These are two questions and two answers:
Question 1:
<span>A
quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe
the solution(s) to the equation by just determining the radicand. Show
your work.
Answer: </span><span>The negative value of the radicand means that the equation does not have real solutions.
Explanation:
1) With radicand the statement means the disciminant of the quadratic function.
2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c
3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20
and the discriminant (radicand) is: (-15)² - 4(3)(20) = 225 - 240 = - 15.
4) The negative value of the radicand means that the equation does not have real solutions.
Question 2:
Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate
method. Show the steps of your work, and explain why you chose the
method used.
Answer: </span> two solutions x = 1 and x = - 8/3x
Explanation:
1) I choose factoring (you may use the quadratic formula if you prefer)
2) Factoring
Given: 3x² + 5x − 8 = 0
Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0
Group: (3x² - 3x) + (8x - 8) = 0
Common factors for each group: 3x(x -1) + 8(x - 1) = 0
Coomon factor x - 1: (x - 1) (3x + 8) = 0
The two solutions are for each factor equal to zero:
x - 1 = 0 ⇒ x = 1
3x + 8 = 0 ⇒ x = -8/3
Those are the two solutions. x = 1 and x = - 8/3
Answer:
Step-by-step explanation:
If you look at the numbers you are given, you see that the first purchase has 3 more adult tickets than the second purchase, and its cost is £24 more. This means an adult ticket costs £24/3 = £8.
Two adult tickets will cost 2×£8 = £16, so three child tickets cost ...
£31 -16 = £15
Each child ticket is then £15/3 = £5.
An adult ticket costs £8; a child ticket costs £5.
The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
Given that the length of the previous deck = 15 feet
The width of the previous deck = 12 feet
Since the new deck will add 5 feet to the length and 4 feet to the width,
The length of the new deck = 15 + 5 = 20 feet
The width of the new deck = 12 + 4 = 16 feet
Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.
So, The length of the deck in the drawing = 20/2.5 inches = 8 inches
The width of the deck in the drawing = 16/2.5 inches = 6.4 inches
Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.
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