How do I factor x^2+7×+6

Mathematics

2 answers:

AlexFokin [52]4 years ago

8 0

$x^2+7x+6\\\\7x=6x+1x\\\\6=6\cdot1\\\\x^2+7x+6=(x+6)(x+1)$

RoseWind [281]4 years ago

3 0

To factor the equation, you need to convert it to the form (x+a)(x+b) and find out what a and b are.
When you multiply (x+a)(x+b), you get x² + (a+b)x + ab.
With the expression x² + 7x + 6, we know that a+b is equal to 7 and a times b is equal to 6.
The only two numbers that add to 7 and multiply to 6 are 1 and 6, leaving us with:
(x+6)(x+1)

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An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2 : S

ziro4ka [17]

Answer:

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

Sample of 421 new car buyers, 75 preferred foreign cars. So $n = 421, \pi = \frac{75}{421} = 0.178$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.151$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.205$

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

8 0

3 years ago

-4rover4+5rover3 please help me

Alchen [17]

$Solution, \frac{-4r}{4}+\frac{5r}{3}=\frac{2r}{3}$

$Steps:$

$\frac{-4r}{4}+\frac{5r}{3}$

$\frac{-4r}{4},\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b},\\-\frac{4r}{4},\\\mathrm{Divide\:the\:numbers:}\:\frac{4}{4}=1,\\-r,\\-r+\frac{5r}{3}$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:r=\frac{r3}{3},\\\frac{5r}{3}-\frac{r\cdot \:3}{3}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c},\\\frac{5r-r\cdot \:3}{3}$