If both the base and height of a triangle are made nine times as long, how many times the area of the original figure is the area of the new figure?

Answers

Answer 1

Answer: To start: A = 1/2bh
Now by increasing both the width and height by 9, you get: A = 1/2(9b)(9h) = 1/2(81)bh

You can see that the increase in area is 81 times the original.

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Divya wants to rent a car to drive for the weekend. The rental company has a special that allows her to rent it for $200 for the weekend, plus $0.07 per mile. Divya only has $230. Write an inequality, solve, and determine her limitations when renting.

Answers

Answer:

$200 + 0.07m \leq 230$

A maximum of $\approx$ 428 miles is the distance what Divya can travel.

Step-by-step explanation:

Given that:

Rent to be paid for the car in the weekend = $200

Charges to be paid per mile = $0.07

Total money available with Divya = $230

To find:

The inequality as per her limitations and solution to the problem.

Solution:

Let the number of miles for which Divya can drive = $m$ miles

Charges for one mile = $0.07

Charges for $m$ miles = $0.07 $m$

Total charges for renting and $m$ miles = Rental charges + Operational charges

Total charges for renting and $m$ miles = $200 + $0.07 $m$

These are charges must be lesser than equal to the amount of money available with Divya.

Therefore, we can write:

$200 + 0.07m \leq 230$

Subtracting 200 from both the sides:

$0.07m \leq 30$

Dividing both sides with 0.07:

$m \leq (30)/(0.07)\nm\leq 428.6$

Therefore, a maximum of $\approx$ 428 miles is the distance what Divya can travel.

What is the measure of ZABD?

Answers

Answer:

Step-by-step explanation:

If ZABC is a 90 degree angle all together and ZDBC is 51 degrees

Subtract 51 from 90 to get the angle for ZABD

90-51=39

1. Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a month? (assume 4 weeks per month)

Answers

$40 per hour
15 students per week
Each hourly student earns them $40 and there are 15 students, so this is multiplication.
40 * 15 = 600 per week
There are 4 weeks per month to earn 600 each week, this is again multiplication.
600 * 4 weeks = 2400 per month
Out of their earned 2400 they must pay for their overhead, the building rent
2400 - 400 = 2000 profit
They are left with $2000 between them.

Answer:

$4400

Step-by-step explanation:

$40 per hour

15 x 40 = 600

Because 'each' of them had 15 students, 600 x 2 = 1200

There are 4 weeks per month to earn 1200 each week, this is again multiplication.

1200 * 4 weeks = 4800 per month

Out of their earned 4800 they must pay for their overhead, the building rent

4800 - 400 = 4400 profit

They are left with $4400 between them.

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Find the distance between the points (1, 2) and -3, 4).