What is the vertex of the parabola f(x) = x^2 – 2x – 8 that has an axis of symmetry at 2 = 12
A (2,-8)
B (1,-9)
C (3,-5)
D (4,0)

Answer:

The function that describes the height of the ball in time is  [tex]h(t) = 32\cdot t -16.087\cdot t^{2}[/tex].

Step-by-step explanation:

Let suppose that ball experiments a free fall motion, which means that the ball is accelerated because of gravity and gravitational acceleration can be considered constant since height reached by the object is too small in comparison with the radius of the Earth. Therefore, we can assume that ball is accelerated uniformly.

Hence, the kinematic formula for the height of the ball ([tex]h(t)[/tex]), in feet, is described below:

[tex]h(t) = s + v\cdot t + \frac{1}{2}\cdot g \cdot t^{2}[/tex] (1)

Where:

[tex]s[/tex] - Initial height with respect to the ground, in feet.

[tex]v[/tex] - Initial velocity, in feet per second.

[tex]t[/tex] - Time, in seconds.

[tex]g[/tex] - Gravitational acceleration, in feet per square second.

If we know that [tex]s = 0\,ft[/tex], [tex]v = 32\,\frac{ft}{s^{2}}[/tex] and [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], then the function that describes the height of the ball in time is:

[tex]h(t) = 32\cdot t -16.087\cdot t^{2}[/tex] (2)

Answer:

2.) 385

Step-by-step explanation:

V=πr2h

3=π·72·7.5

3≈384.8451

rounded=385.

Answer:

600

Step-by-step explanation:

Hope this helps you bro.

We can set this up as a proportion.

[tex]\frac{6}{10}=\frac{x}{1000}[/tex] so 10x=6000 and x=600.

600 out of the 1000 people who went into the store, bought something.

Answer:

56.5 in^2

Step-by-step explanation:

The volume of a cone is π[tex]r^{2}[/tex]h/3. The radius is d/2=6/2=3

V=(3.14 x [tex]3^{2}[/tex] x 6)/3

 =(3.14 x 54)/3

 =169.56/3

 =56.52

Answer:

Let n be the number of 25 cent stamps.Then, 28 - n must be the number of 29 cent stamps.Tim paid $7.60 the stamps.

0.25n + 0.29(28 - n) = 7.60

This means that n stamps at 25 cents a piece plus (28 - n) stamps at 29 cents a piece sum to $7.60.Solve for m.

0.25n + 8.12 - 0.29n = 7.60

-0.04n = -0.52

n = 13

So, Tim bought 13 25-cent stamps and 28 - 13 = 15 29-cent stamps

Step-by-step explanation:

hope this helps:)

Answer: 16,21

Step-by-step explanation:

There are two ways you can solve this problem using substitution and elimination.

In this answer, I'm going to be using substitution.

First, you make two equations based on the information given.

The two equations are 0.15x+0.2y=6.6 and X+Y=37.

In the second problem subtract y to move it to the other side to get X=37-y.  

Now that you got x= make a new equation which should be 0.15(37-y)+0.2y=6.6 use distributive property to get 5.55-.15y+0.2y=6.6.

Then, subtract 5.55 by 6.6 to get 1.05 and 0.2y+-.15y to get 0.05 y.

Now you have 0.05y=1.05 divided 0.05 and 1.05 to get 21.

Now plug 21 into the X+Y=37 equation to get X+21=37 subtract 21 from 37 to get X=16.

So X=16 and Y=21, so the answer is 16,21.

Step-by-step explanation:

7x+10 - (x+2)^2

7x+10 - (x^2 + 2x + 4)

7x+ 10 - x^2 - 2x - 4

5x + 6 - x^2

then if u have to find the value of x then put the value of a = 1,b = 5,c = 6 in quadratic formula (-b + under root b^2 - 4ac / 2a) or (- b - under root b^2 - 4ac / 2a) it will gives the value of x...

HOPE it u..!!

edit - do let me knw that it's right or not..!!

Answer:

x = 9

Step-by-step explanation:

Formula

The secant and tangent lines bear the following relationship

(tangent line )^2 = the outside secant line * length of the whole line

Givens

tangent line = 15

outside secant line = x

length of whole secant line = x + 16

Solution

15^2 = x ( x + 16)

15^2 = x^2 + 16x

225 = x^2 + 16x

x^2 + 16x - 225 = 0

Answer and Discussion

The equation has two factors.

(x - 9)(x + 25) =0

x + 25 has no meaning. There cannot be a negative length in this level of geometry.

The answer is x - 9 = 0

x = 9

9514 1404 393

Answer:

  24π cm²

Step-by-step explanation:

The radius and height of the cone are shown as 3 and 4, so we know the slant height is 5 (a 3-4-5 right triangle is formed by these dimensions). Then the total surface area of the cone is ...

  A = πr² + πrl = πr(r +l)

  A = π(3 cm)(3 cm +5 cm) = 24π cm² . . . . total area of the cone

_____

Additional comment

The (3, 4, 5) Pythagorean triple is one of several involving small integers that regularly appear in math problems. It is worth remembering. In case you need convincing:

  3² + 4² = 5² . . . . sum of squares of sides is square of hypotenuse

  9 + 16 = 25

Answer:

Y= -4.5

Step-by-step explanation:

Hope this helps!

Answer:

y = -4.5

Step-by-step explanation:

6(y + 1.5) = -18

6y + 9 = -18

subtract 9 from each side of the equation:

6y = - 27

divide both sides by 6:

y = -4.5

Answer: I think the answer is B

Step-by-step explanation: My reasoning is that since some houses are expensive, and some houses are very cheap, the average house is in the middle, and that is the median.

Answer:

c bc he should use the median cause it is in the affect the mean

Step-by-step explanation:

Answer:

The required division is 658 and 342.

Step-by-step explanation:

Let the parts be x and y.

47x + 19y = 1000

let try 2digit number for x and y by inspection 14 and 19 best fit.

47*14 + 18*19 = 1000

658 + 342 = 1000

Answer:

$14.85

Step-by-step explanation:

8.98 + 3.27 + 1.5 = 13.75

13.75 x .08 = 1.1

13.75 + 1.1 = 14.85

Answer:

$14.85

Step-by-step explanation:

8.98 x.08= 0.7184

3.27 x .08= 0.2616

1.50 x .08= 0.12

8.98 + 0.72=  9.70

3.27 + .26= 3.53

1.50 + 12 =1.62

9.70+ 3.53 +1.62 = 14.85

Answer:

2.57 and 11/3 and 3.14

Step-by-step explanation:

Answer:

1.) 8x+28      2.) 2(4x+14)

Step-by-step explanation:

simplify it by multiplying the 4

or

after simplifying you could divide by 2

option 1 is the best answer

Answer:

Step-by-step explanation:

Answer:

1. something's missing

2. 120

3. 90

Step-by-step explanation:

Order of operations is: PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction

1. Missing something in this first one

56 ?? 49 x 2

2. 100 + 5 x 4

first multiply:

= 100 + 20

then add:

=120

3. 8 x 12 - 6

first multiply:

= 96 - 6

then subtract:

= 90

Drop the full equation for number 1 in the comments and I'll walk you through it. :)

Answer:

90: D

Step-by-step explanation:

Answer:

1332 1/4

Step-by-step explanation:

(36 1/2)² = (73/2)² = (73 * 73)/(2 * 2) = 5329/4 = 1332 1/4

Answer:

-3,1

The first option is correct.

Step-by-step explanation:

Have a great day!

Answer:

$317

Step-by-step explanation:

Formula for compound interest is;

A = P(1 + (r/n))^(nt)

For melanie;

P = $3800

r = 2⅜% = 0.02375

n = 12/4 = 3

t = 16 years

Thus;

A = 3800(1 + (0.02375/3))^(3 × 16))

A ≈ $5548

For Sébastien;

P = $3800

r = 2¾% = 0.0275

n = 12

t = 16

Thus;

A = 3800(1 + (0.0275/12))^(12 × 16))

A ≈ 5865

Difference between Sébastien and Melanie's final amount = $5865 - $5548 = $317

Answer:

2/3

Step-by-step explanation:

3/4 x 8/9 = 24/36 or 2/3 simplified

Answer:

2/19

Step-by-step explanation:

Answer:

14.90cm [a]

Step-by-step explanation:

To find x, we will apply " sine rule"

that is, [tex]sin[/tex]A/a=[tex]sin[/tex]B/b

here a= x A=90° B=70°anb b =14cm

so we input the values we have

1/x =0.94/14

cross multiply,

0.94x = 14

x = 14/0.94

=14.90cm

Answer:

10 in * 7in

Step-by-step explanation:

Given that :

Volume of block = 350 in³

Height of block = 5 inches

The dimension of block can be expressed cubic units

Volume of a rectangular prism :

V = length * width * height

Let ; length * width = B

350 = B * 5

B = 350 / 5

B = 70 in²

Possible dimension of B:

B = length *width

70 in² = 10 in * 7in

Hence, possible whole number dimension for the base = 10 in * 7in

Answer:

it would be 7 x 10 , 1 x 70 , 2 x 35

Step-by-step explanation:

Answer:

The number cubes needed when we have three cubes along each edge is 27 cubes

Step-by-step explanation:

The given parameters for the building of a cubic prism are;

The number of cubes used to build the 2 by 2 cube = 8 cubes

Let 'x' represent the length of each cube, we have;

The volume of a 2 by 2 cube = 2·x × 2·x × 2·x = 8·x³

Where x³ represents the volume of each cube

When we have three cubes along each edge, the total volume, becomes;

V = 3·x × 3·x × 3·x = 27·x³

The number cubes needed when we have three cubes along each edge, n = (The total volume of the cubes)/(The volume of each cube)

∴ The number cubes needed when we have three cubes along each edge, n = 27·x³/(x³/cube) = 27 cubes.

Answer:

[tex]\frac{x}{y}[/tex]45 long

Step-by-step explanation:

The total area of both the triangles is 56.25 square units.

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

The space occupied by a flat shape or the surface of an object is called area.

Area = (1/2) × base × height

According to the given question.

We have a two triangles, which are similar to each other.

Let the length of the side DE in triangle DEF be x.

Since, ABC similar to DEF

⇒[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]

⇒[tex]\frac{12}{x} =\frac{6}{4.5}[/tex]

⇒[tex]\frac{12(4.5)}{6} = x[/tex]

⇒[tex]2(4.5)=x[/tex]

⇒ [tex]x = 9[/tex]

Now, area of triangle ABC = [tex]\frac{1}{2}(6)(12)=36 square units[/tex]

Area of triangle DEF = [tex]\frac{1}{2} (9)(4.5)= 20.25square units[/tex]

Therefore,

The total area for both the triangles

= 36 + 20.25

= 56.25 square units

Thus option B is correct.

Find out more information about area of similar triangles here:

https://brainly.com/question/16394875

#SPJ2

Answer:

Lateral surface area = 360 cm²

Step-by-step explanation:

Given:

Dimension of small rectangle = (12 cm by 10 cm)

Find:

Lateral surface area

Computation:

Length =√9² + 12²

Length = √81 + 144

Length = 15 cm

Dimension of big rectangle = (15 cm by 10 cm)

Lateral surface area = Area of small rectangle + Area of big rectangle + Area  of slop rectangle

Lateral surface area = (L1 x B1) + (L x B) + (l x b)

Lateral surface area = (12 x 10) + (15 x 10) + (10)(9)

Lateral surface area = 120 cm² + 150 cm² + 90 cm²

Lateral surface area = 360 cm²

The necklaces will be sold for $8.75.

All you have to do is devide 201.25 by 23 and you will get your answer.