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katen-ka-za [31]
3 years ago
12

Which of the following is the equation of an ellipse centered at (5,1) having a vertical minor axis of length 4 and a major axis

of length 6?
Options are in image

Mathematics
1 answer:
Karolina [17]3 years ago
7 0

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

\frac{ {x}^{2} }{ {a}^{2} }  +  \frac{ {y}^{2} }{ {b}^{2} }  = 1

where

  • 2b = vertical axis length
  • 2a = horizontal axis length

(as in the picture)

So it should be like:

\frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} }  +  \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} }  = 1 \\  \frac{ {x}^{2} }{ 9}  +  \frac{ {y}^{2} }{ 4 }  = 1

Since it should be moved to the right and up, the answer would be:

\frac{ {(x - 5)}^{2} }{ 9}  +  \frac{ {(y - 1)}^{2} }{ 4 }  = 1

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Simplify<br> (4i)(–5i)(6i)<br><br> –120<br><br> –120i(incorrect)<br><br> 120i<br><br> 120
professor190 [17]

Answer:

120i

Step-by-step explanation:

;i × i = -1....so hence

4i × (-5i) = -20 i^2...which is -20(-1) = 20....

then you multiply with 6i

20(6i) = 120i

4 0
3 years ago
Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your
Mamont248 [21]

Answer:

14 miles.

Step-by-step explanation:

Let the distance traveled from home to destination = x miles.

Speed while going to friend's house = 35 miles per hour.

Speed while coming back = 40 miles per hour.

Total Time taken for the journey = 45 minutes = 0.75 hours.

Let the time taken while going to friend's house = y hours.

Therefore, the time taken while going to friend's house = (0.75 - y) hours.

To find x and y, model the speeds of both the journeys.

Speed while going to friend's house = Distance/Time.

35 = x/y.

x = 35y (Equation 1).

Speed while coming back = Distance/Time.

40 = x/(0.75 - y).

x = 40(0.75 - y) (Equation 2).

Since x = x, therefore:

35y = 30 - 40y.

75y = 30.

y = 30/75.

y = 0.4 hours.

Put y = 0.4 hours in Equation 1:

x = 35y.

x = 35(0.4).

x = 14.

Therefore, the distance between my friend's house and my house is 14 miles!!!

4 0
3 years ago
Read 2 more answers
On two tests so far this year, a student received a 78 and a 93. The student wants an average between 80 and 90 inclusive. What
Mariulka [41]
<span>240 <= 171 + x <= 270
and now subtract 171 from all and get
69 <= x <= 99
So any score from 69 to 99 will do.</span>
8 0
3 years ago
On tuesday shanice bought five hats. on wednesday half of all the hats that she had were destroyed. equation for... on thursday
wlad13 [49]

If X is the number of hats . . . reading backwards . . .

Thursday = Wednesday + Tuesday

17 = 1/2 X + 5

Solving:

17 - 5 = 1/2 X

12 = 1/2 X

24 = X

So she had 24 on Monday.



8 0
3 years ago
On last week's climb, each climber carried a pack that was 28% of his or her body weight. One climber weighed 78 pounds. What wa
11Alexandr11 [23.1K]
<h3><u>Solution</u> : </h3>

weight of bag :

  • 28   \% \:  \: of \:  \:  \: climber's \:  \: weight

  • \dfrac{28}{100}  \times 78

  • \dfrac{2184}{100}

  • 21.84 \:  \:  \: pounds
8 0
2 years ago
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