x²+10+7=0 by completing the square

A parabola is a mirror-symmetrical U-shape.

From the question, we have:

[tex]\mathbf{Vertex: (h,k) = (80,10)}[/tex]

[tex]\mathbf{Origin: (x,y) = (0,0)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Substitute the values of origin and vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{0 = a(0 - 80)^2 + 10}[/tex]

[tex]\mathbf{0 = a(- 80)^2 + 10}[/tex]

[tex]\mathbf{0 = 6400a + 10}[/tex]

Collect like terms

[tex]\mathbf{6400a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{640}}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

The focus of a parabola is:

[tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

[tex]\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}[/tex]

[tex]\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}[/tex]

[tex]\mathbf{Focus = (80, -11\times 160)}[/tex]

[tex]\mathbf{Focus = (80, -1760)}[/tex]

The equation of the directrix is:

[tex]\mathbf{y = -a}[/tex]

So, we have:

[tex]\mathbf{y = \frac{1}{640}}[/tex] ----- the directrix

The axis of symmetry is:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

We have:

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}[/tex]

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }[/tex]

A quadratic function is represented as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

So, we have:

[tex]\mathbf{a = -\frac{1}{640}}[/tex]

[tex]\mathbf{b = \frac{1}{4}}[/tex]

Recall that:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

So, we have:

[tex]\mathbf{x = -\frac{1/4}{2 \times -1/640}}[/tex]

[tex]\mathbf{x = \frac{1/4}{1/320}}[/tex]

This gives

[tex]\mathbf{x = \frac{320}{4}}[/tex]

[tex]\mathbf{x = 80}[/tex]

Hence, the axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]

Read more about parabola at:

https://brainly.com/question/21685473

Answer:

81+71+x=180

152+x=180

x=180-152

x=28°

Step-by-step explanation:

Hope that this is helpful.

Have a great Day.

Answer:

Using a calculator, if you typed in 517 divided by 7, you'd get 73.8571. You could also express 517/7 as a mixed fraction: 73 6/7.

Step-by-step explanation:

so 73 6/7 is your answer

Answer:

81 4/7

Step-by-step explanation:

Does this help?

Answer:

1)36

2)1g:200g

3)60

4)12

5)132

6)a

7)?sorry

Answer:

Step-by-step explanation:

yan po answer ko

Answer:

Step-by-step explanation:

The ordered pairs from the table:

Find the slope:

Find the y- intercept:

The function is:

Correct choice is D

Take any two pairs

Slope

Equation in point slope form

Answer:

0.4545

Step-by-step explanation:

Just. divide 5 by 11. You're supposed to be in highschool, mate. Just use a calculator.

Step-by-step explanation:

1

3 x2+52x=1440

Step 2: Subtract 1440 from both sides.

1

3 x2+52x−1440=1440−1440

1

3 x2+52x−1440=0

For this equation: a=0.3333333333333333, b=52, c=-1440

0.333333x2+52x+−1440=0

Step 3: Use quadratic formula with a=0.3333333333333333, b=52, c=-1440.

x=

−b±√b2−4ac

2a

x=

−(52)±√(52)2−4(0.333333)(−1440)

2(0.333333)

x=

−52±√4624

0.6666666666666666

x=24,−180

Answer:

x=24,−180

v=30m/s velocity is 30 ms-1

Given :-

To Find :-

Solution :-

According to Question ,

When y = 14 and x = 4 ,

When x = 9 ,

Answer:

5.005

try that, im pretty sure you subtract

Answer:

-6

Step-by-step explanation:

Take the x out for -2

f(-2) is equivalent to x=-2

f(x) = 5x + 4

1. f(-2)=5(-2)+4

2. f(-2)= -10+4

3. -6

Step-by-step explanation:

expanded form is adding each place value together with zeros replacing all other spots

32.28

30.00 + 2.00 + 00.20 + 00.08

Answer:

cheating in exam mmmmmmmm

Answer:

hmmm did you try 14?

Answer:

C) 72cm

Step-by-step explanation:

Multiply 12 x 6

Answer:

(D) : Z+7

Step-by-step explanation:

−

1

+

8

}}

z−1+8

+

7

Answer:

Z-4/4+8

Z - 1 + 8

Z + (-1 + 8)

Z + 7

Answer:

Step-by-step explanation:

0

Answer:

y = x - 4

Step-by-step explanation:

The equation is just y = x shifted down 4 units, so it's y = x - 4. If you have to use all of the symbols, you can write "y = x * 1 - 4 + 0". Otherwise, use the one under "Answer" as it is shorter

Answer:

Step-by-step explanation:

you find slope (y1-y2)/(x1-x2) = (0-1)/(4-5) = -1/-1= 1

then you take a point (4,0)

y-0 = 1(x-4)

I hope this helps!

Answer:

1. -18,-7,-4,3,16

2. -39,-24,-12,20,24

3. -64,-57,-32,0,9

4. -24,-14,-8,-3,-1

Step-by-step explanation:

Negative numbers are always least.

Answer:

heres the square root of 20 4.47214 but i dont know what else to do for this answer. (sorry)

Step-by-step explanation:

√20 = √(4 * 5) = √4 * √5 = 2√5 ≈ 4.47214

Answer:

67

Step-by-step explanation:

you divide the two numbers then you multiply by ten

Answer:

a,khoảng cách từ thị trấn P đến thị trấn Q là

Step-by-step explanat  io  n:

36*5=180(km)

b,Muthu đi xe đạp từ thị trấn P đến thị trấn Q hết số phút là:

180/40=4,5(h)=270(phút)

Step-by-step explanation:

option B is correct answer ( Acute angle triangle)

hope this helps you.

Answer:

Acute triangle

Step-by-step explanation:

Acute triangle have less than 90 degrees

Answer:

p = -1

Step-by-step explanation:

3(2p - 1) - 2*(3p+ 4) = 11p

Use distributive property: a(b +c) =a*b +a*c

3*2p -3*1 -2*3p + (-2)*4 = 11p

6p - 3  - 6p - 8 = 11p

6p - 6p - 3 - 8 = 11p

          - 11 = 11 p

Divide both sides by 11

     -11/11 = p

p = -1

Answer:

7 Hour

Step-by-step explanation:

Divide 660 by 12 to get the unit rate.

660 divided by 12 equals 55.

Hence, in 1 hour, Goran drives 55 miles. Next, divide 385 by 55 to get 7.

Therefore,Goran 7 hours to drive 385 miles.

Answer:

Hello, There!

First we have to find Out How fast Goran can go in one hour and If we dived by 660 ÷ 12 = 55

Now We know that Goran Drove [tex]55[/tex] Miles in 1 hour

Since We figured out How fast Goran can go in one miles we can add/multiply  to get your final Answer

We can add like this 55, 110, 165,  220, 275, 330, 385

Now we Can Stop because the Question says "Goran drove 660 miles in 12 hours.At the same rate, how long would it take him to drive 385 miles"

And Counting the times we Added we Have the Answer 7

Therefore, It took Goran 7 hours Drive 385 Miles

Answer:

x = 9

Step-by-step explanation:

( 17x + 7 )° = ( 13x + 3 )° + 40°

17x + 7 = 13x + 3 + 40

17x - 13x = 43 - 7

4x = 36

x = 9

Answer:

<R=56 degrees; <Q=62 degrees; <S=62 degrees

Step-by-step explanation:

5x+12=4x+22 (This is because the two angles are congruent to each other.)

x+12=22

x=10

Now, plug it in.

5(10)+12=50+12=62 degrees

62(2)=124 degrees (This is because the two angles are congruent and equal)

180-124=56 degrees