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Marat540 [252]
2 years ago
10

Bless me with the answers

Mathematics
1 answer:
vovikov84 [41]2 years ago
8 0
5.) -4
6.) 3
7.) 4
8.) it would be your other choice, i can’t see what it says.
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Write an equation for an ellipse centered at the origin, which has foci at (\pm8,0)(±8,0)left parenthesis, plus minus, 8, comma,
mario62 [17]

Answer:

The equation of the ellipse is \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1

Step-by-step explanation:

The standard form of the equation of an ellipse with center (0 , 0) is

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

  • The coordinates of the vertices are (± a , 0)  
  • The coordinates of the foci are (± c , 0) , where c ² = a² - b²  

∵ The ellipse is centered at the origin

∴ The center of it is (0 , 0)

∵ It has foci at (± 8 , 0)

- The coordinates of the foci are (± c , 0)

∴ c = ±8

∵ It has Vertices at (± 17 , 0)

- The coordinates of the vertices are (± a , 0)

∴ a = ±17

∵ c² = a² - b²

- Substitute the values of c and a to find b

∴ (8)² = (17)² - b²

∴ 64 = 289 - b²

- Add b² to both sides

∴ b² + 64 = 289

- Subtract 64 from both sides

∴ b² = 225

- Take √  for both sides

∴ b = ± 15

∵ The equation of the ellipse is \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

- Substitute the values of a and b in it

∴ \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1 ⇒ \frac{x^{2}}{289}+\frac{y^{2}}{225}=1  

∴ The equation of the ellipse is \frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1

6 0
3 years ago
A right triangle as shown below
anastassius [24]

Answer:

sin a = 7/25

cos a = 24/25

tan a = 7/24

Step-by-step explanation:

Trig. How wonderful. I get tripped up on these types of problems some times, so I decided to try to help! To start, write out the three ratios.

SOH (sine=opposite/hypotenuse) CAH (cosine=adjacent/hypotenuse) TOA (tangent=opposite/adjacent)

Then, label the triangle with “hypotenuse” “adjacent” and “opposite.” This helps us correctly use and find the raitos. Then, use these ratios to find out the ratios of A!

sin a = 7/25

cos a = 24/25

tan a = 7/24

If needed, just divide the ratios to get their decimal form!

6 0
3 years ago
Amaya's test scores in Algebra 1 are 78 and 91. She has one more test left and wants to earn a B for the course, which is from 8
ICE Princess25 [194]
Let x be the score Amaya gets on the final test. She wants her average of all 3 tests to be between 80 and 89: 

<span>80 ≤ (78 + 91 + x) / 3 ≤ 89 </span>

<span>Multiply everything by 3: </span>
<span>240 ≤ 78 + 91 + x ≤ 267 </span>
<span>240 ≤ 169 + x ≤ 267 </span>

<span>Subtract 169 from everything: </span>
<span>240 - 169 ≤ x ≤ 267 - 169 </span>
<span>71 ≤ x ≤ 98 </span>

<span>Answer: </span>
<span>She needs to score between 71 and 98 to get a B for the course.</span>
3 0
3 years ago
Solve each inequality 1 &lt; x -2
ludmilkaskok [199]
Add 2 to both sides...x>3
7 0
2 years ago
Read 2 more answers
A cyclist rides a bike at a rate of 24 miles per hour. What is this rate in miles per minute? How many miles will the cyclist tr
BlackZzzverrR [31]

there are 60 minutes per hour

24/60 = 0.4 miles per minute

0.4*5 = 2

they will ride 2 miles in 5 minutes

4 0
3 years ago
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