Answer:
Step-by-step explanation:
12a)To rationalize the denominator, multiply the denominator and numerator by √5.
b) (a+b)² = a² + 2ab + b²
(1 +√3)² = 1² + 2*1*√3 + (√3)²
= 1 + 2√3 + 3
= 4 + 2√3
a = 4 ; b =2
13) (a + b)(a - b) = a² - b²
So
lets say we have
a/b=2a/2b
we know that if we invert one and multiply it by the other (divide them), we get 1 because a/a=1 where a=a
so
2/3 and 4/6 are equivelent because if you divide them we get 12/12=1
2/3 and 8/12 are equivilent because if you divide them we get 24/24=1
and sinde 2/3=4/6 and 2/3=8/12, 2/3=4/6=8/12
they are equivlent
Plug in (7, 12) for x and y in the equation.
12 = 2(7) + 1
12 = 14 + 1
12 ≠ 15
Therefore, (7, 12) is not on the straight line equation.
The volume of the rectangular prism can be express in standard polynomial as follows:
x³ + 12x² + 35x
<h3>How to find the volume of a rectangular prism?</h3>
volume of a rectangular prism = lwh
where
- l = length
- w = width
- h = height
Therefore,
let
height = x
width = x + 5
length = x + 5 + 2 = x + 7
Therefore,
volume = x(x + 5)(x + 7)
volume = x(x² + 7x + 5x + 35)
volume = x(x² + 12x + 35)
volume = x³ + 12x² + 35x
learn more on volume here: brainly.com/question/2005063
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Answer:
37 polio vaccinations and 23 measles vaccination.
Step-by-step explanation:
Let the number of polio vaccination given=x
Let the number of measles vaccination given=y
Dr. Potter gave a total of 60 vaccinations
x+y=60
Since each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. A total of 184 doses was given out.
4x+2y=184
To find the values of x and y, we solve the two equations simultaneously.
x+y=60 (1)
4x+2y=184 (2)
From (1), x=60-y
Substitute x=60-y into equation 2.
4x+2y=184
4(60-y)+2y=184
240-4y+2y=184
240-184=4y-2y
56=2y
Divode both sides by 2
y=23
Recall earlier that x=60-y
x=60-23=37
Dr Potter gave 37 polio vaccinations and 23 measles vaccination.