Find the equation of the linear function represented by
the table below in slope-intercept form.

The length of the steel band that fastens the three 2-ft cylindrical drums is (6 + 2·π) ft

A cylinder is a three dimensional solid with a horizontal circular cross-section and a vertical rectangular cross section, such that the sides of the cylinder are parallel.

Number of drums = 3 drums

The diameter of each drum = 2-ft

The cross-section of each drum = A circle

The distance between two poinrts of tangency of the steel band = 2 × The radius = The diameter of each drum

Distance between two points of tangency = 2 ft.

The number of distances between two points of tangency on the cylinders = 3

The length of the steel band that curves round each circle is found as using the formular for finding the length of an arc of a circle, as follows;

Angle made at the center of the circle = 90° + 30° = 120°
Length of the arc with angle 120° at the center is therefore;

Length of arc = (120/360)× 2 × π × 1 = (2/3)·π

The total length of the band = 3 × 2 + 3 × (2/3·π) = 6 + 2·π

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Answer:

its C i just did it

Step-by-step explanation:

On applying the formula of perimeter the width of Lewis's cage is obtained as 14.86 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

Mathematically, the perimeter of a rectangle can be calculated by using this formula -

P = 2(L + W)

Where -

P represents the perimeter of a rectangle.

L represents the length of a rectangle.

W represents the width of a rectangle.

For the perimeter of Becky's rectangular cage, calculate the value -

Perimeter, P = 2(L + W)

Substituting the values and solving the equation -

Perimeter, P = 2(15 + 11)

Perimeter, P = 2(26)

Perimeter, P = 52 inches.

For the perimeter of Lewis's rectangular cage, the value given is -

Length of Lewis's rectangular cage is 0.75 times the length of Becky's cage.

L = 0.75W

The value for perimeter will be -

Perimeter, P = 2(L + W)

Solving the equation -

52 = 2(0.75W + W)

26 = (0.75W + W)

1.75W = 26

Width, W = 26/1.75

Width, W = 14.86 inches.

Therefore. the value for width is obtained as 14.86 inches.

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The height of the building, h, found using ratios between similar figures and within similar figures is as follows;

1. The scale factor, r = 17/6

The height of the building is 99 1/6 meters

2. The within figure ratio is 35/60 = h/170

Heiught of the building is 99 1/6 meters

3. The between figure ratio is 35/h = 60/170

Height of the building is 99 1/6 meters

4. The measure of the angle at the top of the building is 60°

Similar triangles are triangles that have corresponding sides that are proportional, such that the sides of each triangle are a constant multiple of the sides of the other.

The distance from the flagpole = 60 meters

Height of the flagpole = 35 meters

The distance from the building = 170 meters

1. The height of the building found using a scale factor is as follows;

The scale factor, s.f. is the know ratio of the distance from the building to the distance from the flagpole

Therefore; s.f. 170/60 = 17/6

The height of the flagpole is 35 meters

Height of the building = Height of the flagpole × Scale factor

Height of the building = 35 m × 17/6 = 99 1/6

The height of the building found using scale factors is 99 1/6 meters

3. The height of the building found using ratios within the two triangles is found as follows;

The triangles are similar, therefore, their interior angles are congruent, and the trigonometric ratios of the angles are the same.

Within the two triangles, we get;

[tex]\frac{Height \ of \ flagpole}{Distance \ from \ flagpole} = \frac{Height \ of \ building}{Disrtance \ from \ building}[/tex]

35/60 = h/170

h = 170 × (35/60) = 99 1/6

Height of the building = 99 1/6 meters

3. The triangles formed with the flagpole and the triangle formed with the building are similar triangles, therefore;

Between the two triangles, we get

[tex]\frac{Height \ of \ the \ flag[pole}{Height \ of \ the \ building } =\frac{Distance \ from \ the \ flagpole}{Distance \ from \ the \ building}[/tex]

Plugging in the known values, we get;

[tex]\frac{35}{Height \ of \ the \ building} = \frac{60}{170}[/tex]

Height of the building = 35 × 170/60 = 99 1/6

The height of the building is about 99 1/6 meters

4, The triangle formed by the flagpole and the building are similar, therefore, the corresponding angles in the triangles are congruent

The angle at the top of the flagpole corresponds with the angle at the top of the building, therefore;

The angle formed at the top of the flagpole is congruent to the angle formed at the top of the building

The measure of corresponding angles are the same, therefore, the anglle at the top of the building is equal to the angle at the flagpole, which is 60°

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The total number of feathers lost in 14 days if you lose 30 feathers every hour is 10,080 feathers.

Feathers lost every hour = 30 feathers

How many feathers is lost in 14 days?

1 day = 24 hours

14 days = 24 × 14

= 336 hours

Total number of feathers lost in 14 days = Feathers lost every hour × number of hours in 14 days

= 30 × 336

= 10,080 feathers

Therefore, the total number of feathers lost in 14 days is 10,080 feathers

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The nightly cost before tax is added is given as follows:

$225.

The nightly cost is obtained applying the proportions in the context of this problem.

The sales tax of 8% means that the total cost is of 108% = 1.08 of the nightly cost x.

As the total cost was of $243, this means that the equation to obtain the value of x is given as follows:

1.08x = 243.

Solving the equation, the nightly cost before tax is added is given as follows:

x = 243/1.08

x = $225.

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In order to write a ratio as a fraction, use a ratio to fraction. When two things are compared in terms of quantity, the ratio is used.

5 : 7 = 5/7  ≅ 0.7142857.

E.g.

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Answer:

  C- The range is the set of all real numbers greater than -4

Step-by-step explanation:

You want an appropriate description of a decreasing exponential function with a horizontal asymptote of y = -4.

The range of the function is the vertical extent of its graph. This exponential function extends from y = -4 to y → +∞.

The range is the set of real numbers greater than -4.

__

Additional comment

The domain is the horizontal extent of the graph. The arrows on the ends of the curve show it extends to infinity in both directions.

The value y=-4 is not actually part of the range. The function comes arbitrarily close to that value, but is never actually that value.

An exponential function is one that has the generic formula y = abx, where a 0, b a positive real number, and b 1. Base b is always the same for exponential functions. In a situation where the set of real numbers is the domain, the exponent x is the independent variable.

4x = 40.5 = 2

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The value for base side is obtained as x = 84.149 yd.

What are trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec) are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

It is seen in the diagram that the above angle with 16° forms a right angle.

Hence, the θ value will be -

90° - 16° = 74°

Now apply the formula for trigonometric ratio sec θ-

sec θ = Hypotenuse/Base

sec 74°= 490/x

x = 490/5.823

x = 84.149

Therefore, the length for x is 84.149 yd.

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The solution of the inequalities is as follows:

1. x > 3

2. x > - 1

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequalities as follows:

-3x + 18 < x + 6

subtract x from both sides of the inequalities

-3x + 18 < x + 6

-3x - x + 18 < x - x + 6

-4x + 18 < 6

subtract 18 from both sides of the inequalities

-4x + 18 < 6

-4x + 18 - 18 < 6 - 18

-4x < -12

divide both sides by -4

x > 12 / 4

x > 3

Let's solve the second inequality

8x - 6 > -3x - 17

8x + 3x > -17 + 6

11x > - 11

divide both sides by 11

x > - 11 / 11

x > -1

The solution are as follows:

1.  x > 3

2. x > -1

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Answer:

x = 4

Step-by-step explanation:

to find the value of x that satisfies both equations, solve them simultaneously.

x + y = 5 → (1)

2x - y = 7 → (2)

add (1) and (2) term vy term to eliminate y

3x + 0 = 12

3x = 12 ( divide both sides by 3 )

x = 4

p+5 is the  algebraic expression for 5 plus a number p

An expression is combination of variables, numbers and operators.

The given sentence is 5 plus a number p

In the given sentence the number p is a variable.

variable is a symbol used to represent a number.

algebraic expression for 5 plus a number p

p+5

Hence, p+5 is the  algebraic expression for 5 plus a number p

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Answer:

Step-by-step explanation:

45436

Answer:

Step-by-step explanation:

A

The value of function f (m + 1) is,

⇒ f (m + 1) = 1 - 3m

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function are,

⇒ f(x) = 4 - 3x

⇒ g(x) = 2x² - 3x + 1

Now, To find the value of f (m + 1), we can substitute the value of x = m + 1 in equation (i), we get;

⇒ f (x) = 4 - 3x

⇒ f (m + 1) = 4 - 3 (m + 1)

⇒ f (m + 1) = 4 - 3m - 3

⇒ f (m + 1) = 1 - 3m

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The result for given linear equations will be 10x=7 i.e. A.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Given 3x+y=3 -->  1

x-3y=-2           -->  2

Multiply linear equation 1 with 3 and add in equation 2

9x+3y+x-3y=9-2

Hence,

10x=7

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A locus, or point, line, or moving surface, is a curve or other shape created in mathematics by all the points that meet a specific equation describing the relationship between the coordinates.

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Liliana is right. A tuple of numbers a, b, c, and d that has the formula a2 + b2 + c2 = d2 is known as a Pythagorean quadruple.

Liliana is right. A tuple of numbers a, b, c, and d that has the formula a2 + b2 + c2 = d2 is known as a Pythagorean quadruple.

They are Diophantine equation solutions, and frequently, only positive integer values are taken into account.

Pythagorean triples are limitless in number. Anytime 2 n + 1 is a square, a Pythagorean triple is formed.

There exists an endless number of Pythagorean triples since 2 n +1 includes all odd integers, every other square number is odd, and there are an unlimited number of odd squares.

(4, 5, 20, 21} should work, or (1, 2, 2, 3}.

[tex]4^{2} + 5^{2} + 20^{2} = 21^{2}[/tex]

[tex]1^{2} + 2^{2} + 2^{2} = 3^{2}[/tex]

so Liliana is right.

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Typically, you could just apply the equations x = r(cos(degrees °)), y = r(sin(degrees °)) to obtain the x, y coordinates on a circle with a known radius and angle.

Three angles in parallel lines facts—alternate angles, co-Interior angles, and matching angles—are used to accomplish this. often referred to as "Z angles." known as "C angles" at times.

The slope-intercept form of a straight line is represented by the equation y = mx + b. In this instance, the points' coordinates are x and y, the gradient is m, and the y-axis' intercept is b.

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1.19 is the cost to download a single song.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that The proportional relationship between the number of songs Nachelle downloads, s, and the total cost in dollars and cents, c, can be represented by the equation c=1.19s

c equal to one point one nine s.

We need to find the cost to download a single song

so s=1

c=1.19×1

c=1.19

Hence, 1.19 is the cost to download a single song.

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Answer:

(-1)/3

Step-by-step explanation:

Simplify the following:

1/6 - 1/2

Put 1/6 - 1/2 over the common denominator 6. 1/6 - 1/2 = 1/6 - 3/6:

1/6 - 3/6

1/6 - 3/6 = (1 - 3)/6:

(1 - 3)/6

1 - 3 = -2:

(-2)/6

The gcd of -2 and 6 is 2, so (-2)/6 = (2 (-1))/(2×3) = 2/2×(-1)/3 = (-1)/3:

Answer: (-1)/3

Answer:

-0.3333

Step-by-step explanation:

According to triangle proportionality theorem:If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

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The angle between Point B and Point A is 0-45° below the horizontal.

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For the given expression, y = a/√4x-b, the range for values of x is, ( -∞, b/4)  ( b/4, ∞)

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression, y = a/√4x-b

by comparing denominator equal to zero,

⇒  4x - b = 0

⇒   x =  b/4

It will be defined for all the values of  x, except, x = b/4

So, the given expression will give definite value for this interval,

x ∈ ( -∞, b/4) , x ∈ ( b/4, ∞)

Hence, The range of values of x is ( -∞, b/4)  ( b/4, ∞)

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x < 0 shows actually the negative side of the x- axis.

x > 2 shows actually the positive side of the x- axis after x = 2 point.

Graph are shown below.

This can be solved using the concept of inequality.

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

There are four fundamental types of inequality: less than ( < ), larger than(>), less than or equal to ( ≤ ), and more than or equal to( ≥ ).

Here, x < 0 shows actually the negative side of the x- axis.

x > 2 shows actually the positive side of the x- axis after x = 2 point.

The graph is attached in the below for better understanding.

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The surface area of the cylinder with diameter 3 cm is 8.4 π cm²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the first cylinder be A

Let the second cylinder be B

Now , the radius of first cylinder r₁ = 8/2 = 4 cm

The radius of second cylinder r₂ = 3/2 = 1.5 cm

Since the two cylinders are similar ,

Area of cylinder 1 / Area of cylinder 2 = ( r₁ / r₂ )²

Substituting the values in the equation , we get

60π / B = ( 4/1.5 )²

On simplifying the equation , we get

60π / B = 7.111

Multiply by B on both sides of the equation , we get

B = 60π / 7.11111

B = 8.4375 π cm²

Hence , the area of second cylinder B = 8.4 π cm²

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Answer: 6 students

A way to solve for this is to use this equation:

(s = number of students)

40 + (30 × s) = amount of money the tutor was paid.

Inserting 6 into the equation, it would look like this:

40 + (30 × 6) = 220

Therefore, the tutor taught 6 students.

Answer:(3.33, 1.67)

Step-by-step explanation: