Solve for x in the equation x^2-12x+36 = 90

Which number line represents the solution set for the given inequality x + 1 < (or equal to) -3 OR -4x < -8

vampirchik [111]

we are given inequalities as

$x+1\leq -3$

Subtract both sides by 1

$x+1-1\leq -3-1$

$x\leq -4$

so, we get interval as

$(-\infty,-4]$

we have

$-4x$

we can divide both sides by -4

$\frac{-4x}{-4} >\frac{-8}{-4}$

$x >2$

so, we get interval as

$(2,\infty)$

now, we can combine them

$(-\infty,-4]$ ∪ $(2,\infty)$

now, we can draw number line and locate this interval

we get

8 0

3 years ago

Read 2 more answers

If there are 5 apples to every 3 oranges in a bin, which graph represents the proportional relationship of the fruit in the bin?

evablogger [386]

Answer:

The answer is D

Step-by-step explanation:

took the test<//3

7 0

3 years ago

Read 2 more answers

How do we do this problem

Zina [86]

What is your problem

4 0

3 years ago

Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an

ipn [44]

Answer:

The sample mean is $\bar{x}=1.24$ and the sample median is 0.56

Step-by-step explanation:

The sample mean $\bar{x}$ of observations $x_1,x_2,...,x_n$ is given by

$\bar{x}=\frac{\sum x_i}{n}$

Applying the above definition we get that

The sum of these 15 sample observations is

$\sum x_i = 0.21+\:0.22+\:0.26+\:0.30+\:0.34+\:0.42\:+0.55+\:0.56+\:1.43+\:1.70+\:1.84+\:2.20+\:2.25+\:3.06+\:3.26\\\\\sum x_i =18.6$

and the sample mean is

$\bar{x}=\frac{18.6}{15}=1.24$

The sample median is obtained by first ordering the <em>n</em> observations from smallest to largest (with any repeated values included so that every sample observation appears in the ordered list). Then,

Sample median = The single middle value if n is odd = $(\frac{n+1}{2} )^{th}$

Sample median = The average of the two middle values if n is even = average of $(\frac{n}{2} )^{th}$ and $(\frac{n}{2}+1 )^{th}$

Applying the above definition we get that

The data is already ordered and n = 15 so,

Sample median = $(\frac{15+1}{2} )^{th}=8^{th}$ = 0.56

8 0

3 years ago

before tomorrow can I have a quick answer and maybe an explanation on how to answer these kinds of questions overall? need some

MA_775_DIABLO [31]

Answer:

a) maximum; the parabola opens downward

b) positive; it must lie above the x-axis

c) x = 1.5

Step-by-step explanation:

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.

The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.

__

If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.

__

The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:

x = (-2 +5)/2 = 3/2

The x-coordinate of the vertex is x = 1.5.

______

<em>Additional comment</em>

The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.

3 0

3 years ago