Plz help ASAP thanks

Use numerals instead of words. If necessary, use / for the fraction bar(s). A parabola is given by the equation y = x2 + 4x + 4.

Anarel [89]

Graph x2 = 4y and state the vertex, focus, axis of symmetry, and directrix.This is the same graphing that I've done in the past: y = (1/4)x2. So I'll do the graph as usual: The vertex is obviously at the origin, but I need to "show" this "algebraically" by rearranging the given equation into the conics form:x2 = 4y Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved
(x – 0)2 = 4(y – 0)This rearrangement "shows" that the vertex is at (h, k) = (0, 0). The axis of symmetry is the vertical line right through the vertex: x = 0. (I can always check my graph, if I'm not sure about this.) The focus is "p" units from the vertex. Since the focus is "inside" the parabola and since this is a "right side up" graph, the focus has to be above the vertex.From the conics form of the equation, shown above, I look at what's multiplied on the unsquaredpart and see that 4p = 4, so p = 1. Then the focus is one unit above the vertex, at (0, 1), and the directrix is the horizontal line y = –1, one unit below the vertex.vertex: (0, 0); focus: (0, 1); axis of symmetry: x = 0; directrix: y = –1Graph y2 + 10y + x + 25 = 0, and state the vertex, focus, axis of symmetry, and directrix.Since the y is squared in this equation, rather than the x, then this is a "sideways" parabola. To graph, I'll do my T-chart backwards, picking y-values first and then finding the corresponding x-values for x = –y2 – 10y – 25:To convert the equation into conics form and find the exact vertex, etc, I'll need to convert the equation to perfect-square form. In this case, the squared side is already a perfect square, so:y2 + 10y + 25 = –x 
(y + 5)2 = –1(x – 0)This tells me that 4p = –1, so p = –1/4. Since the parabola opens to the left, then the focus is 1/4 units to the left of the vertex. I can see from the equation above that the vertex is at (h, k) = (0, –5), so then the focus must be at (–1/4, –5). The parabola is sideways, so the axis of symmetry is, too. The directrix, being perpendicular to the axis of symmetry, is then vertical, and is 1/4 units to the right of the vertex. Putting this all together, I get:vertex: (0, –5); focus: (–1/4, –5); axis of symmetry: y = –5; directrix: x = 1/4Find the vertex and focus of y2 + 6y + 12x – 15 = 0The y part is squared, so this is a sideways parabola. I'll get the y stuff by itself on one side of the equation, and then complete the square to convert this to conics form.y2 + 6y – 15 = –12x 
y2 + 6y + 9 – 15 = –12x + 9 
(y + 3)2 – 15 = –12x + 9 
(y + 3)2 = –12x + 9 + 15 = –12x + 24 
(y + 3)2 = –12(x – 2) 
(y – (–3))2 = 4(–3)(x – 2)Then the vertex is at (h, k) = (2, –3) and the value of p is –3. Since y is squared and p is negative, then this is a sideways parabola that opens to the left. This puts the focus 3 units to the left of the vertex.vertex: (2, –3); focus: (–1, –3)

6 0

3 years ago

Bro I really need this answer (I’ll mark brainliest)

vaieri [72.5K]

Given:

Point G is the centroid of triangle ABC.

FG = x + 8 and AG = 6x - 4

To find:

The value of the variable x.

Solution:

Using rule of centroid:

$$\Rightarrow A G=\frac{2}{3} A F$

$$\Rightarrow A G=\frac{2}{3}(A G+F G)$

$$\Rightarrow 6 x-4=\frac{2}{3}(6 x-4+x+8)$

$$\Rightarrow 6 x-4=\frac{2}{3}(7 x+4)$

Multiply by 3 on both sides, we get

⇒ 3(6x - 4) = 2(7x + 4)

⇒ 18x - 12 = 14x + 8

Subtract 14x from both sides.

⇒ 4x - 12 = 8

Add 12 on both sides.

⇒ 4x = 20

Divide by 4 on both sides.

⇒ x = 5

The value of x is 5.

4 0

3 years ago

How do I find X? Thanks!

Igoryamba

The two labeled angles are alternate exterior angles, and as such, they are equal. This means that we can set up and solve the following equation:

$4x-13=2x+37 \iff 2x = 50 \iff x = 25$

7 0

4 years ago

Six times the difference of a number and three is equal to three less than the number.

icang [17]

Answer:

x=3

Step-by-step explanation:

lets take x as the number

so

6(x-3)=x-3

since it says "6 times" we know that we will have to multiply the difference by 6 and it says the difference of a number and 3 is equal to 3 less than the number so we know that we are subtracting 3 from x

6x-18=x-3

6x-x=18-3

5x=15

x=3

3 0

3 years ago

Jack wants to earn some extra income. His friends suggest that he invest in bonds and stocks. What type of income will James ear

Ne4ueva [31]

Answer:

C. Portfolio income

Step-by-step explanation:

We are told that Jack wants to earn some extra income. His friends suggest that he invest in bonds and stocks.

Let us know the meaning of our given income types.

Earned income: The income which is paid for work is called earned income such as salary.

Passive income: The income which is the result from cash flow received on a regular basis is called passive income such as dividend income.

Portfolio income: The income that comes from investments, dividends, interest and capital gains is called portfolio income such as stocks, bonds, mutual funds, and annuities.

Business income: The income that comes from any business activity is called business income. It is also an earned income.

Since the income received from bonds and stocks is called portfolio income, therefore, option C is the correct choice.

8 0

4 years ago

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