Answer:
9
Step-by-step explanation:
Factors are numbers we can multiply together to get another number.
A common factor is one that is a factor of two (or more) numbers.
The greatest common factor (GCF) is the largest of the common factors.
There are a few ways to find the GCF. One way is to find all the factors of both numbers, then find the ones that are common to both and choose the greatest:
The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54
The factors of 153 are: 1, 3, 9, 17, 51, 153
Therefore, the greatest common factor is 9.
The expression which represents the greatest common factor (GCF) of 54 and 153 is 3×3. Correct option is B.
The greatest common factor (GCF) of two numbers is the largest positive integer that divides both numbers evenly.
To find the GCF of 54 and 153, we need to determine the common prime factors of these two numbers and then multiply those factors together.
The prime factorization of 54:
= 2 × 3 × 3 × 3
= 2 × 3³.
The prime factorization of 153:
= 3 × 3 × 17
= 3² × 17.
The common prime factors of 54 and 153 are two factors of 3, so the GCF is 3 × 3, which can be written as 3².
Hence, 3 × 3 is the expression which represents the greatest common factor (GCF) of 54 and 153. Option B is correct.
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Complete question:
Which expression represents the greatest common factor (GCF) of 54 and 153?
(A) 2×2
(B) 3×3
(C) 2×2×2×3
(D) 2×2×2×3×1
What is the range of the absolute value function below?
Marcel walks due north 50 meters from a tree. Katya walks 20 meters in a straight line away from the same tree but at an angle of 42° from due north, as shown in the diagram below. How far apart are Marcel and Katya to the nearest meter?
The distance from Marcel and Katya is 34 metres
SOH CAH TOA identityFrom the given diagram, we have the following
Hypotenuse = 50mOpposite = xAcute angle given = 42 degrees
According to SOH CAH TOA identity
sin theta = opp/hyp
sin 42 = x/50
x = 50sin42
x = 50(0.6691)
x = 33.46
Hene the distance from Marcel and Katya is 34 metres
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Find the mean of:
1.8, 1.7, 1.3, 1.1, 1.2, 1.6, 1.8
Answer: D.
Step-by-step explanation:
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression that can be used to determine the final cost of the DVD.
Write your answer in your own words, please!
If you don't know the answer, don't type anything.
Answer:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
18. 3
+
11
17
3
4
co
loo
8
Step-by-step explanation:
12. 5
11.
10
10
15. 7
14. 11
Answer:
y= 12% + 3%
y= 0.12 + 0.03
y= 0.12 - 0.03
y= 0.09
Step-by-step explanation:
help plss i need ittttt
Translate the sentence into an inequality.
The product of y and 7 is less than or equal to - 20.
Answer:
[tex]7y \leqslant - 20[/tex]
y > x + 1
y < 2x
x 2 >5
Which points are solutions to the system of inequalities shown below?
Answer:A D F
Step-by-step explanation:
Answer:
Step-by-step explanation:
See attached image.
A high definition radio station charges $200 membership fee for one year in addition to $50 per month for the first 6 months to receive its broadcast. The total cost for the services is determined by the number of months
Answer:
300.00$
50$ per month
6 months
50x6
A sequence is defined by the following: an = 4n – 1 What is a1? What is a8?.
Answer:
a^1=1
a^8=16,384
Step-by-step explanation:
The original equation of a^n=4^n-1 uses n as a placeholder variable for whatever value is needed to solve the equation. For the first question, which gives 1=n, substituting 1 into the equation gives you the answer of 1. 1-1=0. You can not have any number to the power of zero however, so due to the multiplicative identity, you end up with a positive 1.
The second one we are given 8=n. 8-1 equal 7. 4 to the power of seven (multiply 4 by itself 7 times) gets you 16, 384.
Given the sequence defined as [tex]a_{n} = 4n - 1[/tex], [tex]a_{1} =3\ and\ a _ {8} = 31[/tex].
What is an arithmetic sequence?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.
[tex]a_{n} = a_{1} + (n-1)d[/tex]
Given sequence:
[tex]a_{n} = 4n - 1\\\\a_{1} = 4 * 1 - 1 = 4 - 1 =3\\\\a _ {8} = 4 * 8 - 1 = 32 - 1 = 31[/tex]
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Simplify. please help!
Answer:
-3y
Step-by-step explanation:
Take the square root of each term inside the radical to get rid of the radical. The square root of 9 is 3 and the square root of y^2 is y, so the square root of 9y^2=3y. Put the negative back in front and you get -3y.
12 and 300 as decimal
Answer:
12/300 as a decimal is 0.04.
Find the value of x. Round your answer to the nearest tenth.
Answer:
The value of x is 12.24
Step-by-step explanation:
Given;A right angled-triangleTo Find;The value of xNow,
tan 36 = x/17
0.72 = x/17
x = 17 × 0.72
x = 12.24
Thus, The value of x is 12.24
-TheUnknownScientist 72
help me graph this please
Answer:
what do you need help with
Step-by-step explanation:
If CS = 4 and AD = 10, what is the measure of CD? Round to the nearest hundredth. Show all your work.
The measure of the length of line segment CD is; 12.8
Pythagoras theoremPythagoras theorem States that the square of the hypotenus of a triangle is equal to the sum of the square of the opposite and square of the adjacent side.
From the task content, the center of the circle is at point S and since CS = 4;
It follows that CA = 4× 2 = 8.Hence, it follows from Pythagoras theorem that;
CD = √(8² + 10²)CD = √64+100CD = √164.CD = 12.8Read more on Pythagoras theorem;
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The bag contains 20 red marbles, 30 white marbles, and 40 blue marbles.
What is the ratio of red to blue marbles?
What is the ratio of white to red marbles?
Answer:
Red : Blue = 20: 40 = 1 : 2
White: Red = 30 : 20 = 3 : 2
Solve for x.
4 + 3x = 16
To solve this equation we must isolate the variable.
3x = [?]
First subtract 4 from both sides of the equation.
Calculate the new value of the right side of the equation.
Step-by-step explanation:
4 + 3x =16
subtracting 4 on both sides
4-4 + 3x =16-4
0+ 3x = 12
3x = 12
x = 12/3
x= 4
Train 1 travels at a constant speed of 240 miles in 3 hours. Train 2 travels 490 miles in 7 hours. Which train is faster?
Answer:
Train 1
Step-by-step explanation:
Train 1 has constant speed: 240 miles / 3 hours = 80 mph.
Train 2 has constant speed: 490 miles / 7 hours = 70 mph.
So, Train 1 is faster.
Included in the definition of an elliptic curve is a single element denoted O and called the point at infinity or the ____ .
Answer:
Zero Point
Step-by-step explanation:
Two people worked on a car. The first person charged $ 85 per hour, and the second person charged $ 120 per hour. The people worked for a combined total of 15 hours, and together they charged a total of $ 1450. How long did each person work?.
The number of hours the first person worked on the car is 5, while the number of hours for which the second person working on the car is 10.
What is an equation?
An equation is formed when two equal expressions are equated so that the value of a variable can be found.
Let the number of hours for which the first person worked on the car is x
In order to solve the problem, we will make two equations. Now, since we know that the total number of hours for which the two-person worked on the car is 15, therefore, we can write it as,
[tex]x+y =15[/tex]
The amount charged by the first person is $85 per hour, while the amount charged by the second person is $120, and the total cost of the two is $1450 combined. therefore, the total cost can be written as
[tex]85x+120y = 1450[/tex]
As we got the two-equation solving the two-equation, to get our answer.
In the first equation, we will isolate y, in order to get the value of y in terms of x,
[tex]x+y = 15\\y = 15-x[/tex]
As we got the value of y, substitute the value in the second equation,
[tex]85x+120(15-x) = 1450\\85x+1800 - 15x = 1450\\70x = 350\\x = 5[/tex]
As we have the value of x, substitute the value in the first equation,
[tex]x+y=15\\(5)+y=15\\y=10[/tex]
Hence, the number of hours the first person worked on the car is 5, while the number of hours for which the second person working on the car is 10.
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Mike owns a skate shop. He is preparing the cash flow statement for his first year of operation. He had a beginning cash balance of $4,800, $103,000 in total cash sales, $3,500 for utilities, $2,600 in loan payments, and $5,500 for marketing cost. What is Mike's ending cash balance? Ending Cash Balance = Beginning Cash Cash Inflow – Cash Outflow Hint: Do not forget to include the comma to separate the digits and to type the $ symbol! Example: $32,100.
Mike's ending cash balance of the cash flow statement for his first year of operation is $95,400.
What is cash flow?Cash flow is defined as the report which shows the total inflow and outflow of the business for a particular financial period.
Given
Mike owns a skate shop. He is preparing the cash flow statement for his first year of operation.
He had a beginning cash balance of $4,800, $103,000 in total cash sales, $3,500 for utilities, $2,600 in loan payments, and $5,500 for marketing cost.
Total cash inflow = $4,800 + $103,000 = $107,800
Total cash outflow = $3,500 + $2,600 + $5,500 = $11,600
Then the cash flow will be
[tex]\rm Cash\ flow = \$ 107,000 - 11,600\\\\Cash\ flow = \$ 95,400[/tex]
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A large health care system gave all nurses a flat wage increase. A union representative sampled 50
nurses and found that the mean increase in total wages was 5.2%
with a standard deviation of 1.61.
Using a 95% confidence interval, which statement from the union best describes the wage increase for all nurses in the system?
A. The average wage increase for nurses in the system was between 3.6%
3.6% and 6.8%.
B. The average wage increase for nurses in the system was 5.2%.
C. The average wage increase for nurses in the system was 5.205%.
D. The average wage increase for nurses in the system was between 4.76%
4.76% and 5.65%.
Answer:
NOT The average wage increase for nurses in the system was between 3.6% and 6.8%.
Step-by-step explanation:
How do I solve this?
Answer:
By using your brain? XD
Here's the answer:
2:5 of 63
2+5=7
2/7 X 63=18
5/7 X 63= 45
Tina recieves 18/63 (2/7)
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Solve the following linear equations a) a+7 =15
Answer:
a = 8
Step-by-step explanation:
a + 7 = 15
a + 7 - 7 = 15 - 7 Subtract 7 from both sides.
a = 8
Answer is
A = 8
Because 8 + 7 = 15
The other way to explain we need to subtract 7 ( 7 -7 = 0 and 15 - 7 = 8 ) both sides so after subtracting you will get 8
A tree was 4 m tall. One year later, the tree grew f m and became 10 m tall. Write an equation for the height of the tree
Answer:
6m
Step-by-step explanation:
10m-4m=6m
I hope this helped!
Answer:
4+6=10
Step-by-step explanation:
Geometric mean between 9 and 25
Answer:
the answer is 15
The geometric mean of 25 and 9 is 15 . Example 2: ... So, the geometric mean of the three numbers is the cube root of their product.
Answer:
15
Step-by-step explanation:
the geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex] , then
geometric mean of 9 and 25 is
[tex]\sqrt{9(25)}[/tex] = [tex]\sqrt{225}[/tex] = 15
What are the solutions of 12 - x2 = 0?
O x=2,5 and x = -2/3
O x=373 and x = -312
O x= 4/5 and x = -4/3
* x= 6 and x = -6
[tex]12 - 2x = 0 \\ - 2x = 0 - 12 \\ -2x = - 12 \\ - x = - 12 \div 2 \\ - x = - 6 ( - can \: be \: cancelled \: if \: its \: in \: both \: side)\\ x = 6[/tex]
kindly swipe right to left for full solution.
the solutions for the quadratic equation are 3.46 and -3.46
How to solve the quadratic equation?
Here we have the equation:
12 - x^2 = 0
To solve this, first, we add x^2 on both sides:
12 = x^2
Now we can just apply the square root on both sides, to get:
±√12 = x
±3.46
So the solutions are 3.46 and -3.46
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help ill mark brainliest
Answer:
[tex]-2\frac{1}{2}[/tex]
Step-by-step explanation:
Rewriting our equation with parts separated
=[tex]2+\frac{5}{6} -5\frac{1}{3}[/tex]
Solving the whole number parts
[tex]2-5=-3[/tex]
Solving the fraction parts
[tex]\frac{5}{6} -\frac{1}{3}[/tex]
Find the LCD of 5/6 and 1/3 and rewrite to solve with the equivalent fractions.
LCD = 6
[tex]\frac{5}{6} -\frac{2}{6} =\frac{3}{6}[/tex]
Reducing the fraction part, 3/6,
[tex]\frac{3}{6} =\frac{1}{2}[/tex]
Combining the whole and fraction parts
[tex]-3+\frac{1}{2} =-2\frac{1}{2}[/tex]
Hence, the correct answer is -2 1/2
[RevyBreeze]
Your most trustful answer
help me pls!!
find x and y
y= -3x=-19
5x+8y=0
Answer:
x= -8; y= 5
Step-by-step explanation:
5x + 8 ( -3x -19) =0
5x -24x -152 =0
5x -24x= 152
-19x = 152
x= -8
y= -3x -19
y= -3(-8) -19
y= 5
5x + 8y = 0
5(-8) + 8(5) =0
-40 + 40 = 0
can you pls answer 1 and 2 ?? ( i am clueless how to do this )
Answer:
1: M'N'P'Q is NOT the dilation
2. UVW is the dilation
which one of the following rules describes this transformation?