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3 years ago

Which is a valid prediction about the continuous function f(x)?

Mathematics

2 answers:

Bumek [7]3 years ago

8 0

Without seeing the graph, it's impossible to tell. The same can be said if we don't know the function rule. However, we can rule out three non-answers.

Choice B is false because the interval [1,3] has f(x) below zero but the rest of the interval to the right of x = 3 has f(x) not below zero.

Choice C is false. The value x = -1 leads to f(x) = 0 which is not greater than 0

Choice D is false because the values 8 and 4 are positive

After eliminating B, C, & D, we are left with choice A as the answer.

Anastasy [175]3 years ago

6 0

The answer is a i think

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Can u put this from least to greatest 0.5 0.45 3/5

Solnce55 [7]

from Least to Greatest:

0.45 < 0.5 < 3/5

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2 years ago

Find the solution to the system. Write your solution as an ordered pair (x,y) with no spaces, no solution, or infinitely many. -

Ugo [173]

Answer:

<h3>or infinitely many</h3>

Step-by-step explanation:

simplifying the equation -6x + 8y = 12 dividing by 2 would give us the same equation as

-6 / 2x + 8 / 2y = 12/2

-3x + 4y = 6

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2 years ago

Math!!! Need help!!!!!!!

iogann1982 [59]

Thats either 7/5 or 1 2/5 but since theres a whole number i think its 1 2/5

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2 years ago

HELP ME WITH THIS QUESTION PLEASE

lara [203]

Answer:

0.79

Step-by-step explanation:

all you really need to do is multiply your decimal (15.8) by your percent (5) so, you problem would look like 15.8(.05) (note it is .<em>0</em>5 because there need to be 2 decimal places) so, your answer is .79

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2 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0

3 years ago