MATHEMATICS HIGH SCHOOL

A tortoise is walking in the desert. It walks at a speed of 7
meters per minute for
17.5
meters. For how many minutes does it walk?

Answers

Answer 1
Answer: It walks for 2.5 mins.
Answer 2
Answer: The turtle walks for a total of 122.5 minutes.

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Round this number 3.899 to the nearest hundredth

Answers

3.90 is the number rounded to the nearest hundredth.
To round that too the nearest hundredth your answer would be 3.9

[Related Rates]Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm^2? ...?

Answers

Below is the solution: 

A(final)=16cm^2 ds/dT=6 da/dT=? 

A=(s)^2 A=16cm^2 , s=sqrt(A) , s=sqrt(16) , s=4cm 

da/dT=2(s)(6cm/sec) , da/dT=12cm/sec(s) , da/dT=12cm/sec (4cm) 

Answer should be da/dT=48cm^2/sec

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How do you solve x²-10x+9=0 by completing the square?

Answers

x^2-10x+9=0\n\n\underbrace{x^2-2x\cdot5+5^2}_((*))-5^2+9=0\n\n(x-5)^2-25+9=0\n\n(x-5)^2-16=0\ \ \ /+16\n\n(x-5)^2=16\iff x-5=-√(16)\ \vee\ x-5=√(16)\n\nx-5=-4\ \vee\ x-5=4\n\nx=-4+5\ \vee\ x=4+5\n\nx=1\ \vee\ x=9



(*)\ (a-b)^2=a^2-2ab+b^2
x^2-10x+9=0 \n \nx^2-2\cdot5x+5^2-5^2+9=0\n \n(x-5)^2-25+9=0\n \n(x-5)^2=16\n \nx-5=4\ \ \vee\ \ x-5=-4\n \nx=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=1

What is the solution to the proportion? 6/x=9/12

Answers

6/x = 9/12
Product of means = Product of extremes
12 × 6 = 9 × x
x = 12 × 6/9
x = 8

A sum of a number and 14 is at least of 28

Answers

a sum means we are adding.
a number and 14 means we are adding 14 and a number (x)
at least means < 
and to balance the equation out they gave us 28 
so our answer is....
14 + x < 28

Carol and Jan leave from the same place and travel on the same road going the same direction. Carol walks at a rate of 2 miles per hour. Carol left 5 hours earlier than Jan, but Jan rides a bike at a rate of 6 miles per hour. How far did the travel when Jan caught up to Carol?

Answers

Let, the time when Jan cough up to Carol = x

We know, Distance = Speed * Time.

So, Equation would be: 2x + 5*2 = 6x

2x + 10 = 6x

6x - 2x = 10

4x = 10

x = 10/4 = 2.5

Distance traveled in that time = 2.5 * 6 = 15 miles

In short, Your Answer would be: 15 miles

Hope this helps!
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