If Scott started by asking 3 friends to sponsor him and each of those friends asked
three friends, how many sponsors would he have on the 4th week

The flow chart is complete and the answers are given below.

Those figures that have same shape and size are called Congruent Figures.

The flow diagram will be completed as follows

∠2 ≅ ∠4 (  vertical angle theorem )

∠1   ≅  ∠2  ( Given )

∠1  ≅ ∠ 3  ( Vertical Angle Theorem)

∠3   ≅  ∠4  ( Transitive Property of congruence)

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The type of function that best models the data in the table is the quadratic function

The table of values is represented as:

x: 4 6 8 10 12

y : 118 142 150 142 118

From the above table, we can see that:

This is only possible in a quadratic function

Hence, the type of function that best models the data in the table is the quadratic function

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Answer:

32

Step-by-step explanation:

the pattern of sticks from the first 3 diagrams is

7 , 12 , 17 ,..

note the pattern increases by 5 each time , then continue by adding 5 to the previous value.

4th = 17 + 5 = 22

5th = 22 + 5 = 27

6th = 27 + 5 = 32

Answer:

15, 20, 25

Step-by-step explanation:

added in the picture

a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].

c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given points represent on the graph is;

x = 0 , y = 0

x = 120 , y = 0

x = 60 , y = 40

The standard equation is;

[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]

Substitute the value as;

[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

b)

The above equation  in the standard form is found as;

[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]

c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.

Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]

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The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.

The radius r as a function of x will be:

8π - x = 2πr

r = (8π - x)/2π

r = 4 - x/2π

The height has a function of x will be:

r² + h² = 16

h² = 16 - r²

where r = 4 - x/2π

h = √16 - ✓(4 - x/2π)²

h = 4✓(4 - x/2π)²

The volume V of the cone as a function of x will be:

= 1/3 πr²h

= π/3(4 - x/2π)² 4✓(4 - x/2π)²

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Answer: 113 inches cubed

Step-by-step explanation:

Volume of a sphere = 4/3 Pi r^3

Radius = 3 inches

Volume = 113 inches cubed

Hope I helped!

Answer:

3125

Step-by-step explanation:

And

Answer:

every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away

Hope This helps!

Answer:

A

Step-by-step explanation:multiply both sides by two, then subtract b and c from both sides to get a on the right side by itself

Answer:

О A      a = 2s - b - c

Step-by-step explanation:

S = (a+b+c)/2

2s = a + b +c

2s - b - c = a

Graph C represents the following system of inequalities. For clarification refer to the attachment.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

Given relations;

x < - 2x + 4

y < x + 3

x < 3

Hence graph C represents the following system of inequalities.

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A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?

[tex] {p}^{2} > {p}^{2} \: \: and \: \: p {1}^{2} - \: p {2}^{2} \: < \frac{1}{3} [/tex]

Step-by-step explanation:

HOPE ITS HELP

Answer:

5.8

Step-by-step explanation:

According to the given synthetic division, the statements that are true are; Options A, C and E

In the synthetic calculation we use the coefficient of the dividend

with the factors of the function.

Therefore;

3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4

Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4

Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12

- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.

- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.

- The degree of the quotient is 1 and so the he quotient is 3x - 1.

Thus, options A, C and E are correct

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Answer:

2⁶

Step-by-step explanation:

law of indices states multiplication of powers in and out of bracket 3×2=6

[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The value is 64}[/tex]

Therefore the solution to this equation is imaginary given by x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]

A Quadratic equation is an equation that can be written in the form of

ax² +bx+c = 0

The solution of the given quadratic equation

x² -3x +3 = 0

the roots of the equation is given by

[tex]\dfrac { -b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

here a = 1 , b = -3 , c = 3

Substituting the values

The solution is

[tex]\rm \dfrac { 3 \pm \sqrt{(-3)^2 -4*1 *3}}{2}[/tex]

Therefore the solution to this equation is imaginary

given by

x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]

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Answer:

x = 0 y = -5

x = 3 y = 4

Step-by-step explanation:

x² + y² = 25

y - 3x = -5

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

y = 3x-5

x² + y² = 25

x² + (3x-5)² = 25

(3x-5)(3x-5) = 9x² -15x -15x + 25

x² + 9x² -15x -15x + 25 = 25

x² + 9x² -15x -15x = 0

x² + 9x² - 30x = 0

10x² - 30x = 0

x(10x-30)=0

x = 0

10x-30=0

x = 3

y - 3x = -5

y - 3(0) = -5

y = -5

y - 3(3) = -5

y - 9 = -5

y = 4

Answer:

(4,3) and (0,-5) are both solutions where we have (x,y).

Step-by-step explanation:

Here are simplified steps:

https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input

Symbolab is an excellent tool for just most math.

Answer:

Option C is equal to 7^1/3

Answer:

Step-by-step explanation:

Additive inverse:

-3=3

14=-14

-28=28

-1/5=1/5

Multiplicative Inverse:

2/3=3/2

6/18=18/6

5=1/5

11=1/11

Answer:

inverse of -3 is +3

inverse of 14 is -14

inverse of -28 is 28

inverse of -1/5 is 1/5

inverse of 2/3 is 3/2

inverse of 6/18 is 18/6

inverse of 5 is 1/5

inverse of 11 is 1/11

Step-by-step explanation:

Because inverse mean switch it. or opposite of digit

if plus digit then negative digit .

Answer:

2x³ + 2x

Step-by-step explanation:

(x² + x³ + x² + x) - (x² - x³ + x² - x)

= x² + x³ + x² + x - x² + x³ - x² + x

Gathering like terms...

x³ + x³ +x² + x² -x² - x² + x + x

= 2x³ + 2x

The difference of the polynomials is 2(x³+x).

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given are two polynomials (x² + x³ + x² + x) and (x²-x³+x²-x), we need to find the difference,

So,

(x² + x³ + x² + x) - (x²-x³+x²-x)

= x² + x³ + x² + x - x²+x³-x²+x

= 2x²-2x²+x³+x³+x+x

= 2x³+2x

= 2(x³+x)

Hence the difference of the polynomials is 2(x³+x).

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Answer:

see below

Step-by-step explanation:

To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.

The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.

D (2,2)

You could also see this on a graph, see image.

E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.

E is (-1,1)

Then we are able to calculate the slope of DE and BC.

To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.

Slope of DE:

(2-1)/(2--1)

= 1/3

Slope of BC:

(0--2)/(3--3)

=2/6

=1/3

The slopes of BC and DE are equal, so the segments are parallel.

(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)

Answer:

Step-by-step explanation:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

For example, "whatis.com" could be a domain with records for "www.whatis.com" and "www1.whatis.com,"

Answer:

Step-by-step explanation:

The quadratic expression having repeated root is 8x² - 32x + 32.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

We have to find the root of each quadratic expression.

x² - 18x - 81 = 0

Discriminant = [tex]\sqrt{(-18)^2-(4*-81)}[/tex] = [tex]\sqrt{648}[/tex]

x = (18 + √648) / 2 or x = (18 - √648) / 2

Distinct roots

x² - 2x + 3

Discriminant = [tex]\sqrt{(-2)^{2}-(4*3) }[/tex] = [tex]\sqrt{-8}[/tex]

x = (2 + [tex]\sqrt{-8}[/tex]) / 2 or x =  (2 - [tex]\sqrt{-8}[/tex]) / 2

Distinct roots

8x² - 32x + 32

Discriminant = [tex]\sqrt{(-4)^{2}-(4*4) }[/tex] = 0

x = (4 + 0)/ 2 or x = (4 - 0) / 2

x = 2 or x = 2

Repeated roots

Hence the quadratic expression having repeated roots is 8x² - 32x + 32.

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Answer:

Vertical is the answer

By the Pythagorean theorem,

[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]

Answer:

9 dollars per hour

Step-by-step explanation:

We want to use a ratio to find the rate in dollars per hour

72 dollars / 8 hours

Simplify by dividing the top and bottom by 8

9 dollars / 1 hour

9 dollars per hour

Step-by-step explanation:

72$ Per 8 hours, is the same as getting 9$ per hour. How this is possible is simple, All you do when you get a question like this, is that you divide the dollars by the hour, minutes, seconds, etc.

Problem-Connection:

As from this Question we Have 72$ per 8 hours, so we divide 72/8 which results in 9. So Dan Earns 9$ Per Hour.

Answer:

Dan Earns 9$ Per hour.

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A data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.

Thus, a data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.

The given question is incomplete. The complete question is:

"Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as:

A. Symmetric distribution

B. Negatively skewed distribution

C. Positively skewed distribution

D. Bimodal distribution."

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We can actually deduce here the one that uses the reciprocal property to rewrite  [tex]\frac{x}{6} = \frac{28}{3\\}[/tex]  is: C. [tex]\frac{6}{x} = \frac{3}{28}[/tex].

A reciprocal of a number is defined as the number that when it is multiplied by the number, the result is 1. Thus, we deduce here that the product of a number and its reciprocal gives one.

Thus: x/6 x 6/x = 1

Also, if 28/3 x 3/28 = 1

Thus, we see that they use the reciprocal property.

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Answer:

x>0

Step-by-step explanation:

points exist on the right of the graph so the domain is x>0

Answer:

all 50 states

Step-by-step explanation: