Answers
By power algebra method,
a) \(\frac{16}{81}\)
b) \(\frac{2xy}{3}\)
c) \(\frac{16x^4}{y^8}\)
d) \(\frac{3y^2}{x^3}\)
What is dividing power property?According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.
The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.
You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).
a) \((\frac{2}{3})^4\) = \(\frac{2*2*2*2}{3*3*3*3}\) = \(\frac{16}{81}\)
b) \(\frac{2x^2y}{3x}\) = \(\frac{2*x*x*y}{3*x}\) = \(\frac{2xy}{3}\)
c) \((\frac{2x}{y^2})^4\) = \(\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}\) = \(\frac{16x^4}{y^8}\)
d) \(\frac{3xy^4}{x^3}\)\(.\frac{y}{xy^3}\) = \(\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}\) = \(\frac{3y^2}{x^3}\)
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Related Questions
There is a rectangular lot in the garden, with 10 ft in length and 4 ft in width. You plan to expand the lot by an equal length around its
four sides, and make the area of the expanded rectangle 72 ft². How long should you expand the original lot in four directions?
You should expand the original lot by blank in four directions. Please type ft to represent feet.
Answers
Answer:
You should expand the four sides of the original lot by 2 ft.
Step-by-step explanation:
10 x 4 = 40
72 - 40 = 32
32/4 = 8
10 - 8 = 2
10 + 2 = 12
4 + 2 =6
12 x 6 = 72
thirty is equal to twice a number decreased by four
Answers
Answer:
4-(2n)= 30
Step-by-step explanation:
N is 17
find the balance in the account: $3,000 principal, earning 3% compounding annually, after 4 years
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.03}{1}\right)^{1\cdot 4}\implies A=3000(1.03)^4 \implies A \approx 3376.53\)
х
The table of values below represent an exponential function. Write an exponential equation that models the data.
у
-2 23
-1 16.1
0 11.27
1 7.889
2 5.5223
a.
y = 23(0.7)
y = 16.1(1.7)
C. y = 11.27(0.7)
d.
y = 11.27(1.3)
b.
Answers
9514 1404 393
Answer:
C. y = 11.27(0.7^x)
Step-by-step explanation:
The table value (x, y) = (0, 11.27) tells you the multiplier of the exponential term will be 11.27. The decreasing values tell you the base of the exponential term is less than 1. Only answer choice C matches these requirements.
Alana and Petra go to a used book sale , where every book is the same price. Alana buys 4 books and Petra buys 2 books. They run into their friend angus, who really loves to read, and discover that he has bought 16 books. Angus received a $15 discount, but he still spent $5 more than Alana and Petra combined. How much does one book cost?
Answers
Answer:
$2
Step-by-step explanation:
What is the length of the two equal sides?
What is the length of the third side?
Answers
Answer:
the length of the third side is 21
Step-by-step explanation:
let P be the perimeter of the triangle
a the length of the first and second sides
b the length of the 3rd side
…………………………………………………
Then
P = a + a + b
= 2a + b
Where b = a + 6
Therefore
P = 2a + (a + 6)
= 3a + 6
We substitute the numbers we have into the equation:
51 = 3a + 6
⇔ 45 = 3a
⇔ a = 15
Since b = a + 6 then b = 15 + 6 = 21
If f(x) = 3x + 12, g(x) = x + 6, h(x) = x + 1, then (hohohofofog) (0) is (A) 150 (B) 105 (C) 104 (D) 58 (E) 114
Answers
The answer is (C) 104. If f(x) = 3x + 12, g(x) = x + 6, h(x) = x + 1,
What is the function?
A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function is a rule or procedure that takes one or more inputs and produces a corresponding output.
We need to start by evaluating the innermost function first, so:
fog(x) = f(g(x)) = f(x + 6) = 3(x + 6) + 12 = 3x + 30
Next, we evaluate the composition of f and g again, using the result from above:
f×f×g(x) = f(f×g(x)) = f(3x + 30) = 3(3x + 30) + 12 = 9x + 102
Now, we evaluate the composition of h and the result from above:
hohofofog(x) = h(h×f×f×g(x)) = h(h(9x + 102)) = h(9x + 103) = 9x + 104
Finally, we evaluate the entire composition at x = 0:
h×h×f×f×g(0) = 9(0) + 104 = 104
Therefore, the answer is (C) 104. If f(x) = 3x + 12, g(x) = x + 6, h(x) = x + 1,
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3
x < -5
x + 4
f(x) =
x2 – 3x, -5
x4 – 7,
x > 0
Find f(-2)
f(-2) =
P
Answers
Answer: 10
Step-by-step explanation:
Since -2 is in between -5 and 0, we will use the part of the function that says f(x)=x^2 + 3x.
Substituting x=-2, we get (-2)^2 -3(-2)=4+6=10
30 points
The school that Jessica goes to is selling tickets to a fall musical. On the first day of ticket sales
the school sold 6 senior citizen tickets and 5 student tickets for a total of $50. The school took in
$44 on the second day by selling 8 senior citizen tickets and 1 student ticket. Find the price of a
senior citizen ticket and the price of a student ticket.
6C+ SS=50
8C+15=44
Answers
Answer:
The price of a senior citizen ticket to the fall musical is $6
The price of a student citizen ticket to the fall musical is $4
Step-by-step explanation:
C = the price of a senior citizen ticket to the fall musical
S = the price of a student citizen ticket to the fall musical
Day 1:
6C + 5S = 50
Day 2:
8C + 1S = 44
Manipulate the equations so that they have a common coefficient.
Multiple Day 2's equation by 5.
8C + 1S = 44
40C + 5S = 220
Subtract Day 2's equation from Day 1's
(40C + 5S = 220) - (6C + 5S = 50)
(40C + 5S) - (6C + 5S) = 220 - 50
(40C - 6C) + (5S - 5S) = 220 - 50
34C = 170
C = 5
Substitute C into either equation to solve for S.
Day 1:
6C + 5S = 50
6(5) + 5S = 50
30 + 5S = 50
5S = 50 - 30
5S = 20
S = 4
Day 2:
8C + 1S = 44
8(5) + 1S = 44
40 + 1S = 44
1S = 44 - 40
S = 4
PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT (you can use a calculator if you want)
Answers
9514 1404 393
Answer:
BA, EDStep-by-step explanation:
Yes, it is very important. The idea here is that the decimal point in division problems like these can be moved the same number of places in the same direction in each number without changing the result.
__
1. Without a calculator, this is about 8/5, which you know to be more than 1 and less than 4. The only suitable answer choice is the correct one:
B 1.645 ft.
__
2. Moving the decimal point 1 place to the left in both numbers, we have ...
(892×10) ÷ (8×10) = 8290 ÷ 80 . . . . matches A
Moving the decimal point 3 places to the left in both numbers, we have ...
(892×0.001) ÷ (8×0.001) = 0.892 ÷ 0.008 . . . . matches E
The other choices did something other than move the decimal point the same number of places. (Your calculator can verify this.)
__
3. Moving the decimal point 3 places to the right, we have ...
(4367×1000) ÷ (0.004×1000) = 4,367,000 ÷ 4 ≈ 1,000,000
_____
Additional comment
For numbers like the ones in problem 3 that differ substantially in magnitude, it can work well to adjust the decimal points in both numbers so the divisor is between 1 and 10. This lets you easily estimate the position of the decimal point in the quotient.
Of course, if you're doing long division by hand, you always adjust the decimal points so the divisor is an integer (possibly with no trailing zeros).
The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. A juice box is selected at random. What is the probability of the complement of choosing an orange juice box? (first answer will get brainliest)
1/18
4/9
5/9
17/18
Answers
Answer:
\( p(O)=\frac{8}{18}=\frac{4}{9}\)
And since we want the complement of choosing an orange juice box the answer would be:
\( P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}\)
And the nest answer for this case is:
5/9
Step-by-step explanation:
For this case we know that we have 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes, so then the size of the sample space is:
\( 8+4+6= 18\)
Then we can find the probability of selecting an orange juice box with the definition of Laplace given by:
\( p =\frac{possible}{total}\)
And for this case the possible cases are 4 and the total 18 so then the probability is given by:
\( p(O)=\frac{8}{18}=\frac{4}{9}\)
And since we want the complement of choosing an orange juice box the answer would be:
\( P(O') =1 - P(O) = 1-\frac{4}{9}= \frac{5}{9}\)
And the nest answer for this case is:
5/9
can someone help me round 621x29
Answers
Your rounded number is 18010
The reason for this is because when you multiply 621X29, you get 18009. When you round numbers, you want to see how the numbers are. If a number is 4 or below, you will make that number a zero or not count it, whereas numbers above 5 will go up. I hope this helps and if you have any questions, let me know
Answer:
18010
Step-by-step explanation: You see, 621x29=18009 and rounded is 18,010
Gavin is making a scale replica of a tent for his social studies project. The replica is in the shape of a triangular prism. It has an isosceles triangle base with side lengths 6 inches, 5 inches, and 5 inches. The height of the triangle is 4 inches, and the depth of the tent is 7 inches. How much fabric will Gavin need to make the outside of the replica, including the "floor"?
Answers
The fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in²
What is surface area?
Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.
Surface area of triangular prism with isosceles triangle base is find out using the following formula,
\(A_s=[(2a+b)\times l]+2\times A_b\)
Gavin is making a scale replica of a tent for his social studies project.
The replica is in the shape of a triangular prism. It has an isosceles triangle base with side lengths 6 inches, 5 inches, and 5 inches.
The base area of the prism is,
\(A=\dfrac{1}{2}\sqrt{5^2-\dfrac{6^2}{4}}{\times6}\\A=12\rm\; in^2\)
The height of the triangle is 4 inches, and the depth of the tent is 7 inches.
Put the values in the above formula as,
\(A_s=[(2\times5+6)\times 7]+2\times12\\A_s=136\rm \; in^2\)
Thus, the fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in².
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Missing numbers
, 9.8 , 9.1
Answers
Answer:
10.5
Step-by-step explanation:
Missing number, 9.8, 9.1
We see that each time it subtracts 0.7
We take
9.8 + 0.7 = 10.5
So, the missing number is 10.5
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
Answers
A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.
One possible set could be 3 cm, 4 cm, and 5 cm.
To verify if this set forms a right triangle, we can apply the Pythagorean theorem.
Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.
Adding these two values together gives us 25.
Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.
It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.
There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.
These sets are known as Pythagorean triples.
Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.
In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
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Solve using the standard algorithm:
25 x 16
Answers
Answer:
400 !
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
25
x16
____
150
+250
____
400
have a good day! c:
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
Answers
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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Cindy, Inc. sells a product for $10 per unit. The variable expenses are $6 per unit, and the fixed expenses total $35,000 per period. By how much will net operating income change if sales are expected to increase by $40,000?
A) $16,000 increase
B) $5,000 increase
C) $24,000 increase
D) $11,000 decrease
Answers
Answer: it is a $16,000 increase
Suppose you want to buy a new car that cost 32,700 you have no cash only your old car which is worth 2000 as a trade in the dealer says the interest rate is 3% add on for five years find the total interest
Answers
The tοtal interest paid οver the 5-year lοan periοd wοuld be $4,605.
What is Interest?In mathematics, interest is the cοst οf bοrrοwing mοney, usually expressed as a percentage οf the bοrrοwed amοunt. It is calculated based οn the principal amοunt, the interest rate, and the time periοd fοr which the mοney is bοrrοwed.
Assuming that the full purchase price οf the new car is $32,700, and the dealer has οffered a trade-in value οf $2,000 fοr yοur οld car, yοu will need tο finance the remaining balance, which is:
$32,700 - $2,000 = $30,700
If the dealer has οffered a 3% add-οn interest rate fοr a 5-year lοan, we can calculate the tοtal interest paid οver the life οf the lοan using the fοllοwing fοrmula:
Tοtal interest = (Principal × Interest rate × Lοan term) ÷ 2
Substituting the given values intο the fοrmula, we get:
Tοtal interest = ($30,700 × 0.03 × 5) ÷ 2
Tοtal interest = $4,605
Therefοre, the tοtal interest paid οver the 5-year lοan periοd wοuld be $4,605.
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Please tell me fast I am on a time crunch
Answers
Solve for the inequality x
Need help with #6 please help
Answers
Answer:
20 m
Step-by-step explanation:
If 65% of Americans are overweight, how many people would be overweight in a city of 1.5 million?
Answers
Answer:
hey There
Step-by-step explanation:
This compares with 27.5 percent of those age 55 to 64 and 25.6 percent of those age 65 to 74. With respect to being overweight, 31.8 percent of the individuals 75 and older were such, while 37.9 percent of 55 to 64 year olds and 37.8 percent of individuals age 65 to 74 were overweight (figure 1).
Answer:
66.9%
i hope thats right
Let a function f (x) = x² + 1
Find f (4):
Answers
Answer:17
Step-by-step explanation:
Plug in 4 in the place of x and then add 1
\( 👋 \) Hello ! ☺️
Step-by-step explanation:
F(x)= x² +1
\( f(4) = 4 {}^{2} + 1 \)
\( f(4)= 16+1 \)
\(\boxed{\color{gold}{f(4) = 17}} \)
\(<marquee direction="left" scrollamount="2" height="100" width="150">💘Mynea04</marquee>\)
What is the least common denominator of 5/12 and 1/2
Answers
2 I believe I’m not 100% sure tho
If x>0, what is the quotient of 20√ z^6/√ 16z^7 in simplest radical form?
Answers
I suppose you meant z > 0, or meant to use x's in place of z's…
If z > 0, then
\(\dfrac{20\sqrt{z^6}}{\sqrt{16z^7}} = \dfrac{20\sqrt{\left(z^3\right)^2}}{\sqrt{4^2\left(z^3\right)^2z}} = \dfrac{20\left|z^3\right|}{4\left|z^3\right|\sqrt{z}} = \boxed{\dfrac{5}{\sqrt{z}}}\)
because
\(\sqrt{z^2} = |z|\)
and if z is positive, we have |z| = z, and we can eliminate common factors of z in the fraction,
\(\dfrac{\left|z^3\right|}{\left|z^3\right|} = \dfrac{z^3}{z^3} = 1\)
4) Isabel had three times as many dollars as her sister. Isabel has fifteen dollars. How much
money docs her sister have?
Answers
I hope this helps:))
Answer: Her sister has five dollars.
Step-by-step explanation:
15 = 3x
15/3 = 5
= 5
The simplified expression of
5
x
−
8
−
2.25
x
+
3
5x−8−2.25x+3 is
Answers
Answer:
44.5x - 13
Step-by-step explanation:
Combine like term.
The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 10 and 30 minutes late. (b) It is 10 A.M. There is a 20% probability the friend will arrive within how many minutes? part a) what is the probability that the friend is between 10 and 30 minutes late_?
Answers
The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.
The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.
The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.
Therefore, the probability of the friend being between 10 and 30 minutes late is:
P(10 < x < 30) = (height of rectangle) x (width of rectangle)
= (1/30) x 20
= 2/3
≈ 0.6667
So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
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MATHS QUESTIONS PLEASE SOLVE
1. 121 Divided by 11 is
11
10
19
18
2. 60 Times of 8 Equals to
480
300
250
400
3. Find the Missing Term in Multiples of 6 : 6, 12, 18, 24, _, 36, 42, _ 54, 60.
32, 45
30, 48
24, 40
25, 49
4. What is the Next Prime Number after 7 ?
13
12
14
11
5. The Product of 131 × 0 × 300 × 4
11
0
46
45
6. Solve 3 + 6 × ( 5 + 4) ÷ 3 - 7
11
16
14
15
7. Solve 23 + 3 ÷ 3
24
25
26
27
8. What is 6% Equals to
0.06
0.6
0.006
0.0006
9. How Many Years are there in a Decade?
5 years
10 years
15 years
20 years
10. How Many Months Make a Century?
12
120
1200
12000
Answers
2. 480
3. 30, 48
4. 11
5. 0
6. 14
7. 24
8. 0.06
9. 10 years
10. 1200
If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.
Answers
Answer:
To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.
F1 × F2 can be expanded using the distributive property:
F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3
= 36y^2 + 12y - 54y - 18
= 36y^2 - 42y - 18
Now we can subtract F3 from the result:
F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)
= 36y^2 - 42y - 18 + y + 8
= 36y^2 - 41y - 10
Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.
(please mark my answer as brainliest)