3\implies 511.9992\approx r^3 \\\\\\ \sqrt[3]{511.9992}\approx r\implies 7.999996\approx r\implies \stackrel{\textit{rounded up}}{8=r}[/tex]
Lucy and Katy are registering for a sports league for next year. There are 222 sports (volleyball and basketball) and 333 seasons (fall, winter, and spring) to choose from. They each created a display to represent the sample space of randomly picking a sport and a season. Whose display correctly represents the sample space?
Answer:
A. Lucy Only
Step-by-step explanation:
Got it right on Khan Academy
The possible sample space is: FV, WV, SV, FB, WB, and SB
What is probability?Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes
As, the sample space with all possibilities in which lucy and katy register a sports League.
Now, they have 2 sports and 3 seasons for the Sample space.
Mow let us consider, V is registered for Volleyball and B is registered for basketball .
and, F is registered Fall, W is registered for Winter and S is for Spring.
so, that the sample space is:
FV, WV, SV, FB, WB, and SB
where, FV is the registered possibility for fall and in volleyball.
WV is the registered possibility for Winter and in volleyball.
SV is the registered possibility for Spring and in volleyball.
and so on..
Therefore, the correctly representation for the sample space is the one that has all these possibilities.
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circle O is shown below. the diagram is not drawn to scale. 73°
Answer:
Option A
53.5
Step-by-step explanation:
The explicit rule for a sequence is an=5(−2)^n−1
What is the recursive rule for the sequence?
1) an=−2(an+1)
a1=5
2) an=−5(an+1)
a1=2
3) an=−2(an−1)
a1=5
4) an=−5(an−1)
a1=2
Answer:
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
Step-by-step explanation:
Given that the explicit rule for a sequence is [tex]a_n=5(-2)^{n-1}[/tex].
Now we need to find about what is the recursive rule for the sequence and match with the given choices to find the correct choice.
1) [tex]a_n=-2a_{n+1}[/tex], [tex]a_1=5[/tex]
2) [tex]a_n=-5a_{n+1}[/tex], [tex]a_1=2[/tex]
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
4) [tex]a_n=-5a_{n-1}[/tex], [tex]a_1=2[/tex]
Plug n=1 into given formula to get first term
[tex]a_n=5(-2)^{n-1}[/tex]
[tex]a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5[/tex]
base of the exponent part is (-2) so that means we need to multiply -2 to the previous term to get nth term
Hence correct choice is: 3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
Answer:
3) an=−2(an−1)
a1=5
Step-by-step explanation:
You are installing a brick sidewalk. The brick portion of the sidewalk will occupy an area of 100 feet long by 4 feet wide. Each brick will occupy an area 8 inches long by 4 inches wide. What is the minimum number of bricks you will need to build the sidewalk?
Answer:
1,800 bricks are needed
Step-by-step explanation:
First convert the Length and width of the sidewalk into inches
Entire Sidewalk: L= 100x12 =1200in and W= 4 x 12 = 48in
Then we know Area = LxW, so we will do this for both the sidewalk and the brick.
Area of sidewalk: 1200 x 48 = 57600
Bricks ( no need to convert since the measurements are already in inches): 8 x 4 = 32
Now we will divide the area of the entire sidewalk by the area of a single brick to find out how many bricks you need to complete the whole sidewalk:
57600/32= 1,800 bricks
Nicole's cleaning company uses a linear model to determine the amount they charge their clients. They charged $144 for a cleaning job that took 4 hours. They charged $188 for a cleaning job that took 6 hours. Which equation could be used to determine the amount charged, C, for a cleaning job that takes t hours?A.C = 10t + 104B.C = 36t C.C = 44t + 56D.C = 22t + 56
Answer:
D
Step-by-step explanation:
Let the following point represent the first job: (4, $144). Let (6, $188) represent the second. Then we find the equation of the line through these two points. As we go from (4, $144) to (6, $188), x increases by 2 and y increases by $44. Thus, the slope of this line is m = rise/run = $44/(2 hrs), or $22/hr.
Using the slope-intercept formula for a straight line, y = mx + b, we find the equation of this line by finding the y-intercept, b:
Subbing the given info ($22/hr for m, 4 hr for x and $144 for y), we get:
$144 = ($22/hr)(4 hr) + b, or
$144 = $88 + b, which yields b = $56.
Thus, the desired equation is y = mx + b, or y = ($22/hr)x + $56. This matches the last answer (D)
A circle has a diameter of 8 m. What is the approximate area of the circle? 200.96 m2 12.56 m2 25.12 m2 50.24 m2
Answer:
50.24
Step-by-step explanation:
area of a circle =pi r^2
diameter = 2 * radius
radius=8/2=4
area=pi 4^2
=pi 16
=50.26
The length of a rectangle is 3 meters more than the width. The perimeter of the rectangle is 26 meters. If the width is b, which equation represents the situation? How many solutions will this equation have?
Answer:
Thehe answer is 75
Step-by-step explanation:
Answer with Step-by-step explanation:
The length of a rectangle is 3 meters more than the width.
If the width is b.
⇒ Length=b+3
The perimeter of the rectangle is 26 meters.
Since, Perimeter=2(Length+width)
⇒ 2(b+3+b)=26
dividing both sides by 2
⇒ b+3+b=13
⇒ 2b=13-3
⇒ 2b=10
dividing both sides by 2
⇒ b=5
⇒ Width=5 meter
and Length=5+3=8 meter
which equation represents the situation: 2(b+3+b)=26How many solutions will this equation have: UniqueFind the volume of the rectangular prism. Write answer as a fraction. Length=2/3 mm. Width=1/3mm. Height=2/3 mm.
put simply, the volume of a rectangular prism is just the product of all its 3 dimensions.
[tex]\bf V=\cfrac{2}{3}\cdot \cfrac{1}{3}\cdot \cfrac{2}{3}\implies V=\cfrac{4}{27}[/tex]
Given that g(x)=3x^2 -4x+3, find each of the following.
PICTURE DOWN BELOW!!!
Answer:
see explanation
Step-by-step explanation:
To evaluate the expression for the given values.
Substitute the given values for x into g(x)
a
g(0) = 3(0)² - 4(0) + 3 = 0 - 0 + 3 = 3
b
g(- 1) = 3(- 1)² - 4(- 1) + 3 = 3 + 4 + 3 = 10
c
g(2) = 3(2)² - 4(2) + 3 = 12 - 8 + 3 = 7
d
g(- x) = 3(- x)² - 4(- x) + 3 = 3x² + 4x + 3
e
g(1 - t)
= 3(1 - t)² - 4(1 - t) + 3
= 3(1 - 2t + t²) - 4 + 4t + 3
= 3 - 6t + 3t² - 4 + 4t + 3
= 3t² - 2t + 2
A dice game pays a player $5 for rolling a3 ot a 5 with a single die. the player has to pay $2 for any other roll. if a person plays the game 30 times, what is the approximate probability ttrat the person will win at least $15?
The approximate probability that the person will win at least $15 is 0.255.
To solve this problem, we need to calculate the probability of winning at least $15 after playing the game 30 times. Winning at least $15 means that the player must win on at least 6 rolls because winning once pays $5, and $5 times 6 is $30, which is the minimum needed to have a net gain of $15 ($30 won - $15 lost).
First, let's calculate the probability of winning in a single roll. The player wins if they roll a 3 or a 5, which are two favorable outcomes out of six possible outcomes.
[tex]\[ P(\text{win on a single roll}) = \frac{2}{6} = \frac{1}{3} \][/tex]
The probability of losing in a single roll is the complement of the probability of winning:
[tex][ P(\text{lose on a single roll}) = 1 - P(\text{win on a single roll}) = 1 - \frac{1}{3} = \frac{2}{3} \][/tex]
Now, we need to find the probability of winning at least 6 times in 30 rolls. This can be modeled using the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]
where [tex]\( n \)[/tex] is the number of trials (30 in this case), [tex]\( k \)[/tex] is the number of successes (at least 6), [tex]\( p \)[/tex] is the probability of success on a single trial [tex](\( \frac{1}{3} \)), and \( \binom{n}{k} \)[/tex] is the binomial coefficient.
We want to calculate the probability of winning at least 6 times, which is the sum of the probabilities of winning exactly 6, 7, .. up to 30 times:
[tex]\[ P(X \geq 6) = \sum_{k=6}^{30} \binom{30}{k} \left(\frac{1}{3}\right)^k \left(\frac{2}{3}\right)^{30-k} \][/tex]
[tex]\[ P(X \geq 6) \approx 0.255 \][/tex]
Ms.Holmes decided to water her plants.She had 2 1/2 gallons of water.She gave each plant 1/4 gallon of water.Which expression could be used to determine how many plants Ms.Holmes had?
To determine how many plants Ms. Holmes had, divide the total amount of water she had by the amount of water she gave each plant. The expression that can be used is (2 1/2 gallons) divided by (1/4 gallon per plant). Simplifying the expression gives the answer of 10 plants.
Explanation:To determine how many plants Ms. Holmes had, we can divide the total amount of water she had (2 1/2 gallons) by the amount of water she gave each plant (1/4 gallon per plant).
So, the expression that can be used is (2 ½ gallons) ÷ (1/4 gallon per plant). To divide a fraction by a fraction, we multiply the first fraction by the reciprocal of the second fraction. Therefore, the expression simplifies to (2 ½ gallons) × (4 gallons per plant).
Simplifying further, we get 10 gallons. This means that Ms. Holmes had 10 plants.
Learn more about plant watering here:https://brainly.com/question/17021989
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You play a board game with your little brother. You pick a card that sends you back five spaces. On your next turn, you must move back three more spaces. On your third turn, you get to move forward three spaces. Which expression best shows how you could find your new spot on the game board?
Answer:
Step-by-step explanation:
- 5 + (-3) + 3 is the correct option.
Answer:
-5 + (-3) + 3
Step-by-step explanation:
A scatter plot containing the point (5, 29) has the regression equation yˆ=5x+2 . What is the residual e when x = 5? Enter your answer in the box.
e = ?
Answer:
The answer is below
Step-by-step explanation:
Answer:
The residual e=2 when x = 5.
Step-by-step explanation:
A scatter plot containing the point (5, 29), it means the observed value at x=5 it 29.
The given regression equation is
[tex]\hat{y}=5x+2[/tex]
Substitute x=5 in the above regression equation, to find the predicted value at x=-5.
[tex]\hat{y}=5(5)+2=25+2=27[/tex]
The formula to find the residual value e is
e = Observed value - Predicted value
[tex]e=29-27[/tex]
[tex]e=2[/tex]
Therefore the residual e=2 when x = 5.
Find x to the nearest hundredth.
7.73 cm
8.12 cm
20.46 cm
23.78 cm
Answer:
23.78
Step-by-step explanation:
CAH
x/25
cos18=x/25
25cos18=x
x=23.78
Answer:
23.78 cm
Step-by-step explanation:
Since, We know that,
In a right angle triangle,
[tex]cos \theta=\frac{B}{H}[/tex]
Where, B represents base adjacent to [tex]\theta[/tex]
H represents the hypotenuse adjacent to [tex]\theta[/tex]
Thus, by the given diagram,
[tex]cos 18^{\circ}=\frac{x}{25}[/tex]
[tex]\implies x = 25\times cos 18^{\circ}=23.7764129074\approx 23.78\text{ cm}[/tex]
Hence, Last option is correct.
You invest $3000 in an account at 3.5% per year simple interest. How much will you have in the account at the beginning of the 7th year? Round your answer to the nearest whole dollar.
Answer:
$3735
Step-by-step explanation:
The formula for simple interest is I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years. We have everything we need to find the interest, which is the amount your investment earned while it sat there for 7 years. Once we find that interest amount, we will add it to the intial investment to find the total amount after 7 years that your money has grown to.
I = 3000(.035)(7) so
I = 735
3000 + 735 = 3735
Answer:
$3,630
Step-by-step explanation:
You invest $3,000 in an account at 3.5% per year simple interest.
We have to calculate the amount in the account at the beginning of the 7th year. This means we have to calculate the interest for completed 6 years.
Formula for simple interest
A = P(1+rt)
A = Amount after maturity
P = Principal amount ( 3,000)
r = rate of interest in decimal ( 0.035)
t = time in years ( 6 )
Now we put the values in to formula
A = 3,000(1 + 0.035 × 6)
A = 3,000 ( 1 + 0.021 )
A = 3,000 × 1.21
A = $3,630
The amount would be $3,630 at the beginning of the 7th year.
Someone please help??
Answer:
x = 1
Step-by-step explanation:
The base is 3. The value of 3^x will be 3 only when x=1.
_____
The value of any exponential term will be equal to the base when the exponent is 1.
Maryanne began a job that gives her 3 days of vacation each year she is employed up to a maximum of 24 days of vacation time. How many years will she be at the company before she reaches the maximum amount of vacation time?
Answer:
8 years
Step-by-step explanation:
Answer:
she will be at the company for 8 years.
Step-by-step explanation:
The number of days of vacation for each year = 3
Maryanne is employed up to a maximum of 24 days of vacation time.
We need to find the number of years she will be in the company before she reaches the maximum amount of vacation of time.
The number of years she will be in the company = The number of maximum days of vacation time divided by the number of days of vacation for each year
= [tex]\frac{24}{3}[/tex]
= 8 years
Therefore, she will be at the company for 8 years.
A fair coin is tossed 3 times. What is the probability that the coin with land showing heads on all three tosses.
Answer:2/3
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
one way we can solve this is by making a tree using H for heads and T for tails
since it can land H or T, we put them down like this. then we can get H or T again because its a coin, so we put that under each letter. finally we do the same thing again to get 8 possibilities. now we can count how many of them was HHH, which is one
H T
/ \ / \
H T H T
/\ /\ /\ /\
H T H T H T H T
^ this one
or do 2 x 2 x 2 because there are 2 possibilities each three times
Triangle TUV has been dilated to form triangle TꞌUꞌVꞌ.
What is the scale factor?
Answer:
4.4, 4.4 : 1, 22 : 5
Step-by-step explanation:
There are many ways to solve this, but I'll do it by finding the ratio between V'T' and VT.
That's easy, we're given the lengths of these two. The ratio would be 8.8/2. 8.8/2 = 4.4, or (8.8*5)/(2*5) = 22/5
Franco needs to pack 125 bottles of juice. Each box holds 8 bottles. How many boxes are needed to pack all of the juice?
Answer:
16 Boxes
Step-by-step explanation:
Total Bottles:125
Amount of Bottles A Box Is Able To Hold:8
125/8=15.625
Round Up To Nearest Whole Number
16 Boxes Are Needed To Hold 125 Bottles
for the dilation, Do, k = (10, 0 ) —> (5,0) , the scale factor is equal to ____.
•-5
•5
•0.5
•2
Answer:
•0.5
Step-by-step explanation:
We'll assume the dilation was done at the origin point, so it was done evenly.
Since the k point went from (10,0) to (5,0), we know it was reduced... so the scale factor has to be below 1. A scale factor means the size wasn't changed and a dilation/scale factor larger than 1 means it was enlarged.
So, we take the new X-value (5) and divide it by the original X-value (10).
Scale factor = 5/10 = 1/2... so 0.5
Which trigonometric function requires a domain restriction of [-pi/2, pi/2] to make it invertable?
Answer:
[tex]y=\tan x[/tex]
Step-by-step explanation:
The trigonometric function that needs a domain restriction of [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex] to make it invertible is [tex]y=\tan x[/tex].
The function [tex]y=\tan x[/tex] will pass the horizontal line test on this interval therefore making it an invertible function on this interval.
This explains why the inverse tangent function, [tex]y=\tan^{-1} x[/tex] has range [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex].
Answer:
A) [tex]f(x)=sin x[/tex]
Step-by-step explanation:
I just did the test and this was the correct answer.
Identify the coefficient of 13m
Answer: the coefficient of 13m is 13.
Answer:
The coefficient of 13 m is 13.
Step-by-step explanation:
Consider the provided expression.
[tex]13m[/tex]
Numbers appear with variables are called coefficients.
Alphabets in an expression are called variables.
Numbers appear without variables are called Constant terms.
Here we need to identity the coefficient.
From the above definition we know the number appear with the variables are coefficients.
Since m is variable, thus the number 13 must be the coefficient.
Hence, the coefficient of 13 m is 13.
A survey showed that hamburgers are preferred to hot dogs 5 to 3. What percent of those surveyed prefer hamburgers
Final answer:
62.5% of those surveyed prefer hamburgers.
Explanation:
The question is asking to find the percentage of people who prefer hamburgers over hot dogs when given the ratio of 5 to 3.
To calculate this, you would add the two parts of the ratio together to get the total number of parts, which is 5 + 3 = 8.
The number of parts that represent hamburgers is 5.
To find the percentage, you would divide the hamburger part by the total number of parts and then multiply by 100.
This gives you (5/8) × 100, which equals 62.5%.
Therefore, 62.5% of those surveyed prefer hamburgers.
(98 POINTS) (PLEASE HURRY!)
[1] x^2 - xy - x + y =
[2] 1 - x - x^2 + x^3 =
[3] xy + 1 + x + y =
[4] x^2y + y^2x + x^2x + y^3 =
Answer:
1. no like terms
2. x^ 3 − x^ 2 − x + 1
3.x y + x + y + 1
4.x^ 3 + x^ 2 y + x y^ 2 + y^ 3
Lol
In a simple random sample of 90 patients who saw a certain dentist, 8 patients had their teeth whitened. Which interval is the 95% confidence interval for the percent of all the dentists patients who had their teeth whitened?
Answer:
(3.01%, 14.77%)
Step-by-step explanation:
The confidence interval of a proportion is:
CI = p ± SE × CV,
where p is the proportion, SE is the standard error, and CV is the critical value (either a t-score or a z-score).
We already know the proportion: 8/90. But we need to find the standard error and the critical value.
The standard error is:
SE = √(p (1-p) / n)
SE = √((8/90) * (82/90) / 90)
SE = 0.03
To find the critical value, we must first find the alpha level and the degrees of freedom.
The alpha level for a 95% confidence interval is:
α = (1 - 0.95) / 2 = 0.025
The degrees of freedom is one less than the sample size:
df = n - 1 = 90 - 1 = 89
Since df > 30, we can approximate this with a normal distribution.
If we look up the alpha level in a z score table, we find the z-score is 1.96. That's our critical value. CV = 1.96.
Now we can find the confidence interval:
CI = 8/90 ± 0.03 * 1.96
CI = 0.0889 ± 0.0588
CI = (0.0301, 0.1477)
So we are 95% confident that the percent of patients who had their teeth whitened is between 3.01% and 14.77%.
Please Help!
When Mario has to leave the house for a while, he tethers his mischievous puppy to the corner of a 12 ft-by-8 ft shed in the middle of his large backyard. The tether is 18 feet long. Which description fits the boundary of the locus of points in the yard that the puppy can reach?
A. semicircles of radii 18 ft, 10 ft, and 6 ft
B. a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
C. semicircles of radii 18 ft, 12 ft, and 8 ft
D. a three-quarter circle of radius 18 ft, quarter circles of radii 12 ft and 8 ft
Answer:
B. a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
A diagram can be a useful aid to answering this question. At one corner of the shed, 8 ft of rope is no longer available, so the quarter circle has a radius of 18-8 = 10 ft. (That side of the shed is 12 ft, so the area is only a quarter circle.)
At the other corner of the shed, 12 ft of rope is no longer available, so the quarter circle has a radius of 18-12 = 6 ft. (That side of the shed is 8 ft, so the area is only a quarter circle.)
In the attached diagram, the 3/4 circle with radius 18 ft is shown red, and the quarter circles are shown in green.
Can someone help me with these questions please?
1. Which function pass through the points (1, 4), (2, 9), and (3, 16)?
y = (x + 1)2
y = (x + 3)2
y = 7x - 5
2. Suppose that after swimming 1 lap in a pool, you can swim 10 laps in an hour. What is an equation that represents the total number of laps you have swam y in terms of the number of hours x?
y(x) = 10 + x
y(x) = 10(x + 1)
y(x) = 10x + 1
3. Is the following an arithmetic sequence? If so, what is the common difference? {4, 2, 0, -2, -4, -6, …}
Yes, d = -2
No
Yes, d = 2
4. Which function has the following graph?
y = -2x + 4 b. y = 2x + 4 c. y =12x + 4
5. What is the slope of the line containing (3, 5) and (2, 7)?
m = 2 b. m = -2 c. m = 125
6. The graph of a line passes through the point (-3, 2) and has a slope of 4. What is an equation of the line?
y = 4x - 10
y = 4x - 11
y = 4x+ 14
7. Which line is parallel to y = 4x - 2?
y = -14x + 3
y = -4x + 5
y = 4x + 5
8. Which system of equations has (2, 3) as a solution?
y = 2x - 1 b. y = 2x + 1 c. y = 4x - 5
y = x + 1 y = x - 1 y = 2x
Answer:
the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).
Step-by-step explanation:
Note that 4, 9 and 16 are squares of 2, 3 and 4. So it's likely that the parent function is of the form f(x) = x^2. Note that f(1) = 1, f(2) = 4, f(3) = 9 and f(4) = 16.
Let's now determine whether these three points satisfy the first given equation, y = (x + 1)^2: Does 4 = (1 + 1)^2? Does 4 = 2^2? YES.
Does 9 = (2 + 1)^2? Does 9 = 3^2? YES
Does 16 = (3 + 1)^2? YES
So the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).
Final answer:
The detailed answers cover questions related to functions, sequences, equations of lines, slopes, and graphing lines.
Explanation:
Question 1:
The function that passes through the points (1, 4), (2, 9), and (3, 16) is y = (x + 1)^2.
Question 2:
The equation representing the total number of laps swum y in terms of hours x is y(x) = 10x + 1.
Question 3:
The sequence {4, 2, 0, -2, -4, -6, …} is an arithmetic sequence with a common difference of -2.
Question 5:
The slope of the line containing (3, 5) and (2, 7) is m = -2.
Question 6:
For a line passing through (-3, 2) with a slope of 4, the equation of the line is y = 4x + 14.
Combine the following expressions:
ANSWER
[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n}[/tex]
EXPLANATION
The given expression is
[tex] \sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n} [/tex]
We remove the perfect squares under the radical sign.
[tex]\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n} [/tex]
We can now take square root of the perfect squares and simplify them further.
[tex] \sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n} [/tex]
This simplifies to:
[tex]4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n} [/tex]
This further simplifies to:
[tex](4n - 1)\sqrt{3 n} + 3\sqrt{n} [/tex]
Answer:
Option B is Correct
Step-by-step explanation:
[tex]\sqrt{48n^3}+\sqrt{9n} - \sqrt{3n}[/tex]
We need to solve the above expression.
48 can be written as: 2x2x2x2x3
9 can be written as : 3x3
Putting values
[tex]\sqrt{2*2*2*2*3*n*n*n} +\sqrt{3*3*n}-\sqrt{3n}[/tex]
2*2 = 2^2 and n*n = n^2 and 3*3 = 3^2
we also know √ = 1/2
so, putting these values we get,
[tex]\sqrt{2^2*2^2*3*n^2*n} +\sqrt{3^2*n}-\sqrt{3n}\\(2^2)^{1/2} * (2^2)^{1/2} * (3)^{1/2} * (n^2)^{1/2} * n ^{1/2} + ((3^2)^{1/2} *n^{1/2}) -(\sqrt{3n})\\2*2*n * (3^{1/2} *n ^{1/2}) +(3 +n^{1/2}) -(\sqrt{3n})\\4n (\sqrt{3n})+(3 \sqrt{n}) -(\sqrt{3n})\\Rearraninging\\4n(\sqrt{3n}) - (\sqrt{3n})+(3 \sqrt{n})\\Taking \,\,\sqrt{3n} \,\,common\,\, from\,\, 1st\,\, and\,\, 2nd\,\, term\\\sqrt{3n}(4n-1)+(3 \sqrt{n})\\or \,\,it\,\,can\,\,be\,\,written\,\,as\,\,\\(4n-1)\sqrt{3n}+(3 \sqrt{n})[/tex]
So, Option B is Correct.
please help me and plz explain thoroughly i need help asap!
Given the function f(x) = 2(x + 8), find x if f(x) = 12.
2
40
−2
14
f(x) = 2(x+8)
replace f(x) with 12 and then solve for x:
12 = 2(x +8)
Use the distributive Property on the right side:
12 = 2x +16
Subtract 16 from each side:
-4 - 2x
Divide both sides by 2:
x = -4 / 2
x = -2
Answer:
−2
Step-by-step explanation:
f(x) = 2(x+8)
f(x) = 12
12 = 2(x+8)
Divide each side by 2
12/2 = 2/2(x+8)
6 = x+8
Subtract 8 from each side
6-8 =x+8-8
-2 = x