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3 years ago

Find three rational numbers between 1 5 and 0.20.

1 answer:

4 0

2, 3 and 4 is the three rational numbers between

Step-by-step explanation:

True po talaga enanswer ko❤️

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What are the roots of the quadratic equation below?

suter [353]

Answer:

213

Step-by-step explanation:

3131321

4 0

3 years ago

Line v passes through point [6.6] and is perpendicular to the graph of y= 3/4x - 11 line w is parallel to line v and passes thro

lbvjy [14]

Given:

The equation of a line is

$y=\dfrac{3}{4}x-11$

Line v passes through point (6,6) and it is perpendicular to the given line.

Line w passes through point (-6,10) and it is parallel to the line v.

To find:

The equation in slope intercept form of line w.

Solution:

Slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

We have,

$y=\dfrac{3}{4}x-11$ ...(ii)

On comparing (i) and (ii), we get

$m=\dfrac{3}{4}$

So, slope of given line is $\dfrac{3}{4}$ .

Product of slopes of two perpendicular lines is -1.

$m_1\times m_2=-1$

$\dfrac{3}{4}\times m_2=-1$

$m_2=-\dfrac{4}{3}$

Line w is perpendicular to the given line. So, the slope of line w is $-\dfrac{4}{3}$ .

Slopes of parallel line are equal.

Line v is parallel to line w. So, slope of line v is also $-\dfrac{4}{3}$ .

Slope of line v is $-\dfrac{4}{3}$ and it passes thorugh (-6,10). So, the equation of line v is

$y-y_1=m(x-x_1)$

where, m is slope.

$y-10=-\dfrac{4}{3}(x-(-6))$

$y-10=-\dfrac{4}{3}(x+6)$

$y-10=-\dfrac{4}{3}x-\dfrac{4}{3}(6)$

$y-10=-\dfrac{4}{3}x-8$

Adding 10 on both sides, we get

$y=-\dfrac{4}{3}x-8+10$

$y=-\dfrac{4}{3}x+2$

Therefore the equation of line v is $y=-\dfrac{4}{3}x+2$ .

3 0

3 years ago

Please help!

BaLLatris [955]

a) The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) There is a discontinuity at $x = 2$ with a slant asymptote.

a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form $x-r_{i}$ , where $r_{i}$ is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial $f(x)$ has the following form:

$f(x) = (x-6)\cdot (x+1)\cdot (x+3)$

And the expanded form is obtained by some algebraic handling:

$f(x) = (x-6)\cdot (x^{2}+4\cdot x +3)$

$f(x) = x\cdot (x^{2}+4\cdot x + 3)-6\cdot (x^{2}+4\cdot x +3)$

$f(x) = x^{3}+4\cdot x^{2}+3\cdot x -6\cdot x^{2}-24\cdot x -18$

$f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ (1)

The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) In this question we divide the polynomial found in a) (in factor form) by the polynomial $x^{2}-x -2$ (also in factor form). That is:

$g(x) = \frac{(x-6)\cdot (x+1)\cdot (x+3)}{(x-2)\cdot (x+1)}$

$g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ (2)

The slant asymptote is defined by linear function, whose slope ( $m$ ) and intercept ( $b$ ) are determined by the following expressions:

$m = \lim_{x \to \pm \infty} \frac{g(x)}{x}$ (3)

$b = \lim_{x \to \pm \infty} [g(x)-x]$ (4)

If $g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ , then the equation of the slant asymptote is:

$m = \lim_{x \to 2} \frac{(x-6)\cdot (x+3)}{x\cdot (x-2)}$

$m = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x^{2}-2\cdot x} \right)$

$m = 1$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x-2}-x \right)$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x - 18-x^{2}+2\cdot x}{x-2}\right)$

$b = \lim_{n \to \infty} \left(\frac{-x-18}{x-2} \right)$

$b = -1$

The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at $x = 2$ with a slant asymptote.

We kindly invite to check this question on asymptotes: brainly.com/question/4084552

8 0

2 years ago

WHAT IS THE MEDIAN pls help

masya89 [10]

The median is 19.5 :))

7 0

3 years ago

Hey I need helping with solving thank you

Marrrta [24]

Answer:

the answer to this equation is c (10)

6 0

3 years ago