Find the GCF of the numbers 16 and 72

The slope intercept form of the equation is B)y=2x-6.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here let us take any two points \((x_1,y_1)=(0,-6)\) and \((x_2,y_2) =(1,-4)\) .

Now using slope formula slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> slope m = \(\frac{-4+6}{1-0}\) = 2

Now using equation formula \(y-y_1=m(x-x_1)\) then,

=> y-(-6)=2(x-0)

=> y+6=2x

=> y=2x-6

Hence the slope intercept form of the equation is B)y=2x-6.

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The expressions that complete the blanks are

Set A              Set B

4x                      -

-4x                   -4x

-16x                  5x

-6x                   6x - 6

10 - 6x             2x + 10

From the question, we have the following parameters that can be used in our computation:

The expressions

Solving set (a), we have

? = 10x - 6x = 4x

? = 2x - 6x = -4x

? = -10x - 6x = -16x

? = 0 - 6x = -6x

? = 10 - 6x

Solving set (b), we have

? = 6x - 10x = -4x

? = 6x - x = 5x

? = 6x - 6

? = 6x - 4x + 10 = 2x + 10

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The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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Answer:

1) 160×20/100

=32

2) 27/50×100

=54percent

3) no. of girls 25-7=18

=18/25×100

=72percent

5) 45percent

6) 14/25×100

=56percent

7) 225percent

9) 9:5

Answer:

1) 32

2) 54

3) 72

5) 45%

6)56

7) 225%

9) 9:5

Step-by-step explanation:

Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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Answer:

True

Step-by-step explanation:

e^{i\pi} + 1 = 0

Simplifying and therefore meaning that the answer is true.

But in all seriousness 6*3 = 18

6*4a = 24a

So yes it is true :)

Answer:

t is less than or equal to -2

Seven hundred one ten-thousandth can be written in decimal form as:

0.07

Decimal form is a way of representing numbers using the base-10 number system, which uses ten digits (0-9) to represent all possible values.

In decimal form, each digit in a number has a place value based on its position in the number, and the value of the number is equal to the sum of the products of each digit and its corresponding place value.

To get this decimal representation, we multiply 700 by 1/10,000:

700 * 1/10,000 = 700/10,000

                       = 0.0700

                       = 0.07

Thus, seven hundred one ten-thousandth is equal to 0.07 in decimal form.

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Complete Question

write seven hundred one ten-thousandth in decimal form

Answer:

0.15 $

Step-by-step explanation:

the vectors u and v are neither parallel nor orthogonal.

What is Orthogonal?

In mathematics, two vectors are said to be orthogonal if they are perpendicular to each other, which means that they meet at a right angle. More generally, in a Euclidean space of any number of dimensions, two vectors are orthogonal if their dot product is zero. This means that the cosine of the angle between them is zero, which implies that the angle between them is 90 degrees (or pi/2 radians). Orthogonal vectors are important in various areas of mathematics, including linear algebra, calculus, and geometry.

The magnitudes of u and v can be found using the Pythagorean theorem:

\(||u|| = \sqrt{((-7)^2 + (-4)^2)} = \sqrt{(49 + 16)} = \sqrt{(65)}\\v = \sqrt{((-16)^2 + 28^2)} = \sqrt{(256 + 784)} = \sqrt{(1040)}\)

Now we can calculate the dot product of u and v:

u · v = (-7)(-16) + (-4)(28) = 112

Putting it all together, we get:

\(112 = \sqrt{65} \sqrt{1040} cos(\theta)\\cos(\theta) = 112 / (\sqrt{65} \sqrt{1040})\\cos(\theta) = 0.926\)

Since the cosine of the angle θ is positive and greater than zero, we can conclude that the angle is acute and the vectors u and v are not orthogonal.

So, in summary, the vectors u and v are neither parallel nor orthogonal.

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Answer:

The vectors are orthogonal because u⋅v = 0.

Step-by-step explanation:

o7

1. In this scenario, the goalie saves 73% of the opponent's shots. Therefore, any digits from 00 to 72 represent shots that are saved, as they fall within the range of the goalie's saving ability.

2. To win the game, the Iceblades cannot let the other team score any goals. Therefore, the goalie needs to save all 5 shots taken by the other team for a group to be a success.

3. Group 1 is a success because the goalie saves all 5 shots taken by the other team. Since no goals are scored, the Iceblades maintain their one-goal lead and are on track to win the game.

4. In this simulation, the successes are the groups where the goalie saves all 5 shots. Based on the information given, Group 1 is the only success. Therefore, there is one success in the 10 groups.

5. Since there is only one success out of the 10 groups, the estimated probability of the Iceblades winning the game would be 1 out of 10, or 1/10. Expressed as a percentage, this is equal to 10%.

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Algebraic reasoning involves using mathematical structures and processes to analyze and solve problems, and it is an important part of mathematical thinking and problem solving.

What is Algebraic expressions.?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can contain one or more variables, which are usually represented by letters, and they can be simplified or evaluated by substituting numerical values for the variables.

For example, the expression "3x + 2y - 5" is an algebraic expression that contains two variables, x and y, and three constants, 3, 2, and 5. The expression can be evaluated or simplified by substituting specific values for the variables. For instance, if we let x = 2 and y = 1, then the expression becomes "3(2) + 2(1) - 5", which simplifies to 3.

Skip counting, clapping hands rhythmically, and calling out numbers in unison can be helpful activities for students to develop and practice early mathematical concepts. However, they are not necessarily examples of algebraic reasoning.

Algebraic reasoning involves using mathematical symbols and equations to represent and solve problems. It typically involves working with variables, manipulating expressions, and solving equations.

Some examples of algebraic reasoning for students might include:

Writing and solving simple equations, such as "2x + 3 = 7"

Using variables to represent unknown quantities in problems, such as "If x is the number of apples John has, and he gives away 3, how many apples does he have left?"

Recognizing and extending patterns, such as identifying the rule for a sequence of numbers and predicting the next term in the sequence

Simplifying expressions and using the distributive property, such as simplifying "3(x+2) + 2(x+1)" to "5x + 8"

Overall, algebraic reasoning involves using mathematical structures and processes to analyze and solve problems, and it is an important part of mathematical thinking and problem solving.

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Answer:

not a right triangle

Step-by-step explanation:

you can use the pythagorean theorem to prove whether not this is a right triangle

if this triangle is a right triangle then the following equality should be true

a²+b²=c²

(9.75)²+(3.45)²=(10.24)²

(95.06)+(11.90)=(104.86)

106.96≠104.86

since the following equality is not true, this is not a right triangle.

The answers are, a) -2x² + 28x - 35, b) x = 7, c) p = $50 and d) P = $63

a) The profit function P(x) is given by the difference between the revenue function R(x) and the cost function C(x):

R(x) = p(x) · x

P(x) = R(x) - C(x)

First, let's substitute the given price function p(x) = 64 - 2x into the revenue function:

R(x) = (64 - 2x) · x

= 64x - 2x²

Now, substitute the cost function C(x) = 35 + 36x into the profit function:

P(x) = R(x) - C(x)

= (64x - 2x²) - (35 + 36x)

= 64x - 2x² - 35 - 36x

= -2x² + 28x - 35

b) To find the number of units that produces the maximum profit, we need to find the value of x that maximizes the profit function P(x).

This can be done by finding the vertex of the parabola represented by the quadratic function P(x) = -2x² + 28x - 35.

The x-coordinate of the vertex of a quadratic function in the form P(x) = ax² + bx + c is given by:

x = -b / (2a)

In this case, a = -2, b = 28, and c = -35:

x = -b / (2a)

= -28 / (2 · -2)

= -28 / -4

= 7

Therefore, the number of units that produces maximum profit is x = 7.

c) To find the price per unit that produces maximum profit, we can substitute the value x = 7 into the price function p(x) = 64 - 2x:

p = 64 - 2x

= 64 - 2 · 7

= 64 - 14

= 50

Therefore, the price per unit that produces maximum profit is p = $50.

d) To find the maximum profit, we substitute the value x = 7 into the profit function P(x):

P(x) = -2x² + 28x - 35

= -2 · 7² + 28 · 7 - 35

= -2 · 49 + 196 - 35

= -98 + 196 - 35

= 63

Therefore, the maximum profit is P = $63.

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Answer:

A=330

Step-by-step explanation:

im not sure which is the length width height

but if length is 10

width is 3/5

height is 15

A=2(wl+hl+hw)=2·(0.6·10+15·10+15·0.6)=330

then the area would be 330

Answer:

t - 7

Step-by-step explanation:

Answer: t - 7

Step-by-step explanation:

You have “7 less than a number t”, meaning, you have a variable t, and you want to find what 7 less than that is.

So, we would use subtraction.

We would get:

t - 7

Hope this helps! :)

A correlational result can be used to infer causality, but only if the value of r is greater than 0.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:

A 400 sq in

Step-by-step explanation:

10^2*3.14=314, I just rounded to the closest answer sorry if it's wrong.

Answer:    Use Gauth Math. What is the topic about?

Step-by-step explanation:

Answer:

I am pretty sure it is 19 blocks because it is 14 blocks before going back home. She needs to walk 3 blocks west and 2 blocks south. 14+3+2=19

Step-by-step explanation:

Change from rectangular to spherical coordinates: In spherical coordinates, (0, 3, -3) is (3, π/2, 5π/4) and In spherical coordinates, (-6, 6, 6√2) is (√108, π/4, π/2).

In spherical coordinates, a point in three-dimensional space is represented by three coordinates: ρ (rho), θ (theta), and φ (phi).

For part (a), we can use the following formulas to convert from rectangular to spherical coordinates:

ρ = √(x^2 + y^2 + z^2)

θ = arctan(y/x)

φ = arccos(z/ρ)

Plugging in the values (0, 3, -3), we get:

ρ = √(0^2 + 3^2 + (-3)^2) = 3

θ = arctan(3/0) = π/2 (since x = 0 and y > 0)

φ = arccos((-3)/3) = 5π/4 (since z < 0)

Therefore, in spherical coordinates, (0, 3, -3) is (3, π/2, 5π/4).

For part (b), we can use the same formulas to convert from rectangular to spherical coordinates:

ρ = √(x^2 + y^2 + z^2)

θ = arctan(y/x)

φ = arccos(z/ρ)

Plugging in the values (-6, 6, 6√2), we get:

ρ = √((-6)^2 + 6^2 + (6√2)^2) = √108

θ = arctan(6/(-6)) = π/4 (since x < 0 and y > 0)

φ = arccos((6√2)/√108) = π/2

Therefore, in spherical coordinates, (-6, 6, 6√2) is (√108, π/4, π/2).

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Answer:

Yes, the sides are in the ration 2:5!

Step-by-step explanation:

Hope this helps.

Answer:

  The correct answer is B. Yes, the sides are in the ratio 2:5.

Step-by-step explanation:

Hope this helps, and have a wonderful day! :)

Answer:

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The system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the rates for two duplicating companies. There are two different rates as-

[1] > initial fee of $5 and $0.06 per page.

[2] > initial fee of $10.00 and $0.04 per page.

For the [1] company, we can write the equation as -

C[1] = 5 + 0.06x

For the [2] company, we can write the equation as -

C[2] = 10 + 0.04x

So, the system of equations will be -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Therefore, the system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

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After the fifth day, Mary will have $32 left.

1. Start with the initial amount of money: $243.
2. For each day, calculate the amount spent and the remaining amount.
3. Repeat steps 1 and 2 for the five days.

Here's the step-by-step explanation:

Day 1:
- Money spent: $243 x \(\frac{1}{3}\) = 81$
- Remaining money: $243 - 81 = 162$

Day 2:
- Money spent: $162 x \(\frac{1}{3}\) = 54$
- Remaining money: $162 - 54 = 108$

Day 3:
- Money spent: $108 \times \frac{1}{3} = 36$
- Remaining money: $108 - 36 = 72$

Day 4:
- Money spent: $72 x \(\frac{1}{3}\)= 24$
- Remaining money: $72 - 24 = 48$

Day 5:
- Money spent: $48  x \(\frac{1}{3}\)  = 16$
- Remaining money: $48 - 16 = 32$

After the fifth day, Mary will have $32 left.

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we expect there to be one pair of consecutive zeroes in a random bit string of length 5

To find the expected value of the random function x that counts the number of pairs of consecutive zeroes in a random bit string of length n, we need to consider all possible bit strings of length n and count the number of pairs of consecutive zeroes in each one.

Let's first consider the case of a bit string of length 2. There are four possible bit strings: 00, 01, 10, and 11. Only the first-bit string has a pair of consecutive zeroes, so x(00) = 1, while x(01), x(10), and x(11) are all 0. Therefore, the expected value of x for a bit string of length 2 is:

E(x) = (1/4)*1 + (1/4)*0 + (1/4)*0 + (1/4)*0 = 1/4

Now let's consider a bit string of length 3. There are eight possible bit strings: 000, 001, 010, 011, 100, 101, 110, and 111. The bit strings that have pairs of consecutive zeroes are 000 and 100, so x(000) = 1, x(001), x(010), x(011), x(100) = 1, and x(101), x(110), and x(111) are all 0. Therefore, the expected value of x for a bit string of length 3 is:

E(x) = (1/8)*1 + (1/8)*0 + (1/8)*0 + (1/8)*0 + (1/8)*1 + (1/8)*0 + (1/8)*0 + (1/8)*0 = 2/8 = 1/4

We can continue this process for bit strings of longer lengths, but we can also see a pattern emerging. For any bit string of length n, there are n-1 possible pairs of consecutive bits, and each pair has a probability of 1/4 of being a pair of consecutive zeroes. Therefore, the expected value of x for a random bit string of length n is:
   
E(x) = (n-1)*(1/4) = (n-1)/4

So for example, if we have a random bit string of length 5, the expected value of x would be:

E(x) = (5-1)/4 = 1

This means that we expect there to be one pair of consecutive zeroes in a random bit string of length 5.

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Answer:

x= negative goes on the out side of it 15 over 4

Answer:

2x(x + 4)

Step-by-step explanation:

The greatest common factor of 2x^2 and 8x is 2x. So, we can factor out 2x to get:

2x(x + 4)

The definition of a greatest common factor (GCF) is the largest number that is a factor of two or more numbers. In this case, 2x is the GCF of 2x^2 and 8x because it is the largest number that divides both numbers evenly.

Here are the steps on how to factor out the GCF:

In this case, the factored expression is 2x(x + 4).

The answer is:

Work/explanation:

Let's find something that \(\sf{2x^2}\) and \(\sf{8x}\) have in common.

In other words, we find their GCF (greatest common factor).

The GCF of \(\sf{2x^2}\) and \(\sf{8x}\) is 2x.

So I factor it out :

\(\sf{2x(x+4)}\)