Carlton received 45 votes in the school council election, and Will received 60 votes. What percent of the votes did Carlton receive?

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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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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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:

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

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:

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,"

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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A real-life example of a hidden variable would be age in research that checks the correlation between shirt sizes in grade school and reading ability.

In a research that checks whether student shirt sizes (independent variable) have an impact on reading ability, it is found that students with high shirt sizes are better at reading.

A hidden variable here is age. Students who are older will more likely have a higher shirt size and better reading comprehension.

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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]

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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[tex]\log_7(x+9)-\log_710=\log_77\qquad(x > -9)\\\log_7\dfrac{x+9}{10}=1\\\dfrac{x+9}{10}=7\\x+9=70\\x=61[/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.

Your welcome!

Brainly will be greatly appreciated!

Step-by-step explanation:

find the Lcm of 15 and 10 which is 30

multiply the 2fractions by the LCM

8/15*30=16

3/10*30=9

add the products and put them all over the Lcm

(16+9)/30

=25/30 which is equivalent to 5/6 when you divide both the numerator and the denominator by 5

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:

all 50 states

Step-by-step explanation:

Answer:

b. 66

c.56

a 0

Step-by-step explanation:

????????????????????????

Answer:

5.8

Step-by-step explanation:

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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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:

1. Statement C is not true.

2. Option B is correct

3. Option C is correct

4.Option C is correct

Step-by-step explanation:

1. There are 5 Platonic solids : The tetrahedron, cube

,octahedron, dodecahedron ,icosahedron.

therefore statement C is incorrect.

2. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

12 - 18 + F= 2

F = 8.

3. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

V - 30 + 12 = 2

V = 20.

4. Probability is the number of favourable or unfavourable event divided by total events.

therefore denominator always greater than numinator.

so [tex]\frac{8}{7}[/tex] cannot represent the probability

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Step-by-step explanation:

To multiply the fractions, like

[tex] \frac{1}{4} \times \frac{1}{9} [/tex]

Multiply the top,

then multiply the bottom.

[tex] \frac{1}{4} \times \frac{1}{9} = \frac{1 \times 1}{4 \times 9} = \frac{1}{36} [/tex]

Try to use a calculator if you aren't arithmetic heavy, but I suggest you to try to remember them because they are going to be helpful for courses like Algebra, Calculus, Statistics, etc.

To divide fractions, like

[tex] \frac{ \frac{1}{5} }{ \frac{1}{8} } [/tex]

You take the top number,

[tex] \frac{1}{5} [/tex]

Then you flip the bottom number,

[tex] \frac{8}{1} [/tex]

Then multiply the two

[tex] \frac{1}{5} \times \frac{8}{1} = \frac{8}{5} [/tex]

And that is your answer. Comment if you need more clarification

Answer:

15, 20, 25

Step-by-step explanation:

added in the picture

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.)

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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Answer:

x>0

Step-by-step explanation:

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

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 .

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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