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2 years ago

What is the graph of the inequality in the coordinate plane?

Mathematics

1 answer:

miskamm [114]2 years ago

5 0

Answer:

See attached picture.

Step-by-step explanation:

y < -2 is similar to the line y= -2 which is a horizontal line. Since this is not an equal to expression, mark a dashed horizontal line through -2 on the y-axis. It also has a set of solutions which are shaded below or above the line. Since the expression is all y values less than -2, shade below the line for less than values.

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Is the function continuous at x = -17

Pavlova-9 [17]

For a function to be continuous at an x-value, say -17, you need to make sure two things line up:

The limit from the left equals the limit from the right.

$\lim_{x \to -17^{-}} f(x) = \lim_{x \to -17^{+}} f(x)$

This limit equals the functions value.

$\lim_{x \to -17} f(x) = f(-17)$

The left hand limit involves the first piece, f(x) = 20x + 1:

$\begin{aligned} \lim_{x \to -17^{-}} f(x) &= \lim_{x \to -17^{-}} (20x+1)\\[0.5em]&= 20(-17)+1\\[0.5em]&= -339\endaligned}$

The right hand limit invovles the second piece, f(x) = -10x^2:

$\begin{aligned} \lim_{x \to -17^{+}} f(x) &= \lim_{x \to -17^{+}} (-10x^2)\\[0.5em]&= -10\cdot (-17)^2\\[0.5em]&= -2890\endaligned}$

Since the two one-sided limits don't match, the function is not continuous at x=-17.

3 0

2 years ago

Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

Rina8888 [55]

9514 1404 393

Answer:

ΔABC ~ ΔPQR
PQ = 8
PR = 14

Step-by-step explanation:

Angles A and P are marked congruent; angles B and Q are marked congruent, so the triangles are similar by the AA similarity postulate. The similarity statement can be written ...

ΔABC ~ ΔPQR by AA similarity

The ratio of sides of PQR to ABC is the ratio QR/BC = 12/6 = 2. That is, each side in the larger triangle is 2 times the length of the corresponding smaller side.

PQ = 2·AB = 2·4 = 8

PR = 2·AC = 2·7 = 14

The side lengths of interest are ...

PQ = 8, PR = 14

5 0

2 years ago

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equati

amid [387]

In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
$f(x) = a(x - x_1)(x-x_2)(x-x_3)$

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form $(x_n , 0)$

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say $x_1 = 2 , x_2 = 3 , x_3 = 5$

So required equation is
$f(x) = a (x-2)(x-3)(x-5)$
              $= a[(x^2 - 2x - 3x + 6)(x-5)]$
              $= a[(x^2 - 5x+6)(x-5)]$
              $= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)$
              $= a(x^3 - 10x^2+31x-30)$
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
$-5= a (0-0+0 - 30)$
$-5 = -30a$
$a = \frac{-5}{-30} = \frac{1}{6}$
So required equation of cubic polynomial is
$f(x) = \frac{1}{6}(x^3 -10x^2+31x-30)$

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.

4 0

3 years ago

Read 2 more answers

Cual es la relacion entre <a y <b?

RideAnS [48]

Answer:

Angulos suplementarios

7 0

2 years ago

Annie has two equal sized amounts of wax in two different colors she used 5/8 of the green wax and 1/3 of the blue wax to make s

lana66690 [7]

Find a common denominator that 8 and 3 can go into.. which is 24
5/8 = 1/3
15/24 - 8/24
7/24

Hope this helped

6 0

2 years ago