By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.
How to rewrite a power expression according algebra properties
In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:
Step 1 - Write the original expression presented in the statement.
2⁴⁰
Step 2 - By definition of multiplication between real numbers.
2⁽⁸⁾⁽⁵⁾
Step 3 - By the definition of the power of a power.
(2⁸)⁵
The resulting expression is (2⁸)⁵.
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x^2-6x-3=(x-a)^2-b where a and b are constants.Find the values of a and b
Answer:
a = 3, b = 12
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b
Lets expand the right side:
(x-a)^2-b = (x-a)(x-a)-b
(x-a)(x-a)-b = x^2 -2ax + a^2 - b
The left side is equal to the right, as per the original equation:
x^2-6x-3 = x^2 -2ax + (a^2 - b)
Compare each term:
1) x^2 = x^2 OK
2) -6x = -2ax; a = 3 so that -6x = -2(3)x
3) -3 = (a^2-b); a^2 = (b-3)
a = [tex]\sqrt{b-3}[/tex]
a is 3, from above
3 = [tex]\sqrt{b-3}[/tex]
9 = b-3
b = 12
What is the value of the following numerical expression?
-23 +-15+|-17| + -35
A. -56
B.-26
C. 1-261
D. 56
The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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in how many ways can 4 different physics books, 3 different mathematics books, and 2 psychology books be arranged on a bookshelf if the physics books must be together and the mathematics books must be together?
Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.
Here,
There are 3 book,
3!=6
3 different mathematics books,
3!=6
4 different physics books,
4!=24
2 psychology books
2!=2
by fundamental counting principle,
6*6*24*2=1728
There are 1728 different ways to arrange the books because the mathematics and physics books must be together.
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let 0 < a < b < 1,
a) is a^x < b^x, for x>0
b) is a^x < b^x, for x<0
For 0 < a < b < 1, a^x < b^x, for x < 0.
What are inequalities and their types?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, 0 < a < b < 1.
Assuming a = 0.25 and b = 0.5.
∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.
∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.
Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.
Therefore, if 0 < a < b < 1, then a^x < b^x, for x < 0.
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41.153 to the nearest tenth
Answer:
41.2
Step-by-step explanation:
1 is in the tenths place. Because the number the next number is a five, we must round up and 0.20 is the nearest tenth to 0.153.
In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
The total number of skittles in the bag will be 65.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,
N = ( 13 / 20 ) x 100
N = 130 / 2
N = 65
Therefore, the total number of skittles in the bag will be 65.
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Feng invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $70.70. What is the simple percent interest per year?
The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.
As per the given,
Investment = $70
Investment after one year is $70.70
Interset = 70.70 - 70 = $0.70
The interest is given as = PRT/100
0.70 = PR(1)/100
R = (0.70×100)/70
R = 1%
Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".
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Linwood Marcus purchased a new couch for $878 and two end tables for $127 each. What is the sales taz
his purchase if he lives in Florida where the sales tax rate is 6 percent?
A. $57.89
B. $65.67
C. $60.30
D. $67.92
The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92
What is meant by percentage?The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and eventually vanished. The "cento" symbol was simplified to two circles divided by a horizontal line, from which the contemporary "%" symbol was formed.
The abbreviation "pct.", "pct," and sometimes "pc" are also used. A % is a dimensionless (pure) number with no unit of measurement.
Given,
Total purchase=$878
For two tables,
2×127=254
Total=878+254
=1132
6% of 1132 is,
(6/100)×1132
=$67.92
The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92
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Jorge has 20 fish for his dog sled team that he wants to divide into smaller pieces. How many pieces of fish would there be if Jorge divided each fish into tenths?
2,000
200
2
0.2
Answer:
200
Step-by-step explanation:
20*10=200
help is needed, please and thank you
Answer:
f(- 5) = 7
Step-by-step explanation:
f(- 5) means what is the value of y when x = - 5
locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7 ), then
f(- 5) = 7
The football team played 10 games and won 7 games. What was its winning percentage?
Answer:
70%
Step-by-step explanation:
Determine the length of the line segment shown.
line segment from negative 5 comma 5 to 3 comma negative 1
6 units
8 units
10 units
36 units
The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.
How to find the length of a line segment?
A line segment is defined as a line bounded by two points on a line.
The line segment from negative 5 comma 5 to 3 comma negative 1
is found by using the formula
square root of (x2-x1)² +(y2-y1)²
[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]
[tex]\sqrt{8^{2}+6^{2} }[/tex]
[tex]\sqrt{100}[/tex]
=10 units
therefore the length of the line segment is 10 units
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Is (4, 1) a solution to this system of inequalities?
3x + y ≤ 14
3x + 5y < 19
(4, 1) is the solution for the given inequalities
Given,
The system of inequalities;
3x + y ≤ 14
3x + 5y < 19
We have to find that (4, 1) is a solution to the given system of inequalities;
So,
(x, y) = (4, 1)
Then,
Substitute the values of x and y in the equation;
3x + y ≤ 14
3 x 4 + 1 ≤ 14
12 + 1 ≤ 14
13 ≤ 14
Next,
3x + 5y < 19
3 x 4 + 5 x 1 < 19
12 + 5 < 19
17 < 19
Here,
(4, 1) is the solution for the given inequalities
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Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answer:yes
Step-by-step explanation:
for every week he gets 3 cars so it can only incre ment by 3. (1,3) (2,6) (3,9) and so on.
what is the answer what is the answer what is the step by step answer to learn to do it
The approximate percentage of sales tax is 1%
A gymnastics mat priced at $53.
A cost of mat after adding sales tax = $53.53
So, the tax amount would be,
53.53 - 53 = 0.53
We need to find the sales tax percentage.
Let x be the percentage of sales tax.
x = (0.53)/(53.53) * 100
x = 0.0099 * 100
x = 0.99%
x ≈ 1%
Therefore, the approximate percentage of sales tax is 1%
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Which number should be on the bottom left stamp?
Explain what the answer is and how you got it!
The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.
What will the number be?From the first picture, we have 82 and the number below it is 4. This was gotten as:
= 8 ÷ 2
= 4
The second picture has 93 and the number below it is 3. This was calculated as:
= 9 ÷ 3
= 3
The third picture has 61 and the number below it is 6. This was calculated as:
= 6 ÷ 1
= 6
The fourth picture will be:
= 2 ÷ 2
= 1
Therefore the value is 1.
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7. If f(x) = -3x² + 2x - 1 and f(x) = -1, solve for x.
The required values are x=0 and x=2/3.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
f(x) = -3x² + 2x - 1
Substitute f(x) = -1
-1 = -3x² + 2x - 1
-3x² + 2x - 1+1=0
-3x² + 2x = 0
x( -3x+2)=0
=> x=0,
-3x+2 = 0
-3x=-2
x=2/3
The required values are x=0 and x=2/3.
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A, B , C or D ???????? help
Answer:
The Answer is B
Step-by-step explanation:
Since 1.8 times 10 is bigger than 18% meaning its the only one that would be in correct descending order.
Answer:
Pretty sure it’s A
Step-by-step explanation:
18% is 18/100 which is then .18
1/8 is .125
1.8x10 is 18
And .188 is just .188
10 plus the difference of 6 and 2
Answer: 14
Step-by-step explanation: 10 + (6-2) = 14
asking help for a friend
Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).
Given in the graph,
A(4,6) and B(3,5)
Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]
AB = [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]
= [tex]\sqrt{1^{2} +1^{2} }[/tex]
= [tex]\sqrt{2}[/tex]
= 1.414 units
Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Let midpoint of AB be C(x,y)
C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]
= [tex](\frac{7}{2},\frac{11}{2})[/tex]
= (3.5,5.5)
Hence, length is 1.414 units and midpoint is (3.5,5.5).
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Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the intercepts and then
plot the intercepts to create the graph. Label the intercepts, as well as the axis on the graph.
2x+3y=6
The slope and the intercepts of the graph are determined.
Given:
the equation is :
2x+3y=6
we first find the slope of the equation:
m = -a/b
m = -2/3
now solve the intercepts:
to find x intercept, substitute in 0 for y and solve for x.
⇒ 2x+3y=6
⇒ 2x+3(0)=6
⇒ 2x+0=6
⇒ 2x=6
⇒ x=6/2
⇒ x=3
hence we get (3,0)
now, to find y intercept, substitute in 0 for x and solve for y.
⇒ 2x+3y=6
⇒ 2(0)+3y=6
⇒ 0+3y=6
⇒ 3y=6
⇒ y=6/3
⇒ y=2
hence we get (0,2) as the intercepts.
Therefore we plot the required graph.
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What is the slope of the line that passes through the points (1, -9) and (4, -7)? Write your answer in the simplest form.
The slope of the line from the given points will be equal to 3/2 in the simplest form.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given points in the question,
(1, -9) and (4, -7).
x1 = 1 and x2 = 4
y1 = -9 and y2= -7
Slope = (x2- x1)/(y2- y1)
= (4 - 1)/(-7 - (-9))
Slope = 3/2
Therefore, the slope of the line will be 3/2.
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4) Identify all the zeros that make the function
true. f(x) = 2x² - 8
0
-2
2
-4
4
-8
The zero of the function f(x) = 2x² - 8 is ± 2.
Zeros of the function
Zero of the function means the values of x when f(x) is equal to 0. Which means that when f(x) = 0, x is a zero of the function.
Given,
Here we have the function f(x) = 2x² - 8.
Here we need to find the zero of the function.
As per the definition of the zeros of the function,
We have to apply the value of f(x) = 0, then we get,
2x² - 8 = 0
Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,
2x² = 8
Now, move the number 2 to the right hand side then it will be dividing the number 8,
x² = 8/2
x² = 4
x = √4
Therefore, the value of x is ± 2.
So, the zeros of the function is either +2 or -2.
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A line passes through points
(8, - 2) and
(-5, 7). Which ratio can be used to determine the slope of the line?
7+2/
8+5
7-2/
-5-8
8+5/
-2+7
7+2/
-5-8
Answer:
7+2/8+5
Step-by-step explanation:
the chief of police in statville wanted to estimate the number of people above the age of 181818 who are using illegal substances in town. he obtained 200200200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse. once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances. what type of statistical study did the chief of police use?
The chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
In the given question,
The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.
He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.
Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.
We have to explain what type of statistical study the chief of police use.
In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take 200 random names from a computer database. That means he take the sample of 200 random people.
As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
So we can say that the chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
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Answer: Sample Study
No because there’s a great risk of obtaining biased answers.
Is this rat correct tell me tell me NOWWWW teehee
Answer:
No , x = -2
Step-by-step explanation:
When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.
So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect
The correct Answer is
[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 7 minutes and you record the data point of (14,y), what is the value of y? Use slope to justify your answer.
The value of y which the slope formula is 34.
What is slope?Slope can be defined as the rate of change of a body.
To calculate the value of y, we use the formula below.
Formula:
ΔL/t = y/x........... Equation 1Where:
ΔL = Rise in the Level of watert = TimeFrom the question,
ΔL = 17 cmt = 7 minutesx = 14Substitute these values into equation 1 and solve for y
17/7 = y/14y = (17×14)/7y = 17×2y = 34Hence, the value of y is 34.
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pls help ASAP
just fill the blank
Answer:
Use the formula to find distance
ABC is and isosceles triangle. ACDE is a parallelogram. Find BCD
angle bcd is 140. see explanation in image
g(x) = x-2
What is the Parent function and transformation
The parent function is y = x ; shift 2 units downwards.
Given,
In the question:
The function is :
g(x) = x - 2
Now, According to the question ;
Let's know
What is the Parent function and transformation?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
According to the above statement is;
g(x) = x -2
Hence, The parent function is y = x ; shift 2 units downwards.
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