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melisa1 [442]
3 years ago
10

Which of the following accurately shows the range of the function defined below?

Mathematics
1 answer:
tangare [24]3 years ago
5 0

Answer:

[2, positive infinity)

Step-by-step explanation:

the range is the interval of possible y-values or f(x) values.

for x<0 y is always and only 3.

for x between 0 and 2, y = x² + 2.

it clearly increases with increasing x. so, what is y for the smallest x ? the smallest x here is 0.

y = 0² + 2 = 2

for x larger or equal to 2, y = (1/2)×x + 5.

it again increases with increasing x. the smallest x here is 2.

y = (1/2)×2 + 5 = 1 + 5 = 6.

so, the smallest possible value for y is 2. and then it will approach positive infinity, when x approaches positive infinity. but it can never reach that (only after infinite time and at infinite x, so it is officially undefined), so that the interval is open on that end.

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Three vertices of parallelogram ABCD are A(2,-6),B(-1,2),C(5,3).find the coordinates of vertex D
salantis [7]

Check the first picture below.


for a parallelogram, it has to have two pairs of parallel sides, so BC || AD and AB || CD.

if two lines are parallel, they have the same slope, namely the <u>same rise and run</u>.

notice, the line BC has a run of 6 and a rise of 1, <u>arrows in red</u>, therefore, AD must also have a run of 6 and a rise of 1, so if we move from A 6 units over and 1 up, we'd end up at point D.


now, for part atop

Check the 2nd picture, in a parallelogram, opposite sides are parallel and opposite angles are equal, so if WLP is 144°, then PNW is also 144°.

in a parallelogram, diagonals bisect each other, so each cut the other in halves, so if PM is 9 then MW is also 9 and thus PW is just 9+9=18.


now, about QRST.

notice what we said about a parallelogram above, thus


\bf 8x+13=11x-23\implies 8x+36=11x\implies 36=3x \\\\\\ \cfrac{36}{3}=x\implies \boxed{12=x} \\\\[-0.35em] ~\dotfill\\\\ 2y+12=4y-4\implies 2y+16=4y\implies 16=2y \\\\\\ \cfrac{16}{2}=y\implies \boxed{8=y}


so then TQ ==> 2(8) + 12 ==> 16 + 12 ==> 28.

∡Q ==> 8(12) + 13 ==> 96 + 13 ==> 109°.

and since in a parallelogram, adjacent interior angles add up to 180°, then ∡Q + ∡T = 180°.

∡T ==> 180 - 109 ==> 71°.

3 0
3 years ago
If the ratio of the length to the breadth of a rectangle be 5:3 and its perimeter is 144m find the length of the rectangle
Kamila [148]

Answer:

length=45 m (2 sides = 90m)

Step-by-step explanation:

5x +3x=144

8x=144

x=18 (each of the 8 parts of 144 measure 18m)

5(18) + 3(18)=144

90 +54=144

90/2=45 (1 length side)

54/2=27 (1 width side)

The rectangle= 45+45 +27+27 = 144

5 0
3 years ago
Can an exterior angle of a triangle ever be congruent to one of its remote interior angles?
Inga [223]
I do not believe so, no. theres interior angles and exterior angles. hope that helps!
5 0
3 years ago
Find the coordinates of the midpoint of segment MN with endpoints M ( 10, 6 ) and N ( 8, 4 )
victus00 [196]
Use the midpoint formula 
4 0
3 years ago
How do I solve this
Andru [333]
Simply cross multiply:
18*m = 6*15
18m = 90
m = 5
5 0
3 years ago
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