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WARRIOR [948]
3 years ago
7

Rectangle LMNO is rotated 90° clockwise around the origin to create rectangle L'M'N'O'. Which statement would best describe the

relationship between points N and N'?
Mathematics
1 answer:
UNO [17]3 years ago
7 0

Answer:

They are equidistant from origin.

Step-by-step explanation:

Rectangle LMNO is rotated 90° clockwise around the origin to create rectangle L'M'N'O'. Which statement would best describe the relationship between points N and N'?

They are equidistant from origin.

They are midpoints of segment ON and segment O prime N prime.

They are equidistant from point O.

They are midpoints of segment LN and segment L prime N prime.

Answer: If a point with location N(x, y) is rotated 90° clockwise around the origin, the new coordinate N' is at (y, -x). The distance of the two points from the origin O(0, 0) can be calculated using:

ON=\sqrt{(y-0)^2+(x-0)^2}=\sqrt{y^2+x^2}\\  \\ON'=\sqrt{(y-0)^2+(-x-0)^2}=\sqrt{y^2+x^2}

Therefore ON = ON'. The points N and N'are equidistant from the orign

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HELP.
Viefleur [7K]

Answer:

The number of cases in the year 2010 is 266.

Step-by-step explanation:

An exponential function is one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)=aˣ

being a positive real, a> 0, and different from 1, a ≠ 1.

In this case:

r(t) = 207*e^{0.005*t}

where t is the number of years since 1960 and   e is an irrational number of which it is not possible to know its exact value because it has infinite decimal places. The first figures are 2,7182818284590452353602874713527 and is often called the Euler's number. e is the base of natural logarithms.

In this case, you want to know the number of cases r (t) in 2010. So, to know t you must know how many years have passed since 1960. For that, you can simply do the following subtraction: 2010-1960 and you get as a result : 50.

Replacing in the exponential expression r (t):

r(t) = 207*e^{0.005*50}

Solving:

r(t)=265.79 ≅ 266

<u><em>The number of cases in the year 2010 is 266.</em></u>

4 0
3 years ago
What is the volume, in cubic m, of a rectangular prism with a height of 4m, a width of
OleMash [197]

Answer:

72 cubic meters

Step-by-step explanation:

Again to calculate volume you have to take all three measurements given and multiply them like so: x times y times z. In this case x = 4, y = 1 and z = 18. When you multiply all of these terms you get 72 cubic meters.

5 0
3 years ago
Simplified<br> Quickly please
UkoKoshka [18]

Answer:

3a:20d+35

3b:35u+49q+56

4a:15+20t

4b:96k+120t+84

5a:24t+108m+60

5b:56q+28b+35

6a:14q+10w+24

6b:54v+99+27t

7a:16g+24+24c

7b:30a+55+50d

(i think thats what they are but the picture is small so its kind of hard to see)

Step-by-step explanation:

(since theres 10 total ill just give an example on how i solved 5a)

5(4d+7)

simplify into: (5•4d)+(5•7)

multiply: (20d)+(35)

since you do not know what d is, you cannot add them

remove parentheses once done:20d+35

(you don't need parentheses since multiplication come before addition but its easier to just use them)

<h2>Hope this helps</h2>
4 0
3 years ago
What are the zeros of the function f(x) = x2 + 8x + 4, expressed in simplest radical form?
klio [65]

Answer:

x = -4 ± 2√3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the best estimate for the length of a bike
castortr0y [4]
<span>The average length of a bike (including the length of both wheels) is about 68 inches.For finding the true answer we must follow the following convertion rule: 1 inch is equivalent to 0.02 yard, so 68 inches equal to 1.88 yards. Consequently, the value nearest 1.88 yards is 1.5 yards, so the answer is the choice A: 1.5 yards. </span>
8 0
3 years ago
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