[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{14ab^2x^3}{2abx^2}=\dfrac{14}{2}\cdot\dfrac{a}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{x^3}{x^2}=7\cdot1\cdot b^{2-1}\cdot x^{3-2}=\boxed{7bx}[/tex]
Answer:
[tex]7bx[/tex]
Step-by-step explanation:
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{14}{2}=7 =\frac{7ab^2x^3}{abx^2}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:a =\frac{7b^2x^3}{bx^2}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:b =\frac{7bx^3}{x^2}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}[/tex][tex]\frac{x^3}{x^2}=x^{3-2}=x[/tex]
[tex]=7bx[/tex]
Hope this helps!!!
At a farm, Justin picks 3 bushels of fruit. The bushels weigh 8 1/4 pounds, 6 1/2 pounds and 6 5/8 pounds. What is the average weight per bushel .
Answer:
The average weight is 7 1/8 pounds
Step-by-step explanation:
To find the average, we add them up and then divide by how many
average = (b1+b2+b3)/3
= (8 1/4 + 6 1/2+ 6 5/8) /3
Let look at the sum
(8 1/4 + 6 1/2+ 6 5/8)
We need to get a common denominator of 8
8 1/4 *2/2 + 6 1/2 *4/4 + 6 5/8
8 2/8 + 6 4/8 + 6 5/8
20 11/8
20 + 1 3/8
21 3/8
average = (21 3/8) /3
Now we divide by 3
We need to change the mixed number to an improper fraction
21 3/8 = (8*21+3) /8 = 171/8
average = (171/8) /3
We can use copy dot flip
171/8 * 1/3
171/24
We need to change it back to a mixed number
24 goes into 171 7 times with 3 left over
7 3/8
7 1/8
Eliot made a line plot to record the number of birds he saw at his bird feeder .How many more sparrows than blue jays did he see?If you help me answer the question correctly I will give you 48 points and mark u BRAINLIEST
Answer:
He saw 4 more
Step-by-step explanation:
There were 5 sparrows and 1 blue jay 5 - 1 = 4
simplify the expression. 16-4[3+2÷(9-7)]
Answer:
0
Step-by-step explanation:
Answer:
IT ALL EQUALS TO 0.
Step-by-step explanation:
Step 1: Parenthesis:
16 - 4[3 + 2 / 2]
Sep 2: dO DIVISION IN THE BRACKETS:
16 - 4[3 + 1]
Step 3: Add what is in the brackets
16 - 4[4]
Step 4: Multiply
16 - 16
Step 5: Simplify
0
There is a café at the park.
It is 13 metres long and 8 metres wide. What is the area of the café?
Answer:
42 meters
Step-by-step explanation:
because 13 + 13 + 8 + 8 = 42. and that's your answer
Final answer:
The area of the café is calculated by multiplying the length (13 meters) by the width (8 meters), resulting in an area of 104 square meters (104 m²).
Explanation:
The area of the café at the park can be calculated using the formula for the area of a rectangle, which is the product of its length and width. Given that the café is 13 meters long and 8 meters wide, we multiply these two dimensions to find the area.
Step-by-Step Calculation
Identify the length (13 meters) and the width (8 meters) of the rectangle.
Multiply the length by the width: Area = length × width.
Calculate: 13 meters × 8 meters = 104 square meters (104 m²).
Therefore, the area of the café is 104 m².
What percent is equivalent to 18/40 ?
18%
22%
40%
45%
Answer:
45%
Step-by-step explanation:
You do 18 divided by 40
Which is .45
what is the 52nd term for the following sequence ? 14,6,-2,-10,-18
It's an arithmetic sequence:
[tex]a_1=14\\a_2=14-8=6\\a_3=6-8=-2\\a_4=-2-8=-10\\a_5=-10-8=-18\\\vdots\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=14,\ d=-8.\\\\\text{Substitute:}\\\\a_n=14+(n-1)(-8)=14-8n+8=22-8n\\\\\text{We need}\ a_{52}.\ \text{Put n = 52 to the formula}:\\\\a_{52}=22-8(52)=22-416=-394[/tex]
What is the simplified form of (−7x3 + 5x2 − x + 6) − (−8x3 + x2 + 3)?
A. −x3 + 4x2 − x + 3
B. x3 + 4x2 − x + 3
C. x3 − 4x2 − x − 3
D. −15x3 + 6x2 − x + 9
Answer:
B. x3 + 4x2 − x + 3
Step-by-step explanation:
(−7x^3 + 5x^2 − x + 6) − (−8x^3 + x^2 + 3)
Distribute the negative sign
(−7x^3 + 5x^2 − x + 6) + (8x^3 - x^2 - 3)
I like to line them up vertically.
−7x^3 + 5x^2 − x + 6
8x^3 - x^2 - 3
----------------------------------
x^3 +4x^2 -x +3
The simplified form of the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3) is x³ + 4x² – x + 3, corresponding to option B.
To simplify the expression ( –7x³ + 5x² – x + 6) – (–8x³ + x² + 3), we need to remove the parentheses and then combine like terms.
First, distribute the negative sign through the second set of parentheses: –7x³ + 5x² – x + 6 + 8x³ – x² – 3.
Next, combine like terms: (–7x³ + 8x³) + (5x² – x²) – x + (6 – 3).
This simplifies to x³ + 4x² – x + 3.
So, the correct simplified form of the expression is option B. x³ + 4x² – x + 3.
The perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm. Find the length of the other diagonal and area of the rhombus
Hi there! :)
Answer:
Length of the second diagonal: 54 cm
Area of the rhombus: 1,944 cm²
Step-by-step explanation:
1) To find the value of the second diagonal, you first need to know some important properties of rhombuses:
Since the perimeter is 180, and by definition a rhombus has four congruent sides (of equal length), each side length of the rhombus is equal to 45.
The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to half the lengths of the diagonals. In this case one hypotenuse would be equal to 45 and one leg would be equal to 36 (72 ÷ 2 = 36).
We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:
c² = a² + b² → Where "c" is the hypotenus & "a" and "b" are the two other sides.
45² = 36² + b² → Where "b" is the half of the unknown diagonal.
We can now solve this equation for "b":
45² = 36² + b²
45² = 2,025
36² = 1,296
2,025 = 1,296 + b²
Subtract "1,296" from each side of the equation → 2,025 - 1,296 = 729
729 = b²
Square root on each side of the equation → √729 = 27
27 = b
Since "b" represents half of the unknown diagonal, we need to multiply by 2 to find the full length of the diagonal:
27 × 2 = 54 ⇒ Length of the other diagonal.
2) To find the area of the rhombus, you need to multiply the length of the 2 diagonals and divide the answer by 2:
(72 × 54) ÷ 2 = A
Multiply "72" & "54" together → 72 × 54 = 3,888
3,888 ÷ 2 = A
1,944 = A
There you go! I really hope this helped, if there's anything just let me know! :)
Ben made a model that was 5 3/4 inches tall. Laquisha made a model that was 70 11/12 inches tall. How many times as tall was Laquisha’s model?
To determine how many times taller Laquisha's model is compared to Ben's model, convert their heights to improper fractions and divide, simplifying the result to find the ratio.
Explanation:To find out how many times taller Laquisha's model is compared to Ben's model, we divide their heights. Laquisha's model height is
70 11/12 inches, and Ben's model height is 5 3/4 inches. First, convert the mixed numbers to improper fractions. Ben's height as an improper fraction is 23/4 inches. Laquisha's height as an improper fraction is 851/12 inches. Next, divide Laquisha's model by Ben's: (851/12)
÷ (23/4). To divide fractions, we multiply by the reciprocal of the second fraction: (851/12)
× (4/23). Simplify to find the ratio, which represents how many times taller Laquisha's model is.
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answer:
The helicopter still needs to fly up sec 17.0886 at maximum speed.
Step-by-step explanation:
To find out how far the helicopter went down do 100(seconds) * 10.5 and get 1050
Then how much he traveled back up same thing 150 (seconds) * 5.2 and get 780
Next find the difference 780-1050 and get -270 ft it is negative because it is still BELOW GROUND ( That's how you know if it need to fly up or down)
Last to find how many seconds you need you work backwards so instead of multiplying you do the opposite witch is dividing so you take your feet (270) and divide by the maximum speed (15.8). 270/15.8 is 17.08
-7n+4(-6+3n) what is the answer
Answer:
5n - 24
Step-by-step explanation:
distribute the parenthesis by 4
= - 7n - 24 + 12n ← collect like terms
= (- 7n + 12n) - 24 = 5n - 24
Answer:
5n-24
Step-by-step explanation:
-7n+4(-6+3n)
Distribute:-7n-24+12n
Simplify: 5n-24
In Maria's store, the customer count this week is 3000. Maria is planning a promotion and expects a 5% increase in customers next week. How many additional customers is Maria expecting?
Answer:
150
Step-by-step explanation:
3000 * 0.05 = 150
What is the proportion of 19/12 = f/9
Answer:
Alright well solve for f by cross multiplying
Exact form: f = 57/4
Decimal form: f = 14.25 Hope this helps have a nice day :)
Step-by-step explanation:
PLEASE HELP ASAP
Approximately how many times greater is 5 x 10 to the eighth power than 8 x 10 to the fifth power?
Answer:
about 11920.92896
Step-by-step explanation:
what scale factor was used in dilation
Answer: (c) [tex]\bold{\dfrac{3}{4}}[/tex]
Step-by-step explanation:
Chooe any point I am choosing point W.
The W' is closer to C than W so the dilation is less than 1
The only answer choice that is less than 1 is option c.
Why is this the answer? because the side lengths are proportional
[tex]\dfrac{CW'}{CW} = \dfrac{WX'}{WX}= \dfrac{3}{4}[/tex]
i dont know can you help?
Answer:
84
Step-by-step explanation:
42x2=84
multiply 2 with 42 which comes out as 84
solve the inequality. graph your solution |x|>5
[tex]|x|>5\iff x>5\ \vee\ x<-5[/tex]
The value of the digit 4 in 24, 601 is how many times greater then the value digit 4 in 437
Answer:
The Answer is 10 times as much.
Step-by-step explanation:
We know that the 4 in 24,601 is 4000. We also know that the 4 in 437 is 400. If we do 4000/400, we get 10 times as much!
I hope this helps.
Tim answered all the questions on his math test but got 10 answers wrong . He revived 4 points for every correct answer , and there was no penalty for wrong answers . His score was 76 points .
Write an equation to determine the total number of question (q) on Tim’s math test .
76 points/ 4 points per questions means he answered 19 questions correctly
plus the 10 he answered incorrectly
76/4+10=x
19+10=x
29=x
A particular computer takes 13-minutes to download a 52-minute TV show. How long will it take the computer to download a 1.5-hour movie?
The particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
Explanation:In this particular problem, we need to figure out how long a computer will take to download a movie. The computer in question takes 13 minutes to download a 52 minute TV-show, establishing a rate of downloading. We can therefore calculate how long the computer takes to download a minute of TV-show by dividing the download time by the length of the show: 13/52 = 0.25 minutes per minute of show. Next, we convert 1.5 hours (the length of the movie) into minutes, because our rate is in terms of minutes: 1.5*60 = 90 minutes. We then multiply this by our download rate (0.25) to get our answer: 90*0.25 = 22.5 minutes. Thus, this particular computer will take approximately 22.5 minutes to download a 1.5 hour movie.
Learn more about Calculating Download Time here:https://brainly.com/question/33722206
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Which explains whether or not the values in the table represent a direct variation? x 4 6 10 20 y 1 1.5 2.5 5 The table represents a direct variation because the values are proportional. The table represents a direct variation because the values are nonproportional. The table does not represent a direct variation because the values are proportional. The table does not represent a direct variation because the values are nonproportional.
Answer:
Option A is correct.
The table represents a direct variation because the values are proportional.
Step-by-step explanation:
The direct variation says that:
[tex]y \propto x[/tex]
then; the equation is of the form : [tex]y =kx[/tex] where k is the Constant of Variation.
Consider any values of x and y from the table, to solve for k;
Let x = 10 and y = 2.5
then;
[tex]2.5 = 10k[/tex]
Divide both sides by 10 we have;
[tex]k = \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4}[/tex]
Then the equation becomes:
[tex]y =\frac{1}{4}x[/tex]
Therefore, the table represents a direct variation because the values are proportional.
Answer: A The table represents a direct variation because the values are proportional.
Step-by-step explanation:
Rewrite the following expression using the associative property
(4x+9x)+12x
Solve the equation -18=p/2?
Answer:
p=-36
Step-by-step explanation:
-18=p/2
______________________
Multiply both sides by 2
-18(2)= p/2 (2)
______________________
-36 = p
switch the sides of the equation
______________________
p=-36
Which of the following options best describes an algebraic fraction?
Select all that apply.
common denominators
a variable in the numerator
a variable in the denominator
a variable with an exponent
Answer:
Common denominators
A variable in the numerator
A variable in the denominator
Step-by-step explanation:
Note: An an algebraic fraction is the fraction that has some algebraic expression in numerator and some algebraic expression in denominator.
So, if fractions would have common denominators, a variable in the numerator or a variable in the denominator would be an algebraic fraction.
Therefore, following options best describes an algebraic fraction:
common denominatorsa variable in the numeratora variable in the denominatorThere are 38 cube houses with 1000 unit cubes that are 1 meter by 1 meter by 1 meter discribe the dimensions of a cube house using unit cubes
Elizabeth received a car loan for $12,000. She was charged 8% for the bank fees. What is the total amount that she will need to pay the bank back for the loan?
A.
$860
B.
$960
C.
$11,040
D.
$12,960
Answer:
B
Step-by-step explanation:
If you do 12,000 - 92% it gives you 960 and the 92% is = 11,040
What's the lateral area of a right cylinder if the radius of the base is 12mm and the altitude of the cylinder is 5 times the base radius? Use the π key to calculate and round your answer to the nearest whole number.
Answer:
1440π squared mm.
Step-by-step explanation:
Given is the radius of base of cylinder, r = 12mm.
The altitude is five times the base radius, h = 5 times 12mm = 60mm.
The lateral area of the cylinder is the curved surface area of the cylinder.
The formula for curved surface area of cylinder is as follows:-
Curved Surface Area = Circumference of base x altitude of cylinder.
SA = 2πrh = 2π•12•60 = 1440π sq. mm.
Hence, Lateral area of cylinder is 1440π squared mm.
Answer:
1440π
Step-by-step explanation:
We are given the radius of the base of a right cylinder to be 12 mm and its altitude or height to be 5 times the base radius which is equal to (12 x 5) = 60 mm.
We know the formula for the lateral area of a right cylinder:
[tex]A = 2\pi rh[/tex]
So putting in the given values with [tex]\pi[/tex] as it is to get:
[tex]A=2\pi *12*60[/tex]
[tex]A=2(720)\pi[/tex]
[tex]A=1440\pi[/tex]
Therefore, the lateral area of this right cylinder is 1440π.
Which phrase should be inserted on the line to make a true statement
Answer:
[tex]\frac{8}{12}[/tex] equal to [tex]\frac{8}{12}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ------------------------- [tex]\frac{8}{12}[/tex]
Lets compare both the fractions
To compare both the fractions the denominators should be same
Lets make the denominators same
WE try to get 12 in the denominator of first fraction, so we multiply top and bottom by 4
[tex]\frac{2*4}{3*4}=\frac{8}{12}[/tex]
[tex]\frac{8}{12}[/tex] ------------------------- [tex]\frac{8}{12}[/tex]
Both fractions are equal
So [tex]\frac{8}{12}[/tex] equal to [tex]\frac{8}{12}[/tex]
Chris need a graphing calculator for math class c find a $60 model on sale for 15% off if you decide to buy this calculator how much will the sale price be
A)9
B)12
C)51
D)69
Answer:
C) $51
Step-by-step explanation:
Step 1. Calculate the discount
The discount is 15 % of $60
Discount = 60 × 0.15
Discount = $9
===============
Step 2. Calculate the sale price
Sale price = original price - discount
Sale price = 60 - 9
Sale price = $51
The sale price will be $51.
Factor the expression. d2 − 4d + 4
Rewrite it in the form a^2 - 2ab + b^2, where a = d and b = 2
d^2 - 2(d)(2) + 2^2
Use the Square of Difference: (a - b)^2 = a^2 - 2ab + b^2
(d - 2)^2
Answer:
(d - 2)²
Step-by-step explanation:
d² - 4d + 4 ← is a perfect square of the form
(x ± a )² = x² ± 2ax + a²
compare coefficients of like terms
- 2a = - 4 ⇒ a = 2 and a² = 4, hence
d² - 4d + 4 = (d - 2)²