MATHEMATICS HIGH SCHOOL

What is the simplified form of x minus 5 over x squared minus 3x minus 10 ⋅ x plus 4 over x squared plus x minus 12? (6 points)

Answers

Answer 1
Answer:

Answer: Our simplified form will be

(1)/((x+2)(x-3))

Step-by-step explanation:

Since we have given that

(x-5)/(x^2-3x-10)* (x+4)/(x^2+x-12)

So, first we split the middle term of the denominator ,

x^2-3x-10=0\n\n=x^2-5x+2x-10\n\n=x(x-5)+2(x-5)\n\n=(x-5)(x+2)

Similarly,

x^2+x-12=0\n\nx^2+4x-3x-12=0\n\nx(x+4)-3(x+4)=0\n\n(x+4)(x-3)=0

Now, we put in our expression above:

(x-5)/((x-5)(x+2))* (x+4)/((x-3)(x+4))\n\n=(1)/(x+2)* (1)/(x-3)\n\n=(1)/((x+2)(x-3))

Hence, our simplified form will be

(1)/((x+2)(x-3))
Answer 2
Answer: Step 1 is to factor everything! 

After factoring you will get:

x-5 over (x+2)(x+5) times x+4 over (x-3)(x+4)

Step 2 is to remove the duplicate factors!
Remove x+4 and x+5

x-5 over (x+2)(x-5) times 1 over x-3 = 1 over x+2 times 1 over x-3 

Step 3 is to multiply the numerators and the denominators.

End result is 1 over (x+2)(x-3)

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Five less than a number is at least -28

Write 1 2568/10,000 in a decimal notation

Answers

12568/10000

The 10000  has four zeros, write 12568 as 12568.0, simply move the decimal point four places to the left, since 10000 has four zeros.

You have 1.2568 as the answer.
1.2568
It's simple....just follow these steps;
1. See the denominator(the number you are dividing with) which in this case is 10,000.
2. Now, since the denominator is a number that has "1" on the unit place (more examples of such numbers are 10, 100, 1000, 10000 etc.), follow the followig steps.
NOTE:- Do not follow these steps if such is not the case.
3. Count the number of zeros in the denominator.
4. Now, in this case we have 4 zeros, so start counting the digits in the numerator form right.
5. Put the decimal after number of digits equal to the counted zeros.
hope it helps... =)

Estimate the value of the square root of 15.9÷3.8

Answers

Step-by-step explanation:

lets round up for even square roots.

16 and 4 have even square roots

the square root of 16 is 4 and the square root of 4 is 2

4÷2 is 2

i estimate that the square root of 15.9÷3.8 is about 2

Thomas is planning a trip to India. He is currently deciding which cities he would like to visit during his stay. The table below shows possible cities for Thomas to visit, as well as how much money he expects to need at each one. All costs are given in Indian rupees (Rs.). City
Cost (Rs.)
Jaipur
6,920
Mumbai
9,464
Thiruvananthapuram
9,160
Lucknow
5,276
Bhopal
8,268
Bhubaneswar
7,109
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Bengaluru
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Thomas had originally planned to visit Thiruvananthapuram, Mumbai, Bhubaneswar, and Bengaluru, but his budget of Rs. 25,300 makes that impossible. Which of the following itinerary changes will allow Thomas to stay within his budget? (Consider each option individually, rather than as a group.)

I. Swap Thiruvananthapuram for Jaipur and drop Bengaluru.
II. Drop Bhubaneswar.
III. Swap Mumbai for New Delhi, Thiruvananthapuram for Jaipur, and Bhubaneswar for Lucknow.
a.
I and II
b.
III only
c.
I and III
d.
I, II, and III

Answers

The itinerary changes that will allow Thomas to stay within his budget is C. I and III. Check how to reach the result below.

What is a budget?

It should be noted that a budget simply means an estimate of the income and expenditure of an individual.

In this case, the itinerary changes that will allow Thomas to stay within his budget include swapping Thiruvananthapuram for Jaipur and drop Bengaluru and swapping Mumbai for New Delhi, Thiruvananthapuram for Jaipur, and Bhubaneswar for Lucknow.

In this case, a trip to Mumbai costs

9,464 while a trip to New Delhi is 6,303. Therefore, a trip to New Delhi is better in this scenario as it more budget friendly.

Learn more about budget on:

brainly.com/question/6663636
Swap Thiruvananthapuram for Jaipur and drop Bengaluru and  Swap Mumbai for New Delhi, Thiruvananthapuram for Jaipur, and Bhubaneswar for Lucknow.this option is cheaper for thomas

the water level in a leaky swimming pool fell by the same amount each day for 6 days. Over time the water level measure 4 inches lower. What was the change in the water each day

Answers

Answer:

-4/6 of an inch per day (it is negative because the water level is decreasing

Step-by-step explanation:

A car can travel 247 kilometers on 19 liters of gasoline. how much gasoline will it need to go 429 kilometers?

Answers

find the number of miles per 1 liter:

247 kilometers / 19 liters = 13 kilometers per liter.


Divide how may kilometers they want to go by kilometers per liter:

429 kilometers / 13 kilometers per liter = 33 liters are needed.

How many positive integers less than 25 can be formed by using the digits 1,2 and 3

Answers

I tried to think of a fancy formula for it, then decided it's just easier to list them:

1
2
3
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That's 9 of them.
there are 9 numbers that are positive integers that can be formed by the #s 1,2,&3 THAT R LESS THAN 25 1 2 3 11 12 13 21 22 23
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