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Inga [223]
3 years ago
14

Use factoring to solve the quadratic equation x2 − 2x − 3 = 12.

Mathematics
2 answers:
chubhunter [2.5K]3 years ago
8 0

Answer:

x = -3 and x = 5

Step-by-step explanation:

x² − 2x − 3 = 12

x² − 2x − 3  - 12 = 0

x² − 2x − 15 = 0

Product = -15

sum = -2

Factors  are: 3, -5

So the equation becomes;

x² − 2x − 15 = 0

x² + 3x - 5x − 15 = 0

(x² + 3x) - (5x + 15) = 0

x(x + 3) - 5(x + 3) = 0

(x + 3)(x - 5) = 0

∴ (x + 3) = 0

    x = -3  

          or

   (x - 5) = 0

    x = 5

melomori [17]3 years ago
7 0

Answer:

x_1=5\\x_2=-3

Step-by-step explanation:

You have the following quadratic equation given in the problem:

x^{2}-2x-3=12

You must make the equation equal to zero, as following:

x^{2}-2x-3-12=0

Add like terms:

 x^{2}-2x-15=0

Now, to factor the equation, you must find two numbers whose sum is -2 and whose product is -15. Therefore, you have:

(x-5)(x+3)=0\\x_1=5\\x_2=-3

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Fred bought a box of wooden popsicle sticks so that he could make a jewelry box for his mom. He used 58 popsicle sticks to make
aev [14]

Answer:

<h3>p - 34 = 58</h3>

Step-by-step explanation:

Given

Initial number of popsicle sticks in the box to start = p

Amount used = 58 popsicle sticks

Amount left = 34 popsicle sticks

The equation that models the problem is expressed as;

Initial popsicle sticks in the box = Amount used + amount left

Substitute the given values;

p = 58 + 34

p - 34 = 58

<em>hence the required model is p - 34 = 58 </em>

7 0
3 years ago
A ticket cost $4.80 the new ticket price will be 1.25 times the old price what will the new ticket be
PolarNik [594]
It's 6 because you times 4.80 times 1.25 and it's equivalent to 6
7 0
2 years ago
Bob has a standard deck of playing cards. If he randomly draws a J, K, 2, and 2, what is the probability that the next card he d
nlexa [21]

Answer:

The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.


One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):


P(X=k)=(Kk)(N−Kn−k)(Nn)


where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.


P(X=2)=(42)(480)(522)


P(X=2)=61326=1221


In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.


Another way is using simple probabilities and combinations:


P(X=2)=(4C1∗152)∗(3C1∗151)


P(X=2)=452∗351=1221


The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
The pastor divided the 3,000 circulars among 15 teenagers. How many circulars did each young person receive?
pav-90 [236]
Each young person received 200 circulars.

3,000/15= 200
7 0
3 years ago
Write a series of rigid motions that transform pentagon ABCDE to pentagon A′B′C′D′E′
worty [1.4K]

Answer:

We need the following three rigid motions:

i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.

Step-by-step explanation:

We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':

i) Reflection around y-axis:

(x',y') = (-x,y) (Eq. 1)

ii) Translation three units in the -y direction:

(x'',y'') = (x', y'-3) (Eq. 2)

iii) Translation four units in the -x direction:

(x''',y''') = (x''-4, y'') (Eq. 3)

We proceed to proof the effectiveness of operations defined above by testing point D:

1) D(x,y) = (-1, 4) Given.

2) (x',y') = (1,4) By (Eq. 1)

3) (x'',y'') = (1, 1) By (Eq. 2)

4) D'(x,y) = (-3,1) By (Eq. 3)/Result

7 0
2 years ago
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