All categories

4 years ago

Find all real solutions to the equation below. Choices provided in image.

Mathematics

2 answers:

sertanlavr [38]4 years ago

8 0

(x^2 - 9)(x + 2) = 0
(x - 3)(x + 3)(x + 2) = 0

As any of the 3 above factors can equal zero the solutions are

x = 3, -3 , -2.

So the answer is E.

Alex Ar [27]4 years ago

6 0

Given equation (x^2-9)(x+2)=0 ............(1)

By the zero product theorem, when the product of two factors is zero, at least one of the factors equals zero.

Therefore, the solutions of (1) are solutions of
(x^2-9)=0 and (x+2)=0

For (x^2-9)=0 factor (x+3)(x-3)=0 => x=3 or x=-3
For (x+2)=0 => x=-2

So the solution to equation (1) is S={3,-3,-2)
Which means that none of the first four answer options is correct.

You might be interested in

The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 10

serious [3.7K]

Answer:

The rate of change of the height of the box at which is decreasing is $\frac{5000}{130321}$ centimeters per second.

Step-by-step explanation:

From Geometry the volume of a rectangular box ( $V$ ), measured in cubic centimeters, with a square base is modelled by the following formula:

$V = A_{b}\cdot h$ (Eq. 1)

Where:

$A_{b}$ - Area of the base, measured in square centimeters.

$h$ - Height of the box, measured in centimeters.

The height of the box is cleared within the formula:

$h = \frac{V}{A_{b}}$

If we know that $V = 500\,cm^{3}$ and $A_{b} = 361\,cm^{2}$ , then the current height of the box is:

$h = \frac{500\,cm^{3}}{361\,cm^{2}}$

$h = \frac{500}{361}\,cm$

The rate of change of volume in time ( $\frac{dV}{dt}$ ), measured in cubic centimeters per second, is derived from (Eq. 1):

$\frac{dV}{dt} = \frac{dA_{b}}{dt}\cdot h + A_{b}\cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA_{b}}{dt}$ - Rate of change of the area of the base in time, measured in square centimeters per second.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per second.

If we get that $\frac{dV}{dt} = 0\,\frac{cm^{3}}{s}$ , $\frac{dA_{s}}{dt} = 10\,\frac{cm^{2}}{s}$ , $h = \frac{500}{361}\,cm$ and $A_{b} = 361\,cm^{2}$ , then the equation above is reduced into this form:

$0\,\frac{cm^{3}}{s} = \left(10\,\frac{cm^{2}}{s} \right)\cdot \left(\frac{500}{361}\,cm \right)+(361\,cm^{2})\cdot \frac{dh}{dt}$

Then, the rate of change of the height of the box at which is decreasing is:

$\frac{dh}{dt} = -\frac{5000}{130321}\,\frac{cm}{s}$

The rate of change of the height of the box at which is decreasing is $\frac{5000}{130321}$ centimeters per second.

5 0

3 years ago

PLSSS ANSWER!!!!!!!!!!!!

Brums [2.3K]

Look at the picture.

The formula of an area of a triangle:

$A_\Delta=\dfrac{1}{2}ab\sin\alpha$

In the equilateral triangle, the measures of all angles are the same and equal to 60°.

Therefore your answer is:

$\dfrac{1}{2}aa\sin(60^o)=\dfrac{1}{2}a^2\sin(60^o)$

5 0

4 years ago

Ms. Abrams receives a 4% commission plus a salary of $275.00 per week. If her total sales for one week are $2,880.00, how much d

Marta_Voda [28]

390.20 is the answer because 4%of 2880 is 115.20 plus 275.00 is 390.20

8 0

3 years ago

7.4=n-2.6 could you plz solve this or give me some good sites that could solve it for me oh and plz show the steps to thanks

lisov135 [29]

Please try to follow this closely.
Ready ? OK, here goes:

<em> Add 2.6 to each side of the equation.</em>

6 0

3 years ago

Read 2 more answers

Hey guys! Could someone help me with this problem? I got the wrong answer! The answer is B, but I don’t know how to get it! Coul

asambeis [7]

When it says 'which has a greater rate of change' it is referring to 'what has a greater slope.' So, let's calculate each thing's slope:

Table:
I'm going to pick the easiest values to work with, so I'll pick the points (0, -2) and (1, -9/5) - I simplified the mixed fraction. So, here we go, the slope formula is:
$m =\frac{y_2-y_1}{x_2-x_1}$
$m = \frac{- \frac{9}{5} - (-2)}{1-0} = \frac{- \frac{9}{5} - ( -\frac{10}{5} )}{1-0}$
$m = \frac{ \frac{1}{5} }{1} = \frac{1}{5}$

So, the table's slope is -1/5.

Graph
We can, again, pick two points. I'll pick the two given: (5, 0) and (0, -3). Let's start off with the same formula:
$m =\frac{y_2-y_1}{x_2-x_1}$
$m = \frac{-3-0}{0-5} = \frac{3}{5}$

The graph's slope is 3/5.

Now, we just have to decide which is bigger: -1/5 or 3/5. So, clearly:
3/5 > -1/5.

The 3/5 slope was the graph, hence it has the greater rate of change (that's why it's B). If anything doesn't make sense, feel free to DM me or ask!

6 0

3 years ago