What is the area of the polygon below?

Answer:

The steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Answer:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

Answer:

<2, <5

Step-by-step explanation:

<2 is a vertical angle so it is equal to 110

<5 is a corresponding angle and since the lines are parallel it is also equal to 110

Answer:

2 < h <= 3

Step-by-step explanation:

4 + h <= 7

h <= 3          (subtract 4 on both side)

h + 1 > 3

h > 2           (subtract 1 on both side)

So, 2 < h <= 3

Answer is   [tex]h > 1600[/tex]

The convention is to write the variable first on the left side, then the inequality sign, followed by the other side of the inequality.

Writing [tex]h > 1600[/tex] means that h is larger than 1600. Think of an alligator mouth that is represented by the "greater than sign". The mouth opens up to the larger side. In this case, h could be something like 1700 which is larger than 1600. So we'd say [tex]1700 > 1600[/tex] for instance.

Answer:

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Step-by-step explanation:

Well slope-intercept form is [tex]y = ax + b[/tex].

Let's start with the slope.

In this case, finding the slope is easy.

It should have a negative slope.

So we can cross out answer choices A. and C.

Also, we can cross out D. because it just makes no sense, -10/3, if you start from the y-intercept and go down 10 and across 3, yeah that's

not the slope.

So we can cross out D.

The only answer choice left is B.

We can tell the y-intercept is 1/2 because like come on so B is the correct answer.

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Looking at the graph, we can figure out our y-intercept or b simply by looking at the line to see where it intersects the y-axis.

So, we can see that the line intersects the y-axis at 1/2 or 0.5

That means, our y-intercept or b is 1/2 (0.5).

Now, to find out the slope of the line, we can pick two pairs of coordinates on the line and plug it into the slope equation to figure out the slope.

Let's use the two coordinate pairs: (-5, 2) and (0, 1/2).

Plug it in.

1/2 - 2 = - 1.5

0 - - 5 = 5

-1.5/5 = -0.3

Convert it into a fraction: -0.3 = -3/10

Thus, our slope intercept form for this line is: y = -3/10 + 1/2

Answer:

80 pages

Step-by-step explanation:

Let's use a ratio to solve:

pages : seconds

   12    :       9

    4     :       3

    [tex]p[/tex]     :      60

It would seem that [tex]p[/tex] would equal 80. The printer can print 80 pages in 60 seconds or one minute.

Answer:

B

Step-by-step explanation:

Here, we have a grain silo having 2 shapes fused together to make it.

A cylinder and then a hemisphere ( half sphere)

Now, we want to calculate the volume of grain that could completely fill the silo.

Mathematically, to do that, we will need to add the volume of the cylinder to the volume of the hemisphere.

Mathematically,

Volume of cylinder is;

pi * r^2 * h

From the question, r = 6 ft and h = 168 with pi = 22/7

Substituting these values, we have

Volume of cylinder= pi * 6^2 * 168 = 6,048 pi

The volume of the sphere will be;

4/3* pi * r^3= 4/3 * pi * 6^3 = 288 pi

So the total volume of the silo will be;

288 pi + 6,048 pi = 6336 pi

So to have the final result, let’s multiply by value of pi

6336 * 22/7 = 19,193 ft^3

The closest answer here probably due to previous approximations is 19,008 ft^3

Answer:

The answer is below

Step-by-step explanation:

To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.

Equation B: 5x+x=x-4.

Equation A: 5x-2+x=x-4.

Simplifying equation A to be in the form of equation B:

5x -2 + x = x - 4

Adding 2 to both sides:

5x + x -2 + 2 = x - 4 + 2

5x + x = x - 4 + (+2)

= equation A + 2

But 5x+x=x-4 = equation A

Therefore Equation B is the same as Equation A + 2

Answer:ADD/SUBTRACT A QUANTITY TO/FROM ONLY ONE SIDE

And part 2: is NO

Answer:

84

Step-by-step explanation:

Surface area is the combined area of the 2 dimensional planes.

6 × 5 + 3 × 4 × 1/2 × 2 + 6 × 3 + 4 × 6

30 + 12 + 18 + 24

= 84

The surface area is 84 square centimeters.

Answer: 546496.76

Step-by-step explanation:

Given the following :

Current population = 220,000

Population growth rate per year = 7.25%

Population size after 13 years =?

Using the compounding formula :

A = P(1 + r)^t

Where ;

A = final population size

P = current population size

r = growth rate

t = time or period

A = P(1 + r)^t

A = 220,000 ( 1 + 7.25/100)^13

A = 220,000 ( 1 + 0.0725)^13

A = 220,000 (1.0725)^13

A = 220,000(2.484076)

A = 546496.760

The population will be about 546,497 people

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

Answer:

Radius = 6.46 meters

Height = 1.46 meters

Step-by-step explanation:

The volume of a cylinder = πr²h

In the above question, we were given

r = (x + 5) meters

h = x meters

Volume = 192 cubic meters

Hence,

192 = π × (x + 5)² × x

192 = π × (x² + 10x + 25) × x

192 = π × (x³ + 10x² + 25x)

Divide both sides by π

192/π = x³ + 10x² + 25x

61.115498147 = x³ + 10x² + 25x

x³ + 10x² + 25x - 61.12

This Quadratic equation is a polynomial

x = 1.46119

From the above:

Radius = (x + 5)meters

Radius = 1.46119 + 5 = 6.46119 meters

Approximately to 2 decimal places = 6.46 meters

Height = x meters

Height = 1.46119 meters

Approximately to 2 decimal places = 1.46 meters

Answer:

Hope this helps. If not let me know and I'll explain it better

Answer:

All real values of x such that x ≥-3

Step-by-step explanation:

g(x) = sqrt(x+3)

A sqrt must be greater than or equal to zero

sqrt (x+3) ≥ 0

Square each side

x+3≥ 0

Subtract 3 from each side

x ≥-3

The restrictions on x are x ≥-3

That means the domain is x ≥-3

All real values of x such that x ≥-3

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

[tex]g(x)=\sqrt{x+3}[/tex]

A square root must have a value of greater than or equal to 0.

[tex]\sqrt{x+3}\geq 0[/tex]

Square both sides.

[tex]x+3\geq 0[/tex]

Subtract 3 from both sides.

[tex]x\geq -3[/tex]

Answer:

2.5 or 2 1/2

Step-by-step explanation:

i caculated do order of operations

[tex]A = 1500(1.00167)^{12t}[/tex]

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

Explanation:

You could use the formula

[tex]A = P(1+\frac{r}{n})^{nt}[/tex]

to plug in P = 1500, r = 0.02 and n = 12 to get the answer above. This is the compound interest formula. The interest rate r is divided into n = 12 to account for monthly compounding. The original exponent t turns into 12t. So for instance, if t = 2 years go by, then 12*t = 12*2 = 24 months have gone by.

Answer:

8x2-30x+27 has one root (9/4) the square of the other (3/2)

Step-by-step explanation:

8x2+30x+27 = (2*x+3)*(4*x+9)  => solution = {-3/2, -4/9}

One is not the square of the other because squares are positive.

8x2-30x+27 = (2*x-3)*(4*x-9)  =>

solution = {3/2, 4/9}   since (4/9 = (3/2)^2, therefore the preceding question is correct.

Answer:

Step-by-step explanation:

7x² - 4x - 3 = 0

Rewrite - 4x as a difference

That's

7x² - 7x + 3x - 3 = 0

Factorize the expression

7x( x - 1) + 3 ( x - 1) = 0

(7x + 3)( x - 1 ) = 0

7x + 3 = 0 x - 1 = 0

7x = - 3 x = 1

x = -3/7

The solutions are

x = - 3/7 or x = 1

Hope this helps you

Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.

Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.

"a to b"

"a:b"

There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).

a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.

The number in a terms ratio quantities of both numbers are to be positive

Answer:

Step-by-step explanation:

2x − 4y = 6   ⇒   2x = 4y + 6

2x = 4y + 6     and    2x + 4y = -10

so:  4y + 6 + 4y = -10

        4y + 6 = -10

         4y = -16

          y = -4

2x = 4(-4) + 6 = -8 + 6 = -2  

2x = -2   ⇒  x = -1

Answer:

Step-by-step explanation:

To find the hypotenuse we use Pythagoras theorem which is given by

a² = b² + c²

where a is the hypotenuse

So we have

a² = 10² + 3²

a² = 100 + 9

a² = 109

Hope this helps you

Answer:

10.4

Step-by-step explanation:

Answer:

44.8

Step-by-step explanation:

cos α = adjacent leg/hypotenuse

cos 48° = 30/x

x = 30/(cos 48°) = 44.8

Answer:

The number of doughnuts left over are 8 doughnuts

Step-by-step explanation:

The information given are;

The number of doughnuts fried per batch = 20 doughnuts

The number of doughnuts contained in a pack = 13 doughnuts

The number of doughnut batches just fried = 20 batches

The number of packs filled = 44 packs

The number of packs filled with the fried = 44 packs

The number of doughnuts per pack = 13 doughnuts

The number of doughnuts in the pack = The number of packs filled with the fried × The number of doughnuts per pack

The number of doughnuts in the pack = 44 × 13 = 572 doughnuts

Given that the number of batches of doughnuts fried = X batches and the amount of left over = Y doughnuts, where each batch contains 20 doughnuts, we have;

Number of doughnuts fried = Number of batches of doughnuts fried × Number of doughnuts per batch

Number of doughnuts fried = X × 20 =20×X doughnuts

Therefore we have;

Number of doughnuts fried = The number of doughnuts in the pack + The number of doughnuts left over

Which gives;

20×X = 572 + Y where Y < 20

Checking we have multiples of 20 are 560, 580

Given that 520 is the next multiple of 20 after 572, we have;

The number of doughnuts fried = 580 and the number of left over = 580 -  572 = 8 doughnuts.

Answer:

The answer is

Step-by-step explanation:

-31p+79 > -59p+81

Group like terms

Send the constants to the right side of the expression and those with variables to the left side

That's

- 31p + 59p > 81 - 79

Simplify

We have

28p > 2

Divide both sides by 28

We have the final answer as

Hope this helps you

Answer:

C. all whole numbers

Step-by-step explanation:

Well Roberts can’t have a negative income and due to the number of violins being whole numbers, it is impossible to have 2.273 violins.

Hence, the annual income can only be whole numbers

Answer:

c

Step-by-step explanation:

Answer:

The speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.

Since the wind is moving south east, it is at 45 south of east or a bearing of 135.

Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles

Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles

The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles

The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles

The total vertical displacement of the plane is 176.64 miles - 42.43 miles =   134.21 miles

The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles

The direction of this displacement is thus

Ф = tan⁻¹(total vertical displacement/total horizontal displacement)

= tan⁻¹(134.21/62.43)

= tan⁻¹(2.1498)

= 65.05°

= 65.1° to the nearest tenth degree.

The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.

So the speed is 74.0 miles per hour and the angle is 65.1° north-east

Answer:

Step-by-step explanation:

to decrease a number by 40% i would do

100% = number you got

50% divide by 2

10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%

then take the 40% away from the 100%

hope this helps :)

Answer:

2πr + 4a = 8

Step-by-step explanation:

Answer:

H. 1/9.

Step-by-step explanation:

The area of a circle is calculated by solving for π[tex]r^2[/tex].

The smallest circle has an area of π[tex]1^2[/tex] = π * 1 = π.

The middle ring will then have an area of π[tex]2^2[/tex] - π = π * 4 - π = 4π - π = 3π.

The largest ring will then have an area of π[tex]3^{2}[/tex] - π[tex]2^{2}[/tex] = 9π - 4π = 5π.

5π + 3π + π = 9π

So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.

Your answer is H. 1/9.

Hope this helps!

Answer:

I think that it should be

[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

I am done .

I think that it should be

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

{a}^{3}  +  {b}^{3}  +  {c}^{3}   - 3abc = (a + b + c)(  {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca)

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

I am done .