Simplify each exponential expression using the properties of exponents and match it to the correct answer.
Answers
Answer:
2: B, D1: A1/2: CStep-by-step explanation:
Here are the relevant rules of exponents:
[tex]a^{-b}=\dfrac{1}{a^b}\\\\a^0=1\\\\(a^b)(a^c)=a^{b+c}\\\\(a^b)^c=a^{bc}\\\\(ab)^c=(a^c)(b^c)[/tex]
ApplicationWe can use 4 = 2² and 6 = 2·3 to expand each of the given expressions into powers of 2 and 3.
[tex]\boxed{\dfrac{3^{-3}\cdot2^{-3}\cdot6^3}{(4^0)^2}}=\dfrac{3^{-3}\cdot2^{-3}\cdot(2\cdot3)^3}{((2^2)^0)^2}=2^{-3+3-0}\cdot3^{-3+3}=1\cdot1=\boxed{1}[/tex]
[tex]\boxed{\dfrac{3^2\cdot4^3\cdot2^{-1}}{(3\cdot4)^2}}=\dfrac{3^2\cdot(2^2)^3\cdot2^{-1}}{3^2\cdot(2^2)^2}=2^{6-1-4}\cdot3^{2-2}=2\cdot1=\boxed{2}[/tex]
[tex]\boxed{\dfrac{2^4\cdot3^5}{(2\cdot3)^5}}=\dfrac{2^4\cdot3^5}{2^5\cdot3^5}=2^{4-5}\cdot3^{5-5}=2^{-1}\cdot1=\boxed{\dfrac{1}{2}}[/tex]
[tex]\boxed{\dfrac{(3\cdot2)^4\cdot3^{-3}}{2^3\cdot3}}=2^{4-3}\cdot3^{4-3-1}=2\cdot1=\boxed{2}[/tex]
Related Questions
The owner expects you to hand wash each coffee pot before the coffee shop opens. It takes 10 minutes for all of the coffee pots to dry. You spend 82 minutes washing and drying the pots. It takes 4 ½ minutes to clean a coffee pot. How many coffee pots are there? (you only need to put the number)
Answers
step by step explanation:
What is the solution to the equation 4x + 2(x − 2) = 4x + x − 12? (1 point)
Group of answer choices
−8
−1
1
8
Answers
Answer:
-8
Step-by-step explanation:
Multiply the brackets (2x - 4)
Add the x constant together (4x + 2x - 4x - x)
Add the other numbers together (4-12)
x = -8
Have a good day :)
please do all of the parts,, im begging
Use this scenario to answer questions #1-11: Jenny wants to rent a truck. She contacted two companies. Laguna’s Truck Rentals charges $6 for the truck and $2 per mile. Salvatory’s Truck Rentals charges $3 per mile.
1. Identify the independent variable
2. Identify the dependent variable
3. Create an equation to represent the total cost for Laguna’s Truck Rentals.
4. Create an equation to represent the total cost for Salvatori’s Truck Rentals.
5. Select the graph below that best represents the relationship between Laguna's and Salvatory's Truck Rentals. (please see image)
6. Identify and interpret the meaning of the slope for Laguna’s Truck Rentals.
7. Identify and interpret the meaning of the slope for Salvatori's Truck Rentals.
8. Identify and interpret the meaning of the y-intercept for Laguna’s Truck Rentals.
9. Identify and interpret the meaning of the y-intercept for Salvatori's Truck Rentals.
10. Identify and interpret the meaning of the point of intersection.
11. Which of these graphs represents a proportional relationship and why?
if you actually did all of them im giving you a hug.
Answers
Answers:
1. Miles driven
2. Price of rental
3. y = 2x + 6
(The fixed/initial cost is b, the y-intercept. The 2 is the price per mile and the x is the miles driven.)
4. y = 3x
(Since there's no initial cost, the equation is simply 3 times x)
5. A
6. The slope for Laguna is 2. This is the price per mile.
7. The slope for Salvatori is 3. This is the price per mile.
8. The y-intercept for Laguna is 6. This is the initial, fixed cost of renting a truck.
9. The y-intercept for Salvatori is 0. This means there is no initial cost.
10. The point of intersection is the amount of miles driven at which both companies are the same price. If Jenny drives 6 miles, she'll pay $18 either way.
11. I don't know how to do this one, sorry! >_<
I hope I helped on 1-10!
- 7th Grade Work -
Can someone please help me? I really need it.
Answers
Answer:
RentNSave is 0.05x+2.5 more
Step-by-step explanation:
Please help!!!!!!!!!!!!
Answers
Answer: 12?????? i dont know what the question is saying bc ur took a picture of something too close maybe get the whole question?
Step-by-step explanation:
Part A
y varies directly with x, so we know that y = kx for some constant k. Why the letter 'c' isn't used as a constant, instead of k, I'm not entirely sure.
We're told that x = 0.5 and y = 36. Let's use those values to find k
y = kx
36 = k*0.5
36/0.5 = k
72 = k
k = 72
The equation y = kx updates to y = 72x
As a check, plug x = 0.5 in to get,
y = 72x
y = 72*0.5
y = 36
which helps show that we have the correct equation.
Answer: y = 72x===============================================================
Part B
If y = 1/3, then,
y = 72x
1/3 = 72x
72x = 1/3
x = (1/3)*(1/72)
x = (1*1)/(3*72)
x = 1/216
Note how I multiplied both sides by 1/72, which is the same as dividing both sides by 72.
Answer: x = 1/216Monica has a triangular piece of fabric. The height of the triangle is 21 inches and the triangle's base is 12 inches. Monica says that the area of the fabric is 252 in2. What error did Monica make? Explain your answer by entering the correct area of the fabric.
Answers
Answer:
She didnt divide the product of the base and height by 2
Step-by-step explanation:
The correct answer would be 126 inches squared
To find the area of a triangle you have to multiply the base and height together and then divided the product by two
The formula is A=b•h/2
Please answer question below
Answers
Use the box-and-whisker plots to find the interquartile range for both class B and class A?
1. Class A:9 Class B: 14
2. Class A:4 Class B:7
3. Class A:15 Class B:11
4. Class A:5 Class B:7
Answers
Answer:
class a- 10
class b- 15
Step-by-step explanation:
Class b - 15
PLS HELP ME
For any right triangle, the side lengths of the triangle can be put in the equation a2 + b2 = c2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?
Answers
Answer:
Pythagorean theorem:
a² + b² = c²
a is the long leg of the triangle
b is the short leg of the triangle
c is the hypotenuse
side lengths ; 3 inches, 4 inches, 5 inches of a right triangle.
a = 4 inches
b = 3 inches
c = 5 inches
4² + 3² = 5²
16 + 9 = 25
25 = 25
Step-by-step explanation:
Please help! Thanks!
Answers
The answer is 2. I hope this helps.
A group of students were surveyed to find out if they like watching television or reading during their free time.
The results of the survey are shown below:
90 students like watching television
20 students like watching television but do not like reading
80 students like reading
40 students do not like watching television
Make a two-way table on a separate piece of paper to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both watching television and reading? Show your work.
Part B: What is the probability that a student who does not like watching television also does not like reading? Explain your answer.
Answers
B) 30/40 = 3/4 = 0.75
hope you have a great day !
Stan es.pdf Open u 1) Mary has more than 2 pennies in her pocket. + + + + + -5 -4 -3 -2 -1 0 1 2 3 4 5 Inequality: The dot is on because The dot is open/closed because T The arrow points towards the positives/negatives because Т. be 3. Simon has least 1
Answers
Step-by-step explanation:
All numbers belong to the set of numbers known as the real number system. The real number system consists of
every number you have ever dealt with since you were old enough to count. The numbers in the real number system
are divided into two main groups. One group is called the rational numbers and the other is called the irrational
numbers. The set of irrational numbers consists of all numbers that are not rational. This set of irrational numbers
includes those numbers that cannot be written as the ratio of two integers, non-remediate numbers.
and decimals that do not have a repeating pattern of digits. For example, pi(π),
√
2,−2.345876921... are irrational
numbers.
The set of rational numbers includes natural numbers, whole numbers, integers, numbers that can be expressed as
the ratio of two integers, a decimal number that terminates, and decimal numbers that have a repeating pattern of digits.
The natural numbers are the set of positive integers. For example, 1, 2, 3. . . are all natural numbers. The whole
numbers are the natural numbers and zero. For example, 0, 1, 2, 3. . . are all whole numbers. The integers are
the whole numbers and their opposites. For example, -2, -1, 0, 1, 2. . . are all integers. A rational number is any
number that can be expressed in the form of a
b where b 6= 0. When a rational number is expressed as a decimal, it
decimal will terminate (end) or For example, 1
2
,
√
81,−7.456 545 654 are
all rational numbers.
When you classify numbers remember that they can often belong to more than one set of numbers. If you think of
the number 3, you can call it a natural number, a whole number, an integer and a rational number.
The following table may help you to better understand the real number system.
Name a survey that you would like to do and what method of survey are you using?
Answers
Answer:
survey on who like cookie dough ice cream and idek
have a good day :)
Step-by-step explanation:
How do you multiply a fraction by a whole number?
Answers
Multiply the top number of the fraction by the whole number and then place that over the lower number of the fraction. Then you can see if the new fraction can be reduced or rewritten as a proper fraction.
Example:
1/2 x 3 would be (1 x3) / 2 = 3/2 which can be rewritten as 1 1/2
Example: [tex]\frac{2}{5}*10=\frac{2}{5}*\frac{10}{1}=\frac{20}{5}=4[/tex]
Which of the following is an obtuse angle in this figure?
angle DEK
angle FEK
angle DEH
angle DEJ
Answers
Answer:
DEK
Step-by-step explanation:
to be a obtuse angle its required to be over 90 degrees DEK is 150 degrees
Help me save my life from this terrifying math problem
Answers
Perform the operation, Enter your answer in scientific notation.
7 x 10² – 5.5 x 10²
Answers
Answer:
150 or 15^1
Step-by-step explanation:
(?) what is the relationship between the 81 degree angle ? what is the measure of this angle ?
Answers
Answer:
A. They are corresponding and vertically opposite
B. Rigid Motion:
Any way of moving all the points in the plane such that. a) the relative distance between points stays the same and. b) the relative position of the points stays the same. There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.
C: 81
Step-by-step explanation:
Now the angle opposite to x degree will be 82 (alternate angles)
And lastly x degree is equals to 81 degree( vertically opposite angle)
Percentage homeworkkk… (Middle School)
Answers
Answer:
75% for number 2 i think number 3 is 70%
Please help me!
I will give brainly
Answers
Answer:
27
Step-by-step explanation:
You add 63 and 90 (90 being the right angle) and then subtract that from 180 which is the sum of all three angles and you get 27.
Jason has sport cards in his pocket. He has three football cards, one wrestling card and two baseball cards. If Jason reaches into his pocket and selects one card, what is the probability he will get a baseball card? Show your answer in lowest terms.
Answers
Answer:
In lowest terms, there is a 1/3 probability of Jason pulling out a baseball card.
Step-by-step explanation:
There are a total of 6 cards. 4/6 of them are football and wrestling which results in 2 baseball cards. So the probability is 2/6 but since the question wants it in lowest terms, you would have to simplfy 2/6. Divide the top by 2 and the bottom by 2 which gets you 1/3.
Find the slope: y = -2x
Answers
Answer:
-2
Step-by-step explanation:
By definition the slope is value m in the equation y=mx+b. Here, m=-2 and b=0.
Answer:
The slope is -2
Step-by-step explanation:
8 1/4 divided by t = 2/11
Answer for t
Answers
Answer:
1 1/2
Step-by-step explanation:
Turn 8 1/4 into 33/4
Then multiply 33/4*2/11 to get 66/44 then simplify to 1 1/2
Elena wants to add (2.3 x 10⁵)+(3.6 x 10⁶) and writes (2.3 x 10⁵)+(3.6 x 10⁶)=5.9 x 10⁶
Explain to Elena what her mistake was and what the correct solution is.
Answers
Answer:
Step-by-step explanation:
10^5 + 10^6 = 10^5+6
Choose all that correctly describe the pattern of association between the two quantities on the scatter plots.
this is a usatestprep question
i WILL give brainiest to whoever's right
please no links
Answers
The scatter plots are solved and the graph C and graph D are true
What do you mean by Scatter Plot?In a scatter plot, dots are used to represent the values of two separate numerical variables. The values of each data point are represented by the position of each dot on the horizontal and vertical axes. Use scatter plots to see how different variables are related to one another.
Data patterns or trends may be shown using scatter plots, which can also be used to spot any relationships between two variables. The strength and direction of the association between the two variables may be inferred from the scatter plot's shape and orientation.
Given the data ,
Let A, B, C, and D represent the scatter plots.
So, a negative association in a scatter plot describes a relationship between two variables in which a rise in one measure is linked to a drop in the other. This implies that the tendency is for the other variable to decrease as the first variable rises. A trend line or regression line with a falling slope is used to represent it.
Moreover, a positive association in a scatter plot denotes a link between two variables where a rise in one is correlated with a rise in the other. An upward-sloping trend line or regression line is used to represent it.
So , the scatter plots A and B are False
The non-linear and lack of trend charts are therefore accurate.
Go here for additional information about scatter plots.
https://brainly.com/question/29231735
#SPJ3
Solve 7/4x + 5/6=4/3x - 3 for x
Answers
Answer:
x=-46/5
Step-by-step explanation:
1. subtract either 5/6 or add 3 for each side.
2. combine terms
3. x=-46/5
Apple and cranberry juice are mixed in a ratio of 5 to 3. What amount of each juice would be needed to make a 64-fluid ounce pitcher of apple-cranberry juice?
Answers
Answer:
32
Step-by-step explanation:
64/2=32
Answer:
[tex]\text{Apple juice needed: }40\:\mathrm{oz},\\\text{Cranberry juice needed: }24\:\mathrm{oz}[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the amount of apple juice needed, in ounces. Let [tex]c[/tex] be the amount of cranberry juice needed, in ounces. We can set up the following system of equations:
[tex]\begin{cases}a=\frac{5}{3}c, \\a+c=64\end{cases}[/tex]
Solving, we get:
[tex]\frac{5}{3}c+c=64,\\\\\frac{8}{3}c=64,\\\\c=\frac{64\cdot 3}{8}=\boxed{24\:\mathrm{oz}}[/tex]
[tex]a=\frac{5}{3}c,\\\\a=\frac{5}{3}(24),\\\\a=\boxed{40\:\mathrm{oz}}[/tex]
Dean is saving up change so he can go to the arcade with 100 quarters. If he has 363 pennies, 200 nickels, and 23 dimes. How much more money must he save?
A. $ 9.12
B. $ 10.23
C. $ 7.44
D. $ 9.07
Answers
explanation: 363 pennies is equal to $3.36, 200 nickels is equal to $10.00, and 23 dimes is equal to $2.30. all of this change added up is equal to $15.93. since 100 quarters are worth $25, you would take 25-15.93. this equals D.$9.07
Simplify following the order of operations
( 2 + 6 ) ÷ 2 + 4 × 3
3
24
4
16
Answers
Answer: 16
Explanation:
(2+6)÷ 2 + 4 × 3
8÷ 2 + 4 × 3
4 + 4 × 3
4 + 12
16
Use the table to answer the question.
Avocados Price
1 $1.15
2 $2.30
5 $5.75
10 $11.50
How much will 4 avocados cost?
A. $1.15
B. $4.60
C. $3.45
D. $4.45
Answers
Step-by-step explanation:
You can choose one of the prices above to find the proportion.
[tex] \frac{2}{4} = \frac{2.30}{y} \\ 2 \times y = 2.30 \times 4 \\ y = 2.30 \times 2 \\ y = 4.60[/tex]
#CMIIWAnswer: I think its C
Step-by-step explanation: