15. Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same
music store and purchased one CD and five cassette tapes for $76. If all CDs are the
same price and all the cassette tapes are the same price, find the cost of each CD and
each cassette tape.

Using dilation rules, the dilated triangle whose coordinates of the vertices are as follows: A'(-2 , 2), B'(-1,0), C'(1 , 2).

What is the rule for a dilation?

To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:

(x, y) -> (ax, ay).

suppose the coordinates of the vertices of ABC are given as follows:

A(-6,6), B(-3,0), C(3,6).

After a dilation with a scale factor of 1/3, the coordinates of the vertices of A'B'C' will be given as follows:

A'(-2 , 2), B'(-1,0), C'(1 , 2).

These coordinates are derived multiplying the coordinates of A, B and C by 1/3.

For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by 2 to generate the dilated triangle.

A number is divisible by 3 it the sum of its digits is divisible by 3. In this case, we have

which is not divisible by 3. The nearest multiples of 3 are 1623 and 1626. If you divide these numbers by 3, you have

So, the result of our division is between 541 and 542.

If these numbers are too complex to divide, we have to choose easier numbers, but we will lose some accuracy. For example, we can see that 1624 is between 1500 and 1650, which are very easily divisible by 3. We have

So, the result of our division is between 500 and 550. This is still true, but as you can see it is a much looser approximation than the one before.

The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .

We know that the general form of the equation of a circle is given by the following equation:

(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.  

So the general equation of the circle is (x-5)² + (y+3)² = 9² .

Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.

The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.

(x-5)² + (y+3)² = 9²

or, x² + 10x + 25 + y² + 6y + 9 = 81

or, x² + y² + 10x + 6y - 47 = 0

Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.

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The transformations to the graphs of each function are presented as follows:

The parent function is defined as follows:

f(x) = log2(x).

Function p(x) is defined as follows:

p(x) = 7log2(x) - 2.

The transformations are listed as follows:

Function r(x) is defined as follows:

r(x) = -2log2(x) + 3.

The transformations are listed as follows:

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Answer:

its c b a

Step-by-step explanation:

other person was wrong

The amount of fence the farmer will need to buy is 90 ft

The area of rectangle is the product of its length to its width.

i.e., Area of Rectangle= length x width

let the length of the back of his house be x ft.

Thus, if the second side of the garden to be 30 feet longer than the back of his house,

then the length of the second side is; (x + 30) ft.

Now,

Area = Length × width

400 = x (x + 30)

400 = x² + 30x

x² + 30x - 400 = 0

Solving the quadratic equation:

x = -40 or 10

Thus, length of second side = 10 + 30 = 40 ft

Now, Perimeter of 3 sides = 10 + 2(40)

Perimeter of 3 sides = 90 ft

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Answer:

Step-by-step explanation:

The train A speed is 45 mph.  The train B speed is 70 mph.

Answer:

f(x) = 4x
for graph see attachment

Step-by-step explanation:

when the buyer gets 4 points for each movie purchased, the equation for the graph is f(x) = 4x

x being the movies, 4 being the amount of points per movie granted.

The real roots of the function is {0,-2} and there are no repeated roots.

Given function:

f(x) = [tex]x^{2} +2x[/tex]

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

take x as common

x(x+2) = 0

x = 0 and x + 2 = 0

x+2 = 0

x = -2,0.

Therefore the real roots of the function is {0,-2} and there are no repeated roots.

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22 members were present and 8 members were absent.

There are 30 members in a committee.

On a certain day 11/15 of the total members were present.

Let x be the number of members who were present.

So, we get an equation,

x = 11/15 * 30

We solve above fraction.

x = 11 * 2

x = 22

So, 22 members were present.

And 30 - 22 = 8 members were absent.

Therefore, 22 members were present and 8 members were absent.

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The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

C(x) = 11.99 + 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

C(m) = 11.99m + 7

The equation is in the form of y = mx + c

So,

m = 11.99

c = 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

Thus,

The slope of the function is 11.99.

The y-intercept of the function is 7.

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Answer: An investor bought 500 shares of stock , some at $ 3.50 per share and some at $6.00 per share. If the total cost was $ 2187.50, how many shares of each stock did the investor buy?

(a) How will you set up the problem?

Let # of 3.50 shares be "x" ; value is 3.5x dollars

# of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars

EQUATION:

value = value = 2187.50

3.5x + 3000-6x = 2187.5

-2.5x = -812.5

x = 325 (# of 3.50 shares)

500-x = 175 (# of 6.00 shares)

Step-by-step explanation:

The features from the graph of the function are given as follows:

a) The domain is {x | x ≠ -2}.

b) The range is {y | y ≠ 1}.

c) The x-intercept is: x = 0.

d) The y-intercept is: y = 0.

The domain of the function is the set of input values of the function, hence the values of x from the graph.

From the graph, the function is not defined at x = -2, hence the domain is:

{x | x ≠ -2}.

The range of the function is the set of input values of the function, hence the values of y from the graph.

From the graph, the function has an asymptote at y = 1, hence the range is:

{y | y ≠ 1}.

The x-intercept is the value of x at which the function crosses the x-axis, hence:

x = 0.

The y-intercept is the value of y at which the function crosses the y-axis, hence:

y = 0.

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Answer:

5

Step-by-step explanation:

Answer:

Slope [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2x + 5y = 21  Subtract 2x from both sides of the equation

5y = -2x + 21  divide all the way through by 5

y = [tex]\frac{-2}{5}[/tex] x + [tex]\frac{21}{5}[/tex]  The slope is the coeffience of the variable (the number before the x)

Answer:  " x = 1 ".

    The answer for this 'system of equations' is:  " [1, 15] ".

_________

Step-by-step explanation:

To solve for x :

Given:
  y = 3x + 18

  y = 15 ;

_________
 We know that:

 3x + 18 = 15 ;  Now, subtract 18 from Each Side of the equation:

  3x + 18 − 18 = 15 − 18 ;

  to get:

  3x = 3 ; Now, divide Each Side of the equation by 3 ;

     to isolate x on one side of the equation;

      and to solve for x :
 

   3x / 3 = 3 / 3 ;

   to get:    x = 1

_________

The answer is: " x = 1 " ;

 The answer for this 'system of equations' is:
   " [1, 15] " <== { written as:  " [x, y] "} ;

                         in which: " y = 15 " ; is given in the problem.

_________
Hope this answer is helpful.
 Best wishes!
_________

Answer:

D ,

Step-by-step explanation:

4cd(6-9c)

5(x+5)

Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex] \sf x = 4 :: 8 : 2[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\boxed{\: x = \frac{4 \times8}{2} = \frac{32}{2} = 16 }[/tex]Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{16 : 4 :: 8 : 2}[/tex]

The mean number of students per Faculty is 326.

Mean simply means the average of a set of numbers.

In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:

= Total values / 9

= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9

= 2938 / 9

= 326.44

The mean is 326.

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V+12 is the expression that shows how many volunteers there are now

An expression is combination of variables, numbers and operators.

Given,

At the start of the year, the soup kitchen had v volunteers.

During the year, 12 more volunteers joined them

Joined them means added, it means 12 volunteers are added to the v volunteers

v plus twelve.

v+12

Hence v+12 is the expression that shows how many volunteers there are now

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The yards of roadside that Ben is cleaning more than Adam is 26 yards. Sheridan is correct.

The first step is to determine the length of Oakley Street. Pythagoras theorem would be used to determine the length.  Oakley Street is the hypotenuse of the right triangle that is formed by the streets.

The Pythagoras theorem: a² + b² = c²

where:

39² + 52² = c²

1,521 +  2704 = c²

c² = 4,225

c = √4225

c = 65 yards

Total yards Ben picked = 39 + 52 = 91 yards

Yards picked by Adam = 65 yards

Difference in the yards of litters picked = 91 - 65 = 26 yards

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The number of bicycles that are there is 4.

There are a Total of 11 bicycles and tricycles altogether in the shop window.

They have a total of 29 wheels.

Therefore, the number of bicycles that are there can be calculated as follows;

Bicycles has 2 wheels and tricycles has 3 wheels.

Therefore,

let

x = number of bicycle

y = number of tricycle

2x + 3y = 29

x + y = 11

Multiply equation(ii) by 2

2x + 3y = 29

2x + 2y = 22

y = 7

x = 11 - 7

x = 4

Therefore the number of bicycle is 4.

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Answer:

  (a)  as x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞

Step-by-step explanation:

You want to know the end behavior of the 4th-degree function shown in the graph.

The graph has an arrow on each end of the curve shown in the figure. The left arrow points upward, indicating a tendency to +∞ as x gets more negative.

The right arrow also points upward, indicating a tendency to +∞ as x gets more positive.

  As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

The direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

What are the component of force?

If a force acting at some angle [tex]\theta[/tex] with respect to x axis then the force can be resolved into two perpendicular forces ([tex]Fcos\theta[/tex] and [tex]Fsin\theta[/tex]). These perpendicular forces are known as component of forces.

Consider the following diagram of the sialboat.

The component of force along the heading direction is 480N and the component of force perpendicular to the heading is 650N.

If F is the foce the direction of wind then then component of force in the East direction will be [tex]Fcos\theta[/tex] and the component of force in the heading direction is [tex]Fsin\theta[/tex]. Now, take the ratio of these two compnents to find the angle [tex]\theta[/tex] as follows:

[tex]tan\theta=\frac{Fcos\theta}{Fsin\theta}\\tan\theta=\frac{650N}{480N}\\\\\theta=tan^{-1}(1.354)\\=53.6^0[/tex]

Now, calculate the force exerted by the wind. Equate the force in heading direction to find the force.

[tex]Fsin\theta=480N\\F=\frac{480N}{sin\theta}\\=\frac{480N}{sin53.6^0}\\=596.4N[/tex]

Hence, the direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

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The required amount of 25% saline solution is 8 liters.

In mathematics, the equation that used to find an Unknow quantity is known as Linear Equation. Here we use different types of variables to represent the unknown value like x, y, z or a, b, c.. etc.

Here we have

4 liters of a 40% saline  

we need to make it a 30% of saline solution by adding a mount of 25% saline solution

Let us assume that we added x L of 25% of saline solution  

After adding x L of 25% saline into 4 liters of 40% saline to get 30% saline solution then the resultant solution is “x+4” liters of 30% saline.

The mathematical representation for the above line will be

⇒ x litres 25% saline + 4 litres 40% saline = (x+4) litres 30% saline

⇒ x(25%) + 4(40%) = (x+4)(30%)

⇒ 25x/100 + 4(40/100) = (x+ 4)30/100  

⇒ 25x + 160 = (x +4)30  

⇒ 25x + 160 = 30x + 120

⇒ 30x - 25x = 160 - 120

⇒  5x = 40

⇒ x = 8

Therefore

The required amount of 25% saline solution is 8 liters

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The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

Now,

Let the cost of 1 slices of cheese pizza = x

And, The cost of 1 slices of soda = y

Since, Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

Hence, We get;

⇒ 3x + 2y = $8.75  ..(i)

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

So, We get;

⇒ 2x + 4y = $8.50  ..(ii)

Multiply by 2 with (ii);

⇒ 2 (3x + 2y) = 2 × $8.75

⇒ 6x + 4y = $17.5  

Subtract from (ii), we get;

⇒ 6x + 4y - 2x - 4y = $17.5 - $8.50

⇒ 4x = $9

⇒ x = $2.25

And, ⇒ 2x + 4y = $8.50

⇒ 2 × $2.25 + 4y = $8.50

⇒ $4.5 + 4y = $8.50

⇒ 4y = $8.50 - $4.5

⇒ 4y = $4

⇒ y = $1

Thus, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $2.25 + 3 × $1

⇒ $2.25 + $3

⇒ $5.25

Therefore, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

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The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

First, let us know some laws of exponent:

We are given;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].

Now, we will solve one by one;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]

[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]

[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]

[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]

[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]

= 2x

So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.

Now,

[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]

[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]

[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]

[tex]=\frac{1}{(2^{3-1}x^{3-2}y^{3+1})}[/tex]

[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]

= 1 / 4xy^4

So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Please find the figure for the questions below.

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Answer:

angle LHJ is congruent to angle IKL

Answer:

segment JL is congruent to segment JK

segment HL is congruent to segment KI

Angle LJH is congruent to angle KJI

Step-by-step explanation:

we flip the triangles to look for the corresponding sides

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The distance travelled by the tortoise in 1/4 hour is 0.5miles

A rate is a more general measure in which one quantity is divided by another quantity, where both quantities don't necessarily need to have the same unit of measure. For example , Tayo typed 500 words in 50 minutes. This means that the rate of Tayo in typing is 500/50= 10words per minutes.

The tortoise travels 2miles in 1hour. There are two terms of different unit, which are distance in miles and time in hours

if the tortoise travels 2miles in 1hour

then in 1/4 hours,

the tortoise will travel 2×1/4

= 0.5mile

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