Find the 33rd term of 309,303,297

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

14.3%

Step-by-step explanation:

1/7=0.142857142857

round that to the nearest tenth and that is 0.143

make it a percentage and it is 14.3%

The values of the two integers are -43 and -143.

Let the value of the smaller integer be "x".

Since, the sum of two integers is -186.

Smaller integer + Larger integer = -186

x + ( 3x - 14 ) = -186

Solve for x

x + 3x - 14 = -186

4x - 14 = -186

4x = -186 + 14

4x = -172

x = -172/4

x = -43

Hence;

The smaller integer = x = -43

The largere integer = 3x - 14 = 3(-43) - 14 = -143.

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The inverse of the function shown is (x + 5).

What is the inverse of the function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "\(f^{-1}\)" or "\(F^{-1}\)." Here, (-1) should not be confused with an exponent or a reciprocal.

Coordinates of the given line are (8,3) and (-2,-7)

The function of the given graph for two points form is

\(y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )\)

or, \(y-3 = \frac{-7-3 }{-2-8} (x-8 )\)

or, y - 3 = x - 8

or, y = x -8 + 3 = x - 5

y = x - 5

To find the inverse, replace x with y and y with x then, we get

x = y - 5

y = x + 5

\(f^{-1}\) = x + 5

Hence, the inverse of the function shown is (x + 5).

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Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

Answer:

See graph attached

Step-by-step explanation:

Our life is simple because the equation \(y=2x+2\) is already put in slope-intercept form.

This form is called slope-intercept because it states exactly what it's called: The number multiplied by \(x\) (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)

With this info, we can start graphing.

We know that the y-intercept is 2, meaning one point will be (0,2).

We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.

Hope this helped!

The graph of the function y = 2x + 2 is added as an attachment

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

y = 2x + 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

it's 2800

Step-by-step explanation:

2×2×2×2×5×5×7

Answer: The volume of the​ sculpture is 141.84 cubic-feet

Step-by-step explanation: Please see the attachments below

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

PQ = 4cm

QR = 3cm

PR = 5cm

Area = 6cm²

Step-by-step explanation:

Area of triangle = 0.5 × Base × Height

6 = 0.5 × 3 × PQ

6 = 0.5 × 3 × x

\( \frac{6}{0.5 \times 3} = x\)

x = 4cm

PQ = 4cm

Since, it is a right angled triangle applying Pythagoras Theorem,

PR =

\( \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 6} \\ = 5cm\)

PR = 5cm

Answer:

6X²

Step-by-step explanation:

When multiplying terms like this, multiply the numbers by the numbers and the X's by the X's:

3X × 2X

(3×2)(X×X)

(6)(X²)

6X²

Answer:

\(a_{n}\) = \((-\frac{2}{3}) ^{n-1}\)

Step-by-step explanation:

The sequence has a common ratio between consecutive terms , that is

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{a_{3} }{a_{2} }\) = \(\frac{a_{4} }{a_{3} }\) = - \(\frac{2}{3}\)

This indicates the sequence is geometric with nth term

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term

Here a₁ = 1 and r = - \(\frac{2}{3}\) , then

\(a_{n}\) = 1 \((-\frac{2}{3}) ^{n-1}\) = \((-\frac{2}{3}) ^{n-1}\)

Answer:

Step-by-step explanation:

Let y represent the number of yellow sweatshirts sold. Then the total revenue is ...

  $11.95(25 -y) +$12.50(y) = $304.25

  $0.55y +$298.75 = $304.25 . . . simplify

  $0.55y = $5.50 . . . . . . subtract $298.75

  y = 10 . . . . . . . . . . divide by $0.55

  25-y = 15 . . . . the number of white sweatshirts sold

10 yellow and 15 white sweatshirts were sold.

The general form of equation of line is :

y = m(x -a ) + b

where m = slope, (a,b) = passing points

The given equation of line : y = 5x + 7

On comparing it with the general form of line

we get : a = 0, b = 7, m =5

Slope = 5

a) If the two lines are parallel then the slopes of both the lines are equal.

Let the slope of the parallel line is x

slope of the given line is 5

since, the slopes are equal thus x = 5

slope of line parallel to the line y= 5x+7. is 5

b) If the two lines are perpendicular then the product of thier slope is (-1)

Let the slope of the perpendicular line is n

since the slope of the given line is 5

so, from the above statement of slopes of perpendicular lines: 5n = -1

5n = -1

n = -1/5

n = -1/5

slope of line perpendicular to the line y= 5x+7. is -1/5

Answer:

a) slope = 5

b) slope = -1/5

Answer:

Step-by-step explanation:

The HCF ( highest common factor)  of 84 and 96 is 12

option A is not possible because the outcome of 8/12 is not an integer

option C is not possible because the outcome of 45/12 is not an integer

option D is not possible because the outcome of 6/12 is not an integer

option B is possible because the the HCF of 24 and 36 is 12

The maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are:

Lower bound = 9.5

Upper bound = 30

In basketball, players can score 1, 2, 3 (or even 4 or 5 points) during a possession.

Players who score five points are fouled in the act of shooting a three-pointer and making the shot.

Players who score four points attempt a three-pointer and make the subsequent foul shot.

Players who score three points go beyond the 3-point line, in bounds.  

Players who score two points go inside the 3-point line, in bounds.

Players who score one point make free throws.

Basketball scores =  1, 2, 3, 4, 5 points

Median = 3 per possession

9.5   10  12.5   15   15.5   18.5   20  21.5  25    26   30    30

Thus, the maximum lower bound and minimum upper bound for the median number of points the basketball player scored over his last 21 games are 9.5 and 30.

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Relative Frequency of Scores

30 30 26 25 20 15 10 9.5 12.5 15.5 18.5 21.5

Answer:

2,112 inches

Step-by-step explanation:

4 kitchen windows

1 window (22 x 24)

4(22 x 24)

multiplying the brackets by 4 for the 4 windows

4(22 x 24) = 2,112

In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.

The conjugate is the same expression but with the signal between the numbers changed.

So we have:

So the new denominator of the fraction is 2, therefore the correct option is D.

Answer:

\(6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24\)

B is the correct answer.

Amanda and her best friend got $93 each .

To Split a number into two equal half the the number gets divided by 2.

For Example : To split 50 into two equal half , we  divide by 2,

So 50/2 = 25 .

In the question

It is given that Amanda and her best friend found $186

To split the money evenly , the amount needs to be divided into two equal half , that means it should be divided with 2.

that means ,

On dividing 186 by 2

we get

= 186/2

= 93

Therefore , Amanda and her best friend got $93 each .

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-16\(x^{8}\) / -8\(x^{9}\)

= (-16/-8)\(x^{8 - 9}\)

= 2 \(x^{-1}\)

= 2/x

Thus,

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

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The system utilization is mathematically given as 20%.

What is the system utilization?

As per the information provided, a single- server queuing system with a Poisson arrival rate and an exponential service time with the vehicles coming at an average of 20 minutes apart would be the most efficient configuration.

Therefore, the rate of arrival is 20 minutes, and the average amount of time spent providing service is 4 minutes; hence, the rate of providing service is 4 minutes.

The equation for system utilization is  mathematically given as:

system utilization= (the rate of service/the arrival rate)

system utilization= 4/20

system utilization=0.2

Thus, the required system utilization is 20%.

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Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

Slope m = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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It's b i got it right

UR ANSWER LUV WOULD BE

B

HOPES THIS HELPS!:)

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

y = 2x + 6

Step-by-step explanation:

We are given that a line runs through the points (-4,-2) and (-2,2).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.

First, we need to find the slope of the line.

The slope can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points.

Even though we have two points, let's label the values of the points to avoid confusion & mistakes.

\(x_1=-4\\y_1=-2\\x_2=-2\\y_2=2\)

Now let's find the slope (remember: the formula has subtraction):

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{2--2}{-2--4}\)

This can be simplified:

m=\(\frac{2+2}{-2+4}\)

Add the numbers together.

m=\(\frac{4}{2}\)

Divide.

m = 2

The slope of the line is 2.

We can substitute this into the equation for m.

Here is the equation of the line so far:

y = 2x + b

We now need to find b.

As the equation passes through both (-4, -2) and (-2, 2), we can use either one of them to help solve for b.

Taking (-4, -2) for instance:

Substitute -4 as x and -2 as y in the equation we have.

-2 = 2(-4) + b

Multiply.

-2 = -8 + b

Add 8 to both sides.

6 = b

Substitute 6 as b into the equation.

y = 2x + 6

Topic: finding the equation of the line (slope-intercept form)

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