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3 years ago

7

Find all the real values of X for which f(x)=0 F(x)= x^3-x

1 answer:

Natalka [10]3 years ago

5 0

Answer:

x=0,1,-1

Step-by-step explanation:

It factors as

X(x+1)(x-1)=0

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Will the point of the arrow in Figure Bhave the same angle measure as the point of the arrow in Figure A? Explain your answer.

inn [45]

Rotation being a rigid transformation, does not alter the angle and side lengths after transformation.

The arrow in Figure B will have the same angle measure as Figure A

From the complete question (see attachment), we understand that:

Figure A is rotated 90 degrees clockwise around point (2,2)

Rotation is a rigid transformation

This means that: after the transformation

Figure A and figure B will have the same side lengths
Figure A and figure B will have the same measure of angles

The above highlights imply that, the arrow in Figure B will have the same angle measure as Figure A

Read more about rigid transformations at:

brainly.com/question/1761538

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3 years ago

What is 1/5 divided by 1/3?<br><br> a. 3/5<br><br> b. 15<br><br> c. 5/3<br><br> d. 1/15

torisob [31]

The answer should be 3/5

4 0

3 years ago

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Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}

Deffense [45]

Start with a line segment connecting two points, A and B. $\dfrac{DA}{BA}=3$ means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with $\dfrac{DB}{BA}=2$ , or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, $\dfrac{AB}{CB}=\dfrac12$ , so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let $d$ be the length of AB. Then the length of CD in terms of $d$ is $4d$ . We have the coordinates of C and D, and the distance between them is $\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2$ . So

$4d=4\sqrt2\implies d=\sqrt2$

The slope of the line through C and D is

$\dfrac{0-4}{4-0}=-1$

and so the equation of the line through these points is

$y-4=-(x-0)\implies x+y=4$

So the coordinates of A are $(x,y)=(x,4-x)$ . The distance between C and A is $d=\sqrt2$ , so we have

$\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1$

Since A falls to the right of C (in the $x,y$ plane, not just in the sketch), we know to take the positive value $x=1$ . Then the $y$ coordinate is $y=4-1=3$ .

All this to say that A is the point (1, 3), so

$2x+y=2+3=5$

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3 years ago

A circular plot with a 160 foot diameter is watered by a spray irrigation system. To the nearest square foot, what is the area t

Anuta_ua [19.1K]

A circular plot is watered by a sprinkler that rotates through it. The sprinkler only rotates through a semi-circle, or half of the whole circle.

Area of a circle: A = pi x r^2

r = 160 / 2 = 80

A = pi x 80^2

A = 6400pi / 2 = 3200pi

3200pi = 10053.0965

The area water is approximately 10,053 ft^2.

Hope this helps!! :)

4 0

3 years ago

A square storage unit has a volume of 607.5 ft3. The height of the unit is 7.5 ft. What are the length and width of the storage

Eduardwww [97]

Answer:

9ft

Step-by-step explanation:

The base area of the storage is its volume divided by height

$A = \frac{V}{h} = \frac{607.5}{7.5} = 81 ft^2$

Since this base is a square, its length and width is of equal length, which is

$\sqrt{A} = \sqrt{81} = 9ft$

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3 years ago

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