Given:
a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.
To find:
The GCF of given terms.
Solution:
Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.
The given terms are
[tex]a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}[/tex]
Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is
[tex]GCF=a^{24}\times b^{20}[/tex]
[tex]GCF=a^{24}b^{20}[/tex]
Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.
use the rule to write the first five terms of the pattern: Rule: add 8, subtract 4 First term: 13
Answer:
17
Step-by-step explanation:
13 + 8 - 4
Answer:
{13, 17, 21, 25, 29}
Step-by-step explanation:
Add 8 and subtract 4 is equivalent to Add 4.
If the first term is 13, the next is 17;
the second term is 21; and
the third term is 25.
What is the solution of the equation 5* - 1 = 45? Round your answer to the nearest ten-thousandth.
Answer:
The answer is 3.3652
Step-by-step explanation:
Find the number in the thousandth place
5
and look one place to the right for the rounding digit
2
. Round up if this number is greater than or equal to
5
and round down if it is less than
5
.
3.365
which one is the answer
Answer:
Two
Step-by-step explanation:
Here is a diagram of a person standing next to a tree.
The diagram shows two centimeter rulers.
The tree and the person are drawn to the same scale.
The person is approximately 1.75 m tall.
Using the scale diagram, estimate the height of the tree in meters.
15 points + Brainiest + Heart
The estimated height of the tree is approximately 5 meters.
To estimate the height of the tree using the scale diagram, we need to compare the height of the person on the diagram to the height of the tree.
Given that the person's height is approximately 1.75 meters, we can use the scale of the diagram to make the estimation.
Let's assume that the scale on the diagram is such that each centimeter on the ruler corresponds to 1.75 meters in real life.
By measuring the height of the person on the diagram using the ruler, let's say it corresponds to 2 centimeters.
Now, using the scale of 1.75 meters per centimeter, we can calculate the estimated height of the tree:
2 centimeters * 1.75 meters/centimeter = 5 meters
Therefore, based on the scale diagram, the estimated height of the tree is approximately 5 meters.
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Estimate. −49100+1021= ________
Answer:
-48079
Step-by-step explanation:
-(49100-1021)
-48079
digits to write the value of the 5 in this number.587,096
Answer: what does the question even mean
Step-by-step explanation:
A restaurant chef made 4 1/2 pints of mushroom soup Each bowl of soup holds 1/2 of pint. How many bowls of soup will.the chef be able to fill?
Answer:
4 2/4
Step-by-step explanation:
4 1/2 + 1/2 = 4 2/4
i just added em up
Answer:
Step-by-step explanation: 4 1/2 pints / 1/2 pint/ bowl = (9/2) / (1/2) = 9/2 pints x 2 bowl/pint = 18/2 bowls = 9 bowls. QED.
Mrs. Hanley wants to put her 29 students into groups of 6 how many groups of 6 can she make if she puts any remaining students in the smaller group how many students will be in that group. Haley wants to put 29 students into groups of six how many of six can she make if she puts any remaining students in a smaller group how many students will be in
Answer: she can make 4 groups of 6 and there will be 5 left in the other group
Step-by-step explanation: because im right
Jollibee employs a total of 10 cashiers and 15 kitchen crews. The manager selects a team of 2 cashiers and
4 kitchen crews for a graveyard shift. In how many ways can the manager select a team?
Answer:
The manager can select a team in 61425 ways.
Step-by-step explanation:
The order in which the cashiers and the kitchen crews are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In how many ways can the manager select a team?
2 cashiers from a set of 10.
4 kitchen crews from a set of 15. So
[tex]T = C_{10,2}*C_{15,4} = \frac{10!}{2!(10-2)!}*\frac{15!}{4!(15-4)!} = 45*1365 = 61425[/tex]
The manager can select a team in 61425 ways.
all vertical and horizontal cross-sections of any Cube are all the same size and shape what about vertical and horizontal cross-sections of a pyramid are they all the same size are they all the same shape discuss why or why not
Answer:
All the horizontal sections are the same shape like their base, but have different sizes.
All vertical sections through top are triangles, size are different.
The vertical sections not cut through top are 4 sided shapes, sizes are different.
Step-by-step explanation:
50 points I WILL ALSO MARK BRAINLIEST ITS TIMED PLZ HURRY
The coordinates of the vertices of a polygon are shown on the graph below.
On a coordinate plane, point A is at (negative 4, 3), point C is at (0, negative 3), and point B is at (negative 4, negative 3).
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answer:
Triangle
Step-by-step explanation:
Option D. triangle
What is 5/10 = x/100
Answer:
= 50
Step-by-step explanation:
What is the velocity of a car that’s traveled 306 kilometers northeast in 3.4 hours
Answer : -302.6
Step-by-step explanation:
6. Cindy and Sam are 24 miles apart on a path when they start moving
toward each other. Cindy runs at a constant speed of 10 miles per
hour, and Sam walks at a constant speed of 6 miles per hour.
How long does it take until Cindy and Sam meet?
Answer:
2 hours to meet each other
Step-by-step explanation:
Answer:
1.5
Step by step explanation:
Kevin plants a total 72 flowers in a equal row. He plants 6 rows of yellow flowers and 2 rows of red flowers. How many flowers are in each row?
Answer:
9
Step-by-step explanation:
9 is the answer bc
6+2=8
72/8=9
(lol I hope I helped)
Factor to write an equivalent expression for -9x+15y
Answer:
Step-by-step explanation:
-9x +15y = 3(-3x +5y) = -3(3x - 5y)
The required equivalent expression for the given expression -9x + 15y is 3(-3x + 5y).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).
The given expression is given as follows:
-9x + 15y
It is required to find the factorization of the given expression.
As per the question, we have
-9x + 15y
To factor -9x + 15y, we can first factor out the greatest common factor (GCF) of -9 and 15, which is 3:
-9x + 15y = 3(-3x + 5y)
Therefore, the equivalent expression for -9x + 15y is 3(-3x + 5y).
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the triangle Loom is made from wood strips shaped into a 45 45 90 triangle. pegs are placed every half inch along the hypotenuse and every quarter inch along each leg. suppose you make a loom with an 18 inch hypotenuse. approximately how many pegs will you need
Answer:
36 pegs (for the hypotenuse)
About 51 pegs (for the legs)
138 pegs (total)
Step-by-step explanation:
Along the hypotenuse, the pegs are placed every half-inch. That would make 2 pegs per inch. Multiply 2 x 18 to get 36.
The legs are each 9 sqrt 2. This is 12.7279220614. The pegs are placed at each quarter inch for the legs. This is 4 per inch. So multiply 12.7279220614 x 4 to get 50.9116882454. Round this to 51.
Add 51 + 51 for the legs total pegs. You get 102. Add 102 + 36 to get 138 pegs total.
Hope it helps!
Which shows the simplified form of the expression below? 90y^4-120y-360y^3+30y^2
Show all steps you took to get the answer
Answer:
[tex]90y^4-120y-360y^3+30y^2 = 30y((y - 4)(3y^2+1))[/tex]
Step-by-step explanation:
Given
[tex]90y^4-120y-360y^3+30y^2[/tex]
Required
Simplify
[tex]90y^4-120y-360y^3+30y^2[/tex]
Factor out 30y
[tex]90y^4-120y-360y^3+30y^2 = 30y(3y^3 - 4 - 12y^2 + y)[/tex]
Reorder the expression
[tex]90y^4-120y-360y^3+30y^2 = 30y(3y^3 - 12y^2 +y - 4 )[/tex]
Factorize
[tex]90y^4-120y-360y^3+30y^2 = 30y(3y^2(y - 4) +(y - 4) )[/tex]
Combine the factors
[tex]90y^4-120y-360y^3+30y^2 = 30y((3y^2+1)(y - 4))[/tex]
Rewrite as:
[tex]90y^4-120y-360y^3+30y^2 = 30y((y - 4)(3y^2+1))[/tex]
A pool of possible jurors consists of 15 men and 14 women. How many different juries consisting of 5 men and 7 women are possible?
Answer:
6
Step-by-step explanation:
Um so what I did was 15/5=3 and 14/7+2
So for the first group of men, 2 groups. TIMES 3.
Equals 6 options
The diagram shows a logo
Answer/Step-by-step explanation:
✔️Find EC using Cosine Rule:
EC² = DC² + DE² - 2*DC*DE*cos(D)
EC² = 27² + 14² - 2*27*14*cos(32)
EC² = 925 - 756*cos(32)
EC² = 283.875639
EC = √283.875639
EC = 16.85 cm
✔️Find the area of ∆DCE:
Area = ½*14*27*sin(32)
Area of ∆DCE = 100.15 cm²
✔️Since ∆DCE and ∆ABE are congruent, therefore,
Area of ∆ABE = 100.15 cm²
✔️Find the area of the sector:
Area of sector = 105/360*π*16.85²
Area = 260.16 cm² (nearest tenth)
✔️Therefore,
Area of the logo = 100.15 + 100.15 + 260.16 = 460.46 ≈ 460 cm² (to 2 S.F)
Jolyn was paid $340 last week working 17 hours. What was Jolyn’s hourly pay? Do not include the units in your answer
Answer:
20
Step-by-step explanation:
It is mentioned that Jolyn made $340 in 17 hours last week. In order to evaluate this, you'll have to divide the money earned by the hours worked.
[tex]\frac{340}{17} =20[/tex]
Therefore, Jolyn makes $20 an hour as 20 x 17 = 340 which is correct,
CEOLATIONS AND INEQUALITIES
Finding angle measures of a triangle given angles with variables
In the triangle below, suppose that m U=(x+9)°, m = (2x+1), and mW=(7x)".
Find the degree measure of each angle in the triangle.
Answer:
seventeen degrees(17⁰)
Can someone help me ASAP
Answer:
x= (-∞,∞)
Step-by-step explanation:
x could be any value and make this equation true
Anthony borrowed $18,800 at 6% simple interest for 4 months. Determine the amount of interest.
Solve the right triangle round your answer to the nearest tenth
Answer/Step-by-step explanation:
✔️A = 180° - (50° + 90°) (sum of triangle)
A = 40°
✔️Find a:
Reference angle = 50°
Opposite = 17
Adjacent = a
Therefore, using trigonometric ratio, we have the following:
Tan 50 = 17/a
a = 17/tan 50
a = 14.3 (nearest tenth)
✔️Find c using Pythagorean Theorem:
c² = a² + b²
c² = 14.3² + 17²
c = √493.49
c = 22.2 (nearest tenth)
Which expression is the sum of
-5.3m + 3.4n and 2.5n + 2.8m?
A. -2.8m + 6.2n
B. -2.5m + 5.9n
C.-8.1m + 0.9n
D. 2.5m + 5.9n
+
B
Answer:
b
Step-by-step explanation:
its b because you add the 3.4n +2.5n then you subtract -5.3+2.8
36
Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?
(5, 4)
(9, 4)
(2, 9)
(4, 8)
Answer:
9,4
Step-by-step explanation:
Previous balance: $1,221.35; payment: $300; new purchases: $25.90 and$18.53; periodic rate: 1.75%
Answer:
1478.67
Step-by-step explanation:
Suppose a day from this city is selected at random. Let
event A = heavy traffic and event B = bad weather. Are
events A and B independent?
Answer:
The two events are not independent
Step-by-step explanation:
Two events are said to be independent only when the change in one event affect the other event.
Here the two given events are not independent.
Band weathers such as heavy rainfall, snowfall etc. leads to failure of traffic management system and thereby causes heavy traffic. This is easily seen in all major urban cities.
Hence, the two events are not independent as the traffic is affected by the weather conditions.
A flying disc was originally marked at 5$ and has been sold at $3.50. What was the percent of discount?
Answer:
30%
Step-by-step explanation:
Percentage discount
[tex] = \frac{discount}{original \: price} \times 100\% \\ = \frac{5 - 3.50}{5} \times 100\% \\ = 30\%[/tex]
☆ Discount= original price -selling price