Find the length of a segment defined by A(4, 3) and B(8, 0)

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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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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Answer:

224 sq m

Step-by-step explanation:

We are basically finding surface area of a rectangular prism, minus the top side

[tex]2(2)(8) + 2(16)(2) + 16(8)[/tex]

Simplify:

[tex]32 + 64 + 128 = 224[/tex]

Answer:

4 < 7

Step-by-step explanation:

-7 + 11 =

11 - 7 =

4

-4 + 11 =

11 - 4 =

7

4 < 7

Answer:

4<=7

Step-by-step explanation:

-7<=-4

or, -7+11<=-4+11

Therefore 4<=7

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]

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

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:

[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]

The cost of a brush, a sketchbook, and a paint set will be $ 2.38, $ 14.3, and $ 19.067 respectively.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Genevieve brought $35.75 to the art supply store.

She bought a brush, a sketchbook, and a paint set.

Let x be the cost of the paint set.

The sketchbook cost 3/4 the cost of the paint set. Then the cost of the sketchbook will be

[tex]\rightarrow \rm \dfrac{3x}{4}[/tex]

The brush was 1/6 as much as the sketchbook. Then the cost of the brush will be

[tex]\rightarrow \rm \dfrac{3x}{4} \times \dfrac{1}{6}=\dfrac{x}{8}[/tex]

Then the value of the paint set will be

[tex]\begin{aligned} \dfrac{3x}{4} +\dfrac{x}{8} + x &= 35.75\\\\\dfrac{15}{8}x &= 35.75\\\\15x &= 286\\\\x &= \$ 19.067 \end{aligned}[/tex]

Then the cost of the sketchbook will be

→ 3 × 19.067 / 4 = $ 14.3

Then the cost of the brush will be

→ $ 2.38

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Answer: Cristiano scored an 83%

Step-by-step explanation:

1.) plug in 50/60 into a calculator to get the percentage

Answer:

d = 3072.2 ft

Step-by-step explanation:

    Circumference of circle = 9687 ft

                                   πd     = 9687

                                      [tex]\sf \dfrac{22}{7}*d = 9687\\[/tex]

                                              [tex]d = 9687 * \dfrac{7}{22}\\\\d = 3082.2 \ ft[/tex]

Answer:

ANswer A for Reshawn

Step-by-step explanation:

The box plots show data about the heights, in feet, of two different types of trees at a local nursery.

Which statement is best supported by the information in the box plots?

#2^(x-2)

For 2

For 3

For 4

For 5

For 6

#2^x-2

For 2

For 3

For 4

For 5

For 6

Answer:

[tex]\large \begin{array}{| l | c | c | c | c | c |}\cline{1-6}x & 2 & 3 & 4 & 5 & 6\\\cline{1-6} 2^x-2 &2 &6 &14& 30 & 62 \\\cline{1-6} 2^{x-2} & 1&2 & 4& 8& 16\\\cline{1-6}\end{array}[/tex]

[tex]\large \text{$ 2^x-2 $}:[/tex]

[tex]x=2 \implies 2^2-2=2\\x=3 \implies 2^3-2=6\\x=4 \implies 2^4-2=14\\x=5 \implies 2^5-2=30\\x=6 \implies 2^6-2=62[/tex]

[tex]\large \text{$ 2^{x-2} $}:[/tex]

[tex]x=2 \implies 2^{2 -2}=1\\x=3 \implies 2^{3 -2}=2\\x=4 \implies 2^{4 -2}=4\\x=5 \implies 2^{5 -2}=8\\x=6 \implies 2^{6 -2}=16[/tex]

Answer:

x = 0

x = -4

x = -3

Step-by-step explanation:

Hello!

First, lets factor out 3x (GCF) from the whole expression:

Factor the polynomial by grouping:

Set the expression and each factor to 0, and solve for x:

3x = 0

x + 4 = 0

x + 3 = 0

There are 3 roots for this equation: 0, -4, and -3.

Answer:

true because a =b = 0.42

Step-by-step explanation:

I hope it's helpful for you

Answer:

false

Step-by-step explanation:

Answer:

look at the photo

...................................

Answer:

A=e(b-c)-d

A=-2(6-3)-4

A=-12+6-4

A=-6-4

A=-10

Answer:

3.2

Step-by-step explanation:

2e = 6.4

dividing through by 2 in order to make e the subject of the equation

e = 6.4/2

e =3.2

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:

What is (f–g)(x)?

f(x)=

–

2x2+10x

g(x)=11

–

3x2

12

Step-by-step explanation:

Answer:

D. y = -4/5x + 10

Step-by-step explanation:

If you graph it, whether that be on paper or typing the equation out on a website so it can do the graphing for you, it's a straight line with a negative slope unlike the other choices. Therefore, it's a linear function. A quick tip is that, usually, a linear function can be easily shown in the form of y = mx + b (slope-intercept form), and that's the exact form y = -4/5x + 10 is in. y being y (dependent variable, or result/output), -4.5 being m which represents the slope, x being x (independent variable, or input), and +10 being b which represents the y-intercept. If the x is in the denominator like in y = 5/x - 3, it's very likely that it's not a linear function.

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

[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

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

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

Hi!! :D

Answer:

I got 177.46

Step-by-step explanation:

I just used a surface area calculator!

So sorry if this is wrong!

Have a great day! <3

Option A. is correct.  To calculate the lateral surface area triangular prism, the sides B, C and D are need to be added to calculate the area.

A triangular prism is "a polyhedron made up of two triangular bases and three and three rectangular sides. It has 5 faces, 6 edges and 9 vertices".

According to the question,

Formula for lateral surface area  = (a +b +c)h where a, b, c are perimeter of base and 'h' is height of the triangular prism.

From the given triangular prism has B, C and D are perimeter of base.

Hence, to calculate the lateral surface area triangular prism, the sides B, C and D are need to be added to calculate the area.

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Answer:

$36.25

Step-by-step explanation:

Shipping and tax are 25% the price of online book, thus it will be 25/100 x 29 = $7.25

Thus, total will be 29 + 7.25 = $36.25

Step-by-step explanation:

1. completing the square

x² + 10x + ... = (x + a)² = x² + 2ax + a²

10 = 2a

a = 5

so,

x² + 10x + 10 = -22

is

(x + 5)² - 15 = -22

(x + 5)² = -7

x + 5 = i×sqrt(7)

the solutions are

x = i×sqrt(7) - 5

x = -i×sqrt(7) - 5

2. is easy via factoring

that means there has to be an easy way to define

x² + 3x - 40 = (x + a)(x + b)

remember,

(x + a)(x + b) = x² + (a+b)x + ab

since the constant term is -40, we know either a or b had to be negative (and the other positive).

a × b = -40

so, what factors deliver 40 ?

1×40

2×20

4×10

5×8

the x-term factor is 3.

so,

a + b = 3.

therefore, it must be the combination 8-5.

so, the factoring is

(x + 8)(x - 5) = 0

the solutions are therefore

x = -8

x = 5

3. quadratic formula

x² + 3x + 1 = 0

a = 1

b = 3

c = 1

x = (-b ± sqrt(b² - 4ac))/(2a)

x = (-3 ± sqrt(3² - 4×1×1))/(2×1) = (-3 ± sqrt(9 - 4))/2 =

= (-3 ± sqrt(5))/2

the solutions are

x = (-3 + sqrt(5))/2

x = (-3 - sqrt(5))/2

therefore

4. 2 non-real solutions (called also complex or irregular)

5. 2 rational solutions

6. 2 irrational solutions

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!

Answer:

1) 24w + 18
2) 6(4w + 3)

Step-by-step explanation:

Explanation for 1)
Use the Foil method for factoring by multiplying each number inside the bracket [8w + 6] by the number outside the brackets [3]

3*(8w + 6)
3 * 8w + 3 * 6
= 24w + 18

Explanation for 2)
By using the final product in 1) [24w + 18], we can facour it further by using GCF (Greatest Common Factor)

We have to determine first what is the greatest common factor of 24w, and 18

Its 6

So we use 6, and divide it by what we got in explanation 1 to find our 2nd way of writing the expression
24w/6 + 18/6
= 6(4w + 3)

Don't forget to put whatever you divided those numbers by outside of the bracket

Hope this helps :)

Answer:

Step-by-step explanation:

Given

3(8w + 6)

Question

Write in 2 different ways.

Method One

Use the distributive property to remove the brackets.

3(8w + 6)            Given. Remove the brackets. Notice both results

3*8w  + 3 * 6      Combine

24w + 18

Method 2

Take out another common factor. 2 is another common factor.

3(8w + 6)

3*2 (4w + 3)            Combine

6 ( 4w + 3)