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3 years ago

Complete the square for 5x^2-30x=5

Mathematics

2 answers:

xxMikexx [17]3 years ago

8 0

Answer: (x-3)^2=10

Step-by-step explanation:

Nikitich [7]3 years ago

3 0

Solve for x over the real numbers: by completing the square:

5 x^2 - 30 x = 5

Divide both sides by 5:

x^2 - 6 x = 1

Add 9 to both sides:

x^2 - 6 x + 9 = 10

Write the left hand side as a square:

(x - 3)^2 = 10

Take the square root of both sides:

x - 3 = sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

x = 3 + sqrt(10) or x - 3 = -sqrt(10)

Add 3 to both sides:

Answer: | x = 3 + sqrt(10) or x = 3 - sqrt(10)

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A single chocolate muffin has 260 calories, and a blueberry muffin has 240 calories. Both muffins can be bought at the local caf

Stella [2.4K]

Answer:

364 calories

Step-by-step explanation:

1/2 of 240=120 calories

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1/3 of 102=34

120+210+34=364 calories

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3 years ago

Upper bound and lower bound of 17

Licemer1 [7]

Answer:

Step-by-step explanation:

Hey there this si the upper and lower bound for 17

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8 0

3 years ago

SOMEBODY BRO PLEASE HELP ME OUT. Find the measures of the numbered angles in each kite. DUED BY 11:59pmmmmm

amm1812

Answer:

2=90°

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6 0

3 years ago

A small regional carrier accepted 19 reservations for a particular flight with 17 seats. 14 reservations went to regular custome

Ludmilka [50]

Answer:

(a) The probability of overbooking is 0.2135.

(b) The probability that the flight has empty seats is 0.4625.

Step-by-step explanation:

Let the random variable X represent the number of passengers showing up for the flight.

It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.

Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.

Number of reservations = 19

Regular customers = 14

Seats available = 17 - 14 = 3

Remaining reservations, n = 19 - 14 = 5

P (A remaining passenger will arrive), p = 0.52

The random variable X thus follows a Binomial distribution with parameters n = 5 and p = 0.52.

(1)

Compute the probability of overbooking as follows:

P (Overbooking occurs) = P(More than 3 shows up for the flight)

$=P(X>3)\\\\={5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}\\\\=0.175478784+0.0380204032\\\\=0.2134991872\\\\\approx 0.2135$

Thus, the probability of overbooking is 0.2135.

(2)

Compute the probability that the flight has empty seats as follows:

P (The flight has empty seats) = P (Less than 3 shows up for the flight)

$=P(X$

Thus, the probability that the flight has empty seats is 0.4625.

4 0

3 years ago

Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ;
$\sin{\theta} > \cos{\theta}$ if $45^{\circ} < \theta$ ;
$\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

4 0

3 years ago

Read 2 more answers