Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or see transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.


Transformation Real-World Example


translation 1.

2.

3.


reflection 1.

2.

3.


rotation 1.

2.

3.


dilation or stretch 1.

2.

3.

Answer:

slope = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

- [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{4}[/tex] y = 24 ( multiply through by 4 to clear the fractions )

- 2x - 3y = 96 ( add 2x to both sides )

- 3y = 2x + 96 ( divide terms by - 3 )

y = - [tex]\frac{2}{3}[/tex] - 32 ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Answer:

SEE THE IMAGE FOR SOLUTION.

HOPE IT HELPS

Step-by-step explanation:

let :

the job as lifeguard = A

the job as cashier = B

making 2 equations as follows :

(1) A+B = 14 ==> A = 14-B

(2) 10A + 8B = 124

substitute A (equation (1)) into equation (2) :

10(14-B) + 8B = 124

140 -10B +8B = 124

140- 2B = 124

140-124 = 2B

16 = 2 B

B = 8

A = 14-8 = 6

so, as a lifeguard = 6 working hours

and as a cashier = 8 working hours

Answer:

Step-by-step explanation:

Let the lifeguard hours = x

Let the cashier hours= y

x + y = 14

10*x + 8*y = 124           Multiply the top equation by 8 Put it under here.

8x + 8y =     112           Subtract

2x = 12                          Divide by 2

x = 6

He worked 6 hours as a lifeguard.

x + y = 14

6 + y = 14                      Subtract 6 from each side

y = 14 - 6

y = 8                            

He worked 8 hours as a cashier.

check

6*10 = 60

8 * 8 = 64

total    124

Answer:

after 3 seconds, the object hits the ground.

Hope this helps :)

Answer:

75

Step-by-step explanation:

Let's say the unknown number is x

x/5 = 15

x = 15*5

x = 75

Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Answer:

A=13

hope this helped!!!

Answer:

-13

Step-by-step explanation:

-50=6a+28

collect like terms

-50-28=6a

-78=6a

divide both sides by the coefficient of a

-78/6=6a/6

a=-13

Answer:

F = (9/5 ×C) + 32

Step-by-step explanation:

Apply Change of subject

Divide both sides by 5/9

9/5 × C = F - 32

》F = (9/5 ×C) + 32

Answer:

[tex]p = 1[/tex]

Step-by-step explanation:

[tex]5p - 8(6p - 5) = p - 4[/tex]

[tex] - 43p - 40 = p - 4[/tex]

[tex] - 43p - p = - 40 - 4[/tex]

[tex] - 44p = - 44[/tex]

[tex]p = 1[/tex]

Answer:

[tex] p =\frac{22}{27} [/tex]

Step-by-step explanation:

5p - 8(6p - 5) = p - 4

-5p - 48p + 40 = p - 4

-53p + 40 = p - 4

-53p - p = -4 - 40

-54p = -44

p = 44 ÷ 54

p = 44/54

simplify with factor 2

p = 22/27

Answer:

v=20/3

See IMAGE FOR SOLUTION

In the given expression f = uv /(v+t) value of v in terms of t is *4/3t.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given an expression f = uv /(v+t)

Also given

f = 20

u = 5

Hence, From the expression

f =  uv /(v+t)

=> 20 = 5v/(v + t)

Simplifying in the terms of v

20v + 20t = 5v

15v = -20t

v = -4/3t

Therefore, the value of v in the given expression is -4/3t.

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Answer:

no solution

Step-by-step explanation:

14a – (2a + 9) = (12a - 18)

Distribute the minus sign

14a – 2a - 9 = (12a - 18)

12a -9 = 12a -18

Subtract 12a from each side

12a -9-12a = 12a-18-12a

-9 = -18

This is not a true statement so there is no solution

Answer:

x= -6 —> y= 4

x= -11 —> y= 5

Step-by-step explanation:

x= -6 —> y= 4

[tex]f( - 6) = \sqrt{ - ( - 6) - 2} + 2 \\ = \sqrt{6 - 2} + 2 \\ = \sqrt{4} + 2 \\ = 2 + 2 \\ = 4[/tex]

x= -11 —> y= 5

[tex]f( - 11) = \sqrt{ - ( - 11) - 2} + 2 \\ = \sqrt{11 - 2} + 2 \\ = \sqrt{9} + 2 \\ = 3 + 2 \\ = 5[/tex]

I hope I helped you^_^

The value of the function f(x) for the corresponding x = -6 and x =-11 is equal to 4 and 5 respectively.

The function f(x) = √( -x -2) + 2

The value of x and f(x) are ,

x    :   -2   -3    -6    -11

f(x) :   2     3      ?     ?

Now to find the missing value of f(x) substitute the value of x in f(x) we have,

When x = -6

f(x) = √( -x -2) + 2

⇒ f(x) = √( -( -6) -2) + 2

⇒ f(x) = √(6) -2) + 2

⇒ f(x) = √(4) + 2

⇒ f(x) = 2 + 2

⇒ f(x) = 4

And when x = -11

f(x) = √( -x -2) + 2

⇒ f(x) = √( -( -11) -2) + 2

⇒ f(x) = √(11) -2) + 2

⇒ f(x) = √(9) + 2

⇒ f(x) = 3 + 2

⇒ f(x) = 5

Therefore, the missing values of the function are 4 and 5.

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Answer:

the slope is 5

and the intercept is 0

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

HI + IJ = HJ

3x-5 + x-1 = 7x-27

Combine like terms

4x-6 = 7x-27

Subtract 4x from each side

4x-6 -4x= 7x-27-4x

-6 = 3x-27

Add 27 to each side

-6+27 = 3x-27+27

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

Answer:

x=7

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The slope of a line is

Change in y over change in x

This is also known as rise over run

Answer:

[tex](x+2)^2 + (y-1)^2 = 25[/tex]

Step-by-step explanation:

We want to write the equation of a circle with a diameter of 10 units centered on (-2, 1).

Recall that the equation of a circle has the standard form:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where (h, k) is the center and r is the radius.

Since our diameter is 10, our radius is 5.

And since the center is at (-2, 1), h = -2 and k = 1.

Substitute:

[tex]\displaystyle (x - (-2))^2 + (y - (1))^2 = (5)^2[/tex]

And simplify. Hence, our equation is:

[tex](x+2)^2 + (y-1)^2 = 25[/tex]

Answer:

[tex] \sqrt[3]{12} [/tex]

and

[tex] \sqrt[3]{ \frac{1}{18} } [/tex]

because

[tex] \sqrt[3]{12} \times \sqrt[3]{18} = 6 \\ \\ \sqrt[3]{ \frac{1}{18} } \times \sqrt[3]{18 } = 1[/tex]

Answer:

It depends in which direction "away" means. If they are five units to the right then the answer should be 1. if they are 5 points away to the left then the answer would be -9.

Step-by-step explanation:

Basically it depends,

if its indicating to the right the equation would be=

-4+5=x

which to do this negative cancells out its positive, so you can just subtract their absolute values. 5-4=1. And to know which symbol it has you just indicate which factor has the greated absolute value. (aka 5 which is positive so the answer should be positive).

-----------------------------

if its to the left then the equation would be=

-4-5= x

(negative four subtracted by four)

and the easier way to do this would be to turn this equation into addition.

the new equation shall be: -4+(-5)=-9 since they are both negative integers  the sum should be negative.

Answer:

x =36

Step-by-step explanation:

The three angles form a straight line which means they add to 180

2x+2x+x = 180

Combine like terms

5x = 180

5x/5 = 180/5

x =36

Answer:

X=36

Step-by-step explanation:

A straight line like the one shown in the image has 180° by one side.

Following that, we should assume that:

2x+2x+x=180°

5x=180°

x=36°

I hope I have helped you.

Answer:

None of the first 4 do. so I guess the answers E.

Step-by-step explanation:

Answer:

Proven.

Step-by-step explanation:

If 101 is given in base b, then in base 10 you have

[tex]101_b = 1\times b^2 + 0\times b^1 + 1\times b^0 = b^2 + 1[/tex]

For instance, if b = 2, then

101₂ = 2² + 1 = 5₁₀

If b = 3, then

101₃ = 3² + 1 = 9₁₀

If b = 4, then

101₄ = 4² + 1 = 17₁₀

The answer depends entirely on the base of the given number.

Answer:

AC = 22

Step-by-step explanation:

AB + BC = AC , substitute values

4x - 6 + 4 = 2x + 10 , that is

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Then

AC = 2x + 10 = 2(6) + 10 = 12 + 10 = 22

Answer:

Hello,

Step-by-step explanation:

[tex]f(n)=4n-5\\\\g(n)=an+b\\\\(gof)(n)=5n+1\\\\f(g(n))=f(an+b)=4*a*n+4b-5=5n+1\\\\4an=5n ==> a=5/4\\4b-5=1 ==> 4b=6 ==> b=3/2\\\\\\\boxed{g(n)=\dfrac{5n}{4} +\dfrac{3}{2} }\\\\[/tex]

Answer:

8 x 5 x 15 = 600in^3

Answer:

T (6, 5 )

Step-by-step explanation:

Using the section formula

If (x₁, y₁ ) and (x₂, y₂ ) are divided in the ratio m : n , then

( [tex]\frac{nx_{1}+mx_{2} }{m+n}[/tex] , [tex]\frac{ny_{1}+my_{2} }{m+n}[/tex] ) are the coordinates of the internal point

Here (x₁, y₁ ) = A (- 4, 10 ) , (x₂, y₂ ) = B (10, 3) , m : n = 5 : 2

T = ([tex]\frac{2(-4)+5(10)}{5+2}[/tex] , [tex]\frac{2(10)+5(3)}{5+2}[/tex] )

   = [tex]\frac{-8+50}{7}[/tex] , [tex]\frac{20+15}{7}[/tex] )

  = [tex]\frac{42}{7}[/tex] , [tex]\frac{35}{7}[/tex] )

  = (6, 5 )