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Alekssandra [29.7K]

3 years ago

12

3. Which two expressions are equivalent for any value of y? *

1 answer:

-Dominant- [34]3 years ago

5 0

Given:

The pair of expressions in the options.

To find:

The two expressions are equivalent for any value of y.

Solution:

Two expressions are equivalent for any value of y, iff they are equivalent.

$3(3y+3)=3(3y)+3(3)$

$3(3y+3)=9y+9$

Clearly, $3(3y+3)$ is not equivalent to $6y+6$ or $9y+6$ . So, options A and B are incorrect.

$9(y+3)=9(y)+9(3)$

$9(y+3)=9y+27$

$9(y+3)=27+9y$

The expression $9(y+3)$ is not equivalent to $12+9y$ . So, option C is incorrect.

The expression $9(y+3)$ is equivalent to $27+9y$ .

Therefore, the correct option is D.

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Complete the sentence: similar figures have the

umka21 [38]

I'm assuming it would be the same shape? That's also assuming that it's referring to congruent shapes and angles.

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3 years ago

What is the area of this figure?

Karolina [17]

We will do this step by step
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5 0

3 years ago

Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

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

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

If 100 people drink 1.5 cups of coffee a day and the cost per cup is .40 how much would it cost to provide coffee for the whole

N76 [4]

Answer:

It would cost <u>15600</u> to provide coffee for the whole year.

Step-by-step explanation:

Given:

If 100 people drink 1.5 cups of coffee a day and the cost per cup is .40

Now, to find the cost to provide coffee for the whole year if you're place is open 5 days a week.

So, we have the unit rate, and we have to find the cost of 1.5 cup by multiplying 0.40.

<em>1.5 cup of coffee cost </em> $1.5\times 0.40=0.60.$

<em>Thus, 1.5 cup cost 0.60.</em>

<em>If, 100 people drink 1.5 cups. </em>

<em>Then, total cost of 100 people drinking 1.5 cups of coffee = </em> $100\times 0.60=60$ <em />

<em>As, place is open 5 days a week.</em>

So, to get the cost of coffee in 5 days of a week we multiply 5 by 60:

$5\times 60\\\\=300.$

<em>Hence, the cost of coffee in a week is 300.</em>

<em>In 1 year there are 52 weeks.</em>

Now, to get the cost for the whole year we multiply 52 by 300:

$52\times 300\\\\=15600.$

Therefore, it would cost 15600 to provide coffee for the whole year.

6 0

3 years ago

Read 2 more answers

27. It costs $8.65 to ride the train. Ms. Reilly took

frozen [14]

Answer:$164.35

Step-by-step explanation:

You just multiply 19 × 8.65

6 0

3 years ago