MATHEMATICS
MIDDLE SCHOOL

Answer: The answer is 17 I believe, because if you divide 5 by 17, you get the remainder of 4, and both of the two digits are odd.

MIDDLE SCHOOL

What is a equivalent expression for 3y+y+4+y

Answer:

5y+4

we can write it like:

3y+y+y+4

And sum of 3y+y+y is 5y

So answer is 5y+4

MIDDLE SCHOOL

Rewrite the equation x^2-4x+9=5 in the form (x-p)^2=q

Answer:

(x - 2)² = 0

Step-by-step explanation:

given x² - 4x + 9 = 5 ( subtract 5 from both sides )

x² - 4x + 4 = 0

This is a perfect square of the form

(x - a)² = x² - 2a + a²

compare coefficients of the x-term

- 2a = - 4 ⇒ a = 2

⇒ (x - 2)² = 0 ← is the required form

HIGH SCHOOL

Find the exact value of cos(135) and sin(135).

To find the exact value of cos(135), you need the following formula: cos(a+b) = cos a • cos b - sin a • sin b So in this case, it would be: cos (135) = cos ( 45 + 90) = cos 45 • cos 90 - sin 45 • sin 90 = √(2)/2 · 0 - √(2)/2 · 1 = 0 - (√2)/2 = - (√2)/2.

To find the exact value of sin(135), you need the following formula: sin (a+b) = sin a • cos b - cos a + sin b So in this case, it would be sin (135) = sin (90 + 45) = sin 90 • cos 45 + cos 90 • sin 45 = (1 ·(√2)/2) + (0 · (√2)/2) = (√2)/2).

cos (135)= - (√2)/2

sin (135) = (√2)/2

To find the exact value of sin(135), you need the following formula: sin (a+b) = sin a • cos b - cos a + sin b So in this case, it would be sin (135) = sin (90 + 45) = sin 90 • cos 45 + cos 90 • sin 45 = (1 ·(√2)/2) + (0 · (√2)/2) = (√2)/2).

cos (135)= - (√2)/2

sin (135) = (√2)/2

MIDDLE SCHOOL

If you know the rate of a water leak in gallons per hour, how can you find the number of hours it takes for 1 gallon to leak out?

You will need to take the rate it's leaking out at, and figure out how many times that unit goes into one full gallon. Then you will need to multiply your answer by the time given in the rate.

.5 gallon goes into 1 full gallon twice. And 2 x 2 = 4

So figure it out.

.5 gallon goes into 1 full gallon twice. And 2 x 2 = 4

So figure it out.

You will need to take the rate it's leaking out at, and figure out how many times that unit goes into one full gallon. Then you will need to multiply your answer by the time given in the rate.

Example: If the rate is .5 gallon per 1 hour, then we already know that it will take 2 hours...but to calculate it, we will take the .5 gallon and see how many times it goes into a full gallon, Its 2. Now multiply by 1 (since the rate was .5 gallon per 1 hour). So the answer is in fact 2.

Example 2: If the rate was .5 gallon every 2 hours, we will use the same method. If we think about it, we probably already know it will be 4 hours...but lets calculate!

.5 gallon goes into 1 full gallon twice. And 2 x 2 = 4

Example: If the rate is .5 gallon per 1 hour, then we already know that it will take 2 hours...but to calculate it, we will take the .5 gallon and see how many times it goes into a full gallon, Its 2. Now multiply by 1 (since the rate was .5 gallon per 1 hour). So the answer is in fact 2.

Example 2: If the rate was .5 gallon every 2 hours, we will use the same method. If we think about it, we probably already know it will be 4 hours...but lets calculate!

.5 gallon goes into 1 full gallon twice. And 2 x 2 = 4