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3 years ago

Which of the following equations belongs to an ellipse with vertical orientation?

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

6 0

Answer:

d. 16x² + y² = 16

Step-by-step explanation:

Standard form of an ellipse is:

x² / a² + y² / b² = 1

If b > a, the ellipse has a vertical orientation.

We can ignore options b and c, since they have minus signs in them.

Convert the other options to standard form:

a. x² / (1/16) + y² / (1/25) = 1

x² / (1/4)² + y² / (1/5)² = 1

1/4 > 1/5

d. x² + y² / 16 = 1

x² / 1² + y² / 4² = 1

1 < 4

e. x² / 16 + y² = 1

x² / 4² + y² / 1² = 1

4 > 1

Of these three options, only d is a vertical ellipse.

mr Goodwill [35]3 years ago

3 0

The answer to this question is D

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Evan’s family drove to a theme park for vacation. They drove the same speed throughout the trip. The first day, they drove 300 m

Ray Of Light [21]

Answer: Evan's family drove 150 miles on the third day.

Explanation:
Because they had driven the same speed throughout the trip, dividing the miles driven by the hours would result in the miles that they drove per hour. 300/6 and 250/5 = 50. So, Evan's family drove 50 miles per hour. To solve for the hours driven on the third day, you need to multiply the hours driven by the miles that were driven per hour.

3 hrs. x mph (miles per hour) = miles driven on the third day

Hope this helps! Sorry, I don't have the time to reread my answer, but I'm positive that it'll make sense to you somewhat.

6 0

3 years ago

Read 2 more answers

Geometry- Solve the portion. Question#4<br>

kotykmax [81]

Answer:

$d=18$

Step-by-step explanation:

<h3>First let's write our equation</h3><h3 /><h3> $\frac{6}{d-6} =\frac{4}{8}$ </h3><h3 /><h3>Reduce</h3>

<em>Definition - </em><em>reduction refers to the rewriting of an expression into a simpler form</em>

<h3 />

We can reduce $\frac{4}{8}$ to $\frac{1}{2}$

Our equation is now $\frac{6}{d-6} =\frac{1}{2}$

Now we can cross multiply

<em>Definition - </em><em>given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.</em>

$d-6=12$

We are adding because we want our variable to be on one side of the equation

$d=18$

<h3>To check we can show our equation but instead of d we have 18</h3><h3 />

$\frac{6}{18-6} =\frac{1}{2}$

Subtract and we get

$\frac{6}{12} =\frac{1}{2}$

Which makes it true

3 0

2 years ago

10. RECREATION In a game of kickball, Rickie has to kick the

wel

Answer:

The angle Rick must kick the ball to score is an angle between the lines BX and BZY which is less than or equal to 32°

Step-by-step explanation:

The given measures of the of the angle formed by the tangent to the given circle at X and the secant passing through the circle at Z and Y are;

$m\widehat{XZ} = 58^{\circ}$

$m\widehat{XY} = 122^{\circ}$

The direction Rick must kick the ball to score is therefore, between the lines BX and BXY

The angle between the lines BX and BXY = ∠XBZ = ∠XBY

The goal is an angle between $m\widehat{XY}$

Let 'θ' represent the angle Rick must kick the ball to score

Therefore the angle Rick must kick the ball to score is an angle less than or equal to ∠XBZ = ∠XBY

By the Angle Outside the Circle Theorem, we have;

The angle formed outside the circle = (1/2) × The difference of the arcs intercepted by the tangent and the secant

$\therefore \angle XBZ = \dfrac{1}{2} \times \left (m\widehat{XY} -m\widehat{XZ} \right)$

We get;

∠XBZ = (1/2) × (122° - 58°) = 32°

The angle Rick must kick the ball to score, θ = ∠XBZ ≤ 32°

4 0

2 years ago

The ratio of Mary’s downloaded iPad apps to Katie’s is 12 to 8. If Katie has 96 apps how many does Mary have?

sladkih [1.3K]

8×12=96. Katie
12×12=144. Mary
you have to Divide Katie's 96 by 8 to get 12
then take Mary's 12 and multiply it by 12 to get the answer of 144 apps that Mary owns

3 0

2 years ago

Fudgin [204]

Triangle DEF hope that helps

4 0

3 years ago