the product of three consecutive positive integers is $8$ times their sum. what is the sum of their squares?

The linear function that represents the graph of that has the points on the table is: A. .f(x) = 32(3x - 1).

If a point is on a graph of a linear function, its coordinates will make the equation of the linear function true, if plugged into the equation.

Given the table that represents some of the points that are on a linear function graph, use one point, (1, 64), to check which of the functions represents the table.

Substitute x = 1 and .f(x) = 64 into each of the functions given to see which is true:

.f(x) = 32(3x - 1)

64 = 32(3(1) - 1)

64 = 32(3 - 1)

64 = 32(2)

64 = 64 [true]

.f(x) = -32(x - 3)

64 = -32(1 - 3)

64 = 64 [true], however, if we use another set of values, say (5, 448), this function will not be true.

.f(x) = -2(32x - 3)

6 = -2(32(1) - 3)

6 = -2(29)

64 = -58 [not true]

.f(x) = 16(2x - 1)

64 = 16(2(1) - 1)

64 = 16(1)

64 = 16 [not true]

Therefore, the function that represents the table is: A. .f(x) = 32(3x - 1).

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The pre-image and image have the same shape after dilatation, but they are not the same size.

In the given question, we have to explain what is true about an image after a dilation.

The pre-image and image have the same shape after dilatation, but they are not the same size.

The figure is the same from every perspective. The midpoints of the figure's sides and the dilated shape's midpoint are both unchanged. Lines that are parallel and perpendicular to one another in the figure are identical to those in the dilated figure. The pictures stay the same.

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The function that represents the graph will be y = 1 - 2x in interval (∞, 2], y = -3 in interval [2, 3), y = -2 at x = 3, and y = 2(x - 4)² - 2 in interval (3, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

From the graph, the equation of the line that passes through (0, 1) and (2, -3) is given as,

(y - 1) = [(1 + 3) / (0 - 2)](x - 0)

y - 1 = -2x

y = 1 - 2x, (∞, 2]

In intervals [2, 3), the equation is

y = - 3

At x = 3, the value of y is -1.

The vertex of the parabola is at (4, -2). Then the parabolic function is given as,

y = a(x - 4)² - 2

The equation is passing through (0, 5), then we have

0 = a(5 - 4)² - 2

2 = a

The function is y = 1 - 2x in interval (∞, 2], y = -3 in interval [2, 3), y = -2 at x = 3, and y = 2(x - 4)² - 2 in interval (3, ∞).

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No, they cannot form the vertices of a right triangle. The points must be three distinct points and all three must be located in different quadrants.

No, they cannot form the vertices of a right triangle. A right triangle is a three-sided polygon with one 90 degree angle. To form a right triangle, the three points must be three distinct points in different quadrants. In this case, the points (-4 3) and (-1 1) are both in the same quadrant. Additionally, 1/3 is not a point, but a fraction.

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Answer: 4 whole laps plus 1/2 of a lap

Step-by-step explanation:

let x = number of laps

2/3x=3

x=9/2

x=4 1/2

4 whole laps plus 1/2 of a lap

The solution is A = 7

The value of the equation A = 9 - ( 8/S ) when S = 4 is 7

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

The equation A = 9 - ( 8/S )

Now , when S = 4

Substitute the value of S = 4 in the equation , we get

The value of A = 9 - ( 8/S )

The value of A = 9 - ( 8 / 4 )

The value of A = 9 - ( 2 )

The value of A = 7

Therefore , the value of A is 7 when S = 4

Hence , The value of the equation A = 9 - ( 8/S ) when S = 4 is 7

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The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

"Information available from the question"

In the question:

The mean of the quantitative variable of interest in the population is called the

Now, According to the question:

Let's know:

Sample Mean:

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

The mean of the quantitative variable of interest in the sample is called the. Sample Mean. The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

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The value of the given elements are: 0.829.

Given:

The given numbers are: 8,9,33,44,57,60,62,64,73,74,77,86

Here, the largest Number is 86 = Xₐ

and the smallest number is 8 = Xₙ

Now,

Range = Xₐ -Xₙ

           = 86 - 8

           = 78

Therefore,

Coefficient  of Range = Xₐ - Xₙ / Xₐ +Xₙ

                                    = 86 - 8 / 86 +8

                                    = 78 / 94

                                    = 0.829

Therefore, the value is 0.829.

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Answer:

To use coordinates on a coordinate grid, you first need to determine the scale of the grid, which is represented by the proportion M=24R. This means that for every 24 units on the grid, the corresponding real-world distance is equal to R units.

Once you have determined the scale of the grid, you can use the coordinates to locate points on the grid. To do this, you will need to know the coordinates of at least one point on the grid, which is known as the origin. The origin is typically represented by the coordinates (0,0).

To find the coordinates of a point on the grid, you can use the following steps:

For example, if you wanted to find the coordinates of a point that is 5 units to the right of the origin and 3 units above the y-axis, the coordinates of the point would be (5, 3).

The theorem that proves that the triangles are congruent is the Side-Side-Side (SSS) Congruence Theorem.

The Side-Side-Side (SSS) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This theorem is useful for proving that two triangles are congruent without having to use angles. The SSS Congruence Theorem is a useful tool for solving geometry problems involving triangles. It can be used to find the unknown side length of a triangle given the lengths of the other two sides, or in more complicated proofs involving multiple triangles. This theorem is also helpful in determining the area of a triangle, as the area is proportional to the product of the lengths of the sides.

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The probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip is (1/8).

If we toss a coin, we have two possible outcomes: head or tail. Now:

P(E) = Favourable outcomes / Total outcomes

      = 1/2

As per the question, we need heads on the first throw and tails on the next two throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting head on the first throw and B and C be events of getting tails on the second and third throws of dice respectively.

P(A) = P(B) = P(C) = 1/2

So, P(A∩B∩C) = (1/2)*(1/2)*(1/2) = 1/8

So, the Required probability is (1/8)

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The value of C to the nearest tenth, is 70.5.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

We have the triangle ABC.

Where c = 22ft, a = 18ft and b = 20ft

Law of Cosines:

c² = a² + b² - 2ab cosC

Substituting the value of a, b and c to the above equation.

22² = 18² + 20² - 2(18)(20) x cosC

484 = 724 - 720 x cosC

Rearranging

-240 = -720 x cosC

Divide both sides by

-7200.3333333333 = cosC

To find the value of C:

C = Arc cos 0.3333333333

Now the value of arc cos from the trigonometric table,

C = 70.52877936753502

Therefore, the C = 70.5 rounded to the nearest tenth.

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Its means that the addition of natural numbers obeys the closure property.

In mathematics, the closure property is a property that states that if a set is combined with all its limit points, then the combined set is also a limit point. The closure property applies to sets of real numbers, vectors, and matrices. It states that the closure of a set is itself, i.e., the set is closed under the given operation. The phrase "closed under addition" means that when two natural numbers are added together, the result is also a natural number. In other words, natural numbers are part of a closed system concerning addition; the addition operation always produces another natural number.

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The value of the slope is 1 and the value of the y-intercept is 6.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = (10 - 6 ) / ( 4-0)

Slope = 4 / 4 = 1

The y-intercept will be calculated as,

y = mx + c

6 = 0 + c

C = 6

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Answer: the first one

Step-by-step explanation:

Answer: should be this V≈549.78

Step-by-step explanation:

Answer:$ 16.50

Step-by-step explanation:If you are adding, you do

$8.50+

8.00

------------

16.50

0 plus 0 is nothing.

5 plus 0 is 5.

8 plus 8 is 16.

Your answer is now "16.50" .

Answer: y=833.333⇒

Step-by-step explanation:

y=[tex]\frac{3250*40} {40}[/tex]=833.333>

the probability is 68‰

For the normal distribution,

The scores on standardized admissions tests are normally distributed with a mean of 500

Mean (μ)=500

standard deviation(σ)=100

The probability that scores lies between 400 and 600  i.e, P(400

For the standard normal distribution curve

Z=(x-μ)/σ

(400-500)/100<(x-μ)/σ<(600-500)/100

-1

For standard normal distribution mean shifted to zero,  P(x)dx=1/(sqrt(2pi))e^(-z^2/2)dz.

so the probability would be 68‰

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Answer: i-Ready and c

Step-by-step explanation: I hope this helps

Answer:

Step-by-step explanation:

We first rewrite the terms of 48x² +38x + 5 to 48x² + 8x + 30x + 5

We then regroup terms into two proportional parts: (48x² +8x) + (30x + 5)

Factor the expression: 8x(6x + 1) + 5(6x + 1)

We then factor 8x(6x + 1) + 5(6x + 1) to (6x + 1)(8x + 5)

Now that we know (ax + b) and (cx + 1) is (6x + 1)(8x + 5) we just need to apply the numbers to their corresponding letters:

A=8

B=5

C=6

⇒The first step let us find the lowest common denominator to get r of the fraction.

⇒In this case the lowest denominator is 3,meaning3 will multiply all the terms in the equation

⇒[tex]-14(3)=-\frac{4}{3} a(3)\\-42=-4a[/tex]

⇒ Divide all the terms of the equation with the coefficient of the unknown variable to leave it independent.

⇒We are going to divide all the terms of the equation on this case by -4 since it tis the coefficient of the unknown variable

[tex]-\frac{42}{-4} =-\frac{4a}{-4} \\a=10.5[/tex]

∴a=10.5

After solving the system of equation we will get

x = 5y/2 +1  

y = 2/5- 2x/5

First equation is written

−2x+5y=−2

Subtract 5y from both sides.

−2x =−2−5y

The equation is in standard form.

−2x=−5y−2

Divide both sides by −2.

-2x/-2 = -5y-2/ -2

Dividing by −2 undoes the multiplication by −2.

x= −5y-2/-2

​Divide  −2−5y  by −2.

so

x= 5y/2 + 1

Now the second equation is

4x−10y=4

Add 4x to both sides

-10y = 4-4x

The equation is in standard form.

Divide both sides by 10

-10y/10= 4-4x/10

Dividing by 10 undoes the multiplication by 10.

y= 4-4x/10

Divide 4-4x by 10.

so

y= 2/5- 2x/5

​

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Answer:

1 and 5

Step-by-step explanation:

first category and fifth one up

Answer:

Below

Step-by-step explanation:

4 minutes = 4  x 60 = 240 seconds

240 seconds / 15 q   = 16 s/q

The committee can be chosen in 99.98.97.96.95 different ways.

What is a combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

Given

The 5 equal members of the terraforming committee of the united martian colonies are randomly chosen from the council of 99 leaders.

We have to find out how many different ways can this committee be chosen.

For this, we concluded that the committee can be chosen in 99.98.97.96.95 different ways.

Hence,  the committee can be chosen in 99.98.97.96.95 different ways.

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Answer:

The correct equations are 2x +3y=100 and x+y=48. These equations can be used to find the number of multiple-choice and free response questions on the test. The first equation, 2x +3y=100, shows that the total number of points for the multiple-choice questions (2x) plus the total number of points for the free response questions (3y) equals 100. The second equation, x+y=48, shows that the total number of multiple-choice and free response questions on the test is equal to 48. These equations can be solved simultaneously to find the values of x and y.

y = 3x – 2 is the equation of the line which passes through 1/3 and 2 5 with slope.

We can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We know one point on the line, which is (1/3, 2.5). We can calculate the slope by calculating the rise (change in y) divided by the run (change in x), which is (2.5 - 0) / (1/3 - 0) = 2.5 / 0.33 = 7.5. Therefore, the equation of the line is y = 7.5x + b. To solve for b, we can substitute in our point, (1/3, 2.5) into the equation. We get 2.5 = 7.5(1/3) + b, or 2.5 = 2.5 + b. Therefore, b = 0, and the equation of the line is y = 7.5x + 0, or y = 7.5x.

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Answer: -1

Step-by-step explanation: Plug 1 in as x. You get h(1)=-3(1)+2. If you solve this, it is h(1)=-3+2, or h(1)=-1

Answer:

[tex] \sf \: h(1) = - 1[/tex]

Step-by-step explanation:

Given equation,

→ h(x) = -3x + 2

Now the value of h(1) will be,

→ h(x) = -3x + 2

→ h(1) = -3(1) + 2

→ h(1) = -3 + 2

→ [ h(1) = -1 ]

Hence, the value of h(1) is -1.