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Allushta [10]
2 years ago
15

GHLJ and GSTU are both parallelograms. Why is ∠L ≅ ∠T? Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S

in on side G H, and side G U is on side G J.
Mathematics
1 answer:
dybincka [34]2 years ago
3 0

Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.

Step-by-step explanation:

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Subtract. (4x2+8x−2)−(2x2−4x+3) Enter your answer, in standard form, in the box.
Crazy boy [7]

the answer is 2x2+12z-5 (its also in the picture)

3 0
2 years ago
F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.
Whitepunk [10]
Take partial derivatives and set them equal to 0:

\nabla F(x,y)=\langle2x+4,2y-4\rangle=\mathbf 0

We find one critical point within the boundary of the disk at (x,y)=(-2,2). The Hessian matrix for this function is

\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&0\\0&2\end{bmatrix}

which is positive definite, and incidentally independent of x and y, so F(x,y) attains a minimum F(-2,2)=-8.

Meanwhile, we can parameterize the boundary by \mathbf r(t)=\langle9\cos t,9\sin t\rangle with 0\le t\le2\pi, which gives

F(x,y)=F(x(t),y(t))=f(t)=81\cos^2t+81\sin^2t+36\cos t-36\sin t=81+36(\cos t-\sin t)

with critical points at

f'(t)=0\implies 36(-\sin t-\cos t)=0\implies\sin t+\cos t=0\implies t=\dfrac{3\pi}4,\dfrac{7\pi}4

At these points, we get

f\left(\dfrac{3\pi}4\right)=81-36\sqrt2\approx30.0883
f\left(\dfrac{7\pi}4\right)=81+36\sqrt2\approx131.9117

so we attain a maximum only when t=\dfrac{7\pi}4, which translates to (x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right).
3 0
2 years ago
The average density of Styrofoam is 1.00 kg/m^3. If a Styrofoam cooler is made with outside dimensions of 50.0 x 35.0 x 30.0 cm
Nadusha1986 [10]

Answer:

View graph

Step-by-step explanation:

The closest by default to 1100 cubic inches is taking two side and two front covers and that would give you 1080.12 cubic inches since two of the covers you must subtract 3 cm per side and side which would add 6 cm in total so outside would be 35 cm and indoor 29 cm . According the graph

29*50*3= 4350 * 2 lid = 8700 cm3

30*50*3= 4500*2 lid = 9000 cm3

So 8700+9000 = 17700 cm3 to inches 3 = 1080.12 cm3

5 0
2 years ago
John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at speed of 42mph.
elixir [45]

Answer:

47.25 mph

Step-by-step explanation:

Represent the total distance traveled as 2x. Average speed= total distance/total time

When going at 42 mph, the time would be x/42 and when going at 54 mph the time would be x/54 to travel x distance. Add x/42 and x/54 together to get 16x/378. Then divide 2x by 16x/378 to get 47.25 mph. Also this is RSM innit?

5 0
2 years ago
On Monday, the ABC Company stock was at $12.80 per share. On Tuesday it gained $3.42, and then lost $9.70 on Wednesday. What is
solong [7]

Answer:

Step-by-step explanation:

12.80+3.42= 16.22

16.22-9.70= 6.52 that's your answer

6 0
2 years ago
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