Consider the following expanded powers of (a + b)n, where a + b is any binomial and n is a whole number. Look for patterns.
Each expansion is a polynomial. There are some patterns to be noted.
1. There is one more term than the power of the exponent, n. That is, there are terms in the expansion of (a + b)n.
2. In each term, the sum of the exponents is n, the power to which the binomial is raised.
3. The exponents of a start with n, the power of the binomial, and decrease to 0. The last term has no factor of a. The first term has no factor of b, so powers of b start with 0 and increase to n.
4. The coefficients start at 1 and increase through certain values about "half"-way and then decrease through these same values back to 1.
Let's x represents the first odd integer
The next consecutive integer would be represented as x+2.
So x and x+2 being multiplied together will give us 1443:
(x)(x+2)=1443
x^2+2x=1443
x^2+2x-1443=0
By solving the quadratic equation using the quadratic formula, x will equal to 37 and -39.
Since the problem says "integers", so I'm assuming two pairs of consecutive integers would be ok.
With that said you 1st pair will be: 37,39
Your second pair will be: -37,-39.
(-4, 1)
the solution is always where the two points meet!! :)
Answer:
a) Kylie has 8 marbles
b) 7 Cylinders
c) 17 carrots
d) 8 marbles belong to Shauntay
Step-by-step explanation:
5. Identify the type and subtype of each of the fol-
lowing problems.
a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?
Shawn = 15 marbles
S = K + 7
15 = K + 7
K = 15 - 7
K = 8 marbles
Kylie has 8 marbles
b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?
T = 12 blocks
Cubes = 5
Cylinders = the rest
12 blocks = Cubes + Cylinders
Cylinders = 12 - Cubes
Cylinders = 12 - 5
Cylinder = 7
c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?
Number of carrots Peter has before
= Number of carrots he ate + Number of carrots he has now
= 14 + 3
= 17 carrots
d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?
Total number of Marbles = 17
Kelly = 9 marbles
Shauntay = ?
Total = Kelly + Shauntay
Shauntay = Total - Kelly's marbles
= ( 17 - 9) marbles
= 8 marbles
8 marbles belong to Shauntay
