Answers
The given expressions are:
A: 3(x+2)
B: 3x+6
When two expressions are equivalent, it doesn't matter which x-value you use, the result will always be the same, then option C and option D show that these expressions are equivalent, because we will obtain the same result, regardless of the value of x.
Now, the distributive property states:
a(x+y)=a*x+a*y
If we apply this property to expression A, we have:
3*x+3*2=3x+6
Thus, by applying the distributive property we can see that those expressions are equivalent.
The option B which says "Both expressions involve addition" does not show that these expressions are equivalent since we can have different expressions as: 4x+8, x+1, etc... and these are not equivalent.
Thus, the statement which doesn't show that these expressions are equivalent is B. Both expression involve addition..
Now, the
Related Questions
4^4x - 1 = 8^2xSolve for x.
Answers
x = 1
Explanation:
[tex]4^{4x-1}=8^{2x}[/tex]Make the base have the same number:
8 = 2³
4 = 2²
The base becomes 2
[tex]2^{2(4x-1)}=2^{3(}^{2x)}[/tex]Then we simplify:
[tex]\begin{gathered} \text{The base cancels out:} \\ 2(4x-1)\text{ = 3(2x)} \\ 8x\text{ - 2 = 6x} \\ \text{collect like terms: } \\ 8x\text{ - 6x = 2} \\ 2x\text{ = 2} \\ x\text{ = 2/2} \\ x\text{ = 1} \end{gathered}[/tex]Therefore, x = 1
check:
[tex]\begin{gathered} 4^{4(1)-1}=8^{2(1)} \\ 4^{4-1}=8^2 \\ 4^3\text{ }=8^2 \\ 4\times4\times4=\text{ 64} \\ 8\times8\text{ = 64} \\ 64\text{ = 64 (x=1 is correct)} \end{gathered}[/tex]for every 5 tacos,julianna uses 2 cups of shredded cheese. complete the table to show the relationships between the number of tacos and the number of cups of cheese
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For 5 taccos 2 cups cheese is needed.
So 10 taccos is 2*(5 taccos)=2*2 cups cheese =4cups
[tex]\begin{gathered} As\text{ 5 taccos=2cup cheese} \\ 1\text{ tacco=}\frac{2}{5}\text{cup cheese} \\ As\text{5 taccos=2cup cheese} \\ 1\text{ cup cheese=}\frac{5}{2}\text{taccos} \\ So\text{ 10 tacco=10}\ast\frac{2}{5}\text{cup cheese=2}\cdot2=4\text{cups} \\ 10\text{ cup cheese =10}\ast\frac{5}{2}\text{tacco}=5\ast5=25tac\cos \end{gathered}[/tex][tex]35\text{ taccos}=35\ast\frac{2}{5}=7\cdot2=14\text{ cup cheese}[/tex][tex]24\text{ cup cheese=}24\ast\frac{5}{2}=12\ast5=60tac\cos [/tex]So to convert taccos to cups of cheese multiply by 2/5 and from cups of cheese to taccos multiply by 5/2.
Please see the picture for the question and my answer is wrong
Answers
Given sentence:
Five more than half the input is the output
y is the output, x is the input
To interpret the sentence, we should break it into parts:
-half the input: we half the input
- 5 more than we add 5 to the new input
- the sum of these is the output
The equation that represents the given sentence:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]Answer:
[tex]y\text{ = 5 + }\frac{1}{2}x[/tex]10 is what percent of 22 ?Round your answer to the nearest hundredth, if necessary. Type your answer in the box below.
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Answer:
Explanation:
Answer:
We follow the s
Explanation:
To find out what percent of 10 is 22.
We follow the s
1 1/3 divided by 40 using the algorithm
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the given expression is,
1 1/3 = 4/3
[tex]\frac{\frac{4}{3}}{40}=\frac{4}{120}[/tex]is 3/3 x 3/4 less than, greater than, or equal to 3/4
Answers
Given data:
The given expression is 3/3 x 3/4.
The given expression can be written as,
[tex]\begin{gathered} \frac{3}{3}\times\frac{3}{4}=1\times\frac{3}{4} \\ =\frac{3}{4} \end{gathered}[/tex]Thus, the expression 3/3 x 3/4 is equal to 3/4.
Business that offers repayment plan for purchases are required by law to disclose the interest rate but that doesn’t mean they go out of their way to let you know what it is you have to read all the paperwork find the interest rate for the following purchaseTo finance a new laptop Emily is offered a five year payment plan with low monthly payments of $31 and50 Cent the cost of the laptop is $884.43 including tax round to the decimal place if necessary
Answers
Answer:
The number of years for the repayment is
[tex]t=5years[/tex]The amount to be repaid back monthly is
[tex]\text{ \$31.50}[/tex]The cost of the laptop given is
[tex]\text{ P=\$884.43}[/tex]Step 1:
Calculate the total amount of money to be repaid after 5 years
[tex]\begin{gathered} Amount\text{ repayable=monthly payments}\times number\text{ of years}\times12 \\ Amount\text{ repayable=31.50}\times5\times12 \\ Amount\text{ repayable=1890} \end{gathered}[/tex]Step 2:
Calculate the interest on the laptop
[tex]\begin{gathered} interest=Amount\text{ repayable-cost of the laptop} \\ interest=1890-884.43 \\ interest=1005.57 \end{gathered}[/tex]Step 3:
To calculate the interest rate, we will use the formula below
[tex]\begin{gathered} I=\frac{PRT}{100} \\ \frac{100I}{PT}=\frac{PRT}{PT} \\ R=\frac{100I}{PT} \\ T=5,P=884.43,I=1005.57 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} R=\frac{100I}{PT} \\ R=\frac{100\times1005.57}{884.43\times5} \\ R=\frac{100557}{4422.15} \\ R=22.7\% \end{gathered}[/tex]Hence,
The interest rate will be
[tex]\Rightarrow22.7\%[/tex]Find the lowest common multiple of each group. show the factors you used.1) 5,22 and 121
Answers
Solution:
Given:
[tex]5,22,121[/tex]By prime factorization method:
[tex]\begin{gathered} 5=5 \\ 22=2\times11 \\ 121=11\times11 \\ \\ Hence,\text{ the LCM is:} \\ 2\times5\times11\times11 \\ LCM=1210 \end{gathered}[/tex]Therefore, the LCM is 1,210
How can you find a common denominator for one third and one fifth
Answers
Given to find the common denominator for one-third and one-fifth.
Here, the denominators of both fractions are 3 and 5. Since 3 and 5 do not have any factors common. So, the LCD will be the product of 3 and 5, which is equal to 15.
Thus, LCD of 1/3 and 1/5 is 15.
How many solutions does the graph have?
Answers
Answer:
One solution
Step-by-step explanation:
The lines only intersect one time, this indicates that there are only one solution
principal hernadez bought 640 t shirts for the student in his school. the t shirts came in packs of 20. how many packs did he buy
Answers
We know that
• Hernandez bought 640 t-shirts.
,• They came in packs of 20.
To know how many packs he bought, we just need to divide
[tex]\frac{640}{20}=32[/tex]Therefore, principal Hernandez bought 32 packs of t-shirts.solve the system of equations by the addition method 5x + 2y = 64x - 3y = 14
Answers
Given the system
[tex]\begin{gathered} 5x+2y=6 \\ 4x-3y=14 \end{gathered}[/tex]To solve it you have apply the addition method, this means that you have to add both equations.
You have to keep in mind that is only valid to add the terms that have the same variables.
The solution is 9x-y=20
AN Question 7 (5 points) A recent Nielson rating poll contact a random sample of Americans to determine the amount of time their family watched television on a Tuesday night. Exactly 250 people were involved in the poll with 37 people watching no television. 51 people watching 30 minutes of television. 17 people watching 45 minutes of television. 20 people watching 60 minutes of television. 19 people watching 75 minutes of television, 11 people watching 90 minutes of television. 50 people watching 120 minutes of television, and 45 people watching 240 minutes of television. Determine the mean from the given Nielson rating poli. Do not round your answer.
Answers
Mean = sum of the terms/number of terms
Replacing with data:
Mean = (37*0 + 51*30 + 17*45 + 20*60 + 19*75 + 11*90 + 50*120 + 45*240)/250
= 90.84 minutes
A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is 12 in, and the radius of the shaded region is 5 in. Use the value 3.14 for n. Round your answer to the nearest hundredth.
Answers
For this problem, we are given the dimensions of a dashboard. We need to determine the probability a dart will hit the shaded area.
To solve this problem, we need to calculate the area of the whole board (square) and the area of the shaded area (circle). Then we need to divide the area of the shaded circle by the entire board.
The area of a circle can be found as shown below:
[tex]A_{shaded}=3.14\cdot(5)^2=78.5\text{ square inches}[/tex]The area of the square can be found as shown below:
[tex]A_{board}=12^2=144\text{ square inches}[/tex]Now we need to find the probability of the shaded area, which can be done by dividing the area of the circle by the area of the board.
[tex]P(shaded)=\frac{78.5}{144}=0.55[/tex]The probability is 0.55.
Whiteout graphing the function, describe what the graph would look like if b were 8.5
Answers
We have the function y=x+b.
This is a line with b as y-intercept.
When b gets larger, that graph moves parallel and up in the vertical axis.
That is because b is like a "floor" level when x=0, and, as the slope of the line stays the same, the lines stays parallel.
As b becomes negative, the graph goes in the opposite direction (down in the vertical axis).
The lines stays parallel, because the slope does not change.
Please make this simple and easy, and help me quickly, thank you!
Answers
Given:
Total distance = 60 km
Upstream time = 5 hours
Downstream time = 3 hours
Find-:
The rate of boat in still water.
Explanation-:
Let
The speed of the boat in still water is"x"
The speed of the water is "y"
For upstream ( Against the current )
Speed of boat is:
[tex]=x-y[/tex][tex]\begin{gathered} \text{ Distance }=60\text{ km} \\ \\ \text{ Time }=5\text{ hours} \end{gathered}[/tex]Use the formula:
[tex]\text{ Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]For upstream speed is:
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x-y=\frac{60}{5} \\ \\ x-y=12..............(1) \end{gathered}[/tex]For downstream,
[tex]\text{ Speed}=x+y[/tex][tex]\begin{gathered} \text{ Distance}=60\text{ km} \\ \\ \text{ Time}=3\text{ hours} \end{gathered}[/tex]Use the formula of distance
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x+y=\frac{60}{3} \\ \\ x+y=20 \\ \\ y=20-x................(2) \end{gathered}[/tex]From eq(2) put the value of "y" in eq(1) then the value is:
[tex]\begin{gathered} x-y=12...........(1) \\ \\ y=20-x...............(2) \end{gathered}[/tex][tex]\begin{gathered} x-y=12 \\ \\ x-(20-x)=12 \\ \\ x-20+x=12 \\ \\ 2x-20=12 \\ \\ 2x=12+20 \\ \\ 2x=32 \\ \\ x=\frac{32}{2} \\ \\ x=16 \end{gathered}[/tex]The rate of the boat in still water is 16 km/hour
what might a postitive number mean in thid content ,what about a negatuve number
Answers
1.
A positive number might mean that the number of bottles in the machine is bigger than the number of bottles sold.
A negative number might mean that the number of bottles sold is bigger than the number of bottles in the machine.
2.
A cero might mean that the number of bottles sold is equal to the number of bottles in the machine.
12. A block of ice is in theshape of a cube with sidelengths of 1.8 inches. The icehas a density of 876 kg percubic inch. Find the mass ofthe block of ice to the nearesttenth of a kg.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
A block of ice is in the shape of a cube with side lengths of 1.8 inches.
The ice has a density of 876 kg per cubic inch.
Find the mass of the block of ice to the nearest tenth of a kg.
Step 2:
The details of the solution are as follows:
Recall that:
[tex]\begin{gathered} Density\text{ = }\frac{Mass}{Volume} \\ where\text{ Volume of the cube = length x length x length} \\ Volume\text{ of the cube = 1. 8 x 1. 8 x 1. 8 = 5.832 inches}^3 \end{gathered}[/tex][tex]Density\text{ = 876 kg per cubic inch}[/tex][tex]\begin{gathered} Therfore,\text{ mass of of the block of ice = Density x volume} \\ Mass\text{ of the bolock of ice = 876 x 5.832 = 5108. 832 kg}\approx\text{ 5108.8 kg} \\ (\text{ to the nearest tenth of a kg \rparen} \end{gathered}[/tex]CONCLUSION:
The mass of the block of ice to the nearest tenth of a kg =
[tex]5108.8\text{ kg }[/tex]
Find the length of AB.A140/6 inAB = [ ? ]inBRound your answer to the nearest hundredth.
Answers
The length of AB is given by:
AB = θ*r
Basically AB = L
Where:
L = Arc length of the minor sector.
Now:
r = 6 in
θ = 140° = 7/9 π
Therefore:
AB = (7/9 π) * 6 = 14/3 π ≈ 14.66 in
For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert.Here are the items to choose from.ChoicePossible items Appetizer Buffalo wings, Cheese sticks, Potato skins, Nachos Salad Caesar, Southwest, Garden Entree Lamb, Roast turkey, Salmon, Pot roast, Grilled chicken Side dish Mixed vegetables, Baked potato, Rice, French fries, Corn Dessert Chocolate cake, Brownies, Cheesecake How many dinner specials are possible?
Answers
Solution
Step 1:
There are 4 Appetizers, 3 Salad, 5 Entrees, 5 Side dishes, and 3 Desserts.
Step 2:
Possible dinner special
[tex]\begin{gathered} =\text{ 4 }\times\text{ 3 }\times\text{ 5 }\times\text{ 5 }\times\text{ 3} \\ \\ =\text{ 900 } \end{gathered}[/tex]Final answer
900 specials possible dinner.
900
simplify the expression x² - 3xy - 5xy - 7y² + 4x² + 8y²
Answers
x² - 3xy - 5xy - 7y² + 4x² + 8y²
First, let's re-arrange
x² + 4x² - 3xy - 5xy - 7y² + 8y²
5x² - 8xy + y²
For the function f(x) = x2 - 4. construct and simplify the difference quotient f(x+h)-f(x) h
Answers
May I please get help with this. I can’t seem to figure out the right answers for them
Answers
Given
Solution
Using similar triangles
[tex]\begin{gathered} \frac{35}{57}=\frac{22.8}{x} \\ \\ \text{cross multiply} \\ 35x=1299.6 \\ \text{Divide both sides by 35} \\ \frac{35x}{35}=\frac{1299.6}{35} \\ \\ x=37.1314\ldots \end{gathered}[/tex]The final answer
[tex]37m[/tex]Find the slope from real world application. At pizza galore a two topping pizza costs $9. A pizza with four toppings costs $12. How much does each topping cost?
Answers
The slope is:
[tex]m=\frac{12-9}{4-2}[/tex][tex]m=\frac{3}{2}=1.5[/tex]Hence, each topping of the pizza cost $1.5
From a group of 15 women and 16 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?A. 300,540,195B. 778,377,600C. 19,305OD. 82,818,450
Answers
Since we are talking about a group of people the order is not going to matter when we select the different people, then, start to make the combination for the group of women and the group of men separately.
[tex]\begin{gathered} women=15C8 \\ women=\frac{15!}{(15-8)!8!} \\ women=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ women=6435 \end{gathered}[/tex][tex]\begin{gathered} men=16C8 \\ men=\frac{16!}{(16-8)!8!} \\ men=\frac{16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ men=12870 \end{gathered}[/tex]then, multiply the results
[tex]\begin{gathered} 16C8\cdot15C8 \\ 12870\cdot6435 \\ 82,818,450 \end{gathered}[/tex]Special Right Triangles(Radical Answer) Problem I would appreciate the help:0
Answers
In order to determine the value of x, use the
Using a deck of 52 standard playing cards, find the probability for P(Clubs or Spades).
Answers
Solution
There are 13 clubs and 13 spade
=> probability for P(Clubs or Spades) = 13/52 + 13/52
[tex]\frac{13}{52}+\frac{13}{52}\text{ =}\frac{26}{52}=\frac{1}{2}[/tex]How do I solve these?1) Evaluate the expression, 2b+(c-3a) when a= -1/2, b= 3/4, c= 1/4.2) A store manager uses a markup rate of 24% on all appliances. Find the cost of a coffee maker that sells for $77.50. Use formula S=C+r•C, where S is the selling price, C is the cost, and r is the markup rate.
Answers
To evaluate the expression
[tex]2b+(c-3a)[/tex]Plug in the corresponding values that are given and operate, as following:
[tex]\begin{gathered} 2b+(c-3a) \\ \\ \rightarrow2(\frac{3}{4})+(\frac{1}{4}-3(-\frac{1}{2})) \\ \\ \rightarrow\frac{3}{2}+(\frac{1}{4}+\frac{3}{2}) \\ \\ \rightarrow\frac{3}{2}+\frac{1}{4}+\frac{3}{2} \end{gathered}[/tex]At this point, we have to have all our fractions with the same denominator to add them up. To do so, let's find the LCM (Least Common Multiple) between our different denominators (In this case, 2 and 4)
The LCM is 4. Now, we need to find a way for all our fractions to have 4 as a denominator. Notice that we can do so by multiplying both 3/2 by 2 (both in the numerator and denominator), as following:
[tex]\begin{gathered} \frac{3}{2}+\frac{1}{4}+\frac{3}{2}\rightarrow\frac{2\cdot3}{2\cdot2}+\frac{1}{4}+\frac{2\cdot3}{2\cdot2} \\ \\ \rightarrow\frac{6}{4}+\frac{1}{4}+\frac{6}{4} \end{gathered}[/tex]Now, we can add them up:
[tex]\frac{6}{4}+\frac{1}{4}+\frac{6}{4}\rightarrow\frac{6+1+6}{4}\rightarrow\frac{13}{4}[/tex]This way, the answer is 13/4
A local diner purchased a jukebox for $9400 the business makes a down payment of $1000 and agrees to 36 monthly payments of $275 each estimate the annual percentage rate to the nearest 10th of a percent
Answers
Given:-
Jukebox for $9400.
Payment done is $1000.
Agrees to make down payment for 36 months each month of $275.
To find
Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data.(Select all that apply.)(a) Outstanding balance on each account.A. modeB. medianC. mean(b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.).A. modeB. medianC. mean(c) Dollar amount due on next payment.A. modeB. medianC. mean
Answers
Answer:
(a)A,B.C
(b)A
(c)A, B, C
Explanation:
Part A
The outstanding balance on each account can be summarized using the mean, median, and mode since it is quantitative data.
Options A, B, and C are correct here.
Part B
The name of credit cards can only be summarized by frequency. That is, how many belong to each company (i.e. MasterCard, Visa, American Express, etc.)
The only correct option here is Mode. (Option A).
Part C
The dollar amount due on the next payment is a numerical data, we can find the mean, median, and mode for any numerical data.
Options A, B, and C are correct here.