The given line segment has a midpoint at (3, 1).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

y = x
y = x – 2
y = 3x
y = 3x − 8

Definition of average rate of change a function g(x) over an interval [a,b]:

[tex]A = \dfrac{g(b)-g(a)}{b-a}[/tex]

Substitute your function and your interval:

[tex]A = \dfrac{(3^6-6)-(3^0-6)}{3-0} = \dfrac{3^6-6-3^0+6}{3} = \dfrac{3^6-1}{3} = \dfrac{728}{3}[/tex]

The average rate of change of the function gx) = 3(2x) - 6 over the interval [0,3] is calculated as (g(3) - g(0)) / (3 - 0) which equals to 6.

The average rate of change of a function over an interval [a,b] is defined as:

(g(b) - g(a)) / (b - a)

Here, the function g(x) = 3(2x) - 6, and the interval is [0,3]. Let's calculate g(3) and g(0).

g(3) = 3(2*3) - 6 = 12

g(0) = 3(2*0) - 6 = -6

Now, apply these values to the average rate of change formula:

(g(3) - g(0)) / (3 - 0) = (12 - (-6)) / 3 = 18 / 3 = 6.

So, the average rate of change of the function g(x) over the interval [0,3] is 6.

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Answer:

[tex]4c^{7}d^{13}[/tex]

Step-by-step explanation:

[tex](2cd^{4} )^{2} *(cd)^{5}[/tex]

[tex]4c^{2}d^{8} *c^{5} d^{5}[/tex]

[tex]4c^{7}d^{13}[/tex]

The answer is -12 and 9. You have to factor the equation first. Once you do this, than you can set each problem equal to zero and solve. I hope this helps.

Answer:

[tex]\frac{1}{4}[/tex] of the books in the book store are mystery fiction books.

Step-by-step explanation:

Let x represent all the books in the books store.

Then, the fraction of books that are fiction books is [tex]\frac{3}{4}x[/tex]

We have that; [tex]\frac{1}{3}[/tex] of the fiction books are mystery books.

The fraction of the books at the  bookstore that are mystery fiction  books is [tex]\frac{1}{3}\times \frac{3}{4}x=\frac{1}{4}x[/tex].

Therefore [tex]\frac{1}{4}[/tex] of the books in the bookstore are mystery fiction books.

Answer:

1/4

Step-by-step explanation:

Answer:

1= 115

2=45

3=110

4=115

5=115

Step-by-step explanation:

Answer:

1:

[tex]180-(70+45)=65[/tex] degrees(3rd angle of triangle)

Angle 1 is [tex]180-65=115[/tex] degrees.

2:

Angle 2 is 45 degrees as vertically opposite is also 45 degrees.

3:

[tex]180-(65+45)=70[/tex] degrees(third angle of lower triangle)

Its opposite will also be 70 degrees.

So, 3rd can be found as : [tex]360-(70+110+70)=110[/tex] degrees

You can also say that 3 is vertically opposite of 110 degrees.

4:

[tex]180-65=115[/tex] degrees

5:

This is also 115 degrees as its vertically opposite angle to 4.

ANSWER

The second term is 7.

EXPLANATION

The given sequence has it's first term to be:

[tex]t_1 = 3[/tex]

The recursive definition is :

[tex]t_{n+1}=2t_n+n[/tex]

To find the second term , we substitute n=1,

to obtain,

[tex]t_{1+1}=2t_1+1[/tex]

This implies that:

[tex]t_{2}=2t_1+1[/tex]

[tex]t_{2}=2(3)+1[/tex]

Simplify:

[tex]t_{2}=6+1[/tex]

[tex]t_{2} = 7[/tex]

Answer:

The second term of the sequence is 7 ⇒ the 2nd answer

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ The recursive definition is tn+1 = 2 tn + n and t1 = 3

- Lets find the 2nd term

∵ t1 = 3

∵ tn+1 = 2 tn + n

* To find the second term put n = 1

∴ t2 = 2 (3) + 1

∴ t2 = 6 + 1 = 7

∴ t2 = 7

* The second term of the sequence is 7

Answer:

Option  C) 70%

Step-by-step explanation:

we know that

To determine the percentage of games played that won, divide the number of games won by the total number of games played.

so

[tex]P=14/20=0.70[/tex]

Convert to percentage (multiply by 100)

[tex]0.70*100=70\%[/tex]

Answer:

                 [tex]\bold{\dfrac{\,351\,}{275}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac9{10}+\dfrac25\right)\div\left(\dfrac{11}{6}\cdot\dfrac59\right)\ =\ \left(\dfrac9{10}+\dfrac4{10}\right)\div\dfrac{55}{54}=\\\\\\ =\ \dfrac{13}{10}\times\dfrac{54}{55}\ =\ \dfrac{13}{5}\times\dfrac{27}{55}\ =\ \dfrac{351}{275}[/tex]

Answer:

A. 15%

Step-by-step explanation:

percent change = (new number - old number)/(old number) * 100%

The new number is the increased area, 25,587.5 sq yd, and the old number is the original area, 22,250 sq yd.

percent change = (25,587.5 sq yd - 22,250 sq yd)/(22,250 sq yd) * 100%

percent change = (3,337.5 sq yd)/(22,250 sq yd) * 100%

percent change = 0.15 * 100%

percent change = 15%

Since the percent change is a positive number, it is a percent increase.

The percent increase was 15%.

Answer: A. 15%

Answer:

d) The maximum number of footballs the team can purchase is 44.

Step-by-step explanation:

975+34f≤ 2500

Subtract 975 from both sides: 975-975+34f≤ 2500-975

34f≤ 1525

Divide both sides by 34: 34f/34≤ 1525/34

f≤ 44.853

You can't purchase 0.853 of a helmet so the maximum you can buy is 44

The maximum number of footballs the team can purchase is 44.

Inequality directs to the phenomenon of unequal and/or unjust distribution of resources and possibilities among members of a given society. The word inequality may mean different things to various people and in different contexts.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Given

975+34f≤ 2500

Subtracting 975 from both sides: 975-975+34f≤ 2500-975

34f≤ 1525

Dividing both sides by 34: 34f/34≤ 1525/34

f≤ 44.853

so the maximum you can buy is 44

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Answer:

there are no answers it is false just did it

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

3(x + 3) - 2x = 23

3x + 9 - 2x = 23

x + 9 = 23

x = 14

The answer is 16

The Pythagorean theorem is a^2+b^2=c^2

You already have one side and the hypotenuse (c)

15^2+b^2=17^2

15^2= 225

17^2= 289

Now you have 225+b^2= 289

Subtract 225 from both sides and you get

b^2=64

Then take the square root of both sides to get b alone

b=8

Now, since the base of the inner triangle is half of the base of the pyramid, multiply your answer by 2

You will get 16

Answer: [tex]V=11.775\ in^3[/tex]

Step-by-step explanation:

You need to use the formula for calculate the volume of a cone. This is:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the cone-shaped paperweight is 3 inches. Then, you need to divide the diameter by 2 to find the radius:

[tex]r=\frac{3in}{2}\\\\r=1.5\ in[/tex]

Now you know that:

[tex]r=1.5\ in\\h=5\ in\\\pi=3.14[/tex]

Substituting these values into the formula [tex]V=\frac{1}{3}\pi r^2h[/tex], you get that the volume of the  paperweight is:

[tex]V=\frac{1}{3}(3.14)(1.5\ in)^2(5\ in)[/tex]

[tex]V=11.775\ in^3[/tex]

The volume of the paperweight will be 11.76 cubic inches.

Let d be the diameter of the base circle and h be the height of the cone.

Then the volume of the cone will be

V = 1/12 x πd² x h

The cone-shaped paperweight has a diameter of 3 inches and a height of 5 inches.

Then the volume of the paperweight will be

V = 1/12 x π(3)² x 5

V = 1/12 x 3.14 x 9 x 5

V = 11.76 cubic inches

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Answer:

2 miles.

Step-by-step explanation:

Decrease in the temperature: 5.4×5=27°C

Final temperature: 12-27=-15°C

ANSWER

The discriminant is 49.

EXPLANATION

The given quadratic equation is:

[tex]0 =2{x}^{2} + 3x - 5[/tex]

We can rewrite this as

[tex]2{x}^{2} + 3x - 5 = 0[/tex]

Comparing this to

[tex]a{x}^{2} + bx + c = 0[/tex]

We have a=2,b=3, c=-5.

The discriminant is given by:

[tex]D = {b}^{2} - 4ac[/tex]

We plug in the values to get:

[tex]D = {3}^{2} - 4(2)( - 5)[/tex]

[tex]D =9 + 40[/tex]

[tex]D = 49[/tex]

Answer:

D IS THE ANSWER (49)

Step-by-step explanation:

Answer:

85000/100*10.5 = $8925

Step-by-step explanation:

N/A

Answer:

2 reals and 2 rationals.

Step-by-step explanation:

The discriminate gives

b^2 - 4*a*c

b = -7

a = 5

c = 2

(-7)^2 - 4(5)(2)

49 - 40

9

Taking the square root gives you +/-3

The discriminate tells you that there are 2 roots, both real and both rational

x = [(-7) +/- 3  ]/2*5

x = (- 7 - 3)/10 = - 1

x = (- 7 + 3)/10 = -0.4

Answer:

7 ft bRo

Step-by-step explanation:

wow i took 21 and divided it by three and i got SEVEN

how old are you like four

The height of the flat screen TV can be calculated by dividing the given area (21 square feet) by the given width (3 feet). This gives us a height of 7 feet.

In this problem, we are given the area of the flat screen TV and the width. The area of a rectangle is calculated by multiplying the width and the height, so to find the height, we can divide the area by the width.

Let's denote the height as 'h'. So, the formula will be: Width times height = Area of the screen, or in our case, 3 feet times h = 21 square feet. Solving this equation gives us h = 21 ÷ 3 = 7 feet.

So, the height of the TV is 7 feet.

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Answer:

see explanation

Step-by-step explanation:

Note that the sum of the coefficients of g(x)

1 + 2 - 3 = 0

Hence x = 1 is a root of g(x) and (x - 1) is a factor

Note the sum of the coefficients of f(x)

1 - 3 - 13 + 15 = 0

hence x = 1 is a root of f(x) and (x - 1) is a factor

Since (x - 1) is a factor of both

Then f(x) is also divisible by x² + 2x - 3

Step-by-step explanation:

Cir=30π=2πr , thus r=15 , Area=π(r^2)=225 pie meters

The area of circle is 225π m².

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

Given that,

Circumference of the circle = 30π m

Let r be the radius of circle.

Since we know that,

circumference of the circle = 2πr

Therefore,

⇒  2πr = 30π

⇒       r = 15 m

Area of circle = πr²

                      = (15)²π

                      = 225π

Hence required area is 225π square meter.

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Answer:

4

Step-by-step explanation:

-5+9=4

Answer:

A. 0.5

B. 4.5

C. 1.5

D. 0.5

Step-by-step explanation:

y varies inversely with x can be written as:

y = k/x

where k is constant of variation.

1. value of A

x=A, y = 9 and k = 4.5 (given)

y = k/x

9 = 4.5/A

=> A = 4.5/9

=> A=0.5

2. Value of B

x =1, y= B, k = 4.5

y = k/x

B = 4.5/1

B= 4.5

3. Value of C

x=C, y=3. k=4.5

y = k/x

3 = 4.5/C

3C = 4.5

C = 4.5/3

C = 1.5

4. Value of D

x= 9, y=D, k=4.5

y = k/x

D = 4.5/9

D = 0.5

Answer:

[tex]A=0.5[/tex]

[tex]B=4.5[/tex]

[tex]C=1.5[/tex]

[tex]D=0.5[/tex]

Step-by-step explanation:

The form an the equation of inverse variation is:

[tex]y=\frac{k}{x}[/tex]

Being "k" the constant of variation.

Since we know "k" and we have the values given in the table, we can find the missing values:

To find A we need to substitute the [tex]y=9[/tex], the value of "k" and [tex]x=A[/tex] into the equation and solve for "A":

[tex]9=\frac{4.5}{A}[/tex]

[tex]A=\frac{4.5}{9}=0.5[/tex]

To find B we need to substitute the [tex]x=1[/tex], the value of "k" and [tex]y=B[/tex] into the equation:

[tex]B=\frac{4.5}{1}=4.5[/tex]

To find C we need to substitute the [tex]y=3[/tex], the value of "k" and [tex]x=C[/tex] into the equation and solve for "C":

[tex]3=\frac{4.5}{C}[/tex]

[tex]C=\frac{4.5}{3}=1.5[/tex]

To find D we need to substitute the [tex]x=9[/tex], the value of "k" and [tex]y=D[/tex] into the equation:

[tex]D=\frac{4.5}{9}=0.5[/tex]

Answer:

Options B,C,E are true.

Step-by-step explanation:

It has been given in the question ∠ACD is supplementary to ∠ACE and ∠BCD

∠ACD ≅ ∠BCE

Option A. ∠ACE is supplementary to ∠BCD

False. They are not lying on a point of straight line.

∠ACE + ∠BCD ≠180°

Option B. ∠BCE is supplementary to ∠ACE

Since ∠ACD + ∠ACE = 180° [Given]

and ∠ACD ≅ ∠BCE [Given]

Therefore, ∠BCE + ∠ACE = 180°

TRUE.

Option C. ∠BCD is supplementary to ∠BCE

Since ∠ACD + ∠BCD = 180°[Given]

and ∠ACD ≅ ∠BCE [Given]

So ∠BCE + ∠BCD = 180°

TRUE.

Option D. ∠ACE ≅ ∠BCE

Since ∠ACD + ∠ACE = 180°

And ∠ACD + ∠BCD = 180°

This is clear from these equations that ∠ACE is supplementary to ∠BCD.

FALSE :

Option E. ∠BCD is congruent to ∠ACE

As we have already proved in option D. ∠BCD ≅ ∠ACE

TRUE

Therefore, Options B, C, E are TRUE

The probability that Chloe is awarded a blue ribbon in both January and February is 0.1421 or  14.21%.

To calculate this, we simply multiply the probabilities of Chloe being awarded a blue ribbon in January and February:

Probability in January = 0.29

Probability in February = 0.49

Probability in January and February = 0.29 * 0.49 = 0.1421

Explanation:

1. Given probabilities:

  - Probability of Chloe being awarded a blue ribbon in January = 29% = 0.29

  - Probability of Chloe being awarded a blue ribbon in February = 49% = 0.49

2. To find the probability of Chloe being awarded a blue ribbon in both January and February, we multiply the probabilities together:

  - Probability in January and February = 0.29 * 0.49 = 0.1421

Therefore, the probability that Chloe is awarded a blue ribbon in both January and February is approximately 14.21%.

Complete question:

Each month a retail store awards a blue ribbon to its employee of the month. The probability that Chloe is the employee of the month is 29% in January and 49% in February. What is the probability that she is awarded a blue ribbon in both January and February?

Answer:

$24.4

Step-by-step explanation:

We are given that a discount store promises that all items it sells are 40% of their normal asking retail price.

If a shoes have a retail price of $60.99, we are to find the expected price of the shoes at this store.

Expected price of shoes = 40% of $60.99 = [tex] \frac { 4 0 } { 1 0 0 } \times 6 0 . 9 9 [/tex] = $24.4

Answer:

You have walked [tex]\frac{17}{24}[/tex] miles

Step-by-step explanation:

In order to add these two fractions, we must find a common denominator. In this case, I used 24

[tex]\frac{3}{8} +\frac{1}{3} \\\\\frac{9}{24} +\frac{8}{24} =\frac{17}{24}[/tex]

Answer:

3/8 + 1/3 = 9/24 + 8/24 = 17/24

Step-by-step explanation:

Answer:

FIRST OPTION: (-4, -2)

Step-by-step explanation:

Given the inequality [tex]y + x < -5[/tex], substitute each solution given in the options:

1) For (-4, -2) :

[tex](-2)+ (-4) < -5[/tex]

[tex]-6 < -5[/tex] (This is true)

2) For (-3, -2):

[tex](-2)+ (-3) < -5[/tex]

[tex]-5 < -5[/tex] (This is not true)

3) For (-2, -3):

[tex](-3)+ (-2) < -5[/tex]

[tex]-5 < -5[/tex] (This is not true)

4) For (-1, -3):

[tex](-3)+ (-1) < -5[/tex]

[tex]-4 < -5[/tex] (This is not true)

You can observe that (-4, -2) is a solution of [tex]y + x < -5[/tex]

The answer is A.

Hope this helps :)