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Sav [38]
4 years ago
6

How do you graph y < -x

Mathematics
1 answer:
OlgaM077 [116]4 years ago
4 0
First graph the normal graph y = -x
Then since y is less than -x, shade the whole graph below the line.
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A crane is being used to remove a piano from an apartment building. The apartment window is 56 feet directly above the bed of th
gregori [183]
a^2+b^2=c^2\\(42)^2+(56)^2=c^2\\1764+3136=c^2\\4900=c^2\\70=c

70 feet.
7 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 surface area of a cube that measures 3 cm​
kifflom [539]

Answer: Surface area= 54

Step-by-step explanation:

To find the surface area of a cube you do 6 times s^2

S is the side length. In this case that is 3 cm. S^2 is 9

So now you do 6 times 9, and that is 54.

So, the surface area is 54.

8 0
3 years ago
A sporting goods store sells triangular team pennants in two sizes. The base of one pennant is 18 in. and the length of the side
juin [17]
This is a proportion problem because the problem stated that the two team pennants are similar.

Pennant 1 = base = 18 in ; length = 9 inches
Pennant 2 = base =   6 in ; length = x ?

9/18 = x/6
9*6 = 18x
54 = 18x
54/18 = x
3 = x

The length of the  side of the smaller pennant is 3 inches.
6 0
4 years ago
Read 2 more answers
Find the value of k if it is known that the line y=kx+2 goes through point:
MrRissso [65]

Answer:

k = -10/7 and k = -3

Step-by-step explanation:

Given: <em>y</em> = <em>kx</em> + 2

where k is the slope of line and 2 is y-intercept.

∵ line <em>y</em> = <em>kx </em>+ 2 is passing through point <em>P</em> (-7, 12), ∴ <em>x</em> = -7 and <em>y </em>= 12

Now substituting the value of x and y in above equation,

<em>y </em>= <em>kx</em> + 2

12 =<em> k</em>(-7) + 2

-7<em>k</em> = 12 - 2

- 7<em>k</em> = 10

k = \frac{-10}{7}

In the same way, ∵ line <em>y</em> = <em>kx </em>+ 2 is passing through point <em>P</em> (3, -7), ∴ <em>x</em> = 3 and <em>y </em>= -7

<em>y </em>= <em>kx</em> + 2

Now substituting the value of x and y in above equation,

-7 =<em> k</em>(3) + 2

<em>3k</em> = -7 - 2

<em>3k</em> = - 9

<em>k</em> = -3

3 0
4 years ago
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