These are 3 questions and 3 answers:
Question 1) p^2 - 2p - 15 = 0
Solution:
1) factoring:
a) write two parenthesis with p as the first term (common term) of each:
(p ) (p )
b) in the first parenthesis copy the sign of the second term (i.e. - ), and in the second parenthesis put the product of the signs of the second and third terms (i.e. - * - = +)
=> (p - )(p + )
c) search two numbers whose sum is - 2 and its product is - 15. Those numbers are -5 and +3, look:
- 5 + 3 = - 2
( - 5)( + 3) = - 15
=> (p - 5)(p + 3)
d) you can prove that (p - 5) (p + 3) = p^2 - 20 - 15
2) equal the expression to zero and solve:
(p - 5)(p + 3) = 0 => (p - 5) = 0 or (p + 3) = 0
p - 5 = 0 => p = 5
p + 3 = 0 => p = - 3
=> that means that both p = 5 and p = - 3 are solutions.
3) check the solutions:
p = 5 => (5)^2 - 2(5) - 15 = 25 - 10 - 15 = 0 => check
p = - 3 => (-3)^2 - 2(-3) - 15 = 9 + 6 - 15 = 0 => check
4) As a solution set: {5, - 3}
Question 2: (x - 1)(x + 2) = 18
Solution
0) expand, combine like terms and transpose 18:
x^2 + x - 2 - 18 = 0
x^2 + x - 20 = 0
1) factoring:
a) write two parenthesis with x as the first term (common term) of each:
(x ) (x )
b)
in the first parenthesis copy the sign of the second term (i.e. + ),
and in the second parenthesis put the product of the signs of the second
and third terms (i.e. + * - = -)
=> (x + )(x - )
c) search two numbers whose sum is + 1 and its product is - 20. Those numbers are + 5 and - 4, look:
5 - 4 = 1
(5)( - 4) = - 20
=> (x + 5)(x - 4)
d) you can prove that (x + 5) (x - 4)) = x^2 + x - 20
2) equal the expression to zero and solve:
(x + 5)(x - 4) = 0 => (x + 5) = 0 or (x - 4) = 0
x + 5 = 0 => x = - 5
x - 4 = 0 => x = 4
=> that means that both x = - 5 and x = 4 are the solutions.
3) check the solutions:
x = - 5 => (- 5 - 1)(- 5 + 2) = 18
=> (-6)(-3) = 18
=> 18 = 18 => check
x = 4 => (4 - 1)(4 + 2) = (3)(6) = 18 => check
4) As a solution set: {- 5, 4}
Question 3: (k - 6) (k - 1) = - k - 2
Solution:
0) (k - 6)(k - 1) = - k - 2 =>
k^2 -7k + 6 = - k - 2 =>
k^2 -7x + k + 6 + 2 = 0 =>
k^2 - 6k + 8 = 0
1) factor
(k - ) (k - ) = 0
(k - 4) (k - 2) = 0 <-------- - 4 - 2 = - 6 and (-4)(-2) = +8
2) Zero product property:
k - 4 = 0 , k - 2 = 0
=> k = 4, k = 2
3) Check:
a) (4 - 6) (4 - 1) = - 4 - 2
(-2)(3) = - 6
- 6 = - 6 => check
b) (2 - 6)(2 - 1) = - 2 - 2
(-4)(1) = -4
-4 = - 4 => check
4) Solution set: {2, 4}
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
You would subtract x from both sides . then divide the whole equation by 2. your new equation would be y=-1/2x+5 . the graph would going downwards, the line would intercept the y axis at 5, and you would go down one unit and over two units. [to graph it]
<span>An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Source: Google's definition
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1. Make sure you're using the correct formula for the dimensions given. The usual formula gives volume in terms of radius and height. If you are given the diameter, the formula will be different, or you need to compute the radius before you use the formula.
2. Make sure you're using the appropriate value for π. Many calculators have the value built-in. Many problems posted on Brainly require the use of 3.14, which will give different answers. (One recent problem required the use of 3.) If your calculator doesn't have π built in, a reasonable value is 355/113, which is good to 7 significant figures.
3. Make sure the units you are using are compatible (generally, all the same). If your height is in one unit (say inches) and your diameter is in another unit (say centimeters), you need to do units conversion before you put the numbers in the formula. The result of putting your units in the formula with your numbers should be that you end up with units cubed. For example, for a radius of 2 cm and a height of 3 cm, the volume will be
.. V = π(2cm)^2*(3 cm) = 12π cm^3.
4. Compare the dimensions and the volume to things you know. You know the approximate size of a gallon jug, a 2 liter pop bottle, a 5-gallon bucket. Check your answer for reasonableness.
5. Make an estimate based on the dimensions. Round to 1 or 2 significant figures and make a guess as to the approximate result you should get. For this, you can use 3 for π, as you just want to be "somewhere in the ballpark" as opposed to being off by a factor of 10 or more. This requires a certain amount of number sense and knowledge of multiplication tables.
6. Make certain your calculator is being used correctly. If parentheses are involved, make sure you enter the closing parentheses--as opposed to letting the calculator put them in according to its own rules. If division or fractions are involved, make sure you have parentheses around the denominator in every case. 1/2*3 ≠ 1/(2*3) It can be helpful to use a calculator that shows you what it did. (The Google calculator does that, for example.)
7. Sometimes, it helps just to do the calculation twice (possibly in a different order). Inadvertent error can creep in even when you think you're paying attention.
8. If you're doing the math by hand, make use of all available techniques for checking your arithmetic.
