(9.5 minus 3 times 1 and one-half) divided by 0.5 0.5 5 10 19.5

Answer:

x = 6

Step-by-step explanation:

  3          1

- ---- =  - ---- x

   4          8

   3          1

-  ---- =  - ---- x

    4          2³

   3          x

- ----  =  - ----

   4          2³

x = 6

Answer:

Step-by-step explanation:

[tex]f(x)=1-3x\\f(-2) = 1-3(-2)\\= 1+6\\=7[/tex]

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:

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:  ∠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:

a) la altura es de 1.6 metros

b) contendría 3750 litros

Step-by-step explanation:

1000 litros = 1m³

8000 litros = 8000/1000 = 8m³

La formula del volumen de un prisma rectangular es:

v = área de la base * altura

el área de la base es:

ab = 2.5m * 2m = 5m²

entonces:

v = 5 * altura

v = 8m³

así que:

8m³ = 5m²* altura

altura = 8m³/5m²

altura = 1.6 metros

1 metro = 100 centímetros

75 cms = 75/100 = 0.75 metros

entonces:

volumen = 5m² * 0.75m

volumen = 3.75m³

3.75m³ = 3.75*1000 = 3750 litros

El agua que contendría sería de:

3750 litros

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: 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. 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:

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

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:

306 miles

Step-by-step explanation:

68 divided by 2 is 34

34 times 9 equals

Answer:

306 miles

Step-by-step explanation:

68 divided by 2 = 34

a.k.a. 34 miles a gallon

34 times 9 miles = 306 miles

William's car can travel 306 miles with 9 gallons in its tank.

the answer is A right

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

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

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

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)

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: 15 rows with 45 seats each

Step-by-step explanation:

Let x = the number of rows, then 3x= the number of seats in a row.

                                   seats × row= total

                                            3x × x=675

                                                3x²=675

                                                  x²=225

                                                   x=15

Answer:

Step-by-step explanation:

let the number of rows=x

seats in each row=3x

so number of seats=x(3x)=3x²

3x²=675

x²=225

x=15

number of rows=15

and seats in each row=15×3=45

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:

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:

y = 2x - 5

Step-by-step explanation:

y = 2x - 5 is in the form

y = mx + b

which is the slope-intercept form.

Answer: Answer below :)

Answer:

r = 3

Step-by-step explanation:

Here in this question, we are told that the surface area of the sphere varies directly as square of radius;

The first thing to do here is to assign variables;

let s be the surface area and r be the radius;

Now;

Since it is a direct proportional relationship;

s = k•r^2

where k represents the constant of proportionality.

now, let’s get k at first.

From the first part of the question, s = 16 and r = 2; Substituting this, we have

16 = k•2^2

4k = 16

k = 16/4

k = 4

Now from the second part of the question, we want to find r when s = 36

Let’s rewrite our equation;

s = k•r^2

where in this case, r = ? and s = 36

36 = 4 * r^2

4r^2 = 36

r^2 = 36/4

r^2 = 9

r = √9

r = 3

Kindly note we do not pick the negative square root value as radius cannot be negative

The surface area of the sphere when the radius is 5 inches is [tex]100\pi[/tex] and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the surface area S of the sphere:

Step 1 - According to the given data, the surface area S of the sphere varies directly as the square of the radius.

Step 2 - The mathematical expression of the above statement is:

[tex]\rm S= k\times r^2[/tex]    --- (1)

where k is the proportionality constant.

Step 3 - Now, substitute the value of r and S in the above expression.

[tex]\rm 36\pi=k \times 3^2[/tex]

[tex]\rm k = 4\pi[/tex]

Step 4 - Now, substitute the value of [tex]\rm k = 4\pi[/tex] and r = 5 in the expression (1).

[tex]\rm S = 4\pi \times 5^2[/tex]

[tex]\rm S = 100\pi[/tex]

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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.

Answer:

True

Step-by-step explanation:

A perpendicular bisector may be defined as the line segment that intersects some other given line perpendicularly and it also divides it into two congruent or equal parts. Now, two lines are said to be cut at right angles or perpendicular to each other if they intersect in a way that they form ninety degrees to each other.

Constructing a line bisector.

1. Take any line segment of any length.

2. Take your compass and adjust its length to more than the half of the length of the line segment.

3. Placing the compass pointer on one edge at a time cut arcs above and below the line segment.

4. Now mark the points where both opposite arcs meet and join the point to cut the given line segment in two equal parts.

Thus the bisector will divide the line into two equal line segments and it will be at right angles to the given line segment.

Thus it is true that constructing a line bisector is also constructing a perpendicular bisector of the line segment.

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:

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:

8

Step-by-step explanation:

1/4πr² + (2x4) - 1/4πr²

r = 4

8