Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14
Answer:
3x³ + 5x² + 4x + 4
Step-by-step explanation:
Given
(x + 2)(x² + x + 2) + 2(x³ + x²)
To expand the product, each term in the second factor is multiplied by each term in the first factor, that is
x(x² + x + 2) + 2(x² + x + 2) + 2(x³ + x²) ← distribute the parenthesis
= x³ + x² + 2x + 2x² + 2x + 4 + 2x³ + 2x² ← collect like terms
= 3x³ + 5x² + 4x + 4
First of all, a meter is equal to 100cm.
Seb made a jump of
two and a half meters. (
or
)
Multiply 100 by 2.
Now we need the half.
What is half of 100?
50 is half of 100.
So, add 50 to the 200.
Kirsty's jump was
10 centimeters longer.
Add 10 centimeters to the 250 centimeters.
Kirsty's jump was 260 centimeters high, or 2.55 meters.
The sentence sequence is "BDAC".
<u>Step-by-step explanation</u>:
- Derek is rolling a die many times and he is recording when he rolls a dice of three. So we have to identify from largest to smallest.
- The first largest is 30 times. Because of 3*10=30, so he rolls three ten times. So the first option is B.
- The second largest is 20 times. Derek rolled dice three-six times because of 3*6=18. So the second option is D.
- The third-largest is 10 times. In this, he rolls three times. Because of 3*3=9. So the option is A.
- The final option is C. Derek rolls five times. 3*1=3. In this, he rolled only one time. So the sequence is BDAC.
