Solve the equation
(please show work if possible)

Answer:

  27x^6y^6

Step-by-step explanation:

We assume you want to simplify ...

  [tex](3x^2y^2)^3=3^3x^{2\cdot3}y^{2\cdot3}=\boxed{27x^6y^6}[/tex]

__

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

They are on the same side of the transversal cut (both to the left of the transversal) and they are both above the two black lines. It might help to make those two black lines to be parallel, though this is optional.

Other pairs of corresponding angles could be:

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

They are between the black lines, so they are interior angles. They are on alternate sides of the blue transversal, making them alternate interior angles.

The other pair of alternate interior angles is angle 4 and angle 6.

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

Similar to alternate interior angles, but now we're outside the black lines. The other pair of alternate exterior angles is angle 2 and angle 8

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

The other pair of same-side interior angles is angle 4 and angle 5. They are interior angles, and they are on the same side of the transversal.

Answer:  ∠TRa = 30°, ∠aRA = 90°, ∠TRA = 120°

Step-by-step explanation:

I'm not sure if you need the angle of the left triangle only (= 30°)

or if you need the the triangle plus the rectangle (= 120°)

Left Triangle (∠TRa)

The hypotenuse is twice the base so it is a 30° - 60° - 90° triangle

where the base corresponds to the 30° angle.

Rectangle (∠aRA)

A rectangle has four right angles --> four 90° angles.

Angle Sum Theorem

∠TRA = ∠TRa + ∠aRA

          = 30° + 90°

          = 120°

Answer:

b=5

Step-by-step explanation:

-b - 19 = -3b – 9

Add 3b to each side

-b+3b - 19 = -3b+3b – 9

2b -19 = -9

Add 19 to each side

2b-19+19 = -9+19

2b = 10

Divide by 2

2b/2 =10/2

b=5

Answer:

The distance between the grocery store and the school is 4 miles.

Step-by-step explanation:

Given that each point is represented in rectangular form. The staight-line distance ([tex]d[/tex]) between two points on a plane is given by the Pythagorean Theorem:

[tex]d =SF\cdot \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex]

Where:

[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Horizontal locations of points A and B, dimensionless.

[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Vertical locations of points A and B, dimensionless.

[tex]SF[/tex] - Scale factor, measured in miles.

If [tex]SF = 1\,mi[/tex], [tex]A = (6, 4)[/tex] and [tex]B = (6,8)[/tex], the straight line distance is:

[tex]d = (1\,mi)\cdot \sqrt{(6-6)^{2}+(8-4)^{2}}[/tex]

[tex]d = 4\,mi[/tex]

The distance between the grocery store and the school is 4 miles.

Answer:

The actual area is 44,825 mi², and the actual population density of Ohio is 282.3 people per square mile.  I can't answer the estimate part because I don't know what your estimate was.  But you can say my estimate was greater than the actual number or less than the actual number.  And you can say your estimate was greater/less than the actual population density because I didn't know so many people were in each square mile because a square mile isn't that large.

Step-by-step explanation:

Can't really explain this type of question. :v

Step-by-step explanation:

Using distance formula: { origin is (0,0)}

√(x - 0)² + (y - 0)²

√x² + y²

The distance between the origin and the point P(x,y) is √(x² + y²).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The distance between the origin (0,0) and the point P(x,y) is calculated as below:-

Distance = √(x - 0)² + (y - 0)²

Distance = √(x² + y²)

Therefore, the distance between the origin and the point P(x,y) is √(x² + y²).

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Answer:

Step-by-step explanation:

[tex]d = \frac{m}{V} \\Cross\:Multiply\\\\dV = m\\\\Divide\:both \:sides \:of\:the\:equation\:by\:d\\\\\frac{dV}{d} = \frac{m}{d} \\\\\\V = \frac{m}{d}[/tex]

Answer:

8640 m, or 8.64 km, assuming it flew in a straight line

Step-by-step explanation:

Distance = rate (or speed) * time (d = rt)

The rate is 4 m/s and the time is 2160 s.

d = rt

d = 4 * 2160

d = 8640 m, or 8.64 km, assuming it flew in a straight line

Answer:

x = 6

Step-by-step explanation:

  3          1

- ---- =  - ---- x

   4          8

   3          1

-  ---- =  - ---- x

    4          2³

   3          x

- ----  =  - ----

   4          2³

x = 6

Answer:

  1.1783

Step-by-step explanation:

The attached picture shows a cross section of the cylindrical shell that it is convenient to use as a differential of the volume. The radius from the center of revolution is (1-x), so the circumference of the shell is 2π(1-x). Of course, its height is tan(x), so the differential of volume is ...

  dV = 2π(1-x)tan(x)

The indefinite integral does not have a nice closed-form solution, but it can be easily integrated numerically from x = 0 to 1 by most scientific and graphing calculators. The attached shows the volume to be about 1.1783 cubic units.

Answer:

g= 6

j = 2

r= 4

Step-by-step explanation:

Gummy bears = $1.50 per pound

Jelly beans = $1.00 per pound

Runt = $1.00 per pound

Total cost of the mixture = $15.00

Let

g = quantity of gummy bears

j = quantity of jelly beans

r = quantity of runts

g + j + r=12 (1)

1.5g + 1.0j + 1.0r = 15 (2)

three times as many gummy bears as jelly beans.

g=3j

Substitute g=3j into 1

g + j + r = 12

3j + j + r =12

4j + r =12 (3)

Substitute g=3j into 2

1.5g + 1.0j + 1.0r = 15

1.5(3j) + 1.0j + 1.0r =15

4.5j + 1.0j + 1.0r = 15

5.5j + 1.0r =15 (4)

4j + r =12 (3)

5.5j + 1.0r =15 (4)

Subtract (3) from (4)

5.5j - 4j = 15-12

1.5j = 3

Divide both sides by 1.5

j = 3/1.5

= 2

j = 2

Substitute j = 2 into (3)

4j + r =12

4(2) + r =12

8 + r = 12

r= 12-8

r= 4

Substitute j=2 and r= 4 into (1)

g + j + r=12

g + 2 + 4 = 12

g + 6 = 12

g = 12-6

=6

g=6

g= 6

j = 2

r= 4

Answer:

[tex]Mean = 69[/tex]

[tex]Mode = 66[/tex]

[tex]Median = 69[/tex]

Step-by-step explanation:

Given

The frequency table

Required

Determine the mean, median and mode

Calculating Mean

[tex]Mean = \frac{\sum fx}{\sum f}[/tex]

Where

fx = product of frequency and inches

f = frequency

So;

[tex]Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}[/tex]

[tex]Mean = \frac{1587}{23}[/tex]

[tex]Mean = 69[/tex]

Calculating Mode

[tex]Mode = 66[/tex]

Because it highest frequency of 4

Calculating Median

[tex]Median = \frac{\sum f}{2}th\ position[/tex]

[tex]Median = \frac{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}{2}th\ position[/tex]

[tex]Median = \frac{23}{2}th\ position[/tex]

[tex]Median = 11.5th\ position[/tex]

Approximate

[tex]Median = 12th\ position[/tex]

At this point we, need to get the cumulative frequency (CF)

Inches ---- Frequency ---- CF

63 -------------2------------------2

65 -------------1------------------3

66 -------------4------------------7

67 -------------3------------------10

68 -------------1------------------11

69 -------------2------------------13

70 -------------2------------------15

71 -------------1------------------16

72 -------------3------------------19

74 -------------2------------------21

75 -------------2------------------23

From the above table

Since the median fall in the 12th position, then we consider the following data

69 -------------2------------------13

because it has a CF greater than 12

Hence;

[tex]Median = 69[/tex]

Answer:

x = 122

Step-by-step explanation:

Step 1: State what is known

In the picture we can see they marked ∠ABC with a box meaning it is a 90° angle, given that information we can now solve

Step 2: Solve

∠ABC = x - 32

90 = x - 32

90 + 32 = x

122 = x

Therefore 'x' is equal to 122

Answer:

a) La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km

b) El perímetro del área = 84,823 km

El área de la tierra = 572.555 km²

Step-by-step explanation:

a) La distancia desde el punto del borde más cercano a la posición del escáner viene dada por la fórmula de Pitágoras;

r = √a² + b²

Por lo tanto, la distancia = √ (10² + 5²) = √125 = 5 · √5 km

La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km

b) El perímetro está dado por la fórmula para el perímetro de un círculo que es, perímetro, s = π × D

Dónde;

D = El diámetro de la tierra = 27 km.

El perímetro = π × 27 = 84.823 km

El perímetro del área = 84.823 km

El área está dada por la fórmula del área de un círculo = π × D² / 4

El área = π × 27² / 4 = 572.555 km²

El área de la tierra = 572,555 km².

Answer:

Perimeter is irrational

Step-by-step explanation:

The attachment is missing but the question is still answerable

Given

[tex]Area = 24200 yd^2[/tex]

Required

Determine if the Perimeter is rational or not

First, we need to determine the sides of the square;

[tex]Area = Length * Length[/tex]

Substitute [tex]Area = 24200 yd^2[/tex]

[tex]24200 = Length * Length[/tex]

[tex]24200 = Length^2[/tex]

Take Square root of both sides

[tex]\sqrt{24200} = Length[/tex]

[tex]Length = 155.563492[/tex]

The perimeter of a square is calculated as:

[tex]Perimeter = 4 * Length[/tex]

[tex]Perimeter = 4 * 155.563492[/tex]

[tex]Perimeter = 622.253968[/tex]

Because the value of perimeter can't be gotten by dividing two integers, then perimeter is irrational

The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.

In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of

(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s

There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives

(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h

Work Shown:

sin(angle) = opposite/hypotenuse

sin(35) = x/15

15*sin(35) = x

x = 15*sin(35)

x = 8.60364654526569

x = 8.6

Make sure your calculator is in degree mode

Answer:

A

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

the triangle formed by the 2 tangents is isosceles with base angles of 74°

m = 180° - (74 + 74)° = 180° - 148° = 32° ( sum of angles in Δ )

The value of the measured angle of m is 32°.

A tangent of a circle is defined as a single point where a single straight line touches or intersects the circle. A line that never touches the inside of the circle is called a tangent.

The line connecting the outer point will cut the angle between the tangents in bisect and the center are equal to each other.

According to the given figure as

A circle with center O,

Since there are two tangents to the circle drawn from an external point.

therefore the lengths of tangents drawn from an external point to a circle are equal.

So, the triangle formed by the 2 tangents is isosceles with base angles of 74°

We know that sum of angles in the triangle is 180 degrees

So ∠ m = 180° - (74 + 74)°

⇒ ∠ m = 180° - 148°

⇒ ∠ m = 32°

Hence, the value of the measured angle of m is 32°.

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Answer: g(x) =  -(1/2)*x + 3.

Step-by-step explanation:

First, let's define a reflection over the x-axis.

If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).

Now, when we have a function

f(x) = y, the points can be written as:

(x, y = f(x) ) = (x, f(x))

Then, after the reflection over the x-axis, we have:

(x, y = g(x)) = (x, -f(x))

So now we have g(x) = -f(x)

and we know that f(x) = (1/2)*x - 3

then our new function is g(x) =  y = -f(x) = -( (1/2)*x - 3) = -(1/2)*x + 3.

g(x) =  -(1/2)*x + 3.

Answer:

1.5 hours

Step-by-step explanation:

there are 6 hours in between the times of 4 and 10

so 4 sister split up 6 hours equally

to do this, we divide 6 and 4

6/4 = 1.5 hours

each sister can spend 1.5 hours on the computer

Answer:

1 hour and 30 minutes

Step-by-step explanation:

If four sisters get 1 hour each, 2 hours are left.

4 half hours make 2 hours.

Answer:

7+3(-4)(2)= -17

Step-by-step explanation:

7+3(-4)(2)

(-4)*2=-8

∴ 7+3(-8)= 7-24

= -17

Answer:

N= -3

Step-by-step explanation:

Answer:

-3=n or n=-3

Step-by-step explanation:

7+2+4n+3=n+3

9+4n+3=n+3

12+4n=n+3

-3            -3

9+4n=n  

   -4n -4n

9=-3n

______

-3    -3

-3=n or n=-3

Answer:

Sally ends at 3 feet below zero point.

Step-by-step explanation:

Let be [tex]h[/tex] the height with respect to zero point, which is represented by the following sum:

[tex]h = \Sigma_{i=1}^{n} h_{i}[/tex]

Where:

[tex]h_{i}[/tex] - i-th travelled height, measured in feet.

In addition, positive sign means ascension, whereas negative sign means descent.

The statement can be translated into the following mathematical identity:

[tex]h = h_{1}+h_{2}+h_{3}+h_{4}[/tex]

[tex]h = 224\,ft+(-131\,ft)+67\,ft -163\,ft[/tex]

[tex]h = -3\,ft[/tex]

Sally ends at 3 feet below zero point.

the answer is A right

Answer:

1. 80

2. 2400

Step-by-step explanation:

1. what is the change in Dan's total pay for each copy of math is fun he sells?

2. what is Dan's total pay if he doesn't sell any copies of math is fun?

Given

y=80x + 2400

When x=0

y=80(0)+2400

=0+2400

=2400

When x=1

y=80x + 2400

=80(1) + 2400

=80+2400

=2480

change in Dan's total pay for each copy of math is fun he sells is

= 2480 - 2400

=80

2. Dan's total pay if he doesn't sell any copies of math is fun?

y=80x+2400

When x=0

y=80(0)+2400

=0+2400

=2400

Answer:

13x + 3

Step-by-step explanation:

Since there is no value on the left, you just have to simplify this. You always add similar variables together, and the constant is a different value, so 4x + 9x  would result in 13x. 13x + 3 would be the correct simplified answer.

Answer:

13x+3

Step-by-step explanation:

4x+9x+3

You do not add 13x to 3 because 3 does not have an x

Answer:

θ = 36.9°

Step-by-step explanation:

Trigonometric ratios in a right triangle will be,

Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{AC}}{\text{AB}}[/tex]

Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{BC}}{\text{AB}}[/tex]

Tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex] = [tex]\frac{\text{AC}}{\text{BC}}[/tex]

In the picture attached,

Given sides are,

AB = 5 and BC = 4

Therefore, to find the given angle θ only Cosine will be applicable.

Cos θ = [tex]\frac{\text{BC}}{\text{AB}}[/tex]

         = [tex]\frac{4}{5}[/tex]

θ = [tex]Cos^{-1}(0.8)[/tex]

θ = 36.87°

θ ≈ 36.9°

Answer:

8

Step-by-step explanation:

1/4πr² + (2x4) - 1/4πr²

r = 4

8