Consider the statements in the table shown. Select True or False for
each statement about the sequences of transformations that can
verify that triangle ABC is congruent to triangle A'B'C'.

Answer:

9

Step-by-step explanation:

(a-b)^2=a^2-2ab+b^2

(15-12)^2=9

Answer: 96

Step-by-step explanation:

Plug in a and b. so, (15-4(3))2+2(15). so (15-12)2+30. (3)32. Answer is 96.

You need to add 6 red marbles for the ratio to stay the same

The given parameters are:

Black = 6

Red = 4

Represent as ratio

Ratio = Red : Black

This gives

Red : Black = 4 : 6

When you add 4 red marbles, we have:

4 + 4 : 6 + x = 4 : 6

Where x represents the additional number of black marbles

This gives

8 : 6 + x = 4 : 6

Multiply 4 : 6 by 2

So, we have:

8 : 6 + x = 8 : 12

By comparing both sides, we have

6 + x = 12

This gives

x = 6

Hence, you need to add 6 red marbles for the ratio to stay the same

Read more about ratio at:

https://brainly.com/question/2784798

#SPJ1

The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is

                       multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.

According to the question we have been given that

The height of the small plant = [tex]2\frac{1}{2}[/tex] inch

In  1 week the plant grows = [tex]\frac{3}{4}[/tex] inch

We need to find the height of the small plant after 3 weeks.

For that we will first find how much tall it will be in 3 weeks using unitary method that is,

                              1 week = [tex]\frac{3}{4}[/tex] inch

                               3 week = [tex]\frac{3}{4}[/tex]  * 3 inch

                                          = 9/4 inch

Therefore the height of the small plant after 3 weeks will be

                         [tex]=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}[/tex]

hence the height is 19/4 inch

And the method which will not give the correct number of inches is the first option which is

               multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.

Learn more about unitary method here : https://brainly.com/question/8083231

#SPJ9

The expression 6-3/6-4 after simplification will look like 1.5.

Given that the expression is 6-3/6-4.

We are required to find the value after simplification.

Simplification or simplify fractions basically means to simplify a complicated mathematical expression to get a single or direct answer.

We have to use BODMAS rule for the simplification. The full form of BODMAS is Brackets, Open, Division, Multiplication,Addition and Subtraction. Simplication is nothing but to reduce the expression.

The expression is  6-3/6-4.

We have to do division first.

6-3/6-4 =6-0.5-4

Now we have to do subtraction now.

6-0.5-4=5.5-4=1.5

Hence the expression 6-3/6-4 after simplification will look like 1.5.

Learn more about simplification at https://brainly.com/question/723406

#SPJ1

Answer:

You save $ 14.27

Step-by-step explanation:

12 dozen = 11.53

2.15 x 12 = 25.80

25.80 - 11.53 = 14.27

The given statement written as a mathematical expression is c² - c + 14

From the question, we are to write the given statement as a mathematical expression

The given statement is

"The difference between the square of c and the total of c and 14"

The square of c is

c²

and

The total of c and 14 is
c + 14

Thus,

The statement becomes

c² - c + 14

Hence, the given statement written as a mathematical expression is c² - c + 14

Learn more on Writing an expression here: https://brainly.com/question/28419236

#SPJ1

Answer: 17 strings

Step-by-step explanation:

let the number of strings be a

let the number of beads on each string be b

a − b = 10 (first equation)
a × b = 119 (second equation)

From the first equation:

a = 10 + b

substitute first equation into second equation
b × (10 + b) = 119
10b + b² − 119 = 0
b = 7 or b = -17     reject -17

a − 7 = 10
a = 17

Answer:

8.9 ÷ 0.4 = 22.25

so the answer is 22.25

hope this helps

Answer:

22.25 is your answer

Step-by-st

The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]

An equation is an expression that shows the relationship between two or more numbers and variables.

The area of the right triangle is 5 in², the length of the leg is x, hence:

Area = (1/2) * base * height

5 = (1/2) * x * height

height = 10/x

hypotenuse = √[(leg)² + (height)²]

h(x) = √[x² + (10/x)²]

The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

[tex]76000\times1.08=\boxed{82,080}[/tex]

Answer:

82,080

Step-by-step explanation:

To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.

Answer:The cost should be 300,000 dollars

Step-by-step explanation:

Answer:

x^2

Step-by-step explanation:

it's a quadratic equation so the parent function is x^2.

Answer: Slope=5/3

Step-by-step explanation:

my teacher said

Answer:

400

Step-by-step explanation:

Change the 16 and the 64 in the numerator to exponents

2^4 x 10^2 x 4^3/2^4 x 4^2

Simplify

10^2 x 4

100 x 4

The function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The function that models the path of the first kick is given as

y = -0.02(x - 0.30)^2 + 18

A quadratic function is represented as

y = a(x - h)^2 + k

Where

Vertex = (h, k)

In this case, the interpretation of the vertex is

Vertex = (Horizontal distance, Maximum height)

Using the above as a guide, we have

Vertex = (30, 18)

This means that

Horizontal distance = 30

Maximum height = 18

For the second ball, we have

This means that

Horizontal distance = 30

Maximum height = 18 + 6

Evaluate

Horizontal distance = 30

Maximum height = 24

So, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24

Hence, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24

Read more about quadratic functions at

https://brainly.com/question/1214333

#SPJ1

Answer:

-29⁰F

Step-by-step explanation:

Because -19-10=-29.

If total revenue given by the function R=16.5x and has total cost given by C=14x+400, where x is the number of items produced and sold then the number of units that gives break even for the product is 160.

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are commonplace in mathematics and are required for expressing physical relationships in the sciences. The present concept of function was proposed by German mathematician Peter Dirichlet in 1837.

If a variable y is so tied to a variable x that there is a rule that determines a unique value of y whenever a numerical value is assigned to x, then y is referred to as a function of the independent variable x.

If the manufacturer will break even for the products then

Revenue = Cost

F(R) = F(C)

14x+400 = 16.5x

On solving the equation

16.5x - 14x = 400

2.5x = 400

x = 400/2.5

x = 160

In the graph the value of x is 160 as well

Thus, to break the product even the number of units =

160

Learn more about function

https://brainly.com/question/782311

#SPJ1

The justification for each step in the solution of the equation are as follows:

The equation is given as

23x − 13 = 2(x + 2)

Based on the solutions, we can rewrite the given equation as follows

So, we have

2/3x − 1/3 = 2(x + 2)

So, the justification for each step in the solution of the equation are as follows:

2/3x − 1/3 = 2(x + 2) -- Given

By the multiplication property of an equation, we have

2x − 1 = 6(x + 2)

By the distributive property of an equation, we have

2x − 1 = 6x + 12

Next, we collect and evaluate the like terms

2x = 6x + 13

By the subtraction property of an equation, we have

−4x = 13

By the division property of an equation, we have

x =−13/4

Read more about equations at

https://brainly.com/question/1429964

#SPJ1

The slope ( option A) best describes the number 3.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:

a= the slope. It can be calculated for  [tex]\frac{\Delta y}{\Delta x}[/tex].

b= the constant term that represents the y-intercept.

For the given example: a=7 and b=2.

The equation of the question is y=3x+7, when you compare this equation with the  standard form for the linear equation is: y= ax+b. You find that a=3, where a represents the slope.

Read more about the linear equations here:

brainly.com/question/2030026

#SPJ1

Answer:

22, 24

Step-by-step explanation:

Hello!

Consecutive integers are integers that come after each other. We want to find two consecutive even integers that when added give us 46.

Let the first consecutive even integer be x. Since even integers come every 2 integers (even, odd, even), the second even integer should be x + 2.

That means x + 2 should be 24.

The two numbers are 22 and 24.

Answer: x=68

Step-by-step explanation:

(x-5)/3=21

(x-5)*3/3=21*3     ==> Multiply both sides by 3 to remove fractions

x-5=21*3

x-5=63

x+5-5=63+5     ==> Add 5 on both sides to isolate the x variable

x=63+5

x=68

Let's solve the problem,

→ (x - 5)/3 = 21

→ x - 5 = 21 × 3

→ x = 63 + 5

→ [ x = 68 ]

Hence, the value is 68.

Answer:

Step-by-step explanation: 5x=3(x+6)

5x=3x+18

5x-2x=18

3x=18

x=18/3

x=6

The total laps your friend runs is 3.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

A proper fraction is a fraction where the numerator is less than the denominator. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.

The first step is to determine the total miles you run

Total miles run  = length of the side walk x total number of laps

9/10 x (3 + 2)

9/10 x 5 = 45 / 10 = 4.5 miles

The second step is to determine the total number of laps she runs:

4.5 miles / 1 1/2 miles

4.5 / 1.5 = 3 laps

To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498

#SPJ1

The average speed of person during her commute is 28 miles/ hour.

What do you mean by average speed ?

The entire distance that an object travels in a given amount of time is defined as the average speed for that object.

Total time of driving is 12 minutes.

This can be written as hours which will be :

= 12 / 60

= 1/5 hour

Time of stopping at red lights is 3 minutes and speed is 35 miles per hour.

So , the total distance using the formula will be :

Total distance = Speed × time

Here , the time taken will be equal to :

= [(12 + 3) / 60]

= 15 / 60

= 1/4 hour

So ;

Total distance = 35 × (1/4 hour)

Total distance = 7 miles

And the average speed will be ;

Average speed = Distance / Time

or

Average speed = 7 miles / (1/4) hour

Average speed = 7 × 4 miles/hour

Average speed = 28 miles / hour

Therefore , the average speed of person during her commute is 28 miles/ hour.

Learn more about average speed here ;

https://brainly.com/question/553636

#SPJ1

Answer:

-10x-6

Step-by-step explanation:

and simplify and add