Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.
Answers
Answer:
[tex]f(x)=162^\frac{x}{4}[/tex]
[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]
[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[4]{162^{x}}[/tex]
Remember that
[tex]\sqrt[n]{a^{m}}=a^{m/n}[/tex]
[tex](a^{m})^{n}=a^{m*n}[/tex]
so
1) [tex]\sqrt[4]{162^{x}}=162^\frac{x}{4}[/tex]
2) The number 162 decompose in prime factors is
[tex]162=(2)(3^4)[/tex]
substitute
[tex]f(x)=\sqrt[4]{[(2)(3^4)]^{x}}={[(2)(3^4)]^{x/4}={{[(2)(3^4)]^{(1/4)}}^x=[3\sqrt[4]{2}]^{x}[/tex]
3) [tex]f(x)=[3\sqrt[4]{2}]^{x}=[3(2^{\frac{1}{4}})]^{x}[/tex]
therefore
[tex]f(x)=162^\frac{x}{4}[/tex]
[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]
[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]
Answer:
A.B. E.
Step-by-step explanation:
Related Questions
Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music he is supposed to be working on. He has 60 minutes to practice piano and would like to spend at least 35 minutes playing songs instead of practicing scales. So, Sven sets up the following inequality, where t is the number of minutes he spends on each scale, and solves it.
Answers
Answer:
He must spend no more that 25 minutes practising scales.
Step-by-step explanation:
5t + 35 ≤ 60
5t ≤ 25
t ≤ 5.
So the maximum time for practising the scales is 5*5 = 25 minutes.
Answer:
Sven should spend 5 minutes or less on each scale. Maximum times is 25 minutes.
Step-by-step explanation:
Total time to practice piano = 60 minutes
He would like to spend at least 35 minutes playing songs instead of practicing scales.
Let t is the number of minutes he spends on each scale.
The time spend on 5 scales = 5t
Time for playing songs = 60 - 5t
It is given that he would like to spend at least 35 minutes playing songs instead of practicing scales. It means time for playing songs is greater than or equal to 35.
[tex]60-5t\geq 35[/tex]
Subtract 60 from both sides.
[tex]60-5t-60\geq 35-60[/tex]
[tex]-5t\geq -25[/tex]
Divide both sides by -5. If an inequality is divided or multiplied by a negative number, then the sign of inequality is changed.
[tex]t\leq 5[/tex]
Sven should spend 5 minutes or less on each scale.
The maximum value of t is 5, so the maximum time spend on practicing scales is
[tex]\text{Maximum time}=5t\Rightarrow 5(5)=25[/tex]
Therefore, the maximum time is 25 minutes.
Does this table represent a function? Why or why not?
I need help ASAP
Answers
Answer:
B
Step-by-step explanation:
A function has ONE x value and ONE y value.
HELP! PLEASE SHOW WORK.
Answers
Answer:
2⅖
Step-by-step explanation:
Set this up as a proportion:
⅘ ? [parts of the necklace]
__ = __
⅓ 1 [hours]
Divide four-fifths by one-third to get 2⅖.
I am joyous to assist you anytime.
** ⅓ hour = 20 minutes
Point N is on line segment MO. Given MN = x, MO = 3x - 6,
and NO = x + 1, determine the numerical length of MO.
Answers
Answer:
Step-by-step explanation:
N is between points M and O
MN = x
MO = 3x - 6
NO = x + 1
The way it reads MN + NO = MO
x + x + 1 = 3x - 6
2x + 1 = 3x - 6
2x - 2x +1 = 3x -2x - 6
1 = x - 6
1 + 6 = x
x = 7
MO = 3x - 6
MO = 3*7 - 6
MO = 21 - 6
MO = 15
The numerical length of MO, given MN = x, MO = 3x - 6, and NO = x + 1, is 15.
Explanation:Given the conditions of the problem, we can create the equation MO = MN + NO based on segment addition postulate in Geometry. This implies: 3x - 6 = x + x + 1, or 3x - 6 = 2x + 1. Solving this equation for x, you get x equals 7. Substituting x = 7 into MO = 3x - 6 gives you: MO = 3(7) - 6 = 21 - 6 = 15. So, the numerical length of MO, given MN = x, MO = 3x - 6, and NO = x + 1, is 15.
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find each product
1. (-2)(3)
2. (-5)(-7)
3. (8) (-11)
4. (-3) (2) (-2)
Answers
Answer:
1. -6
2. 35
3.-88
4. 12
hope it helps :)
The numbers of calories per serving for various snakes foods are listed below.
Corn chips: 230 calories
Popcorn: 25 calories
Potato chips: 115 calories
Pretzels: 62 calories
What is the mean number of calories per serving for these foods?
A.) 88.5 cal.
B.)108 cal.
C.)230 cal.
D.)432 cal.
Answers
Answer:
B. 108 calories
Step-by-step explanation:
The mean number of a data set is
[tex]\text{Mean}=\dfrac{\text{The sum of all calories in products}}{\text{The number of products}}[/tex]
Corn chips: 230 calories
Popcorn: 25 calories
Potato chips: 115 calories
Pretzels: 62 calories
Thus,
The sum of all calories [tex]=230+25+115+62=432[/tex]
The number of productrs = 4
The mean number of calories [tex]=\dfrac{432}{4}=108[/tex]
When measuring the length a and the width b of a rectangle, it was found that 5.4< a< 5.5 and 3.6< b< 3.7 (in centimeters). Find the possible values of: the perimeter of the rectangle
Answers
Answer:
The possible values of the perimeter of the rectangle is between 18 and
18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
Step-by-step explanation:
* Lets explain how to solve the problem
- The perimeter of any quadrilateral is the sum of the length of its
four sides
- The rectangle is a quadrilateral with each two opposite sides are
equal in lengths, then its perimeter = 2l + 2w, where l, w are its
length and width
∵ The the length of the rectangle is a
∵ 5.4 < a < 5.5 cm
∵ The perimeter of the rectangle = 2a + 2b
- Lets multiply the inequality by 2
∴ 5.4 × 2 < a × 2 < 5.5 × 2
∴ 10.8 < 2a < 11 ⇒ (1)
∵ The width of the rectangle is b
∵ 3.6 < b < 3.7 cm
- Lets multiply the inequality by 2
∴ 3.6 × 2 < b × 2 < 3.7 × 2
∴ 7.2 < 2b < 7.4 ⇒ (2)
- Add inequalities (1) and (2)
∵ 10.8 < 2a < 11
+ 7.2 < 2b < 7.4
∴ 18 < 2a + 2b < 18.4
∵ 2a + 2b represents the perimeter of the rectangle
∴ The possible values of the perimeter of the rectangle is between
18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
The length of an object is measured as 35.8 centimeters. What is this measurement in scientific notation?
A. 358 × 10^1 centimeters
B. 3,580 × 10^2 centimeters
C. 0.358 × 10^2 centimeters
D. 3.58 × 10^1 centimeters
Answers
Answer:
option D is correct
=3.58X 10^1
The subject of the formula below is y.
y = x + a-b
Rearrange the formula to make x the subject.
Pls help
Answers
Answer:
x = y + b - a
Step-by-step explanation:
Given
y = x + a - b ( add b to both sides )
y + b = x + a ( isolate x by subtracting a from both sides )
y + b - a = x
Lainey bought a set of 20 markers for $6
Answers
Final answer:
To find the unit price of markers in a set, divide the total cost by the number of markers to find that each marker costs $0.30 when 20 are purchased for $6.
Explanation:
Lainey's purchase of a set of 20 markers for $6 can be used to illustrate a simple mathematical concept known as unit price, which is the cost per individual item when items are sold in a set or batch. To calculate the unit price, you divide the total cost by the number of items in the set. Here's how you can do this calculation:
Determine the total cost of the set of markers, which is $6.
Count the number of markers in the set, which is 20.
Divide the total cost by the number of markers to find the unit price: $6 ÷ 20 = $0.30 per marker.
Therefore, the cost of each individual marker from the set is $0.30. Starting small, such as with markers, pencils, sharpeners, and erasers, and gradually adding other items like construction paper or magnets, are good practices in both purchasing supplies and understanding incremental costs in financial literacy.
What is the multiplication inverse of 1/4 A. 1.8
B. 1/2
C. 4
D 8/1
Answers
The inverse of 1/4 is 4.
Choice C
-2 (5) + 4 help plzzz
Answers
Answer:
-6
Step-by-step explanation:
-2 * 5 = -10
-10 + 4 = -6
Answer is -6
-2(5)+4
You multiply '-2' to '(5)' which equals to '-10' then you add '4' and the correct answer is '-14'
Hope this helped, my dude
16. A 20.25-gallon gasoline tank is 3/5 full. How many gallons
will it take to fill the tank?
Answers
To fill the tank, multiply 2/5 by the tank's capacity of 20.25 gallons.
Explanation:To find the number of gallons it will take to fill the tank, we need to determine how much more fuel is needed to make the tank full. We can do this by subtracting the current amount of fuel in the tank from its full capacity. The tank is 3/5 full, so the remaining amount of fuel needed to fill the tank is 2/5 of its capacity. Since the capacity of the tank is given as 20.25 gallons, we can calculate the number of gallons needed to fill the tank by multiplying 2/5 by 20.25:
2/5 * 20.25 = 8.1 gallons
Therefore, it will take 8.1 gallons to fill the tank.
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If 7x+4=37, what is the value of 14x-1
Answers
A translation is a transformation of the plane in which a a plane figure slides along a straight line, and changes its position without turning. Each point moves the same distance and in the same direction. Hence all points subjected to the same translation undergo the same displacement.
Solve the inequality
1≥−y4
Question 18 options:
a)
{y | y≥−4}
b)
{y | y≤3}
c)
{y | y≤−4}
d)
{y∣∣y≥−14}
Answers
Answer:
Step-by-step explanation:
1≥−y4
multiply by : -1 -1 ≤ 4y means : 4y ≥ -1
divid by 4 : y ≥ -1/4 answer : d
If n represents a number then write an expression for a number that’s twice than n
Answers
Final answer:
An expression for a number that's twice another number represented by n is written as 2n.
Explanation:
If n represents a number, then the expression for a number that's twice n can be written as 2n. This stems from the definition that multiplying a number by 2 effectively doubles it. To better understand this concept, consider the next statement, N=N*2, which tells us that the new value of N is twice the original value. So, if we substitute N with n, we can express a number that's twice n as 2n.
A 30-mi. stretch of highway has markers every 0.2 mi. The first marker is at the 0.2 mi. mark and the last marker is at the end of the highway at the 30 mi. mark. If n is the number of markers, which equation is true?
A. 30 • 0.2 = n
B. 30 • 0.5 = n
C. 30 • n = 0.2
D. 30 ÷ 0.2 = n
Answers
Tom buys a new phone service. It costs $20 to install, and then costs $15 a month. Write an equation to show the cost of the phone (y) for any number of months (x).
Answers
Answer:
Y=$15x+$20
Step-by-step explanation:
Which equation is equivalent to Vx+11 = 15?
x + 11 = 225
x + 121 = 225
x = 15+11
x = 15-11
Answers
The equation which is equivalent to √x + 11 = 15 is: C. √x = 15 - 11.
Given the following equation:
√x + 11 = 15.To evaluate the given mathematical equation:
How to evaluate an equation.In this exercise, you're required to evaluate the given mathematical equation. Thus, we would make x the subject of formula in the equation and then simplify as follows:
√x = 15 - 11 (equivalent)
√x = 4
Taking the square of both sides, we have:
x = 4²
x = 16.
Read more on equations here: brainly.com/question/13170908
What is n? -4n - 5 = -3n + 4
Answers
Move n terms on one side and other terms on the other side. Note that by moving we are essentially subtracting and adding to both sides so the prefix of a term changes from - to + or from + to -.
[tex]
-4n-5=-3n+4 \\
-4n+3n=4+5 \\
-n=9 \\
n=-9
[/tex]
Hope this helps.
A crayon company makes 87,491 blue crayons, 36,262 red crayons, and 25,063 gray crayons. how many more blue crayons are made than red and gray crayons combined?
Answers
Answer:
26 166
Step-by-step explanation:
Blue = 87 491
Red = 36 262
Green = 25 063
-(Red + green) = - 61 325
Blue - (red + green) = 26 166
The company makes 26 166 more blue crayons than red and green combines.
The local football team won the championship several years ago, and since then, ticket
prices have been increasing $4 per year. The year they won the championship, tickets were
$20. Write an explicit formula for a sequence that will model ticket prices. What will the ticket
price be 10 years after that championship year?
Answers
Answer:
60$
Step-by-step explanation:
if 4$ is per year 20 ÷4 is 5, 5 years have passed and if 10 uears after the champion ship it will be 60 because 4 × 10 is 40 plus the 5 years since it was 20 therefore 20+40 =60
The explicit formula for the ticket price after n years is T(n) = 20 + 4n. Plugging in 10 for n, we find that the price 10 years after the championship will be $60.
Explanation:The question asks us to create an explicit formula to model the increasing price of football tickets after the local team won a championship. If tickets were originally $20 and the price increases by $4 each year, we can use the formula T(n) = 20 + 4n to represent the price of football tickets after n years.
For 10 years after the championship year, we plug 10 into our equation for n: T(10) = 20 + (4 \times 10) = 20 + 40 = $60. Thus, the ticket price will be $60, 10 years after the championship year.
If Tim's top priority is to become famous, his most likely long-term goal is to
become a(n).
Answers
Answer:
Music artist
Why:
Well, if this wasn't the question please explain to me what I'm answering!
5(b+6)=18
solve this, please...!
Answers
Answer:
b = - [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Given
5(b + 6) = 18 ← distribute left side
5b + 30 = 18 ( subtract 30 from both sides )
5b = - 12 ( divide both sides by 5 )
b = - [tex]\frac{12}{5}[/tex] = - 2.4
Good evening
_______
Answer:
b= -12/5
_______________
Step-by-step explanation:
5(b+6)=18
5b+30=18
5b=18-30
5b=-12
b= -12/5.
:)
A 8-oz jar of peanut butter costs $3.18. What is the cost per ounce?
Answers
$3.18 / 8 ounces = $.3975 = $.40 per ounce
Jason needs 3.75 tons of concrete for university path. if his truck holds 1.5 times how many trips most he make?
Answers
Answer:
2 and a half trips?
Step-by-step explanation:
i did 3.75/1.5 and got 2 .5 soooo i think thats it.
Answer:
Three
Step-by-step explanation:
[tex]\begin{array}{rcl}\\\text{Number of tons} & = & \text{Number of trips} \times \dfrac{\text{number of tons}}{\text{1 trip}}\\\text{3.75 t} & = & \text{Number of trips}\times \dfrac{\text{1.5 t}}{\text{1 trip}}\\\dfrac{3.75}{1.5} & = & \text{Number of trips}\\\text{Number of trips} & = & 2.5\\\end{array}[/tex]
Jason can't make 2.5 trips.
He can make two trips carrying a full load and another trip carrying a half-load.
That makes three trips.
I also need some help on this part of the geometry homework.please help me if you can.
Answers
Answer:
They are mirrored
Step-by-step explanation:
When you cut it in half horizontally you can see both sides are mirrored so the lines have the same length
Ryan transformed figure S into similar figure S′.
What scale factor did he use for the dilation?
A. 1/3
B. 1/2
C. 2
D. 3
Answers
Answer:
D. 3
Step-by-step explanation:
Rectangle S is ½ by 1½, so tripling each dimension would give you S':
½ x 3 = 1½
1½ x 3 = 4½
1½ x 4½ are your new dimensions, and are genuine dimensions!
I am joyous to assist you anytime.
Diego Rollins is paid $10.20 an hour for a regular 40-hour week at the
driving range. His overtime rate is 15 times his regular hourly rate.
This week he worked his regular 40 hours plus 8 hours of overtime.
Vhat is Diego's total pay?
Answers
Answer:
$1632
Step-by-step explanation:
Hourly pay for Diego = $10.20
Weekly hours = 40 Hours
Basic earning = 10.20 × 40 = $408
Overtime pay = 15 × Hourly rate = 15 × 10.20 = $153
Total overtime = 8 hours
Overtime earning = 153 × 8 = 1224
Total earning for the week = 408 + 1224 = $1632
In a department store, a $40 dress marked, "save 25%." what is the discount? what is the sales price of the dress?
Answers
Answer:
Discount = $10
Sales Price = $30
Step-by-step explanation:
Discount
= 25% of marked price
= 25% x $40
= (25/100) x 40
= $10
Sales price = Marked price - Discount = $40 - $10 = $30