What is the first step when rewriting y = 3x2 + 9x – 18 in the form y = a(x – h)2 + k?
3 must be factored from 3x2 + 9x
x must be factored from 3x2 + 9x
9 must be factored from 9x – 18
3 must be factored from 3x2 – 18

Answer:

248 acres

Step-by-step explanation:

A forest covers 31,000 acres

0.8% of the forest old growth trees

There are 0.8% × 31000 = 248 acres of old growth trees

Answer:

Step-by-step explanation:

Corresponding angles equal 180 degrees when added

6x + 3x = 180

9x = 180

x = 20

angle CBD is 60 and angle GFH is 120

3(20) = 60

6(20) = 120

Answer:

0.6 ...........................

Answer:

The probability is 4 1 because there is four toys and the probability that the kid will get a Mario toy twice in a row has a low chance becuase, there are three other toys

Step-by-step explanation:

Answer:

A=e(b-c)-d

A=-2(6-3)-4

A=-12+6-4

A=-6-4

A=-10

The measure of the angles are 91.375°and 88.625°. Both the angles are obtained by the supplementary angle principal.

Supplementary angles are two angels whose total is 180 degrees. When a straight line is crossed by a line, two angles develop on each of the examined straight line's sides.

Two sets of additional angles make up those two-two angles. That is, if supplementary angles are placed next to each other, the exterior sides of their exterior sides will form a straight line.

The given data in the problem is;

∠1 = 9y-2

∠2 = 7y+16

The sum of the supplementary angle is 180

⇒9y-2 +7y+16 = 180

⇒16y +14 =180

⇒16y= 166  

⇒ y=10.375

The measure of the angle 1 is;

∠1 = 9y-2

∠ 1 = 9 ×10.375 -2

∠ 1 = 91.375°

The measure of the angle 2 is;

∠2 = 7 × 10.75 +16  

∠2 = 88.625°

Hence, the measure of the angles are 91.375°and 88.625°.

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Answer:

I'm pretty sure the median is 7

Step-by-step explanation:

Well To find the median, first order your data. Then calculate the middle position based on n, the number of values in your data set.

2 2 4 5 5 9 9 12 16 20. Then add the 2 middle numbers. 5 and 9. It is (5+9) divided by 2 is 7.

Hope this helps!

Answer:

The hypotenuse is 4√5.

Step-by-step explanation:

[tex] \sqrt{ {4}^{2} + {8}^{2} } = \sqrt{16 + 64} = \sqrt{80} = \sqrt{16} \sqrt{5} = 4 \sqrt{5} [/tex]

Write 165 as a sum of powers of 2 :

165 = 128 + 37

165 = 128 + 32 + 5

165 = 128 + 32 + 4 + 1

165 = 2⁷ + 2⁵ + 2² + 2⁰

This translates immediately into the decimal expansion of a binary number,

165 = 1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

so that

165₁₀ ≡ 1010 0101₂

Answer:

10100101₂

Step-by-step explanation:

Let us solve it now.

2 |165

2 |82  -  1

2 | 41   - 0

2 |20   -  1

2 |10    - 0

2 | 5   - 0

2 |2      - 1

2 | 1     - 0

    0    - 1

Now write the remainders from bottom to top.

165 = 10100101₂

Answer:

343 cubic inches

Step-by-step explanation:

7 times 7 times 7 is 343

Answer:

18 ft.

Step-by-step explanation:

While you don't have the table provided, this is still a relatively simple problem to solve.

As we know, there are 3 feet per 1 yard (this can be written as 3 ft. = 1 yd. if that's easier to comprehend). So, if we're trying to find how many feet are in 6 yards, you'll write out your equation as 3*6=?. To find what ? is, you'll do the multiplication: 3*6-18.

So, with this, there are 18 feet in 6 yards.

Answer:

[tex]\dfrac 3{10}[/tex]

Step-by-step explanation:

[tex]~~~~~~\dfrac 25 + x = \dfrac 7{10}\\\\\\\implies x = \dfrac 7{10} - \dfrac 25\\ \\\\\implies x = \dfrac 7{10} - \dfrac 4{10}\\\\\\\implies x = \dfrac{7-4}{10}\\\\\\\implies x = \dfrac 3{10}[/tex]

We have the point (3, 22.5), which means every 3 candles, Victor gains 22.5 dollars.

Similarly to the point (7, 52.5), which means every 7 candles, Victor gains 52.5 dollars.

-> Every 1 candle, Victor gains 7.5 dollars.

Solving the inequality, it is found that three values that would make the inequality true are given as follows: y = 12, y = 15, y = 18.

The inequality is given by:

y + 7 > 18.

We solve it similarly to an equality, hence the solution is given as follows:

y > 18 - 7.

y > 11.

Hence three values that would make the inequality true are given as follows: y = 12, y = 15, y = 18.

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Answer:

=69805

Step-by-step explanation:

This is an exponential growth problem.  If the population doubles periodically, it follows a law like this:

P(t) = P(0)e^kt

where P(0) is the initial population at time t=0, and k is a constant with units of years-1.

To find k, let t=0.  Then P(t) = P(0) = initial population = 2183.

Since the population doubles every 28 years, we can write

P(t+28) = 2P(t)

P(0)ek(t+28) = 2[P(0)e^kt] 

Simplifying,

e²⁸k = 2

k = ln(2) / 28 = 0.02475 years-¹

Finally,

P(t) = 2183e⁰.⁰²⁴⁷⁵t, t in years

P(t)= 2183e^0.02475t, t in years

Then at t=140 years from now,

P(140) = 2183e⁰.⁰²⁴⁷⁵×¹⁴⁰

P(140) = 2183e^(0.02475 × 140) = 69804.61168

=69805

Answer: 69,856

Step-by-step explanation: First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.

140÷28=5

The population will double 5 times.

Now figure out what the population will be after it doubles 5 times. Multiply the population by 2 a total of 5 times.

2,18322222=69,856

That calculation could also be written with exponents:

2,18325=69,856

After 140 years, the population will be 69,856 people.

Answer:

He would have to talk 200 minutes.

Step-by-step explanation:

Since 30 divided by .15= 200. And there is a .15 cent cost per minute meaning Javier would have to talk for 200 minutes for the prices to be equal.

Have a great day!

The part of the trip does Annie still have to travel to reach her destination is 24.64.

Annie traveled 2/7 parts of her trip in the first hour, and then 1/8 parts in the second hour. she plans to rest when she has completed half of her trip.

what part of the trip does Annie still have to travel to reach her destination.

We have to determine part of the trip does Annie still have to travel to reach her destination

Annie traveled 2/7 parts of her trip in the first hour, and then 1/8 parts in the second hour.

She plans to rest when she has completed half of her trip.

2/7 Annie traveled in the first hour = 2/7*60 = 17.1428hours

and 1/8 in one hour,

1/8*60=7.5minutes

The distance traveled in the first hour+distance traveled in the second hours=total distance travelled.

Therefore the total distance =7.5+17.14=24.64

The part of the trip does Annie still have to travel to reach her destination is 24.64

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Answer:

184in.³

Step-by-step explanation:

volume of a pyramid = (1/3) • base_area • height

6 • 92 = 552(1/3) = 184

Answer:

In terms of pi: 164.5pi cm squared

Substituting pi for 3.14: 516.53 cm squared

Step-by-step explanation:

3.5^2 = 12.25pi

12.25*2 = 24.5pi

7pi*20 = 140pi

140 + 24.5 = 164.5pi

164.5*3.14 = 516.53

If no letters or numbers are repeated, then the number of possibilities will be 11,232,000. Then the probability that the license plate is ABC123 or MOM678 will be 1/8,788,000.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

A series of license plates are being produced that all have the same pattern of three letters (a-z) followed by three digits (0-9) without any repeats.

If no letters or numbers are repeated, then the number of the possibilities will be

Number of ways = 26 × 25 × 24 × 10 × 9 × 8

Number of ways = 11,232,000

Then the probability that the license plate is ABC123 or MOM678 will be

[tex]P = \dfrac{1}{17,576,000}+\dfrac{1}{17,576,000}\\\\P = \dfrac{1}{8,788,000}[/tex]

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Answer:

She's paid 7.50 pounds an hour

Step-by-step explanation:

7.50 x 8 = 60

The position and nature of the image are magnified,

Focal length, usually represented in millimeters (mm), is the basic description of a photographic lens.

Radius of curvature of the mirror, R = -60 cm

Focal length of the mirror, f = -30 cm

Object distance, u = -20 cm

Let v is the position of the mirror. It can be calculated as :

[tex]\rm \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{-30}-\dfrac{1}{-20}\\\\\\\dfrac{1}{v}=\dfrac{-20 - (-30)}{(-30)(-20)}\\\\\dfrac{1}{v}=\dfrac{10}{(-30)(-20)}\\\\\dfrac{1}{v}=\dfrac{10}{600}\\\\\dfrac{1}{v}=\dfrac{1}{60}\\\\v=60[/tex]

The image is formed at a distance of 60 cm behind the concave mirror.

[tex]\rm m=\dfrac{-v}{u}\\\\m=\dfrac{-60}{-30}\\\\m=2[/tex]

The image is magnified.

Hence, the position and nature of the image are magnified,

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====================================

[tex]\large \sf \underline{Problem:}[/tex]

The perimeter of a rectangle is twice the

sum of its length and its width. The

perimeter is 40 meters and its length is 2

meters more than twice its width.

What is its length?

====================================

[tex]\large \sf \underline{Answer:}[/tex]

The answer is 12 m.

====================================

[tex]

\large \sf \underline{Explanation:}[/tex]

The perimeter (P) of a rectangle is twice the sum of its length (I) and width (w):

P = 2(l + w) P = 34

=>> 2(1+w) = 34

1+ w = 34/2

⇒ I + w = 17

Length is 2 meters more than twice its width:

I = 2w + 2

Now we have the system of equations:

I + w = 17

I = 2w + 2

Use the substitution method and substitute I from the second equation into the first equation:

2w + 2 + w = 17

2w + w = 17 - 2

3w = 15

w = 15/3

w = 5

Now, substitute w into the equation:

I = 2w + 2

I =2* 5+2

I = 10 + 2

I = 12

====================================

The numbers are complex numbers, and the sum of the complex numbers (-4 +i) and (10 - 5i) is 6 - 4i

The expressions are given as:

(-4 +i) and (10 - 5i)

The sum is represented as:

Sum = (-4 +i) + (10 - 5i)

Open the brackets

Sum = -4 +i + 10 - 5i

Collect like terms

Sum = -4  + 10 +i - 5i

Evaluate the like terms

Sum = 6 - 4i

Hence, the sum of the complex numbers (-4 +i) and (10 - 5i) is 6 - 4i

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Answer:

≈ 4.7 mm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the missing side , then

x² + 5.2² = 7²

x² + 27.04 = 49 ( subtract 27.04 from both sides )

x² = 21.96 ( take square root of both sides )

x = [tex]\sqrt{21.96}[/tex] ≈ 4.7 mm ( to the nearest tenth )

Answer:

was less affective on males in the study because only 27 % of them lost weight, whereas 3% of the females lost weight.

Step-by-step explanation:

It had less affective on males in the study. And there is a diffrent amount of males and females who tried the weight loss supplement.

hopefully this helps you

- Matthew

Answer:

573440 kg

Step-by-step explanation:

Given,

Density of copper ( D ) = 8960 kg / m³

Length of cube ( l ) = 4 meters

To find : Mass of solid cube of copper ( m )

Formula : -

Volume of cube = l³

Volume of cube

= l³

= 4³

= 4 x 4 x 4

= 64 meter³

So,

V = 64 meter³

Formula : -

D = m / V

m = D x V

   = 8960 x 64

m = 573440 kg

Hence,

The mass of a solid cube of copper is 573440 kg.

Answer:

B) π/2 units to the right

Explanation:

Function : y = 4sin(2x-π)

f(x) = A * g(Bx - C) + D where C/B is phase shift, D is vertical shift.

Identify: B = 2, C = π, D = 0

Horizontal shift:

Vertical shift:

Answer:

-8 - -11 = 3

Step-by-step explanation:

[tex]-8-x=3\\\\-8-x-3=3-3\\\\-11-x=0\\\\-11-x+x=0+x\\\\-11=x[/tex]

Therefore, the missing number is -11