methane
24/4=6.
The length is 6cm.
What is the value of:
1/2+1/2+1/2+1/2?
(1/2)*4=2.
A pencil costs 50 cents. A notebook costs 3 times as much. You buy 2 notebooks and 1 pencil. How much does it cost in total?
Bonus 10 points if you can give me the answer in dollars.
((50x3)*2)+50
=350 cents, or $3.50
Solve for x:
6x+33+34=85.
So:
6x+33+34=85.
6x+67=85.
6x=18.
x=3.
If a right triangle has hypotenuse=10cm, and one leg=8cm, what is the length of the other leg?
Pythagorean theorem:
a2+b2=c2. So:
82+b2=102 -> 64+b2=100 -> b2=36 -> b=6.
The length of the other leg is 6 centimeters.
5600. We just move the decimal place 3 to the right, because we are multiplying by 103 or 1000, and we get 5600.
A number is multiplied by 6, then 18 is added, then the result is 60. What is the original number?
We can set this up like an algebra equation where x=missing number.
6x+18=60.
6x=42.
x=7.
The original number is 7.
We can also reverse engineer it, subtract 18, then divide by 6, but this is basically the steps of the algebra above.
Find all roots.
(x-3)(x-7)=0
A. x=5 C. x=±√ 6
B. x=3,x=7 D. x=0,x=7
Well, we can see that (x-3) and (x-7) are being multiplied to each other. So, we can see that anything multiplied by 0 is 0. Thus, we have 2 possible solutions: x-3=0 or x-7=0. Solving gives us B. x=3,x=7.
Solve for x.
2x-3=16.
A. x=7 C. x=10
B. x=5 D. x=2
We can notice 16 is a power of 2. we can rewrite this as:
2x-3=24.
Now, we can write this as: x-3=4. Solving for x, we get A. x=7.
If a person has 3 cards, blue, red and green, if they pull out one card from that pile at random, what is the probability that the green card is still there?
So, if the person picks blue or red, we are good. Total no. outcomes: 3. Probability: 2/3 or 66.67%.
A shape is made of two squares stuck together side‑by‑side. Each square has side length 5 cm. What is the perimeter of the whole shape?
A. 20cm C. 10cm
B. 15cm D. 30cm
This one is tricky, because 20 is incorrect. One square's side length is 5, so the side length of the 2 squares combined is 5x2=10. Then, we get perimeter 10+10+5+5, and thus the perimeter is D. 30cm.
A quadratic equation is presented below. Find all values of x.
x2-6x+5=0.
Well, if your brain is fried, you would quadratic equation. But the smarter way is: factoring.
We can find 2 numbers that multiply to 5 and add to -6. Those two numbers are -1 and -5. So:
(x-1)(x-5)=0, and from there, it is clear that x=1 or x=5.
A 3 digit password can contain letters in the first 2 digits, A-Z, and numbers in the last digit, 0-9. Digits/numbers are allowed to repeat. What are the total number of passwords that can be made?
A. 5600 C. 4952
B. 6760 D. 12700
We have 26 letters, and 10 numbers (0 included!!!!)
So:
Total number of passwords: 26x26x10 = B. 6760. (letters for first 2 digits, and number for the last for 3 digit password)
A system of equations is presented below.
x2-y2=175
x+y=5
What is the value of x?
A. 25 C. 10
B. 5 D. 55
x2-y2=175 x+y=5
In this system of equations, we can notice that the -y2 term and +y term could cancel. Thus, we square the second equation:
x2-y2=175 x2+y2=25
Now we see that the terms cancel if we add the 2 equations together, leaving us with 2x2=200. Divide both sides by 2: x2=100. Take the sq. root of both sides, and thus x equals C. 10.