What is the y intercept in the equation y=45x+65

Find the sum and product of the roots. 2x^2 + 6x - 8 = 0

netineya [11]

Suppose you can factorize:

$ax^2+bx+c=a(x-r_1)(x-r_2)$

Then by expanding the right side, you have

$ax^2+bx+c=a(x^2-(r_1+r_2)x+r_1r_2)=ax^2-a(r_1+r_2)x+ar_1r_2$

which means in this case, you have to have

$\begin{cases}6=-2(r_1+r_2)\\-8=2r_1r_2\end{cases}\implies\begin{cases}r_1+r_2=-3\\r_1r_2=-4\end{cases}$

3 0

3 years ago

What is an equation of a line,in point-slope from, that passes through (1, -7) and has a slope of -2/3

il63 [147K]

Answer:

y + 7 = - $\frac{2}{3}$ (x - 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

Where m is the slope and (a, b) a point on the line

Here m = - $\frac{2}{3}$ and (a, b) = (1, - 7), thus

y - (- 7) = - $\frac{2}{3}$ (x - 1), that is

y + 7 = - $\frac{2}{3}$ (x - 1) ← in point- slope form

3 0

3 years ago

Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches. What is

raketka [301]

Answer: 0.5

Step-by-step explanation:

Given : Adult male heights have a normal probability distribution .

Population mean : $\mu = 70 \text{ inches}$

Standard deviation: $\sigma= 4\text{ inches}$

Let x be the random variable that represent the heights of adult male.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x=70, we have

$z=\dfrac{70-70}{4}=0$

Now, by using the standard normal distribution table, we have

The probability that a randomly selected male is more than 70 inches tall :-

$P(x\geq70)=P(z\geq0)=1-P(z$

Hence, the probability that a randomly selected male is more than 70 inches tall = 0.5

4 0

3 years ago

Read 2 more answers

(secx)dy/dx=e^(y+sinx), please help me solve the differential equation. Thanks :)

nalin [4]

First, you must know these formula d(e^f(x) = f'(x)e^x dx, e^a+b=e^a.e^b, and d(sinx) = cosxdx, secx = 1/ cosx

(secx)dy/dx=e^(y+sinx), implies <span>dy/dx=cosx .e^(y+sinx), and then
</span>dy=cosx .e^(y+sinx).dx, integdy=integ(cosx .e^(y+sinx).dx, equivalent of
integdy=integ(cosx .e^y.e^sinx)dx, integdy=e^y.integ.(cosx e^sinx)dx, but we know that d(e^sinx) =cosx e^sinx dx,
so integ.d(e^sinx) =integ.cosx e^sinx dx,
and e^sinx + C=integ.cosx e^sinxdx
finally, integdy=e^y.integ.(cosx e^sinx)dx=e^2. (e^sinx) +C
the answer is
y = e^2. (e^sinx) +C, you can check this answer to calculate dy/dx

7 0

3 years ago

Read 2 more answers

An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline

Allushta [10]

Answer:

The mean is of -0.4 hours.

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Mean of the sample of 64 Duracell:

By the Central Limit Theorem, 4.1 hours.

Mean of the sample of 64 Eveready:

By the Central Limit Theorem, 4.5 hours.

Mean of the difference?

Subtraction of normal variables, so we subtract the means.

4.1 - 4.5 = -0.4

The mean is of -0.4 hours.

8 0

3 years ago