The simplest form of the expression is determined by solving the fractional exponent.
If an exponent of the base (number) is expressed in a fraction, it is called a fractional exponent. In an expression say x^1/y, 1/y is the fractional exponent. Fractional exponent represents the power and root together.
In the given expression, the base term is -32y^15, while the exponent is 1/5.
Since, (ab)^m=a^mb^m
Hence, (-32y¹⁵)^¹/₅=(-32)^1/5*(y^15)^1/5
When a base number has a negative sign, and the power is an odd number, the negative sign is extracted.
(-32)^1/5*(y^15)^1/5=-(32)^1/5*(y^15)^1/5
Since, (a^m)^n=a^m*n
-(32)^1/5*(y^15)^1/5=-32^1/5y^15*1/5
As 32=2*2*2*2*2=2^5
The expression becomes.
-(2^5)^1/5*(y^15^)1/5
Multiplying the powers,
-(25)^1/5*(y^15)^1/5=-(2^5*1/5)(y^15*1/5)=-2y^3
The simplest form of expression is (-32y¹⁵)^¹/₅ is -2y^3.
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At a gymnastics competition, each competitor performed one gymnastics routine. Each routine was at least 3 minutes long, but not longer than 7 minutes. Write a double inequality to represent the possible length, b, of a gymnastics routine at the competition in minutes.
We need to know about inequality to solve the given problem. The double inequality to represent the possible length of a gymnastics routine is given by 3≤b≤7.
Inequality is a realtion which makes comparison between numbers or other expressions. Double inequality means when two or more inequalities are joined together. Here in this question we know that each gymnastic routine is at least 3 minutes long. We assume that the length of a gymnastic routine is b, then we can say from the given information 3≤b. It is also said that no gymnastic routine is longer than 7 minutes, so maximum length of any gymnastic routine is 7 minutes, we can write it as, b≤7. Joining these two inequalities we get the double inequality which describes the possible length of a gymnastic routine.
3≤b≤7
Therefore using the concept of inequality we found the double inequality for possible length of gymnastic routine which is 3≤b≤7.
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Least to greatest x-1, V26, 24/5
V 26
1
<
24
5
Step-by-step explanation:
Scarlett is deciding between two parking garages. garage a charges an initial fee of $11 to park plus $5 per hour. garage b charges an initial fee of $8 to park plus $6 per hour. let a a represent the amount garage a would charge if scarlett parks for t t hours, and let b b represent the amount garage b would charge if scarlett parks for t t hours. write an equation for each situation, in terms of t , t, and determine the hours parked, t , t, that would make the cost of each garage the same.
The number of hours parked for the cost of each garage to be the same is 3 hours.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let t represent the number of hours parked at either garage A or garage B. Hence:
Total charges at garage A (A) = 5t + 11
A = 5t + 11
Total charges at garage B (B) = 6t + 8
B = 6t + 8
If both garages have the same cost:
5t + 11 = 6t + 8
t = 3
The number of hours parked for the cost of each garage to be the same is 3 hours.
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What is an equivalent form of 15(p + 4) − 12(2q + 4)?
15p − 24q + 12
15p − 24q + 8
60p − 72q
−9pq
Answer:
=15p+60-24q-48=15p-24q+12
it's the first one
The equivalent form of the given expression will be 15p - 24q +8. Hence, the first option is correct.
What is an Expression?In mathematics, expressions are assertions that must contain at least two words with variables or terms with numbers in them, or both, and connect them with an operator. It is possible for the mathematical operators to be addition, subtraction, multiplication, or division.
For instance, the equation (x+y) has the terms x and y with an addition operator in between. Numerical expressions, which just contain numbers, and algebraic expressions, which also include variables, are the two types of expressions used in mathematics.
The given expression in the question,
15(p + 4) - 12(2q + 4)
15p + 60 - 24q - 48
15p - 24q + 12.
Hence, it is proved that the equivalent form of the expression is 15p - 24q + 12.
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An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
The number of outcomes in the sample space is 25
First time taking the tile out of urn and marking it down, the possibilities are 1,2,3,4,5
After replacement of the tile, once again there are 5 tiles in the urn.
Second time taking the tile and marking it down, the possibilities are 1,2,3,4,5
The sample space is set of all possibilities, which is
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,3),(2,4),(2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(4,1),(4,2),(4,3),(4,4),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5)}
S=25
The number of outcomes in the sample space is 25
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10)
12
√144
Write the answer as a prime number base ?
Answer:
144
Step-by-step explanation:
12√144
12 × 12
=144
For a number to be classified as a prime number, it should have exactly two factors. Since 144 has more than two factors, i.e. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, it is not a prime number.
The size of a computer monitor is given as the length of the screen's diagonal d in inches. The equation d=5/6√3A models the length of a diagonal of a monitor screen with area A in square inches.
b. Suppose you want to buy a new monitor with a screen that is twice the area of your old screen. Your old screen has a diagonal of 15 inches. What will be the diagonal of your new screen?
The diagonal of the new screen is approximately 21.21 inches.
The diagonal is a straight line that joins two opposite sides of a quadrilateral(polygon with 4 sides).
The length of the diagonal of the square is given as d=5/6√3A where A is the area of the square.
Now when diagonal d=15 cm then we substitute the value of d=15 to calculate area A of the square.
15=5/6√(3A)
or, 3A=15²×6²÷5² (squaring both sides)
or, A=108 square inches
The new monitor has an area of twice the old monitor.
Area of the new monitor =2×108 square inches=216 square inches.
Now we use the value of A=216 to calculate the value of diagonal d for the new monitor.
d=5/6√(3×216)
d=21.213.. inches
Therefore the diagonal of the new screen is approximately 21.21 inches.
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a candidate was to subtract 15 from a certain number but mistakenly added 25 and his answer was 145 calculate the percentage error correct to 1 decimal places
The percentage error of the candidate is 38.1%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, and the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.So, the percentage error:
Let x be the specified number.What he ought to have received is x-15.What he actually obtained is given as x+25, which equals 145.Now,
x+25 = 145x = 120He ought to have received x-15 = 120-15 = 105.
Percentage error = [(what he actually got - what he should have gotten)/what he should have gotten] × 100Percentage error = [(145 - 105)/105] × 100 = 38.1%Therefore, the percentage error of the candidate is 38.1%.
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can anyone help me out?
The value of x and y from the given angles 6x - 25, y and 4x + 15 will be x = 20 and y = 85 degrees.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
The angles are given that 6x - 25, y and 4x + 15
WE can see that the angles 6x - 25 and 4x + 15 are vertically opposite angle, then
6x - 25 = 4x + 15
6x - 4x = 25 + 15
2x = 40
x = 20
Now by linear pair we get
y + 4x + 15 = 180
y + 4(20) + 15 = 180
y = 180 - 80 - 15
y = 100 - 15
y = 85
Therefore, the value of x and y from the given angles 6x - 25, y and 4x + 15 will be x = 20 and y = 85 degrees.
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CHOOSE THE CORRECT INEQUALITY !! HELP PLEASE :))
What is the value of the expression 2x² - 7x +3
when x = -4?
A. -1
B. -57
C. 63
D. 7
I did it with a calculator and got 63
m∠WYX = (2x − 7)° and m∠WYZ = (3x + 2)°. If ∠WYX and ∠WYZ are complementary,
what is the measure of each angle?
A) m∠WYX = 67°; m∠WYZ = 113°
B) m∠WYX = 27°; m∠WYZ = 63°
C) m∠WYX = 31°; m∠WYZ = 59°
D) m∠WYX = 63°; m∠WYZ = 117°
The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
What are complementary angles?Complementary angles are defined as angles that sum up to 90 degrees.
Example:
If x and y are complementary angles, then;
x + y = 90°
From the information given, we have the angles;
m∠WYX = (2x − 7)° m∠WYZ = (3x + 2)since they are complementary, then;
2x - 7 + 3x + 2 = 90
collect like terms
2x + 3x = 90 + 5
Add like terms
5x = 95
Make 'x' the subject of formula
x = 95/5
x = 19
But;
m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°
m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°
Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C
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Between 10 P.M. and 7:36 A.M., the water level in a swimming pool decreased by 6/25 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Answer:
The water level drop in temperature per hour is 40 °C per hour
Unit rate
Hours between 10 P.M. and 7:36 A.M = 9 hours 36 minutes
= 9.6 hours
The total decrease in temperature = 6/25
The unit rate of decrease in temperature per hour = Hours between 10 P.M. and 7:36 A.M ÷ Total drop in temperature
= 9.6 ÷ 6/25
= 9.6 × 25/6
= 240/6
= 40 °C per hour
Therefore, the water level drop in temperature per hour is 40 °C.
14-3m=4m
what is the value of m?
Answer:
2
Step-by-step explanation:
Which is the logarithmic form of the exponential equation 2³=8 ?
(A) logB 2=3
(B) log₈ 3=2
(C) log₃ 8=2
(D) log₂ 8=3
The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=3 .
In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.
The general properties of logarithm for a fixed base are:
logₐa=1logₐx+logₐy=logₐxylogₐx-logₐy=logₐ(x/y)logₐxⁿ=n logₐxlogₓy=(logₐy)/(logₐx)The given exponential equation is 2³=8.
To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.
Taking log₂ on both sides of the equation we get:
log₂(2³)=log₂(8)
Now we know from the properties of logarithms
logₐxⁿ=n logₐx
therefore:
3×log₂(2)=log₂8
Now logₐa=1, so
3×1=log₂8
or, log₂ 8 = 3
Therefore the required logarithmic equation is log₂ 8 = 3.
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Someone pls help! 3x ^2 and x = 10 pls help!
Answer:
300
Step-by-step explanation:
Because of PEMDAS (Order of Operations), you would do the exponent first.
So, 3(x)^2 and 3(100)
Then you get 300
Hope this helps!
Answer:
300
Step-by-step explanation:
3(10^2)
3(100)
300
Find the number that makes the ratio equivalent to 1:5.
5:
Answer:
25
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] = [tex]\frac{5}{x}[/tex] On the top, you need to multiply 1 by 5 to get 5, so multiply the bottom number 5 by 5 to get 25.
Select the correct texts in the passage.
Julian factored the expression 2x4 + 2x³ x²-
At which step did Julian make his first mistake, and which statement describes the mistake?
Step 1
Step 2
Step 3
=
=
2x² + 2x³
x(2x²
= C
-
-
x²
x(2x³ + 2x² x − 1)
-
x (2x² (x + 1))
-
-
- X
-
-. His work is shown.
- 1(x − 1)
1) (x + 1)(x - 1)
Julian should have factored (2x²
Julian incorrectly factored -1 from the second group of terms.
Julian should have factored 2x from all terms instead of x.
Julian incorrectly factored 2x2 from the first group of terms.
1) as a difference of squares.
Julian factored the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the
step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex]) statement is wrong statement.
Julian should have factored (2*2-1) as a difference of squares.
Julian incorrectly factored -1 from the second group of terms.
Julian should have factored 2x from all terms instead of x
Julian incorrectly factored 2*2 from the first group of terms
The expression is, [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]
Factors greatest common factors out,
= [tex]x(2x^{3} +2x^{2} -x-1)[/tex]
Regroup terms into two proportional parts,
= [tex]x((2x^{3} +2x^{2} )+(-x-1))[/tex]
Factor the expression,
= [tex]x(2x^{2} (x+1)+(-x-1))[/tex]
= [tex]x(2x^{2} (x+1)-(x+1))[/tex]
= [tex]x(x+1)(2x^{2} -1)[/tex]
Hence, we can write,
= [tex]2x^{4} +2x^{3} -x^{2} -x[/tex]
= [tex]x(2x^{3}+2x^{2} -x-1)[/tex]
So step 1 is correct.
= [tex]x(2x^{2} (x+1)-(x+1))[/tex]
Then, step 2 is wrong.
Therefore, the expression of [tex]2x^{4} +2x^{3} -x^{2} -x[/tex], then the
step 2 ( [tex]x(2x^{2} +1)) -1(x-1)[/tex] )statement is wrong statement.
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Answer:
Julian should have factored (2x^2-1) as a difference of squares.
Step-by-step explanation:
Quincy was stuck inside for an hour during a storm. He spent 20 minutes reading, 18 minutes
eating lunch, 12 minutes watching television, and 10 minutes drawing.
Match the following ratios to what they describe.
Description
The ratio of time inside to time eating lunch
The ratio of time eating lunch to time watching television
The ratio of time reading to time drawing
Ratio
2:1
10:3
3:2
The ratio of time inside to time eating lunch Ratio: 3:2
The ratio of time eating lunch to time watching television Ratio: 10:3
The ratio of time reading to time drawing Ratio: 3:2
What is the ratio?
A ratio is a mathematical comparison between two numbers that indicates how many times one value is contained within the other.
Description: The ratio of time inside to time eating lunch
Ratio: 3:2
Description: The ratio of time eating lunch to time watching television
Ratio: 10:3
Description: The ratio of time reading to time drawing
Ratio: 3:2
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Answer:
the ratio of time inside to time eating lunch 10: 3
the ratio of time eating lunch to time watching television 3:2
the ratio of time reading to time drawing 2:1
Step-by-step explanation:
I got it wrong following the other person this is what Khan academy says is correct.
Evaluate the following.
||-2|-|3-12||
Answer:
7
Step-by-step explanation:
You want the value of the expression ||-2|-|3-12||.
EvaluationInner groups are evaluated first:
||-2|-|3-12|| = |2 -|-9||
= |2 -9|
= |-7| = 7
The value of the expression is 7.
__
Additional comment
The absolute value function changes negative signs to positive:
|-2| = 2
It has no effect on positive signs.
|2| = 2
Solve for y. −140=18+20y−8
The solution for the variable y according to the one-variable equation given in the task content is; y = -7.5.
What is the solution for the variable y according to the given equation in the task content?It follows from the task content that the equation which is given in the task content and from which the variable y is to be determined is;
−140 = 18 + 20y − 8.
Hence, the equation can be solved as follows;
−140=18+20y−8
Evaluate each side of the equation;
-140 = 10 + 20y
Subtract 10 from both sides;
-150 = 20y
Divide through by 20; we have;
-7.5 = y.
Ultimately, the solution for the variable y as required in the task content is; y = -7.5.
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Evaluate the following expression
Find 2x - 3y - z if x = -2, y = 3, and z = -2
Answer:
-11
Step-by-step explanation:
2x - 3y - z
2(-2) - 3(3) - (-2)
-4 -9 +2
-13+2
-11
Answer:
-11
Step-by-step explanation:
What we are solving for: 2x - 3y - z
x = -2
y = 3
z = -2
We can just plug in the variables.
[tex](2*-2) - (3*3) - (-2)[/tex]
[tex]-4-9+2[/tex]
Therefore, the answer is -11.
Hope this helped!!
how can I cheat on ixl other than the inspect element or a person to help me.
Answer:
Don't cheat, there is your answer.
Step-by-step explanation:
Two financial institutions offer different deals to new customers. The first bank offers an interest rate of 3% for the first year and 2% for the next two years. The second bank offers an interest rate of 2.49% for three years. You decide to invest the same amount of principal in each bank. To answer the following, assume you make no withdrawal or deposits during the three-year period.
a. Write a function that represents the total amount of money in the account in the first bank after three years.
Total amount of money in the account in the first bank after 3 years will be given by the function: P[tex]e^{0.07}[/tex].
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-
A = P[tex]e^{rt}[/tex]
Here, we are given that there are 2 financial institutions-
1st financial institution:
interest rate = 3% for the first year
and interest rate for next two years = 2%
2nd Financial institution:
interest rate = 2.49% for three years
Let the principal amount deposited be P
We assume that the interest is compounded continuously.
Then for the 1st year-Amount = P[tex]e^{0.03}[/tex]
Since, there are no withdrawals or deposits,
The Amount of the 1st year will become the principal for the second year-Amount = (P[tex]e^{0.03}[/tex]) [tex]e^{0.02 * 2}[/tex]
= P × [tex]e^{0.03}[/tex] × [tex]e^{0.04}[/tex]
= P[tex]e^{(0.03 + 0.04)}[/tex]
= P[tex]e^{0.07}[/tex]
Thus, the total amount of money in the account in the first bank after 3 years will be- P[tex]e^{0.07}[/tex].
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Elissa can do a job in 5 hours. Elissa and Lori working together
can do the same job in 2 hours. How long would it take Lori to
do the job alone?
Carrie had 34 tiles. She said that she used all of her tiles to make an array with 5 rows. Could she be correct? Explain why or why not on the lines below.
The mean height of the corn plants of variety A is 43.8 inches. Interpret the value of the mean in the situation.
Type your response in the space below.
The mean or the average height of all the corn plants is 43.8 inches.
There are various mean types in mathematics, especially in statistics.
Each mean is used to summarize a specific set of data, usually to clarify the overall magnitude and sign of the data set.The mean may be mistaken for the median, mode, or midpoint when using descriptive statistics because any of these could be referred to as a "average" (more formally, a measure of central tendency).The arithmetic mean of a set of observations is the sum of all the individual values; however, for skewed distributions, the mean could not be the same as the median or the mode.The average of the frequency distribution is given by the mean of the data set .
Hence the statement here indicates that the average height of all the plants combined is 43.8 inches
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4. The simple interest on a savings account is directly proportional to the amount of the investment.
A savings account with $6,000 earns $75.00 after 1 year. Find a mathematical model that gives the
interest Nafter 1 year in terms of the amount invested P, then calculate the simple interest after
saving an amount of $10,500.
Which function correctly describes the zeros given?
0,−1,2
A) F(x)= x(x+1)(x-2)
B) F(x)= x(x-1)(x+2)
C) F(x)= (x+1)(x-2)
D) None of these
Using the factored form of a polynomial for the given zeros, we can see that option A is the correct one, the function is:
F(x) = x*(x + 1)*(x - 2)
Which function correctly describes the zeros given?For a polynomial with the zeros:
x₁, x₂, x₃, ..., xₙ
The polynomial can be written as:
y = (x - x₁)*(x - x₂)*...*(x - xₙ)
In this case, the zeros are:
0, -1, and 2
Then we can write the polynomial as:
y = (x - 0)*(x + 1)*(x - 2)
If we simplify this, we get:y = x*(x + 1)*(x - 2)Which is the one we can see in option A, so we conclude that option A is the correct one.F(x) = x*(x + 1)*(x - 2)
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Solve each equation. log₂(x²+2 x)=3
The value of x for a given logarithmic expression is 2 or -4.
What is a logarithmic function?
Logarithmic function is the inverse of an exponential function. It is denoted by using the word, log. For example log 10 = 1.
Solving the given equation: log ₂ ( x² + 2x ) = 3
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
Now, the equation becomes,
log ( x² + 2x ) / log 2 = 3
log ( x² + 2x ) = 3 × log 2
log ( x² + 2x ) = log 2³
log ( x² + 2x ) = log 8
Applying exponent both the sides, we get,
e^[log ( x² + 2x )] = e^[log 8]
x² + 2x = 8
x² + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2 or -4
Hence, the value of x for a given logarithmic expression is 2 or -4.
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