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4 years ago

Which expressions are equivalent?

Mathematics

2 answers:

shusha [124]4 years ago

5 0

3(a-b) and 3a-3b. Equivalent

2a(2+b) and 4ab. Not equivalent

kirza4 [7]4 years ago

4 0

Answer:

3(a-b) and 3a-3b. Equivalent

2a(2+b) and 4ab. Not equivalent

Step-by-step explanation:

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Two of your friends go bowling. One friend rents a pair of bowling shoes for $3 and bowls 3 games. The other friend brings his o

Nesterboy [21]

Answer: The cost of each game is $2.50

Step-by-step explanation:

Let's find the equations for each friend:

Friend 1:

Pays $3 for the shoes, and plays 3 games, then if X is the cost of each game, Friend 1 pays a total of:

$3 + 3*X

Friend 2:

This friend buys a soda for $0.50, and he plays 4 games, remember that the cost of each game was X. then this friend pays:

$0.50 + 4*X

And we know that both friends pay the exact same amount, then we can write:

$3 + 3*X = $0.50 + 4*X

And solve this for X.

We need to isolate X, then we can move all the terms with X to the right, and all the terms without X to the left:

$3 - $0.50 = 4*X - 3*X

$2.50 = (4 - 3)*X = X

This means the cost of each game is $2.50

4 0

3 years ago

Question 2(Multiple Choice Worth 5 points) (04.01)The Boardman family walked two over five of a mile in two over seven of an hou

Zolol [24]

Answer:

The unit rate in miles per hour = <em>1.4 miles/hr</em>

Step-by-step explanation:

Given that:

Distance walked by Boardman family = Two over five of a mile = $\frac{2}{5}\ miles$

Time taken by Boardman family = Two over seven of an hour = $\frac{2}{7}\ hour$

To find:

The unit rate in the miles per hour = ?

Solution:

Formula for the rate or the speed can be given as:

$Speed = \dfrac{Distance}{Time}$

Putting the values:

$\Rightarrow \dfrac{\frac{2}5}{\frac{2}7}\\\Rightarrow \dfrac{7}{5}\\\Rightarrow \bold{1.4\ miles/hr}$

So, the unit rate in miles per hour = <em>1.4 miles/hr</em>

4 0

3 years ago

Which expression represents the sum of (2x-5y and (x+y) ?

gayaneshka [121]

I have no clue you have to do something like x2-x1 over y1-y2 and you get yoyu answer from that.

8 0

3 years ago

The height of a triangle is 8 centimeters greater than half its base. The area of the triangle is 48 square centimeters what is

emmainna [20.7K]

Answer:

base = 8 cm

height = 12 cm

Step-by-step explanation:

We will need the formula for area of a trianlge, which is

A = (1/2)bh where b is the base, and h is the height

We are given two formulas...

"The height of a triangle is 8 centimeters greater than half its base" becomes

h = (1/2)b + 8

"The area of the triangle is 48 square centimeters" becomes

48 = (1/2)bh

Plug the first formula into the second to solve for h

48 = (1/2)b[(1/2) + 8] (h becomes (1/2)b + 8)

Now solve for b

48 = (1/4)b² + 4b

**This is a quadratic euquation. Solve using factoring...

(1/4)b² + 4b - 48 = 0 (subtract 48 from both sides)

b² + 16b - 192 = 0 (multiply by 4 so b² is by itself, it's easier to factor this way)

Now factor...

(b + 24)(b - 8) = 0 (you need two numbers that add to 16 and multiply to -192)

Set each binomial equal to zero and solve for b

b + 24 = 0

b = -24

**this anwser is not valid because b is a length, and you can't have negative length

b - 8 = 0

b = 8

Since the other solution is invalid, the base is b

If the base is b, then the height is...

h = (1/2)b + 8

h = (1/2)(8) + 8

h = 4 + 8

h = 12

8 0

4 years ago

What is the justification for the first step in proving the formula for factoring the sum of cubes?

Anna11 [10]

Explanation:

The formula isnt correctly written, it should state:

$a^3+b^3 = (a+b)(a^2-ab+b^2)$

You have to start from $(a+b)(a^2-ab+b^2)$ and end in a³+b³. On your first step, you need to use the distributive property.

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

This is equal to

$a*a^2-a*(ab) + a*b^2 + b*a^2-b*(ab) + b*b^2 = a^3 - a^2b + ab^2 +ba^2 -b^2a +b^3$

Note that the second term, -a²b, is cancelled by the fourth term, ba², and the third term, ab², is cancelled by the fifht term, -b²a. Therefore, the final result is a³+b³, as we wanted to.

5 0

4 years ago