Two numbers are opposites are 12 units apart. What are the two numbers? Answer smaller number, larger number

Find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5.

Elena-2011 [213]

Let's notice, the focus is at (5,0) and the directrix at x = -5.

keep in mind that there's a distance "p" from the vertex to either of those fellows, therefore, if the focus is at 5,0 and the directrix x = -5, the vertex is half-way between them, check the picture below.

notice the distance "p" there, now, is a horizontal parabola, opening to the right, meaning the value for "p" is positive, or just 5, thus

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})}
\\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}})
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=0\\
k=0\\
p=5
\end{cases}\implies (y-0)^2=4(5)(x-0)\implies y^2=20x
\\\\\\
\cfrac{y^2}{20}=x\implies \cfrac{1}{20}y^2=x$

8 0

3 years ago

The right triangle on the right is a scaled

Whitepunk [10]

Answer:

The scale factor is 3.5

6 0

2 years ago

Two altitudes of a triangle have lengths $12$ and $14$. What is the longest possible integer length of the third altitude

nataly862011 [7]

The longest possible altitude of the third altitude (if it is a positive integer) is 83.

According to statement

Let h is the length of third altitude

Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.

From Area of triangle

A = 1/2*B*H

Substitute the values in it

A = 1/2*a*12

a = 2A / 12 -(1)

Then

A = 1/2*b*14

b = 2A / 14 -(2)

Then

A = 1/2*c*h

c = 2A / h -(3)

Now, we will use the triangle inequalities:

a < b+c

2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

b < a+c

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

c < a+b

2A/h < 2A/12 + 2A/14

Solve it and get

h > 6.46

From all the three inequalities we get:

6.46<h<84

So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.

Learn more about TRIANGLE here brainly.com/question/2217700

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8 0

2 years ago

3. Complete the sentence by choosing the proper option from the given choices.

DanielleElmas [232]

Answer:

B. is exactly 1 triangle

Step-by-step explanation:

For any given triangle, the sum of the internal angles is $180^{o}$ . Thus from the given question, adding the given angles;

30° + 70° + 80° = $180^{o}$

Therefore, only one triangle can be produced with the given measure of angles. This implies that there is exactly one triangle. So that the correct option is B.

3 0

3 years ago

the circumference of the circle shown below is 54 centimeters. which expression gives the length in centimeters of XY?

g100num [7]

Answer:

The correct option is C

Step-by-step explanation:

Given the circumference of circle which is 54 cm and also the measure of arc XY is 120°

we have to find the expression for arc length of XY

The arc length can be calculated by the formula

$\frac{\theta}{360}\times 2\pi r$