The Greatest Common Factor of 34 and 51 is 17.
What is Greatest Common Factor?The greatest common factor is the largest number that is a factor of two or more numbers (GCF). The greatest number (factor) divides them, yielding a Natural number. Once all of the number's variables have been identified, there are a handful that are shared by both. The greatest common factor is the largest number found among the common factors. The GCF is often referred to as the Highest Common Factor (HCF)
Given:
We have to find the greatest common factor of 15 and 21 .
So factorizing each number
34 = 2 x 17
51 = 3 x 17
So, the Greatest Common Factor is 17.
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The greatest common factor of 34 and 51 is 17. It is the largest number that divides both numbers without a remainder, and it is found by listing the factors of each number and identifying the greatest one that they have in common.
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 34 and 51, we list the factors of each number:
Factors of 34: 1, 2, 17, 34
Factors of 51: 1, 3, 17, 51
As we can see, the common factors of 34 and 51 are 1 and 17.
Therefore, the greatest common factor of 34 and 51 is 17.
AT THANKSGIVING DINNER, EMMA'S FAMILY ATE 1/3 OF A PUMPKIN PIE. WHAT FRACTION OF THE PIE WAS LEFT OVER?
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Total pumpkin in fraction = 1
= 1 - 1/3
= 2/3
The fraction of the pie left over is 2/3
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Amount of pumpkin pie eaten by the family = 1/3
Let the total pumpkin in fraction = 1
Now,
The fraction of the pie left over.
= 1 - 1/3
= (3 -1)/ 3
= 2/3
Thus,
The fraction of the pie left over is 2/3
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Which law would you use to simplify the expression (x^⁴)⁹ ?
A. product of powers
B. power of a product
C. power of a quotient
D. power of a power
if you see this similar format you will recognize the equation as power of a power ^^•
Five boxes of candles contain a total of 60 candles. each box holds the same number of candles.
Answer:
60/5=12
Step-by-step explanation:
You know that a certain trait occurs in 30% of the population. You want to know how many individuals you have to draw from the population, on average, to get three subjects with the trait.
To find out how many individuals you have to draw from the population, on average, to get three subjects with the trait, you can use the geometric distribution. The average number of trials until the third success can be calculated by dividing 1 by the probability of success.
Explanation:To find out how many individuals you have to draw from the population, on average, to get three subjects with the trait, you can use the geometric distribution.
The probability of success (finding an individual with the trait) is 30% or 0.30, and the probability of failure is 70% or 0.70.
To calculate the average number of trials until the third success, you divide 1 by the probability of success:
1 / 0.30 = 3.33
Therefore, on average, you would have to draw from the population about 3.33 individuals to get three subjects with the trait.
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The radius,
R
, of a sphere is
5.8m
. Calculate the sphere's volume,
V
.
Use the value
3.14
for
π
, and round your answer to the nearest tenth.
a student finds the slope of a line between (14,1) and (18,17). she writes 1-17/18-14 what mistake did she make?
Answer:
Mistake was in denominator.
Step-by-step explanation:
If a line passes through two points ( a, b ) & ( c, d )
Then slope of this line will be = [tex](\frac{d-b}{c-a})[/tex]
Now we come to the question.
a student finds the slope of a line passing through ( 14, 1 ) and ( 18, 17 ) as
slope = [tex](\frac{1 - 17}{18-14})[/tex]
This formula is not the form of [tex](\frac{d-b}{c-a})[/tex]
Accurate answer should be
slope = [tex](\frac{1-17}{14-18})[/tex]
So mistake was in denominator.
Find the coordinates for the vertex of the graph of the function y = 3x^2- 12x + 12
A basketball player is 15 ft horizontally from the center of the basket, which is 10 ft off the ground. At what angle should the player aim the ball if it is thrown from a height of 8.2 ft with a speed of 29 ft/s ?
Which of the following is a factor of 3x3 + 18x2 + 27x?
9x
x3
x + 3
x - 3
If m arc AB = 120°, then which of the following have measures of 60°? (pick as many as you want)
a)∠ADB
b)∠ACD
c)∠BCA
d)∠BAD
e) m arc BC
The correct answers are:
a)∠ADB; and c)∠BCA.
Explanation:
The measure of an intercepted arc is twice as much as the measure of its inscribed angle. AB corresponds with both ∠ADB and ∠BCA. Since the arc is 120°, each angle would be half of that, or 60°.
Point E has a negative x-coordinate, and its y-coordinate is not 0
Where could point E be located on the coordinate plane?
What is 8/25 as a percentage?
The first term in a sequence is x. Each subsequent term is three less than twice thw preceding term. what is the 5th term in the sequence?
A) 8x-21
B) 8x-15
C) 16x-39
D) 16x-45
E) 32x-93 ...?
Philip charges $12 to rake the yard she charges $5 per hour to bag the piles of leaves for 2 hours what is the expression
What is the solution to the equation -2n -2 / 3 =12 ? n =
2-5|5m-5|=-73 absoute value
Which is greater 2 gallons or 8 liters?
Suppose
cos(π/2−x) =3/5, cos x =4/5
find sin, tan, csc, sec, cot
To find the values of sin, tan, csc, sec, and cot, we use trigonometric identities and given information. Sin x = 3/5, tan x = 3/4, csc x = 5/3, sec x = 5/4, and cot x = 4/3.
Explanation:To find the values of sin, tan, csc, sec, and cot, we can use the trigonometric identities. From the given information, we know that cos x = 4/5. Using the Pythagorean identity, sin² x = 1 - cos² x, we can find sin x as:
sin x = sqrt(1 - (4/5)²) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5
Now, we can calculate the remaining trigonometric values:
tan x = sin x / cos x = (3/5) / (4/5) = 3/4
csc x = 1 / sin x = 1 / (3/5) = 5/3
sec x = 1 / cos x = 1 / (4/5) = 5/4
cot x = 1 / tan x = 1 / (3/4) = 4/3
45 equals the quotient of a number n and 3
The equation representing the student's question is 45 = n / 3. To find n, we multiply both sides by 3, resulting in n = 135.
Explanation:The student's question, "45 equals the quotient of a number n and 3," can be translated into a mathematical equation. The word 'quotient' indicates a division operation. We set up the equation as 45 = n / 3.
To find the value of n, we multiply both sides of the equation by 3, giving us 3 * 45 = n. Therefore, n equals 135. The solution to this problem demonstrates how to manipulate an equation to solve for an unknown variable.
In this question, 45 is equal to the quotient of a number, represented by n, and 3.
We can represent this equation as:
45 = n / 3
To find the value of n, we can multiply both sides of the equation by 3:
45 * 3 = n
Therefore, n is equal to 135.
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Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the shape of the graph.
A first number plus twice a second number is 13 twice the first number plus the second totals 20 find the numbers
Evaluate 0!÷1!.
0
1
undefined
Answer:
it is actually not undefined because of the (!), due to this the answer is 1
Step-by-step explanation:
0! 1 5! 120
1! 1 6! 720
2! 2 7! 5,040
3! 6 8! 40,320
4! 24 9! 362,880
those are the factorial calculations
Given the set of numbers (3, 5, 7, 11, 23), what number must be added to the set so that the median of the 6 numbers is 9? what number must be added to the set so that the mean of the 6 numbers is 9?
An electrician charges a $50 house call fee and $65 per hour for work
what is the distance between 0 and 7/10?
SERIOUSLY NEED HELP WITH THIS QUESTION.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
800 cubic feet
1,000 cubic feet
1,200 cubic feet
2,000 cubic feet
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that the volume of cube is 1,000 cubic feet.
The volume of cube is
[tex]V=a^3[/tex]
[tex]1000=a^3[/tex]
[tex]a=10[/tex]
The side length of cube is 10 feet.
It is given that the other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height.
The area of tilted solid is
[tex]V=\text{Area of base}\times \text{height}[/tex]
Since height and base are same, so the area of tilted solid is
[tex]V=(10 \times 10)\times 10=1000[/tex]
The volume of the tilted solid is 1,000 cubic feet. Therefore the correct option is 2.
If you pay for $25.00 for purchase which includes 11% sales tax. how much is the sale tax?
Sales tax is $ 2.75
Further Explanation
How to calculate
Tax = $ 25.00 x (11/100)
Tax = $ 25.00 x 0.11
Tax = $ 2.75
Initial purchase of $ 22.25 + 11% Tax ($ 2.75) = $ 25.00
Or other alternatives:
11% tax
n = sales tax value
11% = $ 25.00 / n
n = $ 25.00 x 11%
n = ($ 25.00 x 11) / 100
n = $ 275/100
n = $ 2.75
So, the sales tax is $ 2.75
Sales tax (VAT) is tax before Value Added Tax (VAT) and is charged each time a sales transaction. A VAT is charged at the manufacturer level / not to retailers (end users). A VAT is collected when delivering goods or services.
Definition of Tax Debt
Debt is an engagement as a result of a special agreement called a debt payable, which requires the debtor to pay the amount of money he has borrowed from creditors.
Sales tax / value-added debt or Sales tax payable is the company's debt to the tax office for sales tax collected by the company from customers for the sale of goods/services. Sales tax rates are deposited by the tax office multiplied by sales / net sales (net sales).
Example
$ 12 cash sale including 10% VAT
Tax Amount: 10 / ÷ 100 × 12 = $ 1.2
Sales Amount: 12 - 1.2 = $ 10.8
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Details
Class: High School
Subject: Mathematics
Keywords: VAT, Tax, Sales
The Shelby University rose garden is a rectangular shape with an area of 192 square feet. The dimensions of the garden are x^2 feet wide by x^2– 61 feet long. How wide is the garden?
a. 3 feet c. 64 feet
b. 8 feet d. 131 feet
...?
A mall distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 2000 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 200 loads per day.
Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents the situation?
Options:
1500x+2000y>=150,000 x+y>=200
2000x+1500y>=150,000 x+y>=200
2000x+1500y<=150,000 x+y<=200
1500x+2000y<=150,000 x+y<=200 ...?
Answer: [tex]2000x+1500y\leq150,000[/tex]
[tex]\Rightarrow x+\leq200[/tex]
Step-by-step explanation:
Let x be the number of loads by land carriers and y be the number of loads by air carriers.
Given: A mall distribution center processes as many as 150,000 pieces of mail each day.
Each land carrier takes 2000 pieces per load and each air carrier 1500 pieces per load.
[tex]2000x+1500y\leq150,000[/tex]
The loading equipment is able to handle as many as 200 loads per day.
[tex]\Rightarrow x+\leq200[/tex]
Hence, the system of inequalities represents the situation is
[tex]2000x+1500y\leq150,000[/tex]
[tex]\Rightarrow x+\leq200[/tex]
Point H is the incenter of triangle ABC. Find DH.
a. 14
b. 7
c. 18
d. 21
Due to a lack of information provided, the length of segment DH in the triangle ABC, where H is the incenter, cannot be determined as provided options could all be possible or might be something entirely different.
Explanation:The question doesn't provide enough information to determine the length of segment DH. In a triangle, the incenter is the center of the inscribed circle (incircle). This is the point where all the angle bisectors of the triangle meet. Segment DH would be a line from the incenter to a point on one of the triangle's sides, in other words, a radius of the incircle. However, without more information such as the length of the sides of the triangle or its area, it isn't possible to determine the length of DH. It could be any of the provided options (14, 7, 18, 21) or something else entirely.
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The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect.
Explanation:The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect. To find the distance DH, we can use the fact that the incenter is equidistant from the three sides of the triangle.
Let AD, BE, and CF be the angle bisectors of triangle ABC, where D, E, and F are the points of intersection with the sides.The incenter H is equidistant from each side of the triangle. So, we have DH = EH = FH.Let DH = x. Then, we have AH = 2x, BH = 2x, and CH = 2x.Therefore, DH = x = (AH + BH + CH)/3 = (2x + 2x + 2x)/3 = 6x/3 = 2x.
Since DH = 2x, the distance DH will be twice the distance from the incenter to any side of the triangle. Without knowing the specific values of the sides of triangle ABC, we cannot determine the exact value of DH. Therefore, none of the given options (a, b, c, d) is the correct answer.
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