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3 years ago

Which of the following is equivalent to the quadratic equation below after

Mathematics

1 answer:

Temka [501]3 years ago

3 0

Answer:

Step-by-step explanation:

x^2 + 10x + 5 - 30 = 0

x^2 + 10x - 25 = 0

x^2 + 10x = 25

x^2 + 10x + 25 = 25 + 25

(x + 5)^2 = 50 <====

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The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacemen

mamaluj [8]

<h2>Answer:</h2>

(a)

The probability is : 1/2

(b)

The probability is : 1/2

<h2>Step-by-step explanation:</h2>

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2) (1,3) (1,4) (1,5)

(2,1) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,5)

(5,1) (5,2) (5,3) (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

We know that it could be calculated by using the formula:

$P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( since, the only outcome out of 20 outcomes is: (3,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

7 0

3 years ago

A kite is inscribed in a square with a side length of 9 units. What is the area of the kite? 27. 5 square units 36. 0 square uni

Rudiy27

45. 0 square units.

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2 years ago

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Alysha’s average speed when walking home from the market was 5 mph, and it takes her 21 minutes longer than when she drives to t

Delicious77 [7]

9514 1404 393

Answer:

3 minutes

Step-by-step explanation:

Let x represent Alysha's time to drive home from the market.

Speed and time are inversely proportional to each other (for the same distance), so we have ...

(walking speed)(walking time) = (driving speed)(driving time)

5(x +21) = (8·5)(x)

x +21 = 8x . . . . . . . . . divide by 5

21 = 7x . . . . . . . . subtract x

3 = x . . . . . . .divide by 7

It takes Alysha 3 minutes to drive home from the market.

3 0

3 years ago

The point C(2,3) is translated along a vector that is parallel to the line y=3x-2. The translation vector has magnitude square r

qaws [65]

Step-by-step explanation:

The translation vector v can be resolved into its x and y components, where x² + y² = 10 (Pythagoras' Theorem) and y = 3x

(parallel to y = 3x - 2, slope = 3).

We have x² + (3x)² = 10,

=> x² + 9x² = 10, 10x² = 10, x = 1 or x = -1.

When x = 1, y = 3. When x = -1, y = -3.

Therefore 2 possible translation vectors

are (1, 3) or (-1, -3).

First new C' = (2 + (1), 3 + (3)) = (3, 6).

Second new C'= (2 + (-1), 3 + (-3)) = (1, 0).

The possible images are (3, 6) and (1, 0).

4 0

3 years ago

(36÷6)÷3=36÷(6÷3) true or false

Jlenok [28]

Answer:

False

Step-by-step explanation:

The left side 2 does not equal to the right side 18 , which means that the given statement is false.

4 0

3 years ago

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