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1 year ago

Graph the image of square RSTU after a rotation 270° counterclockwise around the origin.

Mathematics

1 answer:

djyliett [7]1 year ago

8 0

Rotating 270 degrees counterclockwise about the origin is the same as rotating 90 degrees clockwise about the origin, which can be expressed in coordinate notation $(x,y) \longrightarrow (y, -x)$ .

So, the vertices of the image are:

$U(4,0) \longrightarrow U'(0, -4)\\\\T(5,0) \longrightarrow T'(0, -5)\\\\S(5,-1) \longrightarrow S'(-1, -5)\\\\R(4, -1) \longrightarrow R'(-1, -4)$

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Given that you have 2 parallel lines cut by a transversal, what is the measure of angle 2?

Archy [21]

Step-by-step explanation:

angle 2 = 2x + 10 deg (corresponding angles) or 180 - 4x + 46 deg (angles on a straight line are supplementary)

therefore,

2x + 10 = 226 - 4x

6x = 216

x = 36

hence,

angle 2 = 2(36) + 10 = 82deg

Topic: Angles

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2 years ago

Which equation represents the graph?

frosja888 [35]

Answer:

The answer is A) y+4 =3(x+3)

Step-by-step explanation:

The slope is the rate of change, which you can see from the graph is m = 3/1 = 3.

Your options are given in point-slope form:

y-y1=m(x-x1)

Pick a point from the graph. I used;

(-3, -4). Now plug this into your point slope form equation.

y-(-4) = 3(x-(-3))

y+4=3(x+3)

8 0

2 years ago

find the local and/or absolute extrema for the function over the specified domain. (Order your answers from smallest to largest

Arlecino [84]

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

$f(x)=x^{2}+8\:over\:[-1,4]$

1) Calculating the first derivative

$f'(x)=2x$

2) Now, let's work to find the critical points

Set this

$2x=0\\x=0$

0, belongs to the interval. Plug it in the original function

$f(0)=(0)^2+8\\f(0)=8$

3) Making a table x, f(x) then compare

x| f(x)

-1 | f(-1)=9

0 | f(0)=8 Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.

5 0

2 years ago

a box contains 20 blue marbes, 16 green marbles, and 14 red marbles. two marbles are selected at random. let 3 be the event that

Maksim231197 [3]

Answer:

Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.

Step-by-step explanation:

6 0

2 years ago

8 freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on a committee.

loris [4]

Answer: 11113200

Step-by-step explanation:

We know that , the number of combination of choosing r things from n things is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

$^8C_4\times ^9C_5\times^9C_2\times^7C_3$

$=\dfrac{8!}{(8-4)!4!}\times\dfrac{9!}{(9-5)!5!}\times\dfrac{9!}{(9-2)!2!}\times\dfrac{7!}{3!(7-3)!}\\\\ =\dfrac{8\times7\times6\times5\times4!}{4!4!}\times\dfrac{9\times8\times7\times6\times5!}{4!5!}\times\dfrac{9\times8\times7!}{7!2!}\times\dfrac{7\times6\times5\times4!}{3!4!}\\\\=11113200$

∴ The number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors = 11113200

6 0

2 years ago