Introduction to Writing Proofs - A Geometry Performance project
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Answer:Explanation:

The average rate of change = 3

The average rate of change for a function f(x) is an intervale a < x < b can be calculated using the following equation:

Therefore, the average rate of change of the function h(x) = x^2 – 7x + 6 in the interval 3 < x < 7 is:

Where h(7) and h(3) are equal to:

So, the average rate of change is:

Therefore, the answer is 3.

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

The absolute value function is commonly understood as a function providing the distance the number is from zero on a number line.

y = 3/4|x-6|-8

y = 3/4(-(x-6))-8

y= 3/4( -x + 6) -8

y = 3(-x + 6 - 32)/4

4y = -3x - 24

y = -3(x + 24)/4

For another function of y

y = 3/4|x-6|-8

y= 3/4( x - 6) -8

y = 3(x - 6 - 32)/4

4y = 3(x - 38)

y = 3(x - 38)/4

The absolute value function as piecewise function of y = -3(x + 24)/4 and y = 3(x - 38)/4

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SOLUTION:

Step 1:

In this question, we are given the following:

Can you give me two examples of an absolute value parent function?

Step 2:

What is the parent function for absolute value?

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.

Examples include:

1. The absolute value parent function, written as: f(x)=| x |, is defined as:f(x)={x if x>00 if x=0−x if x<0.

, is defined as:

2. The second example of absolute value function is:

The value of x comes to 78.808 after solving the given expression 1.25x + 1.49 = 100.

So, 1.25x + 1.49 = 100:

Now, solve as follows:

Therefore, the value of x comes to 78.808 after solving the given expression.

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Answer:

Equation of the parabola:

The height of the arch 18 meters from the center is 6.75m

Explanation:

The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0

Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9

Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.

With all this, we can try to find the general form of a parabola. The general form is:

c is the y-intercept. We know that c = 9

We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:

SInce the x-coordinate of the vertex is x = 0

If we solve:

So far we have:

Finally, to find a, we can use the point (36, 0) (one of the roots)

And solve:

Thus, the equation of the arch is:

Evaluating this equation for x = 18, we can find the height of the arch:

Simplification of the given expression to single complex number are as follow :

1. 3i

2. 4i

3. 24

4. 15

5. 1 + √3 i

6.  2 + [tex]\sqrt{5}i[/tex]

As given,

Simplify the following expression to a single complex number,

1) [tex]\sqrt{-9}[/tex] = [tex]\sqrt{9}\sqrt{-1}[/tex] = 3i

where i is the complex number representing [tex]\sqrt{-1}[/tex]

2) √-16 = 4i

3) √-6 √-24

= √6 ×6 ×4

= 6 ×4

= 24

4) √-3 √-75

=√ 3×75

= √3 × 3 ×25

= 3 ×5

=15

5) [tex]\frac{2 +\sqrt{-12} }{2}[/tex]

= (2 + 2√-3) /2

= 1 + √3 i

6) [tex]\frac{4+\sqrt{-20}}{2}[/tex] = [tex]\frac{4+\sqrt{20}\sqrt{-1}}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}\sqrt{-1})}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}i)}{2}[/tex] = [tex]\frac{2(2+\sqrt{5}i)}{2}[/tex] = 2 + [tex]\sqrt{5}i[/tex]

where i is the complex number representing [tex]\sqrt{-1}[/tex]

Therefore, simplification of  the given expression to single complex number are as follow :

1. 3i

2. 4i

3. 24

4. 15

5. 1 + √3 i

6.  2 + [tex]\sqrt{5}i[/tex]

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Answer:

3/16

We assume that the marbles are drawn without replacement.

P(blue and yellow)

= P(b1 and y2) + P(y1 and b2)

= P(b1) P(y2) + P(y1) P(b2)

= (1/4)(1/2) + (1/4)(1/4)

= 1/8 + 1/16 = 2/16 + 1/16 = 3/16

Answer:

72

Step-by-step explanation:

Formula: P (n,r) = n! ÷ (n - r)!

n = Total number of objects in a set

r = The number of items you choose

!/Factorial = Product of all positive numbers less than or equal to the given positive number

9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

7! = 1 x 2 x 3 x 4 x 5 x 6 x 7

P (9,2) = 9! ÷ (9-2)!

362,880 ÷ 5,040 = 72

-3/2 (option A)

The line of green and red are perpendicular.

For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line.

slope of one line (green) = 2/3

slope of red line = negative reciprocal of green line

slope = 2/3

reciprocal of line = 3/2

negative reciprocal of the line = -3/2

The slope of the red line = -3/2 (option A)

The value of the average price per square foot in 2002 is  $101. 5

A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.

The variables are;

Given the function;

P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190

Where;

For the year 2002 , the value of t would be 10

Substitute the value into the formula

P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190

expand the bracket, we have

P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90

multiply through

P(10) = 18 - 2.  + 30. 5 + 55. 90

Add the values

P(10) = $101. 5

Hence, the value is  $101. 5

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Answer:

x = 5

Step-by-step explanation:

Hello!

According to the question, what's the value of 4x-6=x+9

4x-6=x+9

Collect like terms

x - 4x = -6 - 9

-3x = -15

Divide both sides by the coefficient of x which is -3

-3x/-3 = -15/-3

x = 5

When checking

4x-6=x+9

(4)(5)−6 = 5+9

14=14

True

Han is therefore mistaken in what he claims. The area is 8640 [tex]feet^{2}[/tex]

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given Data

Let "x" represent the restaurant's actual space.

You are aware that the map's scale is 1 inch to 12 feet. As a fraction, this is written as follows:

[tex]\frac{1inch}{12feet}[/tex]

Calculate the restaurant's scale drawing area. Such is:

([tex]\frac{1inch}{12feet}[/tex]) ² = [tex]\frac{1inch^{2} }{144feet^{2} } }[/tex]

We can set up this percentage and then solve for "x" to determine the precise location of the restaurant because the restaurant's location is indicated on the map.

Such is:

[tex]\frac{144}{1}[/tex] = [tex]\frac{x}{60}[/tex]

60 (144) = x

x = 8640 [tex]feet^{2}[/tex]

Han is therefore mistaken in what he claims.

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To determine which is the best buy, we need to first find the unit price of each

8 oz $2.40

Unit price

$2.40/8 = $0.3

1 oz = $0.3

24 oz $6.48

Unit price

$6.48/24 =$0.27

1 oz = $0.27

64 oz $14.08

Unit price

$14.08/64 =$0.22

From the above the best best buy is the one with the lowest price which is $0.22

The best buy is;

64 oz $14.08

and the unit rate is $0.22 per oz

[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]

Answer: the andwer to that is C

Step-by-step explanation:

The difference of the values is -12.9 while the product of the expression is 45.9

We have to solve for

2.4 x 10/8

= 2.4 x 1.25

= 3

(9.2 x 10/6)

= 9.2 x 1.667

= 15.3

The difference between the values wpuld be

3 - 15.3

= -12.3

The product of the expressions would be solved by

3 x 15.3

= 45.9

Hence we would say that the difference that is in the values that we have here is -12.9 while the product of these values is given as 45.9

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Answer:

There were 24 cookies in the jar at the beginning.

Step-by-step explanation:

There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.

Answer:

f(2)=8(12-x)-5

=8(12-2)-5

f(2)=8(10)-5

=75

60 and 274.

Step-by-step explanation:

We will operate as follows:

Lines of symmetry, a line that divides a figure into two mirror parts, for example:

As we can see, the only line of symmetry that we can draw in our figure is:

Answer: One

1. The simple interest rate is 80%

2. The interest earned on the account after 10 years is $75

Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.

The formula for simple interest is expressed as;

I = PRT/100

Where;

From the information given, we are to determine the interest rate, R

Substitute the values into the formula, we have;

320 = 200 × R × 2/100

Now, cross multiply, we have;

320(100) = 400R

Find the product of the values

400R = 32000

Divide both sides by the coefficient of the interest rate, we get

R = 32000/400

Find the quotient

R = 80%

If the interest for 2 years is $15

Then in 10 years = $x

cross multiply

x = 150/2

Find the quotient

x = $75

Hence, the rate is 80%

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Scale factor means ratio of the sides of the triangle then the measures of the indicated sides, and the scale factor of CB and AB exists ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.

A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Each pair of given polygons are similar.

Similarity statement for the given polygons:

In ΔDEF and ΔABC,

∠D = ∠A (Angle)

∠E = ∠B  (Angle)

Therefore, ΔDEF  ΔABC (by AA similarity)

If two triangles are similar, then their sides are proportional.

[tex]$\Rightarrow \frac{D F}{A C}=\frac{D E}{A B}$[/tex]

[tex]$\Rightarrow \frac{2.4}{3.6}=\frac{2}{2 x}$[/tex]

By using cross multiplication, we get

⇒ 2.4 × 2x = 2 × 3.6

simplifying the above equation, we get

⇒ 4.8x = 7.2

⇒ x = 1.5

Therefore, the value of x = 1.5.

Substitute x = 1.5 in CB and AB,

CB = 3x – 0.6 = 3(1.5) – 0.6 = 3.9

AB = 2x = 2(1.5) = 3

Scale factor means ratio of the sides of the triangle.

⇒ DF/AC = 2.4/3.6 = 2/3

Therefore, the correct answer is option a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.

The complete question is:

Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.

[tex]$\overline{C B}$[/tex] and [tex]$\overline{A B}$[/tex]

a) ΔDEF -  ΔABC; x = 1.5; CB = 3.9; AB = 3;

b) ΔDEF - ΔCBA; x=3 ; C B=3 ; A B=3.9 ; 2/3

c) ΔDEF -  ΔCBA; x=1 ; C B=3.9 ; A B=3 ; 2/3

d) ΔDEF -  ΔABC; x=1.5 ; C B=3 ; A B=3.9 ; 3/2

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The other endpoint of the segment is (7, 14)

From the question, we have:

On the segment, we have the following endpoints

Endpoint 1, A = (-3,-2)

Midpoint, M = (2,6)

The midpoint of the segment is calculated using

Midpoint (x, y) = 1/2 * (x1 + x2, y1 + y2)

Where

(x1, y1) = (-3,-2)

(x, y) = (2,6)

Substitute the known values in the above equation

So, we have

(2, 6) = 1/2 * (-3 + x, -2 + y)

Multiply both sides of the equation by 2

So, we have

(4, 12) = (-3 + x, -2 + y)

By comparison, we have

-3 + x = 4

-2 + y = 12

Evaluate the like terms in the above equation

So, we have

x = 7

y = 14

When the above solution is represented as a coordinate, we have the following

(x, y) = (7, 14)

Hence, the other endpoint of the segment where the segment has the endpoint (-3,-2) and midpoint (2,6) is (7, 14)

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The student that has the higher standing in the class is Jill

The given parameters are:

Number of students = 200

Jill's position =80th

Nathan's position = Percentile rank  of 80

The above means that

Nathan's position = 80 percentage of the number of students in the class

Substitute the known values in the above equation

So, we have the following equation

Nathan's position = 80 percentage of 200

Rewrite as

Nathan's position = 80 percentage * 200

Express as percentage

Nathan's position = 80% * 200

Express 80% as decimal

Nathan's position = 0.80 * 200

Evaluate the product

Nathan's position = 160

So, we have

Jill's position =80th

Nathan's position = 160th

By comparing the positions, 80th is greater than 160th

Hence, Jill has the higher standing in the class

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The result of the indicated operations are:

(a) -4.324.

(b)  4.324.

(c) 0.9

(a) -1.424-2.9

Calculate the sum of the decimals,

The result is -4.324.

(b) 1.424-(-2.9)

Remove the bracket and change the sign in the middle and add the decimals to get the sum,

1.424 + 2.9 = 4.324.

(c) -1.424-(-2.9) -0.576

Remove the parentheses and change the sign,

-1.424 + 2.9 - 0.576

Add the negative decimal numbers and subtract them from the positive decimal number.

-2 + 2.9 = 0.9

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For the given function f(x) = 7 , the value of x is 5.

We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:

(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)

Where:

(xA , yA) , (xB , yB)  given

to find ,  (xC , yC)

(xA , yA) = (2,0) , (xB , yB) = (5,7)  and yC = 7

to find xC ,

xC - xA = (yC - yA) / (yB - yA) . (xB - xA)

xC =  xA + (yC - yA) / (yB - yA) . (xB - xA)

xC = 2 + (7-0)/(7-0) x (5 - 2)

xC = 2 + (5 - 2)

xC = 2 + 3

xC = 5

so the value of x in given function f(x) = 7 is 5.

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Answer:

13 correct me if i am wrong

Step-by-step explanation:

Answer: (-9/2,-53/4)

Step-by-step explanation:

Answer:

[tex]y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

To find the vertex form of a quadratic equation, complete the square.

Given quadratic equation:

[tex]y=x^2+9x+7[/tex]

Add and subtract the square of half the coefficient of the term in x to the right side of the equation:

[tex]\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}[/tex]

[tex]\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}[/tex]

Factor the perfect square trinomial formed by the first 3 terms:

[tex]\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}[/tex]

Answer:

I'm pretty sure it would be 8 though forgive me if I'm wrong