Factor 1/2 out of (1/2d + 6)

The firework is an illustration of the equation of a parabola.

The x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

The casings hit the ground after 78 seconds.

This means that, a point on the graph is:

[tex]\mathbf{(x,y) = (78,0)}[/tex]

The firework exploded at a maximum of 760.5.

This means that, the vertex is:

[tex]\mathbf{(h,k) = (39,760.5)}[/tex]

The equation of a parabola is:

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

So, we have:

[tex]\mathbf{0 = a(78 - 39)^2 + 760.5}[/tex]

[tex]\mathbf{0 = a(39)^2 + 760.5}[/tex]

Subtract 760.5 from both sides

[tex]\mathbf{a(39)^2 =- 760.5}[/tex]

[tex]\mathbf{1521a =- 760.5}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{760.5}{1521}}[/tex]

[tex]\mathbf{a =- 0.5}[/tex]

Substitute [tex]\mathbf{a =- 0.5}[/tex] and [tex]\mathbf{(h,k) = (39,760.5)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex]

See attachment for the graph of [tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex].

From the graph:

From the equation:

Hence, the x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

Read more about parabolas at:

https://brainly.com/question/5430838

Answer:

[tex]x=\pm i[/tex]

Step-by-step explanation:

[tex]3x^2+5=2[/tex]

[tex]3x^2=-3[/tex]

[tex]x^2=-1[/tex]

[tex]x=\pm i[/tex]

Answer:

It will be true , it is a multiple of 21

Answer:

2.4× 10^4

Step-by-step explanation:

you just sum 1.6 with 0.8

[tex]2.4 \times {10}^{4} [/tex]

Answer:

The answer is -5/8, smaller fractions are always closer to a whole number which make them more, another way to look at it is 5 is 3 numbers away from 8, and 6 is 4 numbers away from 10, which makes -5/8 greater.

Hope this helps!

Answer:

x=6

Step-by-step explanation:

3(6)+1=18+1=19.

Answer:

x=19/2

Step-by-step explanation:

5/x+7=-2

5=-2(x+7)

5=-2x-14

5+14=-2x

19=-2x

Therefore

2x=-19

x=19/2

Answer:

Answer is in the pic

Step-by-step explanation:

A translation is just a movement of the figure so in this case you just add 3 to the x part of the coordinate.

so originally k (-2,5)    m (-3,1)      l (1,1)

add 3 to x so

k (1,5)   m (0,1)   l (4,1)

get a journal and pencil and when you go to sleep, don't put on any alarms. then write down in the morning what you dreamt about. every detail you can thing of. if you have the dream again, write down more details. this will help you begin to lucid dream.

Step-by-step explanation:

8) 125=x+90° (exterior angle= sum of two opposite interior angle)

x= 35°

9) y=80° ( vertically opposite angle)

x= 180-50-80= 50°.

hope this helps you.

Answer:

Answer=69

Step-by-step explanation:

8% of 75=6

75-6=69

Answer:

the answer is Y = -1.5x + 36

Answer:

adjacent angle

Step-by-step explanation:

a linear pair =180 so not it

supplementary and complementary can't be it either due to neither being right angles

not a vertical angle

right next to each other with a common line to connect them so adjacent angle

Answer:

19

Step-by-step explanation:

(48 - 23) + 6 = 31

23 - 6 = 17

(48 - 23) -6 = 19

The answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

It is given that:

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Based on the information we can draw a Venn diagram:

From the Venn diagram:

A + B = 17 + 6

A + B = 23

B = 6

A + B + C = 48

A = 23 - 6 = 17

C = 48 - 17 - 6

C = 25

The total number of pupils who only study Government = 25

The total number of pupils who study Government = 25 + 6 = 31

The total number of pupils who study Economics only = 17

Thus, the answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

Learn more about the Venn diagram here:

brainly.com/question/1024798

#SPJ2

Answer: A: 3x + 6 = 4x + 7                  1: 9x = 4x + 7

B: 3(x+6) = 4x + 7                  2: 3x + 18 = 4x + 7

C: 4x + 3x = 7 - 6                   3: 3x = 4x + 7

                                            4: 3x - 1 = 4x

                                            5: 7x = 1

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

S₄ = 4(4+1)(4+2) = 120

S₃ = 3(3+1)(3+2) = 60

4th term = 120-60=60

Answer:

2

Step-by-step explanation:

Answer:

Laps per minuet

Example:

You are traveling at a rate of 45 miles per hour (or mph). Determine the unit rate and the rate unit.

Solution:

45 is the numerical part of the rate, or the unit rate.

Miles per hour is the unit part of the rate, or the rate unit.

Answer:

2 x 4 − x 3 + x 2 − 9

Step-by-step explanation:

Answer:

Yes

Because

[tex] \frac{pn}{kr} = \frac{pt}{kg} = \frac{tn}{gr} = \frac{1}{2} [/tex]

Also all angles are equal

Answer:

Yes

Step-by-step explanation:

Angle are equal and the ratio of the sides is 2:1.

Answer:

Step-by-step explanation:

[tex](-2)*\dfrac{1}{5}*(-5\dfrac{3}{4})=(-2)*\dfrac{1}{5}*\dfrac{-23}{4}\\\\ = \dfrac{23}{5*2}\\\\=\dfrac{23}{10}\\\\=2\dfrac{3}{10}[/tex]

Answer: i think its all of them are 5

Step-by-step explanation: sorry if im wrong

Answer:

Step-by-step explanation:

an (the nth term ) = a1 + d(n - 1)

=  6 + 3(n - 1).

a17 = 6 + 3(17-1)

= 6 + 48

= 54.

Answer:

the y-intercept is 10

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

arrange the numbers in the other of magnitude

:

2.4,3.3,5.2,5.8,7,7.6,8.4,8.6,9.7

then check for the middle number(s)

median = 7

Answer:

ac = 18.5

Step-by-step explanation:

perimeter of a rectangle =  [tex]2(l+b)[/tex]

= 138m^2= 2(2x + 6 ) + 52

= 4x + 12 + 52 = 138  

= 4x + 64 = 138

= 4x = 138 - 64

= 4x = 74

= x =  74/4

= x = 18.5

Answer:

ok?

Step-by-step explanation:

Answer:

what's your question even-