1. In the formula V = lwh, the variable h needs
1 answer:
Answer:
see the explanation
Step-by-step explanation:
we know that
Using inverse operations, the formula can be rearranged to solve for any one of the variables that might be unknown.
we have
The operation of multiplication is used in the formula
so
The inverse operation of division should be used to isolate the variable H
so
Divide both sides by LW
simplify
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Answer:
1. (4a+3)(4a-3)
2. (2m + 5)(2m-5)
3. (4b-5)²
4. (2x-1)²
5. (3x+1)(3x-1)
6. (n+5)(n-5)
7. (n²-10)²
8. (a²+3)(a²-3)
9. (k²+6)(k²-6)
10. (n²+7)(n²-7)
Step-by-step explanation:
For special products like these, just remember the
Difference of Squares formula:
and
Square of difference formula:
1. 16a²-9 follows the difference of squares form:
a² - b² = (a+b)(a-b)
So all we need to do is get the square root of a and b and follow the form:
(√16a²) - (√9) = (4a +3) (4a - 3)
Let's check through FOIL:
(4a +3) (4a - 3)
16a² - 12a + 12a - 9
16a² - 9
2. 4m² - 25 also follows the same form of difference of squares:
(√4m²) - (√25) = (2m +5) (2m - 5)
Let's check!
(2m +5) (2m - 5)
4m² + 10m - 10m -25
4m² - 25
3. 16b² - 40b + 25 follows the form of square of difference:
a² - 2ab + b² = (a - b)²
√16b² = 4b
√25 = 5
(4b - 5)²
Let's check!
(4b-5)(4b - 5)
16b² - 20b - 20b + 25
16b² - 40b + 25
HEre's another way to look at it:
First multiply the coefficients of the first and last term:
16 x 25 = 400
Next think of two numbers that when you multiply them, you will come up with 400 and sum up to -40. The two numbers would be -20 and -20 which will be the middle term
So it would fill in this way:
16b² - 20b - 20b + 25
Factor the equation:
(16b² - 20b) (-20b + 25)
4b(4b-5) - 5(4b-5)
(4b-5)(4b-5) = (4b-5)²
4. 4x² - 4x + 1 follows that same form:
√4x² = 2x
√1 = 1
(2x - 1)²
Let's check!
(2x - 1)(2x - 1)
4x² - 2x - 2x + 1
4x²- 4x + 1
5. 9x² - 1 follows the form of difference of squares:
√9x² - √1 = (3x + 1)(3x - 1)
Let's check!
(3x + 1)(3x - 1)
9x² + 3x - 3x - 1
9x² - 1
6. n² - 25 follows the form of difference of squares:
√n² - √25 = (n + 5)(n - 5)
Let's check!
(n + 5)(n - 5)
n² + 5n - 5n - 25
n² - 25
7. n⁴ - 100
√n⁴ - √100 = (n² + 10)(n² - 100)
Let's check!
(n² + 10)(n² - 100)
n⁴ + 10n² - 10n² -100
n⁴ - 100
8. a⁴ - 9
√a⁴ - √9 = (a² + 3)(a² - 3)
Let's check!
(a² + 3)(a² - 3)
a⁴ + 3a² - 3a² - 9
a⁴ - 9
9. k⁴ - 36
√k⁴ - √36 = (k² + 6) (k² - 6)
Let's check!
(k² + 6) (k² - 6)
k⁴ + 6k² - 6k² - 36
k⁴ - 36
10. n⁴ - 49
√n⁴ - √49 = (n² + 7) (n² - 7)
Let's check!
(n² + 7) (n² - 7)
n⁴ +7n² - 7n²- 49
n⁴ - 49