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3 years ago

Write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms then use x=3 to show expressions are equivalent

Mathematics

1 answer:

Ket [755]3 years ago

8 0

Answer:

7x + 9

Yes they are equivalent

Step-by-step explanation:

The first expression given to us is

2x + 3 + 5x + 6

Let us call it equation (i)

Now we have to find equivalent expression to it

the given equation is 2x + 3 + 5x +6

similar terms are terms involving x and not involving x

so solving the equation gives

2x + 5x + 3 +6

= 7x + 9

Now we have two equations one is

2x + 3 +5x + 6 ...............(i)

Other is

7x + 9 ..............(ii)

To check they are equivalent or not

Put x = 3 in equation (i)

2(3)+3+5(3)+6= 6 + 3 + 15 + 6

=30

Now put x=3 in second equation

7(3)+9=21 + 9

=30

As the answer of both the equations are 30 so they are equivalent

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On a map, 1.5 centimeters represents a distance of 45 kilometers. If two points on the map are 0.8 centimeters apart, what is th

Dmitry_Shevchenko [17]

Write a proportion
centimeters / kilometers
1.5 / 45 = 0.8 / x
cross multiply
(1.5 * x ) = (45 * 0.8)
1.5x = 36
divide both sides by 1.5
x = 24

The actual distance between the two points is 24 kilometers.

Hope this helps

6 0

3 years ago

Kamila has a rectangular lawn that measures 80 by 150 feet. She wants to lay gravel made from colored rock in a border, 6 feet w

beks73 [17]

A) Diagram

Below is a sketch of the recctangular lawn (the inside rectangle) and the gravel border.

6 ft + 150 yards + 6 ft
-------------------------------
|                                    |
|     ---------------------      |
|     |                        |     |
|     |                        |     |   6 ft + 80 yard + 6 ft
|     |                        |     |
|      ---------------------     |
|                                    |
|------------------------------|

B) How many square feet of the gravel will surround the lawn?

Conversion: 1 yard = 3 feet

=> 80 yard = 80*3 feet = 240 feet

=> 150 yard = 150 * 3 feet = 450 feet

Area of the external rectangle = (6 ft + 240 ft + 6 ft) (6 ft + 450 ft + 6 ft) = 252 ft * 462 ft = 116,424 ft^2

Area of the internal rectangle = 240 ft * 450 ft = 108,000 ft^2

Area of the gravel border = 116,424 ft^2 - 108,000 ft^2 = 8424 ft^2

answer: 8424 ft^2

C) volume

volume = area of the base * depth

2 inches = 2/12 ft = 1/6 ft

=> volume = 8424 ft^2 * 1/6 ft = 1404 ft^3

answer: 1404 ft^3

C) cost

1 yard^3 = $ 30

1yard ^3 = (3 feet)^3 = 27 ft^3

=> cost = $ 30 / 27 ft^3

=> 1404 ft^3 * $30 / 27 ft^3 = $ 1560

answer: $ 1560

7 0

4 years ago

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1

Reptile [31]

Average rate of change over the interval [a,b] for y=f(x) is given by f(b)−f(a)b−a

Hence, average rate of change of from x=−2 to x=6 i.e. over the interval [−2,6] for y=f(x)=12x2 is given rate of change=f(6)−f(−2)6−(−2)

As f(−2)=12(−2)2=2 and f(6)=12(6)2= rate of change=18−28=162=2

3 0

3 years ago

Can help for this questing 1) 2)

Free_Kalibri [48]

Answer:

1. Median

2. Altitude

Step-by-step explanation:

Medians- Bisect the side (Split the side into two equal parts)

Altitude- Makes a right angle

1. Splits the side into two equal parts. Anwser: Median

2. Makes a right angle Answer: altitude

8 0

4 years ago

Verify sin(360º - θ)= -sin θ Show your work

Mekhanik [1.2K]

Answer:

A nice way to show it is through the unit circle.

In the unit circle, the point at angle theta from the origin has a y value of sin theta.

If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).

4 0

4 years ago

Read 2 more answers