The give expression can be written in the simplest form by solving the exponents.
The rules applicable to the expression are rule for negative exponent and power rule of exponents. Either one can be used first. In this case we will multiply the exponents and then solve for the negative exponent.
According to the power rule of exponents, when an exponential expression is raised to a new power, the exponents are multiplied i.e. (a^x)^y=a^xy
(x^2/3)^-3=x^(2/3)*-3=x^-2
According to the rule of negative exponents, the term with the negative exponent can be solved by expressing it as a reciprocal of the term i.e. a^-x=1/a^x
x^-2=1/x^2
The simplest form of the expression (x^2/3)^-3 is 1/x^2.
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z(4−1/2)+4 help please :(((
Answer:
7/2z +4
Step-by-step explanation:
z(4-1/2)+4
=7/2z +4
Answer:
7.5
Step-by-step explanation:
Remove parentheses; z=4-1/2+4
Add the 4s: -1/2+8
convert to fraction: 8*2/2-1/2
combine fractions:8*2-1/2
8*2-1=15
15/2
now convert 15/2 to a decimal, boom, 7.5
At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level.
(a) The expression to represent the difference between the elevations is 5764 - ( - 9).
(b) The answer will be a positive integer.
(c) The difference between the highest and lowest point is 5773 feet.
The elevation of a county is 5764 feet above sea level.
The elevation of the county is 9 feet below sea level at the lowest point.
(a) The highest point = 5764 feet
The lowest point = 9 feet
Then the difference between the highest and the lowest point will be:
difference = Highest - lowest
difference = 5764 - ( - 9)
(b) The answer will be written as a positive integer.
(c) The difference between the highest and lowest points of the county will be:
difference = Highest - lowest
difference = 5764 - ( - 9)
difference = 5764 + 9
difference = 5773 feet
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The complete question is mentioned below:
At its highest point, the elevation of a county is 5764 feet above sea level. At its lowest point, the elevation of the county is 9 feet below sea level. Answer parts (a) through (c).
a. Write an expression using integers to represent the difference between the elevations.
b. Will the answer be written as a positive or negative integer?
c. What is the difference between the highest and lowest points of the county?
(x, y) → (x + 5, y − 4), what are the coordinates of point L′?
Answer: (5,-4)
Step-by-step explanation:
start at zero and go right five because of the adding of five
Then go down 4 because of the minus of zero.
3 (x - 17) < 9 (1 - 3x)
Answer:
x < 2
Step-by-step explanation:
3(x- 17) = 3x - 51
9(1-3x) = 9 - 27x
3x - 51 < 9 - 27x
30x - 51 < 9
30x < 60
X < 2
Landon wants to ride his bicycle 36 miles this week. He has already ridden 4 miles. If he rides for 4 more days, write and solve an equation which can be used to determine mm, the average number of miles he would have to ride each day to meet his goal.
The average number of miles he would have to ride each day to meet his goal is 8 miles
Writing an EquationFrom the question, we are to write an equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal
From the given information,
Landon wants to ride his bicycle 36 miles this week and he has already ridden 4 miles.
The average number of miles, m, he would have to ride for 4 more days to meet his goal is
m = (36- 4)/4
This is the equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal
Now, determine m
m = (36 - 4)/4
m = 32/4
m = 8
Hence, the average number of miles he would have to ride each day to meet his goal is 8 miles
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Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1) Start: 3 End: 10
2) Start: 9 End: 20
3)Start: 100 End: 85
The percent increase or decrease of the starting and ending quantities below are:
233%122%-15%How to find the percent increase?The percent increase can be found by the formula:
= (End - Start) / Start x 100%
The percent increase of these quantities are:
= (10 - 3) / 3 x 100%
= 7 / 3 x 100%
= 2.3333 x 100%
= 233%
= (20 - 9) / 9 X 100%
= 11/9 x 100%
= 1.222 x 100%
= 122%
= (85 - 100) / 100 x 100%
= -15 / 100 x 100%
= -15%
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from x-2 subtract 4x +9
Answer:
I'm pretty sure it is -3x+7
Rebecca collected data and told you that her sample mean was 56 and her sample median was 64. She then draws a histogram based on her data and asks you to guess the shape of it without looking. What would the most likely shape be for her histogram?.
The histogram based on the data distribution where sample mean is less than sample median, the histogram would be skewed to the left.
Histogram is a type of visual (graphical) representation a set of data arranged in a user specific range. It is used summarize data – both discrete and continuous, measured on a interval scale.
When a data whose mean value or average value is less than the median or middle term in an ordered set is represented by a histogram, the shape of the histogram would be skewed to the left. Most of the data in such a histogram will be on the right side of the graph.
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Need help please with math
The equation for red graph is y= f(x-1)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
y = f(x)
Here if look at the graph with black with function f(x) = x
Now, if we look at the graph closely to shift the black graph to red.
There is shifting the graph in the right hand side which which gives the function y= f(x-1)
Hence, the equation for red graph is y= f(x-1)
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What is the value of each logarithm?
b. log₄32
The answer for the given logarithmic function is 5/2
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
loga where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logabc where a is the base is given as logab+logc
loga b/c where a is the base is given as logab-logac
Now it is given to us to find the value of log₄32
where 4 is the base and 32 is the argument
We know that logₐb can be written as log₂b/log₂a
using this identity of logarithm,
our question becomes log₂32/log₂4
32 = 2x2x2x2x2 which is
hence can be written as 2^5
Thus the logarithmic function becomes
log₂2^5/log₂2^2=5log₂2/2log₂2
thus it becomes 5/2
Aa log2/log2 becomes 1
Thus log₄32= 5/2
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i'm stuck on the 'use exact numbers' portion of this .. the equation i came up w/ is: y=2/3x+4 but i know that the 2/3 has to be an exact number .. but how? if i were to divide both of them by 2, i get 1/1.5 ... do i round 1.5 up to 2?
The equation will be 3 y = 2 x + 12 for the graph given.
We are given a graph of the equation.
We need to find the equation of the graph.
Now, first we will see the x and y intercept of the graph.
So, we get that:
x intercept:
( - 6 , 0)
y intercept:
(0 , 4)
Now, we know that equation of the line is given by:
y = a x + b … (1)
Put the points in the equation:
for (-6 , 0)
0 = - 6 a + b
6 a = b … (2)
for (0 , 4)
4 = b
Put in (2)
6 a = 4
a = 4 / 6
a = 2 / 3
Put in equation (1):
y = 2 / 3 x + 4
y = ( 2 x + 12 ) / 3
3 y = 2 x + 12
Therefore, we get that, the equation will be 3 y = 2 x + 12 for the graph given.
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At a party store, packages of 12 noisemakers are $2 each. Packages of 9 party hats are $15 each. Mia wants to buy equal numbers of noisemakers and hats.
To get that many noisemakers and hats: How many packages of noisemakers does Mia need to buy?
How many packages of hats? Explain.
Expand each binomial.
(2 x-y)⁴
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (2x - y)⁴
By using binomial expansion theorem, we get
(2x - y)⁴ = 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴
(2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴
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The radius of a circle can be expressed as r=√A/π inches where r is the radius and A is the area of the circle. If the area of a circle is 169 π in.², what is its radius?
The radius is 169 inches.
As per the known fact, the radius and area of circle are related by the formula -
Area = πr²
So, rewriting the expression in equation -
r=√(A/π)²
As mentioned, r is the radius and A is the area of the circle and π is constant
Keep the value of A in the above mentioned rewritten equation to find the value of radius of circle.
r = √(169π/π)²
On solving the above equation we get the new equation, which is as follows -
r = 169π/π
Cancelling π as it is common in both numerator and denominator
r = 169 inches
Hence, the radius of circle is 169 inches.
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Find the value of x.
Answer:
28 = x
Step-by-step explanation:
We have two similar triangles. The ratio of the sides must be in the same proportion
12 8
------- = -------
x-7 14
Using cross products
12 * 14 = 8(x-7)
168 = 8(x-7)
Divide each side by 8
168/8 = 8(x-7)/8
21 = x-7
Add 7 to each side
21+7 = x-7+7
28 = x
whats the awnser for
$4.98 divied by 24oz
Answer:
0.2075
Step-by-step explanation:
Or $0.2075 per oz
Please answer the question in the photo! [ brainliest ] (20 points)
Answer:
1/4
Step-by-step explanation:
or 90/360
plss help me with this
Answer:
Below in bold.
Step-by-step explanation:
7x - 2 + 9x - 2 + 2(5x) = 2(5x + 5) + 2(4x)
7x + 9x + 10x - 4 = 10x + 10 + 8x
7x + 9x + 10x - 10x - 8x = 10 + 4
8x = 14
x = 14/8 = 7/4
So, ST = 5*7/4 + 5
= 55/4
= 13 3/4
Answer:
ST = 13.75
Step-by-step explanation:
The perimeter of a trapezium is calculated with the following formula:
P = a + b + c + d (a, b: bases, c, d: sides)
The perimeter of a rectangle is calculated with the following formula:
P= 2(a + b) (a: base, b: side)
we will write the following equation to find the length of ST
7x - 2 + 9x - 2 + 5x + 5x = 2(5x + 5 + 4x) first do the inside the parenthesis
2(9x + 5) = 18x + 10
Now,
7x - 2 + 9x - 2 + 5x + 5x = 18x + 10 add like terms on the left side of the equation
26x - 4 = 18x + 10 transfer like terms to the same side of the equation
26x - 18x = 10 + 4 add/subtract
8x = 14 divide both sides by 8
x = 1.75 replace x with this to calculate the lentgh of ST
5x + 5 = 5*(1.75) + 5 and ST = 13.75
Japhet is making small rectangular tiles for a mosaic. each tile has an area of 7 cm 2 and is 1 1/4 cm wide. how long is each tile?
Answer:
28/5
Step-by-step explanation:
7 x 4/5 = 28/5
use keep, change, flip
Answer:
28/5
Step-by-step explanation:
just did it on khan academy.
Find the LCM of 2 and 6 using lists of multiples.
Answer:
6
Step-by-step explanation:
2,4,6,8,10
6,12,18,24
The least number that is on both lists is 6
On Monday, 12 people took 5 hours to clean a number of cars. On Tuesday, 15 people cleaned the same number of cars. Assuming that all the people worked at the same rate,
work out how many hours the 15 people took to clean the cars.
The number of hours the fifteen people took to clean the cars is 4 hours.
Given that, on Monday, 12 people took 5 hours to clean a number of cars. On Tuesday, 15 people cleaned the same number of cars.
What is the rate of work?The rate of doing work is equal to the rate of using energy since the force transfers one unit of energy when it does one unit of work.
Assuming that all the people worked at the same rate, work out how many hours the 15 people took to clean the cars.
Now, based on the given conditions, formulate 12 × 5 ÷ 15
= (12 × 5) ÷ 15
= 60 ÷ 15
= 4 hours
Therefore, the number of hours the fifteen people took to clean the cars is 4 hours.
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8.2/3 of the students in a class are boys, 3/4 of the boys are right-handed There are 18 right-handed boys. How many students are there in the class?
Answer:
36
Step-by-step explanation:
3/4x = 18 multiply both sides by 4/3
(4/3)(3/4)x = (18/1) (4/3)
x = 24 There are 24 boys in the class.
2/3x = 24 Multiply both sides by 3/2
(3/2)(2/3)x = (24/1)(3/2)
x = 36
By solving a linear equation , we get the total number of students in the class are 36
What is a linear equation in one variable?An linear equation is a mathematical statement consists of expressions of only one variable that too with power 1 and constants and compares two such expressions by equating them.
Standard form of linear equation in one variable : ax +b = c
x = (c-b)/a
Let the total number of students in the class are x
Given that 2/3 of the students in a class are boys
∴ The number of boys = 2/3(x) =(2x)/3
Then given that 3/4 of the boys are right handed and there are 18 right-handed boys
∴ 3/4( no of boys ) =18
⇒3/4 *(2x/3) =18
⇒(3*2x)/(4*3) =18
⇒x/2 =18
Multiplying both sides by 2
⇒x = 2*18 = 36
Therefore, the total number of students in the class are 36
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Question 15
The recipe calls for 3/4 cup of brown sugar. Neih is trying to half the recipe. How much brown sugar should she use?
O 1/2 cup
O 3/8 cup
O 1/4 cup
O 1 and 1/8 cup
Answer:
3/8 cup
Step-by-step explanation:
You simply divide 3/4 by 2 and get a 0.375
We turn the decimal into a fraction and get 375/1000 then simplify the fraction to 3/8
Find the GCF of
12 and 54
Answer: GCF = 6
Step-by-step explanation:
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
Then the greatest common factor is 6.
a bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. after 4 hours there will be 2640 bacteria. (a) express the population after t hours as a function of t. population: equation editor (function of t)
Answer:
T=x(T*2) where X=660
Step-by-step explanation:
If it has been 2 hours than t=2
plug in 2 for t and you get x*4
SUPER URGENT!!!
Joel sells ice cream cones at the county fair. He has to rent the equipment for $36 and spend $0.52 on ingredients for each cone. What is the minimum number of ice cream cones Joel must sell at $1.40 each in order to make a profit?
Please explain ALL OF THE STEPS, or your answer is useless. Thanks!!
Denote by x the number of cones sold or produced.
Denote by C(x) the total cost.
Denote by R(x) the revenue made.
Denote by P(x) the net profit accumulated.
[tex]C_{T}(x)=C_{fixed}+C_{variable} \: \\ C_{T}(x)=36+0.52x[/tex]
[tex]R_{T}(x)=selling \: price \: x \\ R_{T}(x)=1.4x[/tex]
[tex]P(x)=R_{T}(x)-C_{T}(x) \\ P(x)=1.4x-(36 + 0.52x) \\ P(x)=1.4x - 36 - 0.52x \\ P(x)=0.88x - 36[/tex]
If there exists profit, then P(x) has to be positive.
[tex]P(x) > 0 \\ 0.88x - 36 > 0 \\ 0.88x > 36 \\ x > \frac{36}{0.88} \\ x > 40.90909 \\ x = 41[/tex]
Do All sides of a parallelogram have the same length.
Answer:
Step-by-step explanation:
No, They do not.
Answer:
All sides of a parallelogram have the same length.
Step-by-step explanation:
A parallelogram can have one pair or two pairs of parallel sides. All sides of a parallelogram have the same length. All angles of a parallelogram have the same measure.
Write 750 in scientific notation
Answer:
7.5 × 10[tex] {}^{2} [/tex] (scientific notation)
Step-by-step explanation:
➟ 750 = 7.5 × 10[tex] {}^{2} [/tex] (scientific notation)
What are the steps for divide in one bye one
Which expression is equivalent to (5x−5y3)−2?
whoever gets it right gets a crown!!
Step-by-step explanation:
5 minus 5 is 0,then 3 minus 2 is 1,therefore the answer is 1xy