Page 1:
(MC 02.03)
What set of reflections and rotations would carry rectangle ABCD onto itself?
(4 points)
1) Rotate 180°, reflect over the x-axis, reflect over the line yox
2) Reflect over the x-axis, rotate 180°, reflect over the x-axis
3) Rotate 180°, reflect over the y-axis, reflect over the line y=x
4) Reflect over the y-axis, reflect over the x-axis, rotate 180°

Answer:

The length of the floor is [tex](15x^{2}+4x)\ ft[/tex]

Step-by-step explanation:

we know that

The area of a rectangle ( classroom floor) is equal to

[tex]A=LW[/tex]

in this problem we have

[tex]A=(30x^{3}+8x^{2})\ ft^{2}[/tex]

[tex]W=2x\ ft[/tex]

substitute in the formula and solve for L

[tex](30x^{3}+8x^{2})=2x(L)[/tex]

Divide by 2x both sides

[tex]L=(15x^{2}+4x)\ ft[/tex]

Answer:

D it is a horizontal line . .  .horizontal lines do not have a slope

Step-by-step explanation:

Answer:

B. the slope is zero

Step-by-step explanation:

The line shown is a horizontal line.  Horizontal lines have zero slope.

Vertical (up and down) lines do not have a slope ( or what we usually call undefined slope)

The answer is:

Range: All the real numbers or (-∞,+∞)

To solve the problem, we need to rewrite the variable "x" as "y" and the variable "y" as "x", and then, isolate "y". Then, we need to look if there is any restriction to the resulting value of "y".

We are given the function:

[tex]y=log_8(x)[/tex]

Now, rewriting we have:

[tex]x=log_8(y)[/tex]

Then, isolating we have:

[tex]8^{x} =8^{(log_8(y))}\\\\8^{x}=y[/tex]

Therefore, we can see that the resultant function is a quadratic or polynomial function, we need to remember that there is no restriction for this type of functions, it means that the range of the function is equal to the Real numbers where the values of  "x" exist.

Hence, the answer is:

Range: All the real numbers or (-∞,+∞)

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

√(3)/2

Step-by-step explanation:

To find the quotient, rationalize the denominator by multiplying both the numerator and denominator by √(6)

3√(8)*√(6)    =     3√(48)

4√(6)*√(6)              24

Next, simplify the top radical

12√(3) =  √(3)/2, This is the answer, it cannot be simplified any further.

 24  

For this case we must find the quotient of the following expression:

[tex]\frac {3 \sqrt {8}} {4 \sqrt {6}} =[/tex]

We combine [tex]\sqrt {6}[/tex] and [tex]\sqrt {8}[/tex] into a single radical:

[tex]\frac {3 \sqrt {\frac {8} {6}}} {4} =\\\frac {3 \sqrt {\frac {4} {3}}} {4} =\\\frac {3 \frac {\sqrt {4}} {\sqrt {3}}} {4} =\\\frac {3 \frac {2} {\sqrt {3}} * \frac {\sqrt {3}} {\sqrt {3}}} {4} =[/tex]

[tex]\frac {3 * \frac {2 \sqrt {3}} {3}} {4} =\\\frac {\frac {6 \sqrt {3}} {3}} {4} =\\\frac {6 \sqrt {3}} {12} =\\\frac {\sqrt {3}} {2}[/tex]

Answer:

[tex]\frac {\sqrt {3}} {2}[/tex]

Answer:

Step-by-step explanation:

Let the base of the board is x feet away from the wall .

And the hypotenuse, which is represented by the length of the board be 15 foot .

So here we have adjacent represented by the base and the hypotenuse .

And cosine function relates adjacent and hypotenuse , which is cos 60=15/x

And the value of cos 60 is half .

Performing cross multiplication

1/2=15/x

Dividing both sides by 2

x=7.5ft

Answer:

7.5 feet.

Step-by-step explanation:

The boardgame resting against the wall is creating a triangle rectangle and as it is forming a 60º angle with the ground that would be solve with the cosine of 60, which is the value of the division of the hypotenuse by the adjacent side, which would be the distance from the base of the board game to the wall:

Cos60= .5

cos60=adjacent side/hypotenuse

.5= adjacent side/15

adjacent side= 15x.5

Adjacent side=7.5 feet

Answer:

C

Step-by-step explanation:

In division when bases are same you do top exponent minus bottom exponent.

So here you do t^(12-6) which is t^6.

[tex]\huge{\boxed{5.5x+10}}[/tex]

We multiply the class fee by the number of classes. [tex]\bf{5.5x}[/tex]

A registration is a one-time fee, so it is simply added. [tex]5.5x \bf{+10}[/tex]

Answer:

Volume= 82.4in³

Step-by-step explanation:

Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic"

To find the volume of sphere, we will use the following formula of Volume:

Volume = 4/3 πr³

Put the values in the formula:

As we know that the value of π is 22/7 or 3.14

Radius = 2.7

According to the formula:

Volume = 4/3 * 3.14 *(2.7)³

Volume= 4/3* 3.14(19.683)

Volume=4/3(61.80462)

Volume=247.21848/3

Volume= 82.4in³....

Answer:

16 packs

Step-by-step explanation:

u just have to divide 224 by 14 to get 16

the school wants to get 224 clocks, they clocks come in packs of 14, so each pack has 14 clocks, how many packs are needed?

well, how many times does 14 go into 224? 224 ÷ 14, and you know what that is.

On this line, for all y-values, the x-value will always be -3.

Since it is a vertical line it has no run, only a rise. This makes the slope undefined.

This said, the equation for this line is x = -3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

7m

Step-by-step explanation:

The volume of a pyramid is given by the following formula: 1/3bh. Where 'b' represents the area of the base and 'h' the height of the pyramid.

The area of the base is: b = (3m)(4m) = 12m^2

Now, we know that the volume is 28m^3, then:

28m^3 = (1/3)(12m^2)(h)

Solving for 'h':

h = 7m

Answer:

Part 1) [tex]f(x)=\frac{2x-1}{x+2}[/tex] -------> [tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

Part 2) [tex]f(x)=\frac{x-1}{2x+1}[/tex] -------> [tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

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

Part 4) [tex]f(x)=\frac{x+2}{-2x+1}[/tex] ----> [tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]

Part 5) [tex]f(x)=\frac{x+2}{x-1}[/tex] -------> [tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]

Step-by-step explanation:

Part 1) we have

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

Find the inverse  

Let

y=f(x)

[tex]y=\frac{2x-1}{x+2}[/tex]

Exchange the variables x for y and t for x

[tex]x=\frac{2y-1}{y+2}[/tex]

Isolate the variable y

[tex]x=\frac{2y-1}{y+2}\\ \\ xy+2x=2y-1\\ \\xy-2y=-2x-1\\ \\y[x-2]=-2x-1\\ \\y=\frac{-2x-1}{x-2}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

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

Part 2) we have

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

Find the inverse  

Let

y=f(x)

[tex]y=\frac{x-1}{2x+1}[/tex]

Exchange the variables x for y and t for x

[tex]x=\frac{y-1}{2y+1}[/tex]

Isolate the variable y

[tex]x=\frac{y-1}{2y+1}\\ \\2xy+x=y-1\\ \\2xy-y=-x-1\\ \\y[2x-1]=-x-1\\ \\y=\frac{-x-1}{2x-1}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

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

Part 3) we have

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

Find the inverse  

Let

y=f(x)

[tex]y=\frac{2x+1}{2x-1}[/tex]

Exchange the variables x for y and t for x

[tex]x=\frac{2y+1}{2y-1}[/tex]

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

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

Part 4) we have

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

Find the inverse  

Let

y=f(x)

[tex]y=\frac{x+2}{-2x+1}[/tex]

Exchange the variables x for y and t for x

[tex]x=\frac{y+2}{-2y+1}[/tex]

Isolate the variable y

[tex]x=\frac{y+2}{-2y+1}\\ \\-2xy+x=y+2\\ \\-2xy-y=-x+2\\ \\y[-2x-1]=-x+2\\ \\y=\frac{-x+2}{-2x-1} \\ \\y=\frac{x-2}{2x+1}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

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

Part 5) we have

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

Find the inverse  

Let

y=f(x)

[tex]y=\frac{x+2}{x-1}[/tex]

Exchange the variables x for y and t for x

[tex]x=\frac{y+2}{y-1}[/tex]

Isolate the variable y

[tex]x=\frac{y+2}{y-1}\\ \\xy-x=y+2\\ \\xy-y=x+2\\ \\y[x-1]=x+2\\ \\y=\frac{x+2}{x-1}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

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

Answer:

Step-by-step explanation:

Answer:

C. y = x2 + 8x + 12

Step-by-step explanation:

To find x intercept/zero, substitute y = 0

0 = x^2 + 8x + 12

x^2 += 8x + 12 = 0

x^2 + 8x + 12 = 0

Solve the quadratic equation

x = -8±[tex]\sqrt{8^2 -4(12)[/tex] / 2(1)

any expression multiplied by 1 remains the same

x= -8±[tex]\sqrt{8^2 - 4(12)[/tex] / 2(1)

Evaluate the power

8^2

write the exponentiation as a multiplication

8(8)

multiply the numbers

64

x = -8±[tex]\sqrt{64 - 4(12)[/tex] / 2(1)

multiply the numbers

x = -8±[tex]\sqrt{64 - 48[/tex] / 2(1)

any expression multiplied by q remains the same

x = -8±[tex]\sqrt{64-48[/tex] /2

subtract the numbers

x = -8±[tex]\sqrt{16[/tex] / 2

calculate the square root

x= -8± 4 / 2

x= -8 + 4 / 2

x= -8 - 4 / 2

simplify the expression

x = -2

x = -8 - 4 / 2

x = -2

x = -6

final solutions are

x1 = -6, x 2 = -2

Answer:

A. 14 meters

B. 24 meters

Step-by-step explanation:

A. Mellisa starts at 29 meters deep, then rises 15 meters.  So her final depth is 29 − 15 = 14 meters.

B. Melissa starts at 40 meters deep, then rises 2 m/min for 8 minutes.  That means she rises a total distance of 2 × 8 = 16 meters.  So her final depth is 40 − 16 = 24 meters.

Answer:

At one point, Mellisa is 29 meters below the surface of the water.

A.

As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters.

So, her final depth at the end of the 12 minutes = [tex]29-15=14[/tex] meters

B.

Mellisa is at a depth of 40 meters. Every minute, she rises 2 meters.

So, in 8 minutes she will rise [tex]2\times8=16[/tex] meters

Her depth will be = [tex]40-16=24[/tex] meters

Answer:

V =91.845 ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = pi (1.5)^2 *13

Letting pi = 3.14

V = 3.14 (1.5)^2 * 13

V =91.845 ft^3

Answer:

V=91.89

Step-by-step explanation:

Given:

radius, r= 1.5 ft

height, h=13 ft

volume of cylinder= pi *r^2 *h

V=3.14 *(1.5)^2 *13

V=91.89 ft^3 !

Answer:

[tex]\tt{(8^{-3})}^{-4}; \ \ \ {(8^{1})}^{12}; \ \ \ {(8^{6})}^{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\tt {(a^m)}^n=a^{m\cdot n}}\\\\\\ \tt{(8^{-3})}^{-4}=8^{-3\cdot(-4)}=8^{12}\\\\{(8^{1})}^{12}=8^{1\cdot12}=8^{12}\\\\{(8^{6})}^{2}=8^{6\cdot2}=8^{12}\\\\[/tex]

Answer:A,D,F

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

5x + 2 = 3x + 4(2x - 1)

Distribute the 4

5x + 2 = 3x + 8x - 4

Combine like terms

5x + 2 = 11x - 4

Subtract 5x from each side

5x -5x + 2 = 11x - 5x - 4

2 = 6x-4

Add 4 to each side

2+4 = 6x-4+4

6 = 6x

Divide each side by 6

6/6 =6x/6

1= x

The value of x is 1 for equation 5x + 2 = 3x + 4(2x - 1).

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Given,

[tex]5x+2=3x+4(2x-1)\\[/tex]

[tex]5x+2=3x+8x-4[/tex]

On transposing like terms on one side of the equation.

[tex]5x-3x-8x=-4-2\\-6x=-6[/tex]

On multiplying -1 on both sides,

[tex]-6x\times(-1)=-6(-1)\\6x=6[/tex]

On dividing by 6 on both sides,

[tex]\frac{6x}{6}=\frac{6}{6}\\x=1[/tex]

Hence, the value of x is 1.

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Answer:

Susanne is 16 years old.

Step-by-step explanation:

You're gonna need three equations.

Key: B = Bob, D = Dakota, s = Susanne

B = 4s

D = s - 3

B + D + s = 93

Now plug in B and D into the third equation:

4s + (s - 3) + s = 93

Now solve it:

4s + s - 3 + s = 93

6s - 3 = 93

+3 +3

6s = 96

6s/6 = 96/6

s = 16

Bob's age is 4 times greater than Susanne's age, and Dakota is 3 years younger than Susanne.

The sum of their ages is 93. Susanne's age is 16.5.

Let's assign variables to represent the ages of the individuals involved:

We are given that Bob's age is 4 times greater than Susanne's age, so we can write the equation B = 4S.

We are also told that Dakota is three years younger than Susanne, so we can write the equation D = S - 3.

The sum of their ages is given as 93, so we can write the equation B + S + D = 93.

Substituting the first equation into the second equation, we get D = 4S - 3.

Substituting the values from the second and third equations into the fourth equation, we have (4S - 3) + S + (S - 3) = 93.

Simplifying this equation, we get 6S - 6 = 93. Adding 6 to both sides, we have 6S = 99. Dividing both sides by 6, we find that S = 16.5.

Therefore, Susanne's age is 16.5.

Answer:

7

Step-by-step explanation:

The quadratic equation looks like:

ax + by + c = 0

"c" is the variable that stands for the "constant", or the number that does not have an extra variable attached, and so is "unchanging". In this case, your answer is 7, which is the constant of the equation. Once defined, the number cannot be changed.

~

Answer:

20 in

Step-by-step explanation:

The radius is half the diameter.

You are given the diamter is 40 in.

So the radius is half of 40 in.

Half of 40 in means what is 40 in divided by 2.

Half of 40 in or 40 in ÷ 2 is 20 in.

The radius is 20 in.

Answer: 20 inches

Step-by-step explanation: A radius is half of the circle, and a diameter is a whole circle. 2 radius are equal to one diameter. So divide the diameter by 2 to get the radius.

40/2 = 20

The radius of the circle is 20 inches.

Answer:

To make something as small as possible or easier for something in particular.

Hope I helped!

Answer:

ab( b+c)

Step-by-step explanation:

abb +abc

There is an a and  b in each term

What remains goes inside the parentheses

ab( b+c)

Answer:

ab(b+c)

Step-by-step explanation:

Take out each variable like you would any other number

abb+abc

ab(b+c), This is the answer, with the distributive property, you can convert it back to its original form.

ab*b+ab*c=ab^2+abc

Answer:

They are 2 and 3.

Step-by-step explanation:

2 * 3 = 6

Answer:

So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]

Step-by-step explanation:

Since we are dividing by a linear factor, I'm going to use synthetic division.

Since the linear factor that we are dividing by is (x-5), I'm going to put 5 on the outside:

5    |     1       -12       8

      |              5      -35

      |--------------------------

           1         -7      -27

So the quotient x-7 while the remainder is -27.

So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]

You could do long division if you prefer:

           x-7

         ------------------------

(x-5) |   x^2-12x+8

        - (x^2-5x)

        --------------------------

                -7x+8

              -(-7x+35)

         ---------------------

                     -27

You still get the same thing that the quotient is x-7 and the remainder is -27.

Answer:

5m^6 + 2m^4 + 5m^3

hope this works!!!!

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², simplify each term by subtracting 2 from the exponents. The result is 5m⁶ + 2m⁴ + 5m³. The correct answer is D).

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², follow these steps

Write the given expression: (10m⁸ + 4m⁶ + 10m⁵) / 2m².

Divide each term in the numerator by 2m² separately:

(10m⁸ / 2m²) + (4m⁶ / 2m²) + (10m⁵ / 2m²).

Simplify each term:

5m⁶ + 2m⁴ + 5m³.

The final result is 5m⁶ + 2m⁴ + 5m³.

The correct option is D).

In this division, we use the rule of exponents: when dividing terms with the same base, subtract the exponents.

The division by 2m² reduces the power of 'm' in each term by 2. So, 10m⁸ becomes 10m⁶, 4m⁶ becomes 2m⁴, and 10m⁵ becomes 5m³. The constants 10 and 4 remain unchanged. The simplified expression is the final result.

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Answer:

The vertex is (-2,-17).

Step-by-step explanation:

We have given y=2x²+8x-9

To find the x-coordinates we use:

xv= -b/2a

where a=2 and b=8

Now put the values in the formula:

xv= -(8)/2(2)

xv=-8/4

xv= -2

Now to find the y coordinates, we will simply substitute the value in the given equation:

y=2x²+8x-9

y=2(-2)²+8(-2)-9

y=2(4)-16-9

y=8-16-9

y=-8-9

y= -17

Therefore the vertex is(-2, -17)....

Answer:

59.25 cm

Step-by-step explanation:

The perimeter means the sum of all the sides of a figure.

The perimeter of a triangle would be sum of all 3 sides (triangle has 3 sides).

The measure oof 3 sides are given, so we just need to add them to get the perimeter.

Perimeter = 16.3 + 18.75 + 24.2 = 59.25 cm

To find the perimeter of the triangle, add the side lengths of 16.3 cm, 18.75 cm, and 24.2 cm to get a total of 59.25 cm. The formula used is simple addition of all side lengths.

To find the perimeter of a triangle, you need to add up the lengths of all its sides. The side lengths given are 16.3 cm, 18.75 cm, and 24.2 cm.

Therefore, the perimeter of the triangle is 59.25 cm.

Answer:

the number of $10 bills = 17

the number of $20 bills = 37

Step-by-step explanation:

Let x be the number of $10 bills  and y be the number of $20 bills

Total bills = 54

So [tex]x+y= 54[/tex]

Total value of money is $910

[tex]10x+20y= 910[/tex]

now we solve for x  and y

Solve the first equation for y

[tex]x+y= 54[/tex]

[tex]y=54-x[/tex]

Now replace y in second equation

[tex]10x+20y= 910[/tex]

[tex]10x+20(54-x)= 910[/tex]

[tex]10x+ 1080-20x= 910[/tex]

[tex]1080-10x= 910[/tex]

Subtract 1080 from both sides

[tex]-10x= -170[/tex]

Divide both sides by -10

x= 17

[tex]y=54-x[/tex]

Replace x with 17

[tex]y=54-17=37[/tex]

the number of $10 bills = 17

the number of $20 bills = 37

Your question asks how much money was collected at the toll for a period of 8 hours.

To find the answer, we would need to gather some important information from the question.

Important information:

With the information above, we can solve the problem.

First, let's find how much money the toll makes in one hour. To find this, we need to multiply 1.50 by 160 cars, since the toll costs $1.50 and 160 cars go through it per hour.

[tex]1.50*160=240[/tex]

The toll makes $240 per hour.

Now, since we need to find how much the toll makes in 8 hours, we need to multiply 240 by 8.

[tex]240 * 8=1,920[/tex]

When you're done solving, you should get 1,920.

This means that the toll makes $1,920 in 8 hours.

Answer:

Given that the function is a model of miles per hour with x being representative of time in seconds, you simply have to plug 2 into the equation for each x.

Therefore,

g(x) = x^4 - 4x^2 + 7x - 8

becomes

g(x) = 16 - 16 + 14 - 8 = 6 miles per hour.

So, 6 mph is your answer!!

At rate of 6 miles per hour the rollercoaster travelling at 2 seconds.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

g(x) = [tex]x^4[/tex] - 4x² + 7x - 8

where x is time measured in seconds.

Now, the speed of roller-coaster for t= 2 seconds

g(2) =  [tex]x^4[/tex] - 4x² + 7x - 8

g(2) =  [tex]2^4[/tex] - 4(2)² + 7(2) - 8

g(2)= 16 - 16 + 14 - 8

g(2) = 6 miles per hour.

Hence, the speed 6 miles per hour.

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