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3 years ago

Transform x2 + 6x + 8 = 0 into the form (x − p)2 = q?

2 answers:

7 0

Step 1x2 + 6x + 8 + 1 = 0 + 1
Step 2x2 + 6x + 9 = 1
Step 3(x + 3)2 = 1
Your answer is (x +3)2 = 1
Hope I helped <3

liraira [26]3 years ago

5 0

So hmmm x²+6x+8=0

alrite.. let's do some grouping now
( x² + 6x + [?]²) + 8 = 0

notice above, we have a missing fellow in order to get a perfect square trinomial... hmm who would that be?

let's take a peek at the middle guy of the trinomial.. 6x.. hmmm let's factor it, 2*3*x, wait a minute! 2 * 3 * x... we already have x² on the left-side, since the middle term is just 2 * the square root of the other two terms, that means that the guy on the right, our missing guy must be "3"

alrite, let's add 3² then, however, bear in mind that, all we're doing is borrowing from our very good friend Mr Zero, 0

so if we add 3², we also have to subtract 3², let's do so

(x² + 6x +3² - 3²) + 8 = 0

(x² + 6x +3²) + 8 - 3² = 0

(x+3)²=3² - 8

(x+3)² = 1

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Point, line and plane

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3 years ago

John jogs 2 7/10 miles to the park. Marsha jogs 4/5 miles to the park. How much farther does John jog?

Elden [556K]

Answer:

1.9 miles.

Step-by-step explanation:

John jogs 2 7/10 miles to the park. Marsha jogs 4/5 miles to the park.

Convert the fractions into decimals:

2 7/10 = 2.7

4/5 = 0.8

Subtract '0.8' from '2.7':

$2.7-0.8=1.9$

John should jog 1.9 miles farther than Marsha.

Hope this helps.

7 0

3 years ago

Read 2 more answers

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti

melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

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:

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

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that $m = 100, \mu = \frac{1}{100} = 0.01$

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

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

This is P(X > 190). So

$P(X > 190) = e^{-0.01*190} = 0.1496$

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

$P(X > x) = 0.08$

$e^{-0.01x} = 0.08$

$\ln{e^{-0.01x}} = \ln{0.08}$

$-0.01x = \ln{0.08}$

$x = -\frac{\ln{0.08}}{0.01}$

$x = 252.6$

Capacity of 252.6 cubic feet per second

5 0

3 years ago

Mrs. McClure's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to m

bezimeni [28]

Answer:

Amount of butter need for 1 cup of oil = 2 cup of butter

Step-by-step explanation:

Given:

Amount of butter need for 1/2 cup of oil = 1 cup

Find:

Amount of butter need for 1 cup of oil

Computation:

Amount of butter need for 1/2 cup of oil = 1 cup

1 cup butter = 1/2 cup oil

So,

Amount of butter need for 1 cup of oil = 1 / [1/2]

Amount of butter need for 1 cup of oil = 1 / [0.5]

Amount of butter need for 1 cup of oil = 2 cup of butter

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3 years ago

Trejon rides his bike 2 1/4 miles each day. Which equation can be used to find r, the number of miles he will ride in 8 days?

LiRa [457]

Answer:

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3 years ago