Before we begin, remember the following:
-ve * -ve = +ve
-ve * +ve = -ve
+ve * -ve = -ve
+ve * +ve = +ve
Now, for each of the given expression, we will expand the brackets, combine like terms and then compare the final output with the given expressions.
First expression:
(x² + 15x + 65) + (2x - 5)(3x + 8)
x² + 15x + 65 + (2x*3x + 2x*8 - 5*3x - 5*8)
x² + 15x + 65 + (6x² + 16x - 15x - 40)
x² + 15x + 65 + 6x² + 16x - 15x - 40
x²(1+6) + x(15+16-15) + 65-40
7x² + 16x + 25
This expression corresponds to letter B
Second expression:
(4x + 1)(3x - 4) - (5x² - 10x - 12)
4x(3x) + 4x(-4) + 1(3x) + 1(-4) - (5x² - 10x - 12)
12x² - 16x + 3x - 4 - 5x² + 10x + 12
x²(12-5) + x(-16+3+10) - 4+12
7x² - 3x + 8
This expression corresponds to letter D
Third expression:
(8x² + 19x + 4) + (3x + 2)(x - 5)
8x² + 19x + 4 + (3x*x + 3x*(-5) + 2*x + 2*(-5))
8x² + 19x + 4 + (3x² - 15x + 2x - 10)
8x² + 19x + 4 + 3x² - 15x + 2x - 10
x²(8+3) + x(19-15+2) + 4-10
11x² + 6x - 6
This is equivalent to letter A
Fourth expression:
(6x + 1)(3x - 7) - (7x² - 34x - 20)
6x(3x) + 6x(-7) + 1(3x) + 1(-7) - (7x² - 34x - 20)
18x² - 42x + 3x - 7 - 7x² + 34x + 20
x²(18-7) + x(-42+3+34) - 7+20
11x² - 5x + 13
This is equivalent to letter C
Hope this helps :)
Answer:
a right triangle
Step-by-step explanation:
because if you rotate your head, then you can see that the top is at a 90 degree angle
I assume you mean the product of mixed numbers,
3 1/2 × 3 1/2
If we write this as
(3 + 1/2) × (3 + 1/2) = (3 + 1/2)²
we can use the identity
(a + b)² = a² + 2ab + b²
so that
3 1/2 × 3 1/2 = 3² + (2 × 3 × 1/2) + (1/2)²
3 1/2 × 3 1/2 = 9 + 3 + 1/4
3 1/2 × 3 1/2 = 12 1/4
Alternatively, we can first write 3 1/2 as a mixed number:
3 + 1/2 = 6/2 + 1/2 = (6 + 1)/2 = 7/2
Then
3 1/2 × 3 1/2 = 7/2 × 7/2 = (7 × 7) / (2 × 2) = 49/4
and
49/4 = (48 + 1)/4 = ((4 × 12) + 1)/4 = 12 + 1/4
Answer:
79.25
Step-by-step explanation:
Answer:
15,435
Step-by-step explanation: thts the anwser
