The first step is to write this equation into general form. The
general form of an equation is:
ax^2 + bx + c = 0
To make this equation to general form, you have to simplify
the equation first.
2/3(x-4) (x+5) = 1
2/3 (x^2 + 5x – 4x – 20) = 1
2/3(x^2 + x -20) = 1
2/3x^2 + 2/3x – 40/3 = 1
2/3x^2 + 2/3x – 40/3 – 1 = 0
2/3x^2 +2/3x – 43/3 = 0
Therefore, a = 2/3 ; b = 2/3 ; c = -43/3
Answer: hope this helps
Step-by-step explanation:
Simplifying
1.17 + -0.07a + (-3.92a) = 0
Combine like terms: -0.07a + (-3.92a) = -3.99a
1.17 + -3.99a = 0
Solving
1.17 + -3.99a = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1.17' to each side of the equation.
1.17 + -1.17 + -3.99a = 0 + -1.17
Combine like terms: 1.17 + -1.17 = 0.00
0.00 + -3.99a = 0 + -1.17
-3.99a = 0 + -1.17
Combine like terms: 0 + -1.17 = -1.17
-3.99a = -1.17
Divide each side by '-3.99'.
a = 0.2932330827
Simplifying
a = 0.2932330827
Step-by-step explanation:
24÷(45÷25)= 21
x=21
Hope this helped!
Answer:
False
Step-by-step explanation:
The triangles are similar because the angles are the same
We know nothing about the side lengths, so we can say nothing about concurrency. They may or may not be congruent.
These are 6 questions and 6 answers.
To find each probability we will use the definition of probability:
Probability = number of positive outcomes / number of total possible outcomes
1) <span>P(Jack or ten)
</span>
<span>Answer: 2/13 ≈ 0.12
</span>
Justification:
i) Positive outcomes: A standard deck of cards has 4 jacks and 4 tens, then those are 4 + 4 = 8 different positive outcomes.
ii) Possible outcomes: a standard deck of cards has 52 different cards, so, that is a total of 52 different possible outcomes
iii) Probability, P
P = number of positive outcomes / number of total possible outcomes
P = 8 / 52 = 2/13 ≈ 0.15
<span>
2.P(red or black)
</span>
Answer: 1
Justification:
i) Positive outcomes
Half of the cards are red and half of the cards are black, so they both add for the total of the cards = 52
ii) Possible outcomes: 52 cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 52 / 52 = 1
<span>
3.P(queen or club)
</span>
Answer: 4/13 ≈ 0.31
Justification:
i) Positive outcomes
There are 4 Queens.
There are 1/4 of 52 clubs = 1/4 × 52 = 13 clubs.
But you cannot add all of them, because one club is the Quenn of Clubs.
Then, the total number of different Queens and clubs is 4 + 13 - 1 = 16
ii) Possible outcomes: 52 different cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 16 /52 = 4 / 13 ≈ 0.31
<span>
4.P(red or ace)
</span>
Answer: 7 / 13 ≈ 0.54
Justification:
i) Positive outcomes
Half of the cards are red: 26
There are 4 aces.
Since 2 aces are red, the number of different red and aces cards is: 26 + 4 - 2 = 28
ii) Possible outcomes: 52 different outcomes
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 28 / 52 = 7 / 13 ≈ 0.54
<span>
5.P(diamond or black)
</span><span>
</span>
Answer: 1/2 = 0.5
Justification:
i) Positive outcomes
There are 52 / 4 = 13 diamonds
There are 26 black cards.
All the diamonds are black cards.
Then, the number of different diamond or black cards is 13 + 26 - 13 = 26
ii) Possible outcomes: 52 different cards.
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 26 / 52 = 1/2 = 0.5
6.P(face card or spade)
Answer: 11/26 ≈ 0.42
Justification:
i) Positive outcomes
Face cards are jacks, queens and kings. That is 3 × 4 = 12 different cards.
The spades are 13 cards.
Since, 3 of the faces are spade cards, the number of different cards of those types are 12 + 13 - 3 = 22
ii) Possible outcomes: 52 different cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 22 / 52 = 11 / 26 ≈ 0.42
