Maria has 2 dogs. Her friend bought her h more dogs. Write an expression that show how many dogs Maria has now.

Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)

Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

Learn more about factorizing a quadratic expression at

brainly.com/question/52959

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5 0

8 months ago

At the start of the experiment substance is measured to be 70°C, and by the end of the experiment its temperature is measured as

11Alexandr11 [23.1K]

9514 1404 393

Answer:

-130 °C

Step-by-step explanation:

The change is found by subtracting the start temperature from the finish temperature. It is ....

-60 °C - 70 °C = -130 °C

3 0

2 years ago

When x=8 y=20. What is y when x=42?

Sergeu [11.5K]

If you would like to know what is y when x = 42, you can calculate this using the following steps:

x = 8 ... y = 20
x = 42 ... y = ?

8 * y = 20 * 42 /8
y = 20 * 42 / 8
y = 105

The correct result would be: y = 105 when x = 42.

3 0

2 years ago

Read 2 more answers

6463/4 show your work first to answer get brainlist

masya89 [10]

Answer:

1 6 1 3 r.11

Step-by-step explanation:

1 6 1 3 r.11

4 $\sqrt{6463\\}$

-4

$_________________\\$ ____________

2463

-24

____________

63

-4

____________

23

-12

____________

11

7 0

2 years ago

Social Sciences Alcohol Abstinence The Harvard School of Public Health completed a study on alcohol consumption on college campu

Scilla [17]

Answer:

a) There is a 6.69% probability that a randomly selected female student abstains from alcohol.

b) If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.

Step-by-step explanation:

This is a probability problem:

We have these following probabilities:

-20.7% of a woman attending an all-women college abstaining from alcohol.

-6% of a woman attending a coeducational college abstaining from alcohol.

-4.7% of a woman attending an all-women college

- 100%-4.7% = 95.3% of a woman attending a coeducational college.

(a) What is the probability that a randomly selected female student abstains from alcohol?

$P = P_{1} + P_{2}$

$P_{1}$ is the probability of a woman attending an all-women college being chosen and abstaining from alcohol. There is a 0.047 probability of a woman attending an all-women college being chosen and a 0.207 probability that she abstain from alcohol. So:

$P_{1} = 0.047*0.207 = 0.009729$

$P_{2}$ is the probability of a woman attending a coeducational college being chosen and abstaining from alcohol. There is a 0.953 probability of a woman attending a coeducational college being chosen and a 0.06 probability that she abstain from alcohol. So:

$P_{2} = 0.953*0.06 = 0.05718$

So, the probability of a randomly selected female student abstaining from alcohol is:

$P = P_{1} + P_{2} = 0.009729 + 0.05718 = 0.0669$

There is a 6.69% probability that a randomly selected female student abstains from alcohol.

(b) If a randomly selected female student abstains from alcohol, what is the probability she attends a coedücational colege?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

Here:

What is the probability of a woman attending a coeducational college, knowing that she abstains from alcohol.

It can be calculated by the following formula:

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

We have the following probabilities:

$P(B)$ is the probability of a woman from a coeducational college being chosen. So $P(B) = 0.953$

$P(A/B)$ is the probability of a woman abstaining from alcohol, given that she attends a coeducational college. So $P(A/B) = 0.06$

$P(A)$ is the probability of a woman abstaining from alcohol. From a), $P(A) = 0.0669$

So, the probability that a randomly selected female student attends a coeducational college, given that she abstains from alcohol is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{(0.953)*(0.06)}{(0.0669)} = 0.8287$

If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.

4 0

2 years ago