12a^2b^3 / 3ab
Factor 3 out of the numerator:
3(4a^2b^3) / 3ab
Cancel out the common factors:
4a^2b^3 / ab
Cancel out the common factors again to get the final answer:
4ab^2
Colin and Jezebel are employees at Game Zone. They recorded the number of computer games they sold each week for the past 9 weeks.
Colin 15 20 21 9 3 16 9 14 17
Jezebel 10 14 20 11 4 26 5 8 20 (a) All of the games sold of which person had the greatest spread? Explain how you know. (b) The middle 50% of the games sold of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Colin’s and Jezebel’s sold games?
Answer:
a) The sold games of Jezebel had the greatest spread.
b) The middle 50% of the games sold by Colin has the least spread.
c) Jezebel sold more games than colin.
Step-by-step explanation:
Range is sued to calculate the spread of the given data.
Range is given by:
[tex]Range=Max\ Value-Min\ Value[/tex]
So,
Part a)
For Collin:
Range=21-3=18
For Jezebel:
Range=26-5=21
Part b)
Middle 50% of the values will be the values between 1st quartile and 3rd quartile
So, to find quartiles:
For Colin:
=3,9,9,14,15,16,17,20,21
The median is 15.
The lower half is 3,9,9,14
Q1 = (9+9)/2= 18/2 = 9
The upper half is 16,17,20,21
Q3 = (17+20)/2= 37/2= 18.5
The middle 50% is first quartile subtracted from third quartile
So, the spread is:
18.5-9=9.5
For Jezebel:
4,5,8,10,11,14,20,20,26
The median is 11.
The lower half is 4,5,8,10
Q1 = (5+8)/2=13/2=6.5
The upper half is 14,20,20,26
Q3 = (20+20)/2=40/2=20
The middle 50% values' spread is:
20-6.5=13.5
Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..
Sheila bought a new computer for $2000 and has agreed to finance it at 12% interest, with $100 payments each month. When she makes her first payment next month, how much will she pay for interest alone?
Answer:
rate per month = .01 agreed = r
Luckily they only ask for the first month so it is 0.01 * 20 .
Later months get more complicated and it is like paying off a mortgage with the term unknown but the rate and payment known.
Payment = principal value [ r / {1-(1+r)^-n } ]
100 = 2000 [ .01 / {1 - (1.01)^-n } ]
5 = 1/ {1 - (1.01)^-n }
.2 = 1 - (1.01)^-n
.8 = 1.01^-n
log .8 = -n log 1.01
n = 22.4 months :)
so over the almost two years pay 2240 total :)
* Hopefully this helps:) Mark me the brainliest:)!!!
Final answer:
For Sheila's first payment on her new computer financed at 12% annual interest with $100 monthly payments, she will pay $20 towards interest and the remaining $80 will go towards the principal.
Explanation:
Sheila bought a new computer for $2000 and agreed to finance it at 12% annual interest, with $100 monthly payments. To calculate the interest she will pay with the first payment, we need to find 1% of $2000 (since 12% per year is equivalent to 1% per month).
(1% of $2000) = 0.01 * $2000 = $20
Therefore, when Sheila makes her first monthly payment of $100, $20 will go towards interest, and the remaining $80 will reduce the principal on her loan.
(HELP ASAP PLEASE)
Zoe often orders party trays from her favorite Mexican food restaurant for company events. For a recent company party, she spent $239 on 4 burrito platters and 5 taco platters. For a company meeting, she spent $208 on 3 burrito platters and 5 taco platters. How much does each type of platter cost?
Each burrito platter costs $___ and each taco platter costs $___ .
Answer:
Each burrito platter costs $_31__ and each taco platter costs $_23__ .
Step-by-step explanation:
Let the cost of a burrito platter be x and the cost of a taco platter be y;
4 burrito platters and 5 taco platters would cost;
4x + 5y = 239
3 burrito platters and 5 taco platters would cost;
3x + 5y = 208
We can solve the two equations simultaneously via elimination method. We subtract the two equations in order to eliminate y and solve for x;
4x - 3x = 239 - 208
x = 31
Using the first equation, substitute x = 31 and solve for y;
4(31) + 5y = 239
124 + 5y = 239
5y = 115
y = 23
Find the radius of a sphere with a surface area of 64(pie) sq.m. Round your answer to the nearest whole number.
a.
8 m
c.
16 m
b.
2 m
d.
4 m
[tex]\bf \textit{area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=64\pi \end{cases}\implies 64\pi =4\pi r^2 \\\\\\ \cfrac{64\pi }{4\pi }=r^2\implies 16=r^2\implies \sqrt{16}=r\implies 4=r[/tex]
The radius of the sphere will be 4 meters. Thus, the correct option is D.
What is the surface area of the sphere?Let r be the radius of the sphere. Then the surface area of the sphere will be given as,
SA = 4πr² square units
The surface area of the sphere is 64π square meters. Then the radius of the sphere is calculated as,
64π = 4 x π x r²
r² = 16
r = 4 meters
Thus, the correct option is D.
More about the surface area of the sphere link is given below.
https://brainly.com/question/29251585
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what is 10 radical 12 times 6 radical 6
Answer:
360 radical 2 or 509.11688
Step-by-step explanation:
simplify the radicals
12 =2 radical 3
calculate the products
10* 2 radical 3 * 6 radical 6
= 120 radical 18
again simplify
360 radical 2
Answer:
360 radical 2
Step-by-step explanation:
The Venn diagram represents the results of a survey that asked participants whether they would want a fish or turtle as a pet. Complete the table.
have a don't have Total
fish. a fish.
have turtle __. __. ___
don't have turtle__. __. ___
Total__. __. ___
Answer:
[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]
Step-by-step explanation:
From the Venn diagram:
have both turtle and fish - 6 participants;have only fish - 11 participants;have only turtle - 15 participants;don't have pets - 12 participants;So, in total,
6+11+15+12=44 participants took part in survey.
The two-way table looks like
[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]
Someone help PLEASE
Answer:
Q4. (-7)Q5. (-8)Step-by-step explanation:
The perfect square:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Q4
We have
[tex]y^2+14y+49=0\\\\y^2+2(y)(7)+7^2=0\\\\(y+7)^2=0\iff y+7=0\qquad\text{subtract 7 from both sides}\\\\\boxed{y=-7}[/tex]
Q5
We have
[tex]y^2+16y+64=0\\\\y^2+2(y)(8)+8^2=0\\\\(y+8)^2=0\iff y+8=0\qquad\text{subtract 8 from both sides}\\\\\boxed{y=-8}[/tex]
Suppose a helium balloon is filled with 1,000 cm3 of helium. Each day, the balloon loses half its helium. Identify the amount of helium that will be in the balloon on the second and third days.
Answer:
the answer is 500cm^3 and 250cm^3
Step-by-step explanation:
This is the correct answer to your question. Btw I wasn't able to answer it before so I commented on the answer above but now I can answer it like this, hope it helps! :)
The on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
A helium balloon is filled with 1,000 cm3 of helium.
First day of the balloon has 1000 cubic cm helium gas
Each day, the balloon loses half its helium.
After second day the amount of helium gas = 1000/2 = 500 cubic cm
After third day, the amount of helium gas = 500/2 = 250 cubic cm
Thus, the on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.
Learn more about the sequence here:
brainly.com/question/21961097
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A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = −16t2 + 94t + 12
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
2.9375 < t < 6
2 < t < 5
1 < t < 4
0 < t < 3
Answer:
Well I think it is A because domain is the x values.
Step-by-step explanation:
So when you plug this in your calculator (mine is a ti-84 plus ce) you would hit graph. After it graphs it press Zoom, 0 to center it then press 2nd, trace which pulls up parabola menu's. Press 0 and find the left bound, right bound and then press enter which would give you x values of 2.9375 < t< 6
At the same time I don't know if this is right. I never really excelled at parabolas just trying to help.
Check the picture below.
so the domain will be the values that "x" gets, now, the maximum height of the ball is when it reaches the vertex or U-turn up above, well, what is the x-coordinate anyway?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+94}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{94}{2(-16),}\qquad \qquad \right)\implies \left( \cfrac{487}{16},\qquad \qquad \right)\implies (2.9375,\qquad \qquad )[/tex]
so then x = 2.9375 at the vertex, now, what is "x" when it hits the ground? recall y = 0 at that instant.
[tex]\bf \stackrel{f(t)}{0}=-16t^2+94t+12\implies 0=-2(8t^2-47t-6) \\\\\\ 0=(8t+1)(t-6)\implies t= \begin{cases} \boxed{6}\\ \begin{matrix} -\frac{1}{8} \\[-0.5em]\cline{1-1}\\[-5pt]\end{matrix} \end{cases}[/tex]
so then, the values for "x" or namely the domain from the vertex till the ball hits the ground is 2.9375 < t < 6.
Help! What is the probability that a card drawn from a standard 52 card deck is a diamond or a three?
Answer:6.5%
Step-by-step explanation:
There are 4, number three cards and 4 diamond cards in a deck of 52 cards. Divide 52 by 8.
Answer:
30.8% or 4/13
Step-by-step explanation:
There are 52 cards in a deck of cards.
There are 4 nines (4/52) and 13 (13/52) diamonds in a deck of cards.
When you add them together, you get 17/52. Then, you have to subtract the card that is both a nine and in a diamond suite, so you subtract -1 because there is only one card that fits both categories. You should have 16/52, which simplifies to 4/13 / 30.8%.
A flagpole broke in a storm. 777 meters are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 242424 meters away horizontally.
How tall was the flagpole before it broke?
The broken flagpole forms a right triangle, where the vertical leg is the piece still standing and the hypotenuse is the broken piece.
So, the original length is the sum of the hypotenuse and the vertical leg.
The hypotenuse can be found using the pythagorean theorem:
[tex]h=\sqrt{7^2+24^2}=25[/tex]
So, the flag was originally [tex]7+25=32[/tex] meters long.
A bookstore receives a shipment consisting of two boxes. There is no empty space in either of the boxes. The first box contains 16 books, each measuring 3/2 in by 8 in by 11 in. The second box contains 30 books, each measuring 3/4 in by 5 in by 8 in.
Explain which of the two boxes is larger and how you know. Show your work to support your explanation.
To find the answer, I used:
Volume = Length • Height • Width
Each book in box 1 has a volume of 132 inches^3 and there are 16 of them, so I multiplied 132 inches^3 by 16 and got a total volume of 2,112 inches^3 in box 1
Each book in box 2 has a volume of 30 inches^3 and there are 30 of them, so I multiplied 30 inches^3 by 30 and got a total volume of 900 inches^3 in box 2
2,112 inches^3 is greater than 900 inches^3 so box 1 should be more than twice as big as box 2
2112 cubic inches.
To determine which of the two boxes is larger, we need to calculate the volume of each box. For the first box, containing books each measuring 3/2 in by 8 in by 11 in, the volume of one book is calculated as:
Volume of one book = (3/2) * 8 * 11 = 12 * 11 = 132 cubic inches.Total volume for 16 books = 132 * 16 = 2112 cubic inches.For the second box, containing books each measuring 3/4 in by 5 in by 8 in, the volume of one book is calculated as:
Volume of one book = (3/4) * 5 * 8 = 3.75 * 40 = 150 cubic inches.Total volume for 30 books = 150 * 30 = 4500 cubic inches.Comparing the two totals, the second box, with a total volume of 4500 cubic inches, is larger than the first box, which has a total volume of 2112 cubic inches. Hence, we know that the second box is larger because it has a greater total volume.
If f(x)= x^2-2x and g(x)= 6x+4 for which value of x does (f+g)(x)=0
Answer:
x = - 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4 ← equating to 0
x² + 4x + 4 = 0 ← in standard form
(x + 2)² = 0 ← in factored form, thus
x + 2 = 0 ⇒ x = - 2
Rhombus LMNO is shown with its diagonals.
Angle MNO measures 112°. What is the measure of angle LMN?
34°
45°
56°
68°
Answer:
The measure of angle LMN is 68° ⇒ the last answer
Step-by-step explanation:
* Lets revise the properties of the rhombus
- The rhombus has 4 equal sides in length
- Every two opposite angles are equal in measure
- Every two adjacent angles are supplementary (their sum = 180°)
- The two diagonals bisect each other
- The two diagonals perpendicular to each other
- The two diagonals bisect the vertices angles
* Lets solve the problem
∵ LMNO is a rhombus
∴ ∠LMN and ∠MNO are adjacent angles
∴ ∠LMN and ∠MNO are supplementary
∴ m∠LMN + ∠MNO = 180°
∵ m∠MNO = 112°
∴ m∠LMN + 112° = 180° ⇒ subtract 112 from both sides
∴ m∠LMN = 68°
* The measure of angle LMN is 68°
Answer:
68
Step-by-step explanation:
What’s the perpendicular slope of 4/3
Answer:
-3/4
Step-by-step explanation:
Perpendicular slopes are reciprocal opposites of the original slope. This means that the reciprocal of 4/3 is 3/4, and the opposite of 3/4 is -3/4.
To find the perpendicular slope you must take the given slope take the opposite reciprocal (aka switch the sign and flip the fraction)
so...
[tex]\frac{-3}{4}[/tex]
^^^slope perpendicular to 4/3
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the volume of the prism shown
Answer:
The answer is 450
Step-by-step explanation:
V = l*w*h
V = 15*10*3
V= 450
ANSWER
[tex]450 {cm}^{3} [/tex]
EXPLANATION
The prism shown is a rectangular prism or cuboid.
The volume of a cuboid is given by:
[tex]Volume=l \times b \times h[/tex]
From the diagram, the length is l=15cm ,the breadth is b=10cm and the height is h=3cm.
We substitute the values into the formula to obtain,
[tex]Volume=15 \times 10 \times 3[/tex]
We simplify to get,
[tex]Volume=450 {cm}^{3} [/tex]
If a function f(x) is defined as (4x)/(1-x), what is the expression for f(x + h)
ANSWER
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h}[/tex]
EXPLANATION
The given expression is
[tex]f(x) = \frac{4x}{1 - x} [/tex]
To find an expression for f(x+h), we substitute x+h, wherever we see x in the given expression.
This implies that,
[tex]f(x + h) = \frac{4(x + h)}{1 - (x + h)} [/tex]
We simplify to obtain;
[tex]f(x + h) = \frac{4x + 4h}{1 - x - h} [/tex]
Answer:
A
Step-by-step explanation:
(4x+4h)/(1-x-h)
Here are two steps from the derivation of the quadratic formula.
What took place between the first step and the second step?
*Apex
ANSWER
C. Factoring a perfect square trinomial.
EXPLANATION
The first step shown is:
[tex] {x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
Observe that the left hand side is a perfect square trinomial.
In other words, the left hand side is of the form,
[tex] {m}^{2} + 2mn + {n}^{2} [/tex]
which can be factored as:
[tex] {m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2} [/tex]
When we factor the perfect square trinomial on the left hand side, we obtain:
[tex]( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]
The correct answer is C
Answer:
FACTORING A PERFECT SQUARE TRINOMIAL!
Step-by-step explanation:
GOT IT CORRECT ON 3.8.3 AP-EX...
it's not sq root because that comes afterwards.
it's not completing the square because that's
x^2+ bx/a +(b/2a)^2=-c/a+(b/2a)^2
Then from there it's
x^2 + bx/a + b^2/4a^2 = -c/a + b^2/4a^2
(x + b/2a)^2 = b^2/4a^2 -c/a
Then that step ends. If you don't believe me look at study 3.3.1 page 13.
This will help!
HELP!!!! Which of the following is a counterexample that proves the conditional statement false?
If a number is divisible by four, then it is divisible by eight.
12
16
24
48
Answer:
12 I think........?....
Answer:
The answer is 12
Step-by-step explanation:
In this case, we just have to try with all of them:
12/4=312/8=1,5Then it is not divisible (it is not integer). This proves the statement false.
Let's try with the others as well, just to check:
16/4=416/8=224/4=624/8=348/4=1248/8=6All the others don't prove false that statement.
Please Help Me With This Problem
Answer:
[tex]Area=1,325\ yd^2\\Perimeter=204\ yd[/tex]
Step-by-step explanation:
You can use the following formula to calculate the area of the triangle:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
You can observe in the figure that:
[tex]b=53\ yd\\h=50\ yd[/tex]
Then, the area is:
[tex]A=\frac{(53\ yd)(50\ yd)}{2}=1,325\ yd^2[/tex]
To find the perimeter you must add the lenght of each side of the triangle. Then, this is:
[tex]P=97\ yd+53\ yd+54\ yd\\\\P=204\ yd[/tex]
Solve for :
(x+3)/2=6
Answer:
x=9
Step-by-step explanation:
(x+3)/2=6
Multiply each side by 2
2*(x+3)/2=6*2
x+3 = 12
Subtract 3 from each side
x+3-3 = 12-3
x = 9
find the midpoint of the line segment with the given endpoints.
(14, -6), (13, 14)
Answer:
Step-by-step explanation:
23
Answer:
([tex]\frac{27}{2}[/tex], 4 )
Step-by-step explanation:
Use the midpoint formula
midpoint = [[tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
with (x₁, y₁ ) = (14, - 6) and (x₂, y₂ ) = (13, 14), hence
[[tex]\frac{1}{2}[/tex](14 + 13), [tex]\frac{1}{2}[/tex](- 6 + 14) ]
= ([tex]\frac{27}{2}[/tex], 4)
leon is installing a fence around a rectangular vegetable garden with a perimeter of 60 feet. the garden is 12 feet wide. how long is the garden?
The wide side of the garden is 12 feet, so the other side would be 12 feet aswell.
12+12=24
To find the length of each long side, you subtract 60-12, then divide by 2.
60-12=48/2=24
Simplify the following expression (3i+4-i+4(6+2i)
Answer:28 + 10i
Step-by-step explanation: You first distribute.
(3i+4-i+4(6+2i)
3i +4-i+24+8i (Distribute)
3i - i = 2i + 8i= 10i and 4 + 24= 28 (Combine like terms)
10i + 28 or 28 + 10i
Answer:
Answer: 28 + 10i
Step-by-step explanation:
A P E X
1. What are the mean, median, mode and range of the data set given the altitude of lakes in feet: –
11, –28, –17, –25, –28, –39, –6, and –46?
(1 point)
A. mean = –25; median = –26.5; mode = –28; range = 40
B. mean = –25; median = –40; mode = –26.5; range = 28
C. mean = –26.5; median = –25; mode = –28; range = 28
D. mean = –26.5; median = –28; mode = –25; range = 40
2. Given the data 21, 13, 13, 37, 13, 23, 25, 15:
A. What is the outlier in the data?
B. What is the mean with the outlier?
C. What is the mean without the outlier?
A. 13; 21; 17.6
B. 37; 20; 17.6
C. 37; 17.6; 20
D. 13; 17.6; 21
Answer:
cdc
Step-by-step explanation:
1. The option is (A) mean = –25; median = –26.5; mode = –28; range = 40.
2. The option is (C) 13; 17.6; 20.
What is the median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.
To find the mean, median, mode, and range of the data set, we first need to arrange the data in order:
–46, –39, –28, –28, –25, –17, –11, –6
Mean: To find the mean, we add up all the values and divide by the total number of values:
Mean = (-46 + -39 + -28 + -28 + -25 + -17 + -11 + -6) / 8
Mean = -25
Median: To find the median, we need to find the middle value of the data set.
Since there are 8 values, the median is the average of the 4th and 5th values:
Median = (-28 + -25) / 2
Median = -26.5
Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is –28, since it appears twice and no other value appears more than once.
Range: To find the range, we subtract the smallest value from the largest value:
Range = -6 - (-46)
Range = 40
Therefore, the answer is (A) mean = –25; median = –26.5; mode = –28; range = 40.
2.
A. The outlier in the data set is 37, since it is much larger than the other values.
B. To find the mean with the outlier, we add up all the values and divide by the total number of values:
Mean = (21 + 13 + 13 + 37 + 13 + 23 + 25 + 15) / 8
Mean = 17.6
C. To find the mean without the outlier, we need to exclude the value 37 and then calculate the mean using the remaining values:
Mean = (21 + 13 + 13 + 13 + 23 + 25 + 15) / 7
Mean = 17.6
Therefore, the answer is (C) 13; 17.6; 20.
To learn more about the median;
https://brainly.com/question/28060453
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Please show your work
Let a,b & c be the number of cookies Adrian, Bobby and Calvin baked respectively.
(a+b+c)/3 =138
(a+b)/2 =136
a+b=272
a=272-b
(b+c)/2 =125
b+c=250
c=250-b
Sub a=272-b and c=250-b into (a+b+c)/3 =138,
(a+b+c)/3 =138
[(272-b)+b+(250-b)]/3 = 138
272-b+b+250-b = 414
-b = -108
b=108
From the above,
a=272-b
=272-108
a=164
c=250-b
=250-108
c=142
∵ a=164
b=108
c=142
∴ Adrian baked 164 cookies.
Bobby baked 108 cookies.
Calvin baked 142 cookies.
A cylinder has a circular base with a radius that measures 9 inches. Determine the diameter of the base of the cylinder.
3 inches
4.5 inches
18 inches
81 inches
The answer is 18 inches.
Let r=radius and d=diameter
2r=d
2(9)=d
18=d
Hope this helps!
Answer:
18 inches
Step-by-step explanation:
What is the value of X in the equation 2x+3y=36, when y=6?
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Answer:
x = 9
Step-by-step explanation:
Substitute y=6 into 2x+3y=36
2x+3(6) =36
2x + 18 = 36
2x = 18
x = 9
Solve for x. show your work
6/9 = x+2/24
Simplify 6/9 to 2/3
2/3 = x + 2/24
Simplify 2/24 to 1/12
2/3 = x + 1/12
Subtract 1/12 from both sides
2/3 - 1/12 = x
Simplify 2/3 - 1/12 to 7/12
7/12 = x
Switch sides
x = 7/12
What are the domain and range of f(x) =(1/6)^x + 2?
A.domain: {x | x > - 1/6} ; range: {y | y > 0}
B.domain: {x | x > 1/6} ; range: {y | y > 2}
C.domain: {x | x is a real number}; range: {y | y > 2}
D.domain: {x | x is a real number}; range: {y | y > –2}
Answer:
[tex]\large\boxed{C.\ domain:\ \{x\ |\ x\ \text{is a real number}\};\ range:\ \{y\ |\ y>2\}}[/tex]
Step-by-step explanation:
[tex]f(x)=\left(\dfrac{1}{6}\right)^x+2\\\\\text{The domain:}\ x\in\mathbb{R}\to\{x\ |\ x\ \text{is a real number\}}\\\\\lim\limits_{x\to\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=0+2=2\\\\\lim\limits_{x\to-\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to-\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\{y\ |\ y>2\}\\\\\bold{Look\ at\ the\ picture}[/tex]
Answer: Option C
domain: {x | x is a real number}; range: {y | y > 2}
Step-by-step explanation:
We have the function [tex]f(x) =(\frac{1}{6})^x + 2[/tex]
Note that f(x) is an exponential function.
By definition the exponential functions of the form [tex]a(b)^x +k[/tex] have as domain all real numbers and as range {y | y > k} if [tex]a>0[/tex], [tex]b>0[/tex]
Where a is the main coefficient, b is the base and k is the vertical displacement.
In this case [tex]k = 2[/tex], [tex]b=\frac{1}{6}[/tex], [tex]a=1[/tex]
Therefore the domain of f(x) is all real numbers and the range of f(x) is
{y | y > 2}