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3 years ago

What is the area of a rectangle whose sides measure 2g and (g+5)

Mathematics

1 answer:

zvonat [6]3 years ago

4 0

Answer:

2g² + 10g

Step-by-step explanation:

Let the,

Length of the rectangle be " l ".

Base of the rectangle be " b ".

l = 2g

b = g + 5

Formula : -

Area of the rectangle = lb

Area of the rectangle

= 2g ( g + 5 )

= 2g ( g ) + 2g ( 5 )

= 2g² + 10g

Therefore,

the area of a rectangle whose sides measure 2g and ( g + 5 ) is 2g² + 10g.

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Use the Distributive Property to expand 9(3 + x).

tankabanditka [31]

Distribute the 9 to each term in the parentheses with multiplication.

9(3 + x) = 27 + x

But this is usually written as x + 27

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3 years ago

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The distance between capeton & Jonesville is 80 miles. The scale on the map is 0.75 in 10 Mi how far part are the cities on

ikadub [295]

Answer:

6 in = 80 miles

Step-by-step explanation:

Given that:

Distance between Capeton and Jonesville = 80 miles.

Map scale : 0.75 in = 10 miles ; this means 0.75 inches on the map represents 10 miles on land.

Hence, If ;

0.75 inches = 10 miles

x inches = 80 miles

Cross multiply :

10 * x = 80 * 0.75

10x = 60

10x / 10 = 60 / 10

x = 6 inches

Hence,

6 in = 80 miles

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3 years ago

There are 2 questions pls answer fast

Furkat [3]

Answer:

Q1: B. UHWXUQV

Q2: None of these answers equal 12 so I'll just tell you the answers for all of them in case you mistyped.

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3 years ago

Find the 89th term of 25,35,45

MAXImum [283]

Answer:

The 89th term would be 895.

Step-by-step explanation:

There is a pattern of adding 10 each time. Notice that the 5 at the end doesn't change and that the first number continues (i.e. 2, 3, 4, 5, 6). All you have to do is add an 89 in front of the 5 and that is your answer, 895.

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3 years ago

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Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

2 years ago