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3 years ago

9x^2+4y^2 = 36

Mathematics

2 answers:

Vladimir [108]3 years ago

7 0

Answer:

c.(0, -√5) and (0, √5)

Step-by-step explanation:

The equation represents an ellipse centered on origin (0,0). First, the formula is rearranged to its cannonical form:

$\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

The foci are located in the lines of the semimajor axes, so, the distance between the center and any of the foci is:

$c = \sqrt{9 - 4}$

$c = \sqrt{5}$

The foci are located at $(0, -\sqrt{5})$ and $(0,\sqrt{5})$ . Hence, the answer is C.

Afina-wow [57]3 years ago

6 0

The answer is c
hope this would help you

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A pattern follows the rule "Starting with one, every consecutive line has a number one more than twice the previous line".

gtnhenbr [62]

Answer:

The fourth line will have 15 marbles

Step-by-step explanation:

The third line has 7 marbles. So, you double that and add one in order to find the number of marbles in the fourth line.

7*2=14

14+1=15

4 0

2 years ago

4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513

dimaraw [331]

Answer:

Part 4) $sin(\theta)=\frac{12}{13}$

Part 10) The angle of elevation is $40.36\°$

Part 11) The angle of depression is $78.61\°$

Part 12) $arcsin(0.5)=30\°$ or $arcsin(0.5)=150\°$

Part 13) $-45\°$ or $225\°$

Step-by-step explanation:

Part 4) we have that

$cos(\theta)=-\frac{5}{13}$

The angle theta lies in Quadrant II

The sine of angle theta is positive

Remember that

$sin^{2}(\theta)+ cos^{2}(\theta)=1$

substitute the given value

$sin^{2}(\theta)+(-\frac{5}{13})^{2}=1$

$sin^{2}(\theta)+(\frac{25}{169})=1$

$sin^{2}(\theta)=1-(\frac{25}{169})$

$sin^{2}(\theta)=(\frac{144}{169})$

$sin(\theta)=\frac{12}{13}$

Part 10)

Let

$\theta$ ----> angle of elevation

we know that

$tan(\theta)=\frac{85}{100}$ ----> opposite side angle theta divided by adjacent side angle theta

$\theta=arctan(\frac{85}{100})=40.36\°$

Part 11)

Let

$\theta$ ----> angle of depression

we know that

$sin(\theta)=\frac{5,389-2,405}{3,044}$ ----> opposite side angle theta divided by hypotenuse

$sin(\theta)=\frac{2,984}{3,044}$

$\theta=arcsin(\frac{2,984}{3,044})=78.61\°$

Part 12) What is the exact value of arcsin(0.5)?

Remember that

$sin(30\°)=0.5$

therefore

$arcsin(0.5)$ -----> has two solutions

$arcsin(0.5)=30\°$ ----> I Quadrant

$arcsin(0.5)=180\°-30\°=150\°$ ----> II Quadrant

Part 13) What is the exact value of $arcsin(-\frac{\sqrt{2}}{2})$

The sine is negative

The angle lies in Quadrant III or Quadrant IV

Remember that

$sin(45\°)=\frac{\sqrt{2}}{2}$

therefore

$arcsin(-\frac{\sqrt{2}}{2})$ ----> has two solutions

$arcsin(-\frac{\sqrt{2}}{2})=-45\°$ ----> IV Quadrant

$arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°$ ----> III Quadrant

5 0

3 years ago

Keiko sold less than three fourths of his sister's sales

sertanlavr [38]

The correct question is
<span>Keiko sold 3 less than three-fourths of his sister’s sales. Which expression represents what Keiko sold?

Let
S----------------> </span><span>the amount that Keiko's Sister sold
</span>K----------------> the amount that Keiko sold

we know that
Keiko sold 3 less than three-fourths of his sister’s sales
K=(3/4)*S-3

the answer is
K=(3/4)*S-3

6 0

3 years ago

Suzie Chambers sells cars for a living. She earns $450 per week plus a commission of 5% on

Greeley [361]

Answer:

$930

Step-by-step explanation:

450 + 9600(.05)

450 + 480

$930

6 0

2 years ago

Read 2 more answers

FIFTY POINTS!! Please help! I'll give brainliest

melomori [17]

Answer:

4851 ways

Step-by-step explanation:

The fish have 3 choices. They can make it above, below, or though the pipe. Keep in mind there are 100 fish total:

group 1 + group 2 + group 3 = 100

If we keep group 3 (the fish that swim below the pipe) constant, say 1, and increment the other two (group 2 starting off at 1) we find 98 possibilities.

98 + 1 + 1 = 100,

97 + 2 + 1 = 100,

96 + 3 + 1 = 100

. . . 98 possibilities

Now we take group 1 as one greater (1 + 1 = 2) and then start incrementing group 2 starting from 1 as done before. So 97 + 2 + 1 = 100. Followed by 96 + 3 + 1, 95 + 4 + 1...97 possibilities

If we continue this pattern, we have 98 + 97 + 96... + 1 total possibilities to partition this school of fish.

98 + 97 + 96... + 1,

Sum = n(n + 1)/2 = 98(98 + 1)/2 = 98(99)/2 = 4851

8 0

2 years ago