All categories

2 years ago

What equation results from completing the squre and then factoring x^2+10=15

Mathematics

1 answer:

nlexa [21]2 years ago

6 0

For this case we must complete squares:

$x ^ 2 + 10x = 15$

We add the square of half the coefficient of the term "x",

$(\frac {b} {2a}) ^ 2$ on both sides of the equation:

$x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15$

According to the perfect square trinomial we have:

$(a + b) ^ 2 = a ^2 + 2ab + b ^ 2$

Rewriting the expression we have:

$a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40$

ANswer:

$(x + 5) ^ 2 = 40$

You might be interested in

The price of an item is $45.00. After a discount, the price is $38.25. What is the percent of the discount?

Nataly_w [17]

Answer:

92.5% before discount 100% after discount is 92.5%

7 0

2 years ago

Maylin and Nina are making fruit baskets. They have 36 apples, 27 bananas, and 18 oranges. They want each basket to contain the

allochka39001 [22]

Nina is correct,

Hope this helped

XD XD XD XD XD

4 0

2 years ago

What is 44/12 as a simplified mixed fraction

Marat540 [252]

3 67/100

3 will stay a whole number so you put that as the whole number. 67 is 67 percent of a whole. so you put it over 100.

7 0

3 years ago

Read 2 more answers

Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. Wha

Art [367]

Answer:

0.4204 probability, option b.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour

13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of $\mu = \frac{13}{60} = 0.2167$

What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?

This is P(X > 4). So

$P(X > 4) = e^{-0.2167*4} = 0.4204$

So the correct answer is given by option b.

3 0

2 years ago

A shipping container shaped like a rectangular prism must have a maximum volume of 10 cubic yards. If the container is 2 1/2 yar

denpristay [2]

Answer:

$1\frac{1}{7} yards$

Step-by-step explanation:

The maximum volume the shipping container can have is 10 cubic yards.

The volume of a rectangular prism is given as:

V = L * W * H

where L is length, W is width and H is height.

To find the maximum height of the container, make H the subject of formula:

$H = \frac{V}{L * W}$

We have been given the length and width of the container as 2 1/2 yards and 3 1/2 yards respectively.

Hence, the maximum height is:

$H = \frac{10}{2\frac{1}{2} * 3\frac{1}{2} } \\\\H = \frac{10}{\frac{5}{2} * \frac{7}{2} }$

$H = \frac{10}{\frac{35}{4} } \\\\H = \frac{10 * 4}{35} \\\\H = \frac{40}{35} = \frac{8}{7} = 1\frac{1}{7}$

The maximum height of the container is $1\frac{1}{7} yards$ .

7 0

2 years ago