Answers
Answer:
Option A) [tex]-6r^2s^4t^3[/tex] is correct
Therefore the result is [tex]\frac{18r^4s^5t^6}{-3r^2st^3}=-6r^2s^4t^3[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{18r^4s^5t^6}{-3r^2st^3}[/tex]
To find the result of the given expression:
That is solve the fractional expression as below:
[tex]\frac{18r^4s^5t^6}{-3r^2st^3}[/tex]
[tex]\frac{18r^4s^5t^6}{-3r^2st^3}=\frac{-6r^4s^5t^6}{r^2st^3}[/tex]
[tex]=-6r^4s^5t^6.r^{-2}s^{-1}t^{-3}[/tex] ( using the properties [tex]\frac{1}{a^m}=a^{-m}[/tex] and [tex]a^m.a^n=a^{m+n}[/tex])
[tex]=-6r^{4-2}s^{5-1}t^{6-3}[/tex]
[tex]=-6r^2s^4t^3[/tex]
Therefore [tex]\frac{18r^4s^5t^6}{-3r^2st^3}=-6r^2s^4t^3[/tex]
Therefore the result is [tex]-6r^2s^4t^3[/tex]
Therefore option A) [tex]-6r^2s^4t^3[/tex] is correct
Related Questions
30 points
Which expression is equivalent to | a | ≤ 4 ?
1. a ≥ –4 and a ≤ 4
2. a ≤ –4 or a ≥ 4
3. a ≤ –4 and a ≥ 4
4. a ≥ –4 or a ≤ 4
Answers
Answer:
1. a ≥ –4 and a ≤ 4
Step-by-step explanation:
Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4
:)
For any two integers x + y, |x+y|=|x|+|y|
Answers
Answer:
Sometimes true.
Step-by-step explanation:
The statement is sometimes true and sometimes false depending on the values of x and y.
Here's an example that shows it to be true.
|x+y|=|x|+|y|
Let x = 5 and y = 6.
|x+y|=5 + 6 = 11
|x|+|y| = |5| + +|6| = 5 + 6 = 11
In this case, both sides equal 11, and the expression is true.
Here's an example that shows it to be false.
|x+y|=|x|+|y|
Let x = -5 and y = 5.
|x+y|= |-5 + 5| = |0| = 0
|x|+|y| = |-5| + |5| = 5 + 5 = 10
The left side equals 0, and the right side equals 10. The sides are different, and the expression is false.
Find the Lowest Common Multiple of 108 and 120
Answers
Answer:
Step-by-step explanation:
108 = 2*2*3*3*3=2² * 3³
120 = 2*2*2*3*5=2³*3*5
LCM = 2³*3³*5 = 8*27*5= 1080
To find the LCM of 108 and 120, first find their prime factorizations and then multiply the highest power of each prime factor.
Explanation:To find the Lowest Common Multiple (LCM) of 108 and 120, we can first find their prime factorizations. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, while the prime factorization of 120 is 2 × 2 × 2 × 3 × 5. We can then find the LCM by taking the highest power of each prime factor from both numbers. So, the LCM of 108 and 120 is 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2,160.
The Lowest Common Multiple (LCM) of 108 and 120 is 1080. This is found by finding the prime factors of each number, and then multiplying together the highest power of each factor.
Learn more about LCM here:https://brainly.com/question/35898348
#SPJ2
How to you use a unit rate to solve a rate problem for any number of units?
Answers
Answer:
Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.
Step-by-step explanation:
We are asked the way to use a unit rate to solve a rate problem for any number of units.
Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.
Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.
Since [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)
If an employee earns $20.00 per hour plus $1.50 per hour for vacation and you pay $2.00 per hour in tax and $9.00 for every $100.00 in payroll for workers compensation what is the total hourly wage for the employee ?
Answers
- 2 = 19.5
so hourly he gets paid $19.50
Maria is starting a small business selling flowers. She has to pay $150 for a vendor’s permit. Each bouquet costs her $7 and she sells them for $15. How many bouquets must Maria sell to break even?
Answers
22 bouquets must Maria sell to break even.
bouquet costs per unit $7
vendor permit $150
number of bouquet need to sell to meet break even 22 item (150/7)
22 item need to selled to meet the break even.
What is sale?A sale is a deal involving two or more people when tangible or intangible commodities, services, or assets are exchanged for cash. A seller may occasionally receive assets in addition to money.
In the financial markets, a sale can also be defined as an agreement between a buyer and a seller specifying the purchase price and delivery details of a financial security.
A sale is essentially a contract between a seller of a certain good or service and a buyer who is willing to pay for that good or service, regardless of the environment.
To learn more sale, refer;
https://brainly.com/question/15375944
#SPJ2
Explain the Pythagorean Theorem
Answers
Answer:
Pythagorean theorem theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle
100/60 is exactly 1.66666666667. When I do long division my answer comes up as 1.6 with the decimal repeating, am I doing anything wrong
Answers
Answer:
I don't think you are doing anything wrong. Just ignore it and write the repeating decimal. If you're asked to do it, round it up instead.
Answer:
No you aren't doing anything wrong, it's just that the calculator is rounding the answer. So yes 1.6 repeating is correct
16
Select the correct answer.
For Al, its atomic number is 13 and its mass number is 27. How many neutrons does it have?
O
A.
13
ه
ن
م
نا
40
Reset
Next
Answers
Answer:
14.
Step-by-step explanation:
The number of neutrons = the mass number - atomic number
= 27 - 13 = 14.
The correct answer is that Aluminium (Al), with an atomic number of 13 and a mass number of 27, has 14 neutrons.
To find the number of neutrons in an atom, one subtracts the atomic number (which is the number of protons) from the mass number (which is the sum of the number of protons and neutrons).
For Aluminium:
- The atomic number (Z) is 13, which means it has 13 protons.
- The mass number (A) is 27, which means the total number of protons and neutrons is 27.
The number of neutrons (N) can be calculated using the formula:
[tex]\[ N = A - Z \][/tex]
[tex]\[ N = 27 - 13 \][/tex]
[tex]\[ N = 14 \][/tex]
Therefore, Aluminium has 14 neutrons.
The function y = – 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?
Answers
The range of the function y = -3, graphed over the domain {x | -8 < x < 8}, is a singular value, which is y = -3.
Explanation:The question asks for the range of the function y = -3 which is graphed only over the domain {x | -8 < x < 8}. This function is a horizontal line, which means that for any value of x within the domain, the value of y will always be -3.
Therefore, the range of this function is simply the single value y = -3, because no matter what x-value we have (as long as it's between -8 and 8), the y-value remains constant at -3.
fractions greater than 1
Answers
These are all fractions that are greater than 1. You can create any of these by putting a bigger number on the top than on the bottom of the fraction
Answer:
Anything with a numerator (top) greater then the denominater (bottom) here are some examples:
[tex] \frac{11}{2} [/tex]
[tex] \tfrac{8}{5} [/tex]
[tex] \frac{399}{7} [/tex]
[tex] \frac{6}{2} [/tex]
Hope this information helps my friend!
An online store is offering 15% off all items in your order. Before the discount is applied, the items in your cart are: shampoo for $6.35, conditioner for $6.35, granola bars for $12.50, dish soap for $13.40, and toothpaste for $2.50. What is the discounted total price for all the items, assuming no sales tax is added? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.
Answers
Answer:
The total discounted price is 34.93
Step-by-step explanation:
The items in the cart are:
Shampoo for $6.35Conditioner for $6.35Granola bars for $12.50Dish soap for $13.40 Toothpaste for $2.50Total cart = $ 41.10
Discount = 41.10 * 0.15 = $ 6.17
Discounted total price = 41.10 - 6.17
Discounted total price = 34.93
Answer:
34.94.
Step-by-step explanation:
First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.
Next, we can calculate the discount: =(15/100)×$41.10=$6.165.
Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.
What is the algebraic expression for the following word phrase: the quotient of 6 and z?
A. 6+z
B. 6z
C. 6-z
D. 6/z
Answers
Answer:
Step-by-step explanation:
the quotient is the result of division
the quotient of 6 and z...
6/z <===
** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6
A rectangle park measures 300 ft by 400 ft. A sidewalk runs diagonally from one comer to the opposite corner. Find the length o
the sidewalk
a 400 ft
c 250 ft
b. 500 ft
d. 650 ft
Answers
The length of side walk is 500 feet
Solution:
Given that, A rectangle park measures 300 ft by 400 ft
Length = 300 feet
Width = 400 feet
A sidewalk runs diagonally from one comer to the opposite corner
We have to find the length of side walk
Which means, we have to find the length of diagonal of rectangle
The diagonal of rectangle is given by formula:
[tex]d = \sqrt{w^2+l^2}[/tex]
Where,
d is the length of diagonal
w is the width and l is the length of rectangle
Substituting the values in formula, we get
[tex]d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500[/tex]
Thus length of side walk is 500 feet
This year's Super Bowl will be the 54th. There have been 53 Super Bowls and
the NFC has won 3 more Super Bowls then the AFC. How many games did each
conference win?
Answers
Answer:
Therefore NFC won 28 games and AFC won 25 games.
Step-by-step explanation:
i) let the number of Super Bowls won by NFC be x
ii) let number of Super Bowls won by AFC be y
iii) therefore it is given that x + y = 53
iv) and also it is given that x = y + 3
v) substituting the equation in iv) into the equation in iii) we get
(y +3) + y = 53 ⇒ 2y = 50 therefore y = 25.
vi) substituting the value of y from v) into the equation iv) we get
x = 25 + 3 = 28.
Therefore NFC won 28 games and AFC won 25 games.
To solve this mathematics problem, we formulate an equation based on the information that total Super Bowls were 53 and NFC won 3 more than AFC. By solving the equation, we find that NFC won 28 games and AFC won 25 games.
Explanation:To solve this problem, let's start with the total number of games, which is 53. If the NFC has won 3 more Super Bowls than the AFC, that means the number of games won by both conferences adds up to 53. Let's denote the number of games won by the AFC as 'x'. So, the equation will be:
x + (x + 3) = 53By combining like terms, we get:
2x + 3 = 53Subtracting 3 from both sides, we have:
2x = 50Finally, when we divide by 2, we solve for x:
x = 25This means that the AFC has won 25 games, and the NFC, having won 3 more, has won 28 games.
Learn more about Algebraic equation here:https://brainly.com/question/953809
#SPJ12
You estimate that your friend is 50 inches tall. That actual height of your friend is 54 inches. Find the percent error.
Answers
To find the percent error, calculate the absolute difference between the estimated height and the actual height, and divide it by the actual height. Finally, multiply the result by 100 to get the percentage.
Explanation:To find the percent error, we need to calculate the absolute difference between the estimated height and the actual height, and then divide it by the actual height.
Finally, we multiply the result by 100 to get the percentage.
Step 1: Determine the difference between estimated and actual height.
Difference = Actual height - Estimated height
Difference = 54 inches - 50 inches
Difference = 4 inches
Step 2: Calculate the absolute value of the difference.
Absolute value of the difference = |4 inches|
Absolute value of the difference = 4 inches
Step 3: Divide the absolute difference by the actual height and multiply by 100% to get the percent error.
Percent Error = (Absolute difference / Actual height) × 100%
Percent Error = (4 inches / 54 inches) × 100%
Percent Error ≈ 7.41%
Therefore, the percent error in your estimation of your friend's height is approximately 7.41%.
How would I solve (6r +3)2 and show my work?
Answers
Answer:
12r+6
Step-by-step explanation:
2(6r+3)
2(6r)+2(3)
12r+6
Roger served 5/8 pound of crackers, which was 2/3 of entire box. What was the weight of crackers originally in box?
Answers
Answer:
original weight of the box = 15 / 16 pounds
Step-by-step explanation:
Identify a decimal number between 0.25 and 0.125
Answers
Answer: 0.126?
Step-by-step explanation:
A decimal number between 0.25 and 0.125 could be 0.2 or 0.15. These numbers sit within the specified range and comply with the principles of decimal number placement.
Explanation:The task here is to identify a decimal number that lies between 0.25 and 0.125. To achieve this, we can carefully select a decimal value that stands in the middle of these two numbers. An example of a suitable decimal would be 0.2, as it comfortably sits within this specified range. Another example could be 0.15. These are both valid decimal numbers that reside between 0.25 and 0.125, and their selection adheres to the principles of decimal number placement on a number line.
Learn more about Decimal Number Placement here:https://brainly.com/question/34233482
#SPJ3
How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30 % sugar syrup?
Answers
Answer:
5 liters of water.
Step-by-step explanation:
Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.
Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or
[tex]Sugar\:syrup =0.3(15+y)[/tex]
And since this must equal the amount of syrup we had before:
[tex]0.3(15+y)=0.4(15)[/tex]
[tex]4.5+0.3y=6[/tex]
[tex]0.3y=1.5[/tex]
[tex]\boxed{y=5}[/tex]
Thus, 5 liters of water must be added to obtain 30% sugar syrup.
Answer:
5 liters of water
Factor the polynomial: 2x(x - 4) + 7(x-4)
O A. 14x(x-4)
O B. (x – 4)(2x- 7)
O C. (2x - 4)(x+7)
O D. (x – 4)(2x+7)
Answers
Answer:
D
Step-by-step explanation:
Given
2x(x - 4) + 7(x - 4) ← factor out (x - 4) from each term
= (x - 4)(2x + 7) → D
Show step by step for equation -8/3x + 4(x + 9/4) = -2/3(x + 12/8) + 3
Answers
Answer:
see attached picture please
Is 15/18 an equivalent ratio
Answers
Answer:
no
Step-by-step explanation:
bc
15/18 cant be simplified no matter what
Answer:
No
Step-by-step explanation:
15/18 can not be simplified
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
3
0.98
1.21
0.33
Answers
Answer:
0.33
Step-by-step explanation:
Aight so all we do is use the formula, as shown here:
[tex]\frac{\Delta x}{\Delta y}[/tex]
[tex]x[/tex] is this amount it changed, which is 0.99. So we plug that for [tex]\Delta x[/tex]:
[tex]\frac{0.99}{\Delta y}[/tex]
Then, we find the amount of times the storm changed, and we plug that for [tex]\Delta y[/tex]:
[tex]\frac{0.99}{3}[/tex]
So, now that we have utilized the formula, we can now solve!
[tex]\frac{0.99}{3} = 0.33[/tex]
Good luck!
Answer:
0.33
Step-by-step explanation:
A baby goes to sleep at 8 p.m., wakes up after two hours, stays awake for 15 minutes, and then goes back to sleep. If the baby repeats this sleep pattern until she is awakened at 6 a.m., what percent of the time from 8 p.m. to 6 a.m. was the baby asleep?
Answers
Answer:
Step-by-step explanation:
If the baby repeats this sleep pattern until she is awakened at 6 a.m., what ... We have 10 hours between 8PM and 6AM = 10 * 60 = 600 minutes ... Awake 12:15 - 12:30 ... There are 4 periods of 2 hour sleep and 1 period of 1 hour sleep = 4*2(60) + 1(60) ... So 540/600 = 54/60 = 9/10 = 90% of the time asleep.
Answer:
87.5%
Step-by-step explanation:
I am not sure how to set this up....so I am just gonna try to figure this a different way....without any formula
8 p.m - 10 pm.......awake for 15 minutes
10 pm - 12 am......awake 15 minutes
12 am - 2 am.......awake 15 minutes
2 am to 4 am.....awake 15 minutes
4 am to 6 am....awake 15 minutes
so from 8 pm to 6 am....that is a total of 10 hrs.....and in those 10 hrs, the baby was awake 5(15) = 75 minutes.....change 10 hrs to minutes.....1 hr = 60 min...so 10 hrs = (10 * 60) = 600 minutes
so in 600 minutes, the baby was awake 75 minutes.....that means the baby was asleep (600 - 75) = 525 minutes
525/600 = 0.875 = 87.5% <=== baby was asleep
or maybe this way....for every 2 hrs, the baby was awake 15 minutes....means the baby was asleep (120 - 15) = 105 minutes.
2 / 105 = 10 / x
2x = 1050
x = 1050/2
x = 525 minutes.....so the baby was asleep 525 minutes out of 600 minutes.
525/600 = 0.875 = 87.5%
I am getting the same answer either way
trigonometry help (angles of evaluation and depression)
Answers
Answer:
240.3
Step-by-step explanation:
Remember SohCahToa for the trig. ratios. You always divide two sides.
'o' is opposite side. 'a' is adjacent side. 'h' is hypotenuse side.
Using alternating angles you can find the angle I marked blue (see diagram below). Because the 31° is parallel to the bottom side of the triangle, you can use alternating angles (Z pattern), where both 'insides' of the Z have the same measure.
The blue angle will be our angle of reference (angle we are talking about) represented by this symbol θ.
Since we need to find 'y', the opposite side, and we know 400ft is the adjacent side, use the tangent ratio.
tanθ = opposite / adjacent
tan31° = y / 400ft Substitute what you know.
y = (400ft)tan31° Isolate 'y'. Multiply 400ft and tan31°.
y = 240.344......ft Exact answer on calculator
y ≈ 240.3ft Answer rounded to nearest tenth
The nearest tenth is the first decimal. Since the second decimal is '4 or less', you round down, keeping the digit of the first decimal the same.
If the second digit was '5 or more', then you would round up.
Find the quotient. 22x2y2 ÷ 11x2y2
Answers
Quotient = 2
Solution:
Given expression is [tex]22x^2y^2\div11x^2y^2[/tex].
To find the quotient.
[tex]22x^2y^2\div11x^2y^2=\frac{22x^2y^2}{11x^2y^2}[/tex]
In numerator 22 can be written as 2 × 11.
[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{2\times11x^2y^2}{11x^2y^2}[/tex]
Take common term out in the numerator and denominator.
[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{(11x^2y^2)(2)}{11x^2y^2}[/tex]
Common terms in the numerator and denominator will be cancelled.
[tex]\frac{22x^2y^2}{11x^2y^2}=2[/tex]
Hence the quotient is 2.
Answer:
The guy up top is right its 2 with no mistake.
Step-by-step explanation:
If 5 is an element in the domain of f(x)= 8x-21/5, what is the corresponding element in the range?
Answers
The corresponding element in the range when 7 is an element in the domain is f(5)=179/5
Step-by-step explanation:
Given that the 5 is an element in the domain of f(x)
The function f is defined by f(x)=8x-21/5
To find the corresponding element in the range:
That is put x=5 in the given function f(x)
Therefore f(x) becomes
f(5) = 8(5)-21/5
=40-21/5
=179/5
Therefore corresponding element in the range when 5 is an element in the domain is f(5)=179/5
Learn more about how to find the domain of a function here:brainly.com/question/1369616
Rewrite the following expression using the distributive property and the GCF: 36+48
Answers
Answer:
12(3+4)
Step-by-step explanation:
Answer:
Etc: 12 34
Step-by-step explanation:
Can you help me on a math problem?
Answers
Answer: -3 and +3
Step-by-step explanation: