find the greatest common factor of the numbers 20,45

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

haro has more

Step-by-step explanation:

Answer:

Which expression is equivalent to ((4^((5)/(4)).4^((1)/(4)))/(4^((1)/(2))))^((1)/(2))?

Since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.

An included side is a side that is in between two angles in a triangle, where the rays of the angles overlap.

Thus, in triangle ABC, side AC lies in between angle A and angle C.

Therefore, since angle A and angle C forms side AC, AC is included between: A. ∠A and ∠C.

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Answer: A

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

1 2 are the only numbers below 3

therefore 2/6= 1/3

a. The amount of copper in a bronze of 360g is 324g

b. The mass of bronze with 670.5g of copper is 745g

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The ratio of copper to Tin is 9:1. The total ratio is 10

a.therefore the amount of copper = 9/10 × 360

= 324g

b. The mass of copper = 670.5g

therefore the mass of the bronze =

= 9/10× y = 670.5

9y = 670.5 × 10

9y = 6705

y = 6705/9

y = 745g

therefore the total mass of the bronze is 745g

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Answer:

If two triangles are proven to be congruent, then every single corresponding side and angle between those two triangles are congruent by CPCTC Theorem. CPCTC stands for Corresponding parts of congruent triangles are congruent.

Explanation:

CPCTC Theorem states that if two triangles are congruent, then their

Using Algebraic expression solution ,

The cost of three hats is $18 .

We have given that,

A hat company charge for design fee $4 per hat .

i.e design fee of one hat = $4

total cost of 5 hats = $30

let the cost of one hat without design fee be $x and total cost of one hat is $(x+4) .

using the above statement, we get an algebraic expression,

5( x+ 4)= 30

we solve the above algebra expression,

=> 5x + 20 = 30

=> 5x = 10

=> x = 2

so, cost of a hat without design fee is $2

and total cost of one hat is $6.

we have to calculate cost of 3 hats .

cost of one hat in hat company= $ 6

cost of three hats in hat company= $(6×3)

= $18

Hence, the total cost of 3 hats is $18.

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Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

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To find the definite integral of a function over an interval using the limit definition, we divide the interval into smaller subintervals and approximate the integral by summing the areas of corresponding rectangles.

The width of each subinterval is determined by dividing the length of the interval by the number of subintervals.

In this case, the interval is [2, 5], and we are dividing it into n subintervals. To find the width of each subinterval, we calculate the length of the interval by subtracting the lower endpoint from the upper endpoint:

Length of interval = upper endpoint - lower endpoint = 5 - 2 = 3.

Then, we divide the length of the interval by the number of subintervals (n):

Width of each subinterval = Length of interval / Number of subintervals = 3 / n.

So, the width of each subinterval is 3/n.

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The fuel-flow indicator rotor and needle in a motor-impeller and turbine indicating system are driven by a mechanism that measures and displays the rate at which fuel is flowing to the engine.

The fuel-flow indicator rotor and needle play a crucial role in providing real-time information about the rate of fuel consumption in an engine. The rotor is typically connected to a turbine or impeller, which is driven by the flow of fuel passing through it. As the fuel flows, it causes the rotor to rotate, and this rotational motion is then translated into the movement of a needle on the indicator display. The position of the needle corresponds to the fuel flow rate, allowing the operator or pilot to monitor and control the fuel consumption.

This indicating system is important for several reasons. Firstly, it enables operators to monitor fuel usage, ensuring that the engine is receiving an appropriate amount of fuel for efficient operation. Secondly, it provides valuable information for fuel management, allowing adjustments to be made if necessary to optimize performance or conserve fuel. Additionally, the indicator system helps identify any anomalies or irregularities in fuel flow, which can be indicative of potential issues or malfunctions within the engine or fuel system. Overall, the fuel-flow indicator rotor and needle serve as critical components in maintaining engine performance, efficiency, and safety.

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The required answer is the value of z-sub-c for a 94% level of confidence is approximately 1.88.

Explanation:-

To determine the value of z-sub-c (critical value) for a 94% level of confidence, we need to find the z-score that corresponds to a cumulative probability of 0.97 (since the confidence level is 94%).

The z-sub-c value can be obtained using statistical tables or a calculator. For a two-tailed test at a 94% level of confidence, the remaining probability is (1 - 0.94)/2 = 0.03.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to a cumulative probability of 0.97 is approximately 1.88 (rounded to two decimal places).

Therefore, the value of z-sub-c for a 94% level of confidence is approximately 1.88.

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The probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

To find the probability that a random student will be taking both Algebra 2 and Chemistry, we need to use the concept of conditional probability.

Let's denote the event of taking Algebra 2 as A and the event of taking Chemistry as C. We are given that P(A) = 0.08 (8% probability of taking Algebra 2) and P(C|A) = 0.17 (17% probability of taking Chemistry given that the student is taking Algebra 2).

The probability of taking both Algebra 2 and Chemistry can be calculated using the formula for conditional probability:

P(A and C) = P(C|A) * P(A)

Substituting the given values:

P(A and C) = 0.17 * 0.08

P(A and C) = 0.0136

Therefore, the probability that a random student will be taking both Algebra 2 and Chemistry is 0.0136 or 1.36%.

It is important to note that the probability of taking both Algebra 2 and Chemistry is determined by the intersection of the two events, which means students who are taking both courses. In this case, the probability is relatively low, as it depends on the individual probabilities of each course and the conditional probability given that a student is taking Algebra 2.

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Answer:

1.58 meters

Step-by-step explanation:

Answer: 105

Step-by-step explanation:

Given

The ratio of men to women working for a company is 4:7

There are total of 165 employees

Suppose, there is  4x men and 7x women such that the ratio remains constant

\(\therefore 4x+7x=165\\\Rightarrow 11x=165\\\Rightarrow x=15\)

\(\text{Men= }4\times 15=60\\\text{Women= }7\times 15=105\)

Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

Answer:

your mom

1234567891011

810 minutes

if u add ten to 219 each time u will get 13 and 5 left which is 13.5 and 13.5 in minutes equals 810

The probability that exactly two couples state incompatibility as the reason is equal to the probability of two couples citing incompatibility and two couples not citing it.

HTML formatted answer: Given: 65% of all divorce cases cite incompatibility as the underlying reason. To find: Probability that exactly two will state incompatibility as the reason. Solution: As per the given data, The probability of citing incompatibility as the underlying reason for divorce is 65%.

Then, the probability of citing any other reason is (100% - 65%) = 35%.Let the probability of citing incompatibility by any couple as A, and the probability of not citing incompatibility by any couple as B. Here, the total couples filing for divorce = 4. Probability of two couples citing incompatibility and two couples not citing it.P(2C, incompatibility and 2C, not incompatibility)= \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35²The probability of choosing any 2 out of 4 couples = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] = 6The probability of 2 couples citing incompatibility = 0.65²The probability of 2 couples not citing incompatibility = 0.35²Hence,The probability that exactly two couples state incompatibility as the reason isP(2C, incompatibility) = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35² = 6 × 0.4225 × 0.1225 = 0.3218Therefore, the required probability is 0.3218.

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Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.

A deposit ticket is a little paper where you are required to fill in the details of the deposit that you seek to make into your savings account. All information in the ticket ought to be filled accurately.

The teller may have declined to receive the ticket due to incorrect total amount filled on the ticket. Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.

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Answer:

a. the subtotal is calculated incorrectly

Step-by-step explanation:

I'm good at math ;)

Answer:

42 tubes of toothpaste.

The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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Answer:

28 cm

Step-by-step explanation:

The perimeter (P) is the sum of the sides

P = LE + EF + ( FG + HI + JK ) + ( GH + IJ + KL )

   = 8 + 6 + 8 + 6

   = 28 cm

Answer:

so when factorising, you first remove the common factors. in this case it is (x+3)

so what is remaining is the x and 4

you group that together.

my teacher explained that when factorising, after removing the common factor then you divide each term by the common factor, and then group the answers to that in brackets.

so it will be,

\(x(x + 3) + 4(x + 3) \\ (x + 3)( \frac{x(x + 3)}{x + 3} + \frac{4(x + 3)}{(x + 3)} \)

so basically whats left after dividing, is x and 4 because the x+3 cancel off.

and thats how you get the answer of

(x+3)(x+4)

hope this helps;)

The value of the function g(x) at g = 4 is 18.

Given is a function g(x) as follows -

g(x) = 3x² - 5(x + 2)

We have the following function as -

g(x) = 3x² - 5(x + 2)

For g(4), we can write -

g(4) = 3 x (4)² - 5(4 + 2)

g(4) = 3 x 16 - 5 x 6

g(4) = 48 - 30

g(4) = 18

Therefore, the value of the function g(x) at g = 4 is 18.

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Answer:

24.83

Step-by-step explanation:

74.50 divided by 3

Answer:

51

Step-by-step explanation:

since 1 = 39 degrees, it'd be complementary if you were to open it up if it were a C, it would be 90. So since its this way, i believe you would take 39 and do 90 - 39 to get your answer.  Im sorry if this is wrong but i hope it helps you!!

To find the length of the diagonal of square C, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Since square C has equal sides, we only need to find the length of one side and then multiply it by the square root of 2 to get the length of the diagonal.

Using the coordinates given, we can find the length of one side by subtracting the x-coordinate of one vertex from the x-coordinate of the other vertex (11 - 1 = 10). We then multiply this by the conversion factor given in the problem (1 square unit = 25 feet) to get the length in feet (10 * 25 = 250). Finally, we multiply this by the square root of 2 to get the length of the diagonal (250 * sqrt(2) ≈ 353.55 feet).

Therefore, if square C has an area of 2500 square units and each unit is equal to 25 feet, then a square with a diagonal length of approximately 353.55 feet would be an accurate representation of square C.

Answer:

C

Step-by-step explanation:

Using Pemdas:

3 (1 + 4) / 3 + 4^2

3 (5) / 3 + 4^2

3 (5) / 3 + 16

15 / 3 + 16

Answer:

A

Step-by-step explanation:

First you have to simplify the equation, you should use PEMDAS. This means you first have to simplify the parenthesis.  simplify it, multiply 3 by 1 and 4. This makes the equation 3+12/3+4^2. Then following PEMDAS, you simplify the exponent. 4^2 is the same as 4x4 so 4^2 is 16. 3+12/3+16, then you can simplify either side first. 3+12/18, then you simplify the only part left. 15/18. The GCM of this fraction is 3 so you divide both sides by 3. 15/3/18/3. Simplify this to get 5/6.

When you simplify equation A, you get 15/3/6. First simplify 15/3 to get 5. This equation answer is 5/6 which is equal to 5/6 so this is the correct answer.

When you simplify equation B, you get 15/3/8. Simplify 15/3 again and get 5. This equation answer is 5/8 which is not equal to 5/6 so this is not the correct answer.

When you simplify equation C, you get 15/3/16. Simplify 15/3 first and get 5. 5/16 is not equal to 5/6 so this is not the correct answer.

Therefore, Equation A is the correct answer.

Answer:

Step-by-step explanation:

\(Midpoint of AC = \left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2} \right)\\\\x_{1}=-2 \ and \ y_{1}=-4\\\\\left(\dfrac{-2+x_{2}}{2},\dfrac{-4+y_{2}}{2} \right) = \left(6 ,8 \right)\\\\\\Compare \ x-coordinates \ and \ y-coordinates\\\\\dfrac{-2+x_{2}}{2}=6 \ ; \dfrac{-4+y_{2}}{2}=8\)

-2 + x₂ = 6*2           ; -4 + y₂ = 8*2

-2 + x₂  = 12            ; -4 + y₂ = 16

        x₂ = 12+2        ;        y₂ = 16+4

        x₂ = 14            ;         y₂ = 20

Point C(14, 20)