Knowledge Check Questio Calculate the distance between the points C=(-7,6) and E=(-2,2)

The value of the expression is A = 6xy

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 2 ( x ) ( 3 ) ( y )

On simplifying the equation , we get

A = ( 2 ) (3 ) ( xy )

A = 6xy

Therefore , the value of A is 6xy

Hence , the expression is A = 6xy

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The expression can be written as a single logarithm using the laws of logarithms as: 2logx(y)+logx(z/y).

The exponent or power to which a base must be increased in accordance with the laws of logarithms to arrive at a certain number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n

Using the laws of logarithms, we can combine the given expression as follows:

2 log(x) - log(y) + log(z)

Now, using the law of logarithmic addition, we can combine the second and third terms as follows:

2 log(x) + log(z/y)

Therefore, the given expression as a single logarithm is:

2 log(x) + log(z/y)

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All of the possible outcomes in which Hana wins the game is {6, 8, 10, 12, 14, 16}.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain to occur.

To win the game, the sum of the two spinners must be an even number greater than 6. Let's list all the possible outcomes:

So the possible outcomes in which Hana wins the game are: 2 + 4 = 6, 2 + 8 = 10, 4 + 2 = 6, 4 + 4 = 8, 4 + 6 = 10, 4 + 8 = 12, 6 + 2 = 8, 6 + 4 = 10, 6 + 6 = 12, 6 + 8 = 14, 8 + 2 = 10, 8 + 4 = 12, 8 + 6 = 14, and 8 + 8 = 16.

Therefore, all of the possible outcomes in which Hana wins the game is {6, 8, 10, 12, 14, 16}.

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The 100th term of the arithmetic sequence: 7, -1, -9 is -785.

To find the 100th term of an arithmetic sequence, we can use the formula: an = a1 + (n - 1)d where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

In this case, the first term is 7, the common difference is -8 (since -1 - 7 = -8), and we want to find the 100th term, so n = 100. Plugging these values into the formula, we get:

a100 = 7 + (100 - 1)(-8)

a100 = 7 + (99)(-8)

a100 = 7 - 792

a100 = -785

Therefore, the 100th term of the arithmetic sequence is -785.

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The number of cubic centimeters of space that 3 ping pongs would have is 339. 29 cm ³

A ping pong ball takes the shape of a sphere and the volume of a sphere is ;

= 4 / 3 x π x radius ³

Given the radius of 3 cm, the volume of one ping pong ball is :

= 4 / 3 x π x 3 ³

= 113. 09734 cm ³

If there are three ping pong balls, the volume would then be :

= 113. 09734  x 3 ping pongs

= 339. 29 cm ³

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A percentage of 25% οf the kids were οn the winning team.

Percentage is a way οf expressing a prοpοrtiοn οr fractiοn as a number οut οf 100. It is denοted by the symbοl "%".

Tο find the percentage οf kids οn the winning team, we can use the fοrmula:

percentage = (part/whοle) x 100%

In this case, the "part" is the number οf kids οn the winning team, which is 15. The "whοle" is the tοtal number οf kids whο played, which is 60. Substituting these values, we get:

percentage = (15/60) x 100% = 0.25 x 100% = 25%

Therefοre, 25% οf the kids were οn the winning team.

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If f(x)=2x+1 and g(x)=x^2 +5, the value of  g(f(2)) = 30.

The question is asking to evaluate the composition of the two functions, g(f(2)). This means that first the innermost function, f(2), needs to be evaluated, and the result substituted in place of f(2) in the expression for g(f(2)).

First, evaluating f(2) yields f(2) = 2*2 + 1 = 5. Then, substituting 5 in place of f(2) in the expression for g(f(2)) yields g(f(2)) = g(5) = 5^2 + 5 = 30.

Therefore, the answer to the question is g(f(2)) = 30.

A composite function is a function evaluated on another function.

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The ordered pair (1,-3) is a solution to the given system, while the ordered pair (0,0) is not

practice is a great way to help you understand how to determine whether ordered pairs are solutions to a given system. In this case, we are looking at the system:

3x+y=0

x+2y=-5

To determine whether the ordered pairs (0,0) and (1,-3) are solutions, we need to plug them into the equations and see if they make the equations true.

For the first ordered pair (0,0), we plug in x=0 and y=0 into the equations:

3(0)+(0)=0

(0)+2(0)=-5

The first equation is true, but the second equation is not. Therefore, (0,0) is not a solution to the system.

For the second ordered pair (1,-3), we plug in x=1 and y=-3 into the equations:

3(1)+(-3)=0

(1)+2(-3)=-5

Both equations are true, so (1,-3) is a solution to the system.

In conclusion, the ordered pair (1,-3) is a solution to the given system, while the ordered pair (0,0) is not.

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Using the slope-intercept form we know that Astrid is correct as the slope of the line is -4.

You can use the slope-intercept formula, y = mx + b, when you know the slope of the line to be studied and the provided point is also the y-intercept (0, b).

The formula's symbol b stands for the y value of the y-intercept point.

y=mx+b is a formula that expresses a line's slope and y-intercept.

The point where the line crosses the y-axis is known as the y-intercept and is typically represented in coordinate form as (0,b).

So, according to the given description of the slope-intercept form, we know that:

m = -4 and b = 1/3

Hence, we know that Astrid is correct.

Therefore, using the slope-intercept form we know that Astrid is correct as the slope of the line is -4.

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Answer:

Neil:

Sima:

Step-by-step explanation:

Neil:

Sima:

The value of x is 18.4.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given that,

sin (2x + 7)° = cos (3x - 9)°  [Equation 1]

We have the trigonometric rule that,

cos (θ) = sin(90 - θ)

So, cos (3x - 9)° = sin (90 - (3x - 9))

So from equation 1,

sin (2x + 7)° = sin (90 - (3x - 9))

Equating,

2x + 7 = 90 - (3x - 9)

2x + 7 = 90 - 3x + 9

2x + 7 = 99 - 3x

5x = 92

x = 18.4

Hence the value of x is 18.4.

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99 as a product of primes is, 99 = 3² * 11

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

To Write 99 as a product of primes,

we get,

99 = 3 * 3 * 11

99 = 3² * 11

Hence, 99 as a product of primes is, 99 = 3² * 11

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The given matrices are checked and their status is mentioned in the following list below :a. Reduced echelon form [100 010 000 -10-100] b. Not in echelon form [ -8000 -4200 -8110 -9101 -8130] c. Reduce echelon form [11 10 -4 -10] d. Echelon form [ 100 001 000 -502] Echelon form and reduced echelon form of matrices

The Matrix A is in the reduced echelon form if and only if the following conditions are satisfied:All rows having 0s are at the bottom of the matrix.There must be no 0 rows in the matrix.In each row of the matrix containing the leading nonzero element, all entries above and below the leading entry are 0.

The leading coefficient of a nonzero row is always strictly to the right of the leading coefficient of the row above it.In each column containing a leading coefficient, all other entries are zero.

For a matrix to be in echelon form, it must fulfill the following conditions : All rows containing all zero elements are located at the bottom of the matrix. All leading coefficients in any nonzero row are always strictly to the right of the leading coefficient in the row above it.

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Answer:

Ava has 25 books initially, then gives away 7 books, leaving her with 25 - 7 = 18 books.

After Tom gives her 12 books, she will have 18 + 12 = 30 books.

Therefore, Ava has 30 books now.

Answer:

She would have 30 books

Step-by-step explanation:

25 - 7 + 12 = 30

The expression can be simplified using the rule of exponents. The value of the expression 0.5a²b³ * (-2b)⁶ is 32a²b¹⁵.

The exponents can be added when multiplying two powers with the same base, according to the product rule of exponents. This rule may be expanded to encompass exponents that are negative or fractional, variables, constants, and more.

The expression can be simplified using the rule of exponents.

0.5a²b³ * (-2b)⁶ = 0.5a²b³ * 64b⁶

Using the power rule of the exponents we have:

= 32a²b⁹ * b⁶

Simplifying the above value we have:

= 32a²b¹⁵

Hence, the value of the expression 0.5a²b³ * (-2b)⁶ is 32a²b¹⁵.

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Expression 0.5a²b³ times (-2b)⁶ is -32a²b⁹

An algebraic expression is a combination of variables, constants, and mathematical operations. It represents a mathematical relationship between quantities and can be used to model real-world situations or solve problems.

Algebraic expressions can contain variables, which are symbols that represent unknown values, constants, which are fixed values, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.

We can simplify this expression using the rules of exponents:

0.5a²b³ times (-2b)⁶ = 0.5a²b³ times (-64b⁶)

Multiplying the coefficients, we get:

-32a²b⁹

Therefore, the simplified expression is -32a²b⁹.

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The implied domain of the function y = (-6x^2 - 4x)/8 is found to be (-∞, ∞).

The first step in determining the implied domain of the function is to isolate the dependent variable, in this case y, on one side of the equation.

We can do this by adding 5y to both sides of the equation and subtracting 4x from both sides of the equation:

-6x^2 - 4x = 8y

Next, we can divide both sides of the equation by 8 to get y by itself:

(-6x^2 - 4x)/8 = y

Now we have the function in terms of y:

y = (-6x^2 - 4x)/8

The implied domain of the function is the set of all x-values for which the function is defined.

In this case, there are no restrictions on the values of x that can be used in the function, so the implied domain is all real numbers.

Therefore, the implied domain of the function y = (-6x^2 - 4x)/8 is (-∞, ∞).

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The average rainfall for these seven states is 53.14 inches per year.

The rainfall for the seven different states can be represented using the following list: [83, 57, 48, 97, 20, 36, 31].
To find the average rainfall for these seven states, we need to add up all of the values in the list and then divide by the number of values.
Step 1: Add up all of the values in the list:
83 + 57 + 48 + 97 + 20 + 36 + 31 = 372
Step 2: Divide the sum by the number of values in the list:
372 / 7 = 53.14

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The missing sides are 6.9 cm and 9.8 cm

A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees, which is known as a right angle. The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs or the adjacent and opposite sides.

We know that;

Sin 35 = opposite/12

Opposite = 12 sin 35

= 6.9 cm

Cos 35 = adjacent/12

adjacent = 12 cos 35

adjacent = 9.8 cm

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Each child will receive 0.8 (or 4/5) of a cake.

To solve this problem, we need to divide 4 small cakes equally among 5 children. This means we need to divide the total number of cakes by the number of children.

To represent this visually, we can draw 4 small cakes and divide them into 5 equal parts. Each part represents the portion of a cake that each child will receive.

The drawing is in the image attached.

Therefore, each child will receive 0.8 (or 4/5) of a cake.

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We can use the notation definition to show that Π does not perform too differently between two environments vj and v0 by comparing the performance of Π in both environments and calculating the difference between them.

In order to show that Π does not perform too differently between two environments vj and v0, we can use the notation definition to compare the performance of Π in both environments.

First, we can use the notation Π(vj) to represent the performance of Π in environment vj and Π(v0) to represent the performance of Π in environment v0.

Next, we can compare the two performances by calculating the difference between them using the notation |Π(vj) - Π(v0)|.

If the difference is small, then we can say that Π does not perform too differently between the two environments. However, if the difference is large, then we can say that Π performs differently in the two environments.

In conclusion, we can use the notation definition to show that Π does not perform too differently between two environments vj and v0 by comparing the performance of Π in both environments and calculating the difference between them.

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Answer:

490 newtons

Step-by-step explanation:

The linear equation that shows a proportional relationship is y = 5x/6, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. A proportional relationship is one where two variables are related in such a way that when one variable changes, the other changes by a constant factor. In other words, the ratio of the two variables remains constant.

We are given that;

Linear equations to chose from

Now,

when x increases by a certain amount, y increases by a corresponding amount that is exactly 5/6 times as much. In other words, the ratio of y to x is always 5/6, which means that the two variables are proportional to each other.

Therefore, the linear equation will be y = 5x/6.

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Minimum: 112

Quartile Q1: 129.5

Median: 138

Quartile Q3: 154.5

Maximum: 156

Another inequality that describes the solutions would be: x ∈ (4, ∞)

What is inequality ?

In mathematics, an inequality is a statement that compares two values, expressions, or quantities, and asserts that they are not equal. Inequalities are often expressed using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality 3x > 12 can be solved by dividing both sides by 3:

3x/3 > 12/3

x > 4

This means that all values of x greater than 4 are solutions to the inequality 3x > 12.

This notation represents the interval of all real numbers greater than 4, including 4 itself. The symbol "(" means that 4 is not included in the interval, while "∞" indicates that the interval extends indefinitely to the right.

Therefore, Another inequality that describes the solutions would be: x ∈ (4, ∞)

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Answer:

V(t)= 900(0.8) ^t

Step-by-step explanation:

900[tex]x^{3}[/tex]=460.8

      [tex]x^{3}[/tex]=0.512

        x=0.8

Answer:

b

Step-by-step explanation:

The ratio of Anson's savings to Billy's savings after the book fair was 20 : 3

Let's start by setting up some equations:

Let A be the amount of money Anson had before giving 1/10 of his savings to Billy, and let B be the amount of money Billy had at that time.

We know that the ratio of Anson's savings to Billy's savings was 3:11 before the transfer, so:

A/B = 3/11

We also know that after the transfer, Anson had 9/10 of his original savings left, so:

Anson's new savings = 9/10 A

And Billy had 1/10 of Anson's original savings, plus his original savings, so:

Billy's new savings = B + 1/10 A

We're also told that both Anson and Billy spent the same amount of money at a book fair.

Let's call that amount X.

So after the book fair:

Anson's new savings = 9/10 A - X

Billy's new savings = B + 1/10 A - X

Finally, we're told that the ratio of Anson's savings to Billy's savings was 1:9, and that Billy had $264 more than Anson. So:

(9/10 A - X)/(B + 1/10 A - X) = 1/9

B + 1/10 A - X = 264 + (9/10 A - X)

Simplifying the second equation, we get:

1/10 A + X = 264

Substituting X = 1/10 A + 264 into the first equation, we can solve for B:

(9/10 A - (1/10 A + 264))/(B + 1/10 A - (1/10 A + 264)) = 1/9

8/9 A - 2640 = B/9

B = 8/9 A - 23760

Now we can substitute this expression for B into the equation we found for X:

X = 1/10 A + 264

And we can substitute both expressions into the equation we found for Billy's new savings:

(B + 1/10 A - X) = (8/9 A - 23760 + 1/10 A - (1/10 A + 264))

Simplifying, we get:

B = 8/9 A - 23760

X = 1/10 A + 264

B + 1/10 A - X = 7/9 A - 24024

So we know that Anson had 7/9 of his original savings left after the book fair, and Billy had 2/9 of Anson's original savings plus $264:

Anson's new savings = 7/9 A

Billy's new savings = 2/9 A + 264

We also know that before the transfer, the ratio of Anson's savings to Billy's savings was 3:11. So we can set up another equation:

A/B = 3/11

Substituting our expression for B from earlier, we get:

A/(8/9 A - 23760) = 3/11

Solving for A, we get:

A = $83160

So Anson had $83160 before giving 1/10 of his savings to Billy, and Billy had $30360 at that time.

After the book fair, Anson had $50400 left, and Billy had $8316 + $264 = $8580.

Therefore, the ratio of Anson's savings to Billy's savings after the book fair was:

50400/8580 = 20/3 = 20 : 3

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Answer:

18/40

or

9/20

Step-by-step explanation:

13 marbles are initially removed.

40 - 13 = 27

1/3 of that is removed.

27 - 9 = 18

We take whatever is left over (18 marbles), and put it in a fraction to represent what fraction is left over from 40.

18/40

or

9/20

The exact value of sin(6/11π) is -sin(6/11π).

The exact value of sin(6/11π) can be found by using the reference angle of 6/11π. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. In this case, the reference angle is (6/11π) - π = (-5/11π).

To find the exact value of sin(-5/11π), we can use the fact that sin(-θ) = -sin(θ). So, sin(-5/11π) = -sin(5/11π).

Next, we can use the fact that sin(θ) = sin(π - θ) to find the exact value of sin(5/11π). So, sin(5/11π) = sin(π - 5/11π) = sin(6/11π).

Therefore, the exact value of sin(6/11π) is -sin(6/11π).

In conclusion, the exact value of sin(6/11π) is -sin(6/11π).

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The solution to the inequality is x ≤ 6.8. This means that Elise can afford to rent the paddle boat for a maximum of 6.8 hours if she has $15 to spend.        

Why does inequality matter?

Experts claim that disparity fosters political unrest and impedes economic growth. Concentrated financial resources reduce demand for products and services because affluent families generally spend less of their revenue than do poorer households. If low-income people have fewer choices, the company might suffer.

To solve the inequality 1.25x + 6.50 ≤ 15, we can start by isolating x on one side of the inequality:

1.25x + 6.50 ≤ 15

Subtract 6.50 from both sides:

1.25x ≤ 8.50

Divide both sides by 1.25:

x ≤ 6.8

Therefore, the solution to the inequality is x ≤ 6.8. This means that Elise can afford to rent the paddle boat for a maximum of 6.8 hours if she has $15 to spend.

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The area in square miles (rounded to the nearest integer) is:

area = 2,492 square miles.

Here we need to perform a change of units from acres to square miles. We know the relation:

1 square mile = 640 acres.

And we want to find the area of a park with 1,505,011 acres in square miles.

We can rewrite the relation above as:

1 acre = (1/604) square miles.

Then the area of the park will be:

Area = 1,505,011 acres  = 1,505,011*(1/604) square miles

Area = 2,491.74 square miles.

Rounding to the nearest integer we will get:

area = 2,492 square miles.

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