MATHEMATICS HIGH SCHOOL

240/2,304 simplest form

Answers

Answer 1

Answer:

Answer:

5/48

Step-by-step explanation:

Answer 2

Answer:

Answer:

5/48

Step-by-step explanation:

to simplify this we should know the least common fact of the two which would be 48 then divide 240 and 2304 by 48 to get 5/48

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Tara incorrectly estimates 36,591,000,000 meters as 4x10^6 meters explain tara's mistake?

Answers

Answer:

4 * 10¹⁰

Step-by-step explanation:

Estimation:

The estimate value of 36,591,000,000 is 40,000,000,000.

40,000,000,000 = 4 * 10¹⁰

Answer: 4 * 10¹⁰

Choose the two equations you would use to solve the absolute value equation below. Then solve the two equations.|x + 5| = 55

Answers

$|x+5|=55\n\nx+5=55\ \vee\ x+5=-55\n\nx=55-5\ \vee\ x=-55-5\n\nx=50\ \vee\ x=-60$

Please help!!!!!The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to
serve the ferry operator's needs?

Answers

The boat must go 9mph on the lake in order for it to serve the ferry operator's needs

Represent the speed of the boat on the lake or in still water with x

Given that:

The current in a river has a speed of 6 mph.

When the boat goes upstream, the speed is x - 6;
When the boat comes downstream, the speed is x + 6;

So, the time taken by the boat each trip are:

$t_1= 22.5 * (x - 6)$

$t_2= 22.5 * (x + 6)$

$T = 9 * (x + 6) * (x - 6)$

The equation that calculates the required time (x) is:

$t_1 + t_2 =T$

This gives

$22.5 * (x - 6) + 22.5 * (x + 6) = 9 * (x + 6)* (x - 6)$

Expand

$22.5x - 135 + 22.5x + 135 = 9x\² - 324$

Evaluate the like terms

$45x = 9x\² - 324$

Divide through by 9

$5x = x\² - 36$

Collect like terms

$x\² -5x - 36 = 0$

Factorize

$(x + 4) (x - 9) = 0$

Solve for x

$x = 9\ or\ x = - 4$

x cannot be negative.

So, we have:

$x = 9$

Hence, the boat must go 9mph on the lake in order for it to serve the ferry operator's needs

Read more about speed and distance at:

brainly.com/question/4931057

Answer: the speed of the boat on the lake is 9 mph

Step-by-step explanation:

Let x represent the speed of the boat on the lake or in still water.

The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.

Time = distance/ speed

Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is

22.5/(x - 6). The time taken to travel downstream is

22.5/(x + 6)

Since the total time is 9 hours, it means that

22.5/(x - 6) = 22.5/(x + 6)

Cross multiplying, it becomes

22.5(x + 6) + 22.5(x - 6) = 9

Multiplying through by (x + 6)(x - 6), it becomes

22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]

22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)

22.5x + 22.5x = 9x² - 324

9x² - 45x - 324 = 0

Dividing through by 9, it becomes

x² - 5x - 36 = 0

x² + 4x - 9x - 36 = 0

x(x + 4) - 9(x + 4) = 0

x - 9 = 0 or x + 4 = 0

x = 9 or x = - 4

Since the speed cannot be negative, then x = 9

An ice cream shop's goal is to sell a mean of 45 ice cream cones per day. In one week, it sold the following numbers of ice cream cones each day.54, 45, 33, 39, 48, 40, 41

How many more ice cream cones would it have had to sell during the week to meet its goal?

A. 15
B. 25
C. 35
D. 5

Answers

To achieve its goal, it needed to sell at least a total of 45*7 = 315 cones each week. but it only sold 54+45+33+39+48+40+41= 300 cones.
therefore it needs 315 - 300 = 15 more cones to meet its goal.

Answer:

15 !

Step-by-step explanation:

What is the height of a rectangular prism with a base of 147cm and a volume of 1323cm

Answers

What is the meaning of science

Water coming out from a fountain is modeled by the function f(x) = −x2 + 8x + 2 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.What does the average rate of change of f(x) from x = 1 to x = 4 represent?

Answers

Average rate of change of f(x) from x = 1 to x = 4 represents the average speed with which the water is falling between the first second and the fourth second.

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