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4 years ago

Find the solutions to 6x^2- 54x = 0

Mathematics

1 answer:

Nina [5.8K]4 years ago

4 0

Answer:

A. x = 9

D. x = 0

Step-by-step explanation:

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$6x^{2} -54x=0$

$a=6\\b=-54\\c=0$

substitute in the formula

$x=\frac{-(-54)(+/-)\sqrt{-54^{2}-4(6)(0)}} {2(6)}$

$x=\frac{54(+/-)54} {12}$

$x=\frac{54(+)54} {12}=9$

$x=\frac{54(-)54} {12}=0$

therefore

The solutions are x=0 and x=9

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What is the length of in the right triangle below? A. B. 24 C. 576 D. 36 E. 16 F. 260

harina [27]

Answer:

B. 24

Step-by-step explanation:

To find this, use Pythagorean Theorem

a^2+b^2=c^2

a is 10, and c is 26. We know 26 is the hypotenuse because it is opposite the right angle

10^2=b^2=26^2

100+b^2=676

Subtract 100 on both sides

b^2=576

Take the square root of both sides

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Hope this helps! :)

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3 years ago

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3 years ago

Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs.

Evgen [1.6K]

To solve this problem, let us first assign variables. Let us say that:

x = volume of 67% herbicide solution

y = volume of 46% herbicide solution

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x + y = 42

x = 42 – y --> 1

The component mass balance on the pure herbicide would be:

0.67 x + 0.46 y = 0.55 (42) --> 2

Substituting equation 1 to 2:

0.67 (42 – y) + 0.46 y = 23.1

28.14 – 0.67 y + 0.46 y = 23.1

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4 years ago

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A survey of magazine subscribers showed that 45.2% rented a car during the past 12 months for business reasons, 56% rented a car

IgorLugansk [536]

Answer:

a. 0.692 or 69.2%; b. 0.308 or 30.8%.

Step-by-step explanation:

This is the case of the probability of the sum of two events, which is defined by the formula:

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$ (1)

Where $\\ P(A \cup B)$ represents the probability of the union of both events, that is, the probability of event A plus the probability of event B.

On the other hand, $\\ P(A \cap B)$ represents the probability that both events happen at once or the probability of event A times the probability of event B (if both events are independent).

Notice the negative symbol for the last probability. The reason behind it is that we have to subtract those common results from event A and event B to avoid count them twice when calculating $\\ P(A \cup B)$ .

We have to remember that a sample space (sometimes denoted as S) is the set of the all possible results for a random experiment.

<h3>Calculation of the probabilities</h3>

From the question, we have two events:

Event A: event subscribers rented a car during the past 12 months for business reasons.

Event B: event subscribers rented a car during the past 12 months for personal reasons.

$\\ P(A) = 45.2\%\;or\;0.452$

$\\ P(B) = 56\%\;or\;0.56$

$\\ P(A \cap B) = 32\%\;or\;0.32$

With all this information, we can proceed as follows in the next lines.

The probability that a subscriber rented a car during the past 12 months for business or personal reasons.

We have to use here the formula (1) because of the sum of two probabilities, one for event A and the other for event B.

Then

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$\\ P(A \cup B) = 0.452 + 0.56 - 0.32$

$\\ P(A \cup B) = 0.692\;or\;69.2\%$

Thus, the probability that a subscriber rented a car during the past 12 months for business or personal reasons is 0.692 or 69.2%.

The probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.

As we can notice, this is the probability for the complement event that a subscriber did not rent a car during the past 12 months, that is, the probability of the events that remain in the sample space. In this way, the sum of the probability for the event that a subscriber rented a car plus the event that a subscriber did not rent a car equals 1, or mathematically:

$\\ P(\overline{A \cup B}) + P(A \cup B)= 1$

$\\ P(\overline{A \cup B}) = 1 - P(A \cup B)$

$\\ P(\overline{A \cup B}) = 1 - 0.692$

$\\ P(\overline{A \cup B}) = 0.308\;or\;30.8\%$

As a result, the requested probability for a subscriber that did not rent a car during the past 12 months for either business or personal reasons is 0.308 or 30.8%.

We can also find the same result if we determine the complement for each probability in formula (1), or:

$\\ P(\overline{A}) = 1 - P(A) = 1 - 0.452 = 0.548$

$\\ P(\overline{B}) = 1 - P(B) = 1 - 0.56 = 0.44$

$\\ P(\overline{A \cup B}) = 1 - P(A \cup B) = 1 - 0.32 = 0.68$

Then

$\\ P(\overline{A \cup B}) = P(\overline{A}) + P(\overline{B}) - P(\overline{A\cap B})$

$\\ P(\overline{A \cup B}) = 0.548 + 0.44 - 0.68$

$\\ P(\overline{A \cup B}) = 0.308$

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3 years ago

On January 1, 2006, you have $100 in a savings account that earns interest at a rate of 1% per month. On the last day of every m

WINSTONCH [101]

Answer:

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Step-by-step explanation:

On January 1, 2006, I have $100 in a savings account that earns interest at a rate of 1% per month. On the last day of every month, I deposit $75 in the account, beginning in January.

So, at the end of the month of January, the added amount to the account is $75 and 1% of $100 i.e. 1$.

Then, total $(75 + 1) = $76 is being added at the end of each month.

So, the recursive rule for account balance at the beginning of the nth month will be given by $b_{1} = 100$ and $b_{n + 1} = b_{n} + 76$ where, n = 1, 2, 3, ..... (Answer)

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3 years ago