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2 years ago

What are the solutions of the quadratic equation?

2 answers:

8 0

We have x^2 + 2 · x · (11/2) + (11/2)^2 = - 24 + (11/2)^2;
Then, ( x + 11/2 )^2 = -24 + 121/4;
( x + 11/2 )^2 + 96/4 - 121/4 = 0;
( x + 11/2 )^2 - 25 / 4 = 0;
( x + 11/2 )^2 - (5/2)^2 = 0;
( x + 11/2 - 5/2)·( x + 11/2 + 5/2 ) = 0;
( x + 6/2 )·( x + 16/2 ) = 0;
( x + 3 )· ( x + 8 ) = 0;
x = - 3 or x = -8;
The first choice is the correct answer.

sineoko [7]2 years ago

3 0

Original equation:
x^2 + 11x = -24
Move everything to the left hand side of the equation. To do this, add 24 to each side.
x^2 + 11x + 24 = 0
Now figure out a combination of two numbers that when added equals 11 but when multiplied equals 24. The answer is 8 and 3.
(x + 8)(x + 3) = 0
You can check the result by doing FOIL.
There are two values for which the equation works: x = -8 and x = -3.

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Answer:

We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 31.7 milligrams

Sample mean, $\bar{x}$ = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s = 2.8 milligrams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}$

We use One-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429$

Now, $t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

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2 years ago

Draw a picture to show the product of 4:7 x 3. Then write the product

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Answer:

¹²/₇

Step-by-step explanation:

Model ⁴/₇ × 3

Assume that you have three pies, each dived into seven slices.

There are only four slices remaining in each pie, that is, there is ⁴/₇ pie in each pie plate

The picture represents ⁴/₇ × 3.

Model the product

Now, transfer slices to get as many filled pie plates as possible.

Count the total slices.

You have 12 slices, and each slice represents ⅐ of a pie.

You have ¹²/₇ pie.

∴ ⁴/₇ × 3 = ¹²/₇

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