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After graphing the parabola [tex](x+1)^2=2(y-3)[/tex], she can fill the boxes as follows:

Gigi identifies that the vertex of the parabola is [tex](-1, 3)[/tex]. The parabola opens up, and the focus is [tex]\frac{1}{2}[/tex] unit away from the vertex. The directrix is [tex]1[/tex] unit from the focus. The focus is the point [tex](-1, \frac{7}{2})[/tex]. The directrix of the equation is [tex]y=\frac{5}{2}[/tex].

Since Gigi's parabola has the x-term squared, then the parabola has the general formula

[tex](x-h)^2=4p(y-k)[/tex]

So,

[tex]x-h=x+1 \implies h=-1[/tex]

[tex]y-k=y-3\implies k=3[/tex]

The vertex is

[tex](h,k)=(-1,3)[/tex]

The focus is

[tex](h,k+p)=(-1,3+\frac{1}{2})\\=(-1,\frac{7}{2})[/tex]

The directrix is

[tex]y=k-p=3-\frac{1}{2}=\frac{5}{2}[/tex]

The other values can be computed as follows;

Direction the parabola opens: Since the value of p is positive, the parabola opens up.

Distance of focus from vertex: The focus and vertex both have the same x position, so the distance will be in terms of the y-coordinates only. The distance from the focus to the vertex is

[tex]\frac{7}{2}-3=\frac{1}{2}\text{ unit}[/tex]

Distance of directrix to focus: The directrix is the line [tex]y=2.5[/tex]. The distance of the directrix to the focus will be

[tex]\frac{7}{2}-\frac{5}{2}=1 \text{ unit}[/tex]

Learn more about conic sections here: https://brainly.com/question/12854078

Answer:

I took the quiz.

Step-by-step explanation:

Answer:

37/40

Step-by-step explanation:

                                      3/8                              7/10

      80/40                   -       15/40              -          28/40                   =  37/40

two whole shampoo  -      uses at home    -      uses on holiday     =  left

Answer:

?? No questions asked here

Answer:

5 minutes

Step-by-step explanation:

72/1 = 360/5

Step-by-step explanation:

i think the greatest from is 0.02 T

Answer:

I might be wrong i think its C but double check and dont put it in until you are sure its right

Step-by-step explanation:

Answer:  The number is 8

Please mark brainliest

Step-by-step explanation:

8 is the value of the unknown number 'x' from the equation 5x + 7 =47.

" Linear equation is defined as the algebraic expression which has highest power of the given variable equals to one."

According to the question,

'x' represents the unknown number.

As per the condition given linear equation we get,

   5x + 7 = 47

Add (-7) both the sides

5x + 7 + (-7) = 47 + (-7)

⇒5x = 40

Divide by 5 both the sides we get,

(5x) / 5 = 40 / 5

⇒ x = 8

Hence, 8 is the value of the unknown number 'x' from the equation 5x + 7 =47.

Learn more about linear equation here

https://brainly.com/question/11897796

#SPJ2

Answer:

9/40

i think it may be like this

Step-by-step explanation:

3/5.3/8

9/40

Answer:

[tex](-3,4)[/tex]

Reasoning:

This problem is telling you that if y equal 4, what does x equal?

You can easily insert the y value to find the constant x.

[tex]4=-3x-5[/tex]

[tex]9=-3x[/tex]

[tex]\frac{9}{-3} =\frac{-3x}{-3}[/tex]

[tex]-3=x[/tex]

Answer:

I think it's. y=-2/1x+2

Answer:

$640

Step-by-step explanation:

im actually not too sure. i think thats right

Answer:

320

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

So, the first step to solving the problem is to find out what type of triangle it is

and what rule of goemetry we can use to solve it.

Finding What Theorem We Can Use

So, the first step is to figure out what theorem we can use to solve the problem and how they can help us. By looking at it, we can see that it is an Isosceles Triangle due to the two sides being equal and 1 side not being equal.

One Theorem used on the Isosceles Triangle is the Base Angles Theorem. This states that the bottom two angles of the sides on the Isosceles triangle are equal to each other. So in this case if we letter the triangle A on the top, B as the Left, and C as the right. It would say this:

[tex]<ABC= <ACB[/tex]

Since we know this rule, we can solve for the equation.

Solving

We can solve for this by using two things that we know:

+ Sum of all angles in a triangle is 180 degrees.

+ Bottom two sides are congruent.

Since we know that, we can solve for the answer:

[tex]1) <ABC + <BAC+<BCA=180\\2) <BAC = 80\\3) <ABC + <BCA=100\\4) 2<ABC=100\\5)<ABC=<BCA=50[/tex]

After solving, we know that x is 50 degrees!

Cheers!

(Feel free to comment a question if you didn't understand something!)

Answer:

x = 3

Step-by-step explanation:

2 - 2x = -3 - -1

2 - 2x = -4

-2x = -6

-2x / -2 = 1x

-6 / -2 = 3

ur answer is then 1x = 3 or x = 3.

Answer:

- 42

Step-by-step explanation:

The opposite of 42 is negative 42.

Answer:06-16

Step-by-step explanation:

Engineering

Answer:

Only whole numbers of people, n, are assumed in the calculation.

Step-by-step explanation:

The function relating the number of people, n, to the revenue, r, implicity assumes that only whole people will purchase tickets.  13.5 would mean that 13 normal people and 1/2 of a person bought tickets.  This can't be in the domain, since the ticket saleperson would run away if 1/2 of a person showed up:  thus no ticket sale.

Actually, it may depend on how one defines a person.  Is it 1/2 physically, or 1/2 mentally?  I've personally seen the latter show up at some fundraisers.

Answer:

( AB )² + 12 = 162

Step-by-step explanation:

By Pythagoras theorem,

( AB )² + ( BC )² = ( AC )²

( AB )² + ( 2√3 )² = ( 9√2 )²

( AB )² + 12 = 162

Step-by-step explanation:

it's a right angled triangle so to find the measures of 3rd side we use hypotenuse formula which is,

h² = a² + b²

here in the given figure we have to find base or b²

(AC)² = (CB)² + (AB)²

we know,

AC = 9√2

CB = 2√3

now,

162 = 12 + AB

THEREFORE, OPTION B is correct.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

a.  3

b. -10

c. 0

dddwdwcd

Answer:

The person is saying that everyone has their own view of God.

A example is...

That is someones view on God.

Answer:

30yd^3

Step-by-step explanation:

dimensions are 3*5*2 (count the number of blocks) so multiply to get 30 yd^3

Answer:

Hey mate...

Step-by-step explanation:

This is ur answer.....

The sum of the lengths of any two sides of a triangle must be greater than the third side. (a)(8,11,19)⇒8+11 not greater than 19 , (N.G.) (d)(13,4,8)⇒4+8<13 , (NG). Hence, option (b) is the only answer.

Hope it helps!

Brainliest pls!

Follow me! :)

Answer:

desculpa,mais eu preciso de ponto para ajudar meu irmão

Answer:

60

Step-by-step explanation:

Answer:

[tex]LCD[/tex] [tex]is[/tex] [tex]60[/tex]

Step-by-step explanation:

We look for the [tex]LCM[/tex] between these 3 number

[tex]12: 12,24,36,48,60\\6:6,12,18,24,30,36,42,48,54,60\\5:5,10,15,20,25,30,35,40,45,50,55,60[/tex]

Our [tex]LCM[/tex] is 60

that means our [tex]LCD[/tex] is [tex]60[/tex]

Brainliest please

Answer:

a = 7

Step-by-step explanation:

Equation of line : y = mx + b

m = slope

Plug in coordinates:  

Slope = Change in y/Change in X

Slope = 13-4/5-2 = 9/3 = 3

Plug in coordinates:

y - intercept = b

13 = 5(3) + b

13 = 15 + b

b = -2

Equation: y = 3x - 2

Input 3 for x

y = 3x - 2

y = 9 - 2

y = 7

-Chetan K

Answer:

solution,

x+85+24=180 (being sum of angle of triangle)

x+109=180

x=180-109

x=71

therefore, the third angle is 71

Answer just below :-

Step-by-step explanation:

Let the third angle be x

Then;

24°+85°+x = 180 ( sum of interior angles of a triangle is 180°)

or; 109°+x = 180°

or; x = 180°-109°

:x=71°

Therefore the measure of third angle is 71°