A cylinder has a radius of 6 inches and is 15 inches tall. What is the approximate volume of the cylinder? Express the answer in terms of pi.

Answer:

sin(B)=cos(90-B)

Step-by-step explanation:

sin(B)=cos(90-B) is a co-function identity.

We can also prove it using the difference identity for cosine.

Let's do that:

cos(90-B)

equals

cos(90)cos(B)+sin(90)sin(B)

0cos(B)+1sin(B)

0+sin(B)

sin(B)

Therefore cos(90-B)=sin(B).

Answer:

So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.

Step-by-step explanation:

I think your function is off... but I can look at your ordered pairs.

(1,10)

(2,50)

(3,250),..

As the x increases by 1 the y is being multiply by a factor of 5 each time.

So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.

Answer:

78

Step-by-step explanation:

The given functions are:

[tex]f(x) = - 2x - 7[/tex]

and

[tex]g(x) = - 4x + 6[/tex]

[tex](f \times g)(x) = f(x) \times g(x)[/tex]

[tex](f \times g)(x) = ( - 2x - 7)( - 4x + 6)[/tex]

When we plug in x=-5, we get:

[tex](f \times g)( - 5) = ( - 4 \times - 5 + 6)( - 2 \times - 5 - 7)[/tex]

[tex](f \times g)( - 5) = ( 20 + 6)( 10 - 7)[/tex]

[tex](f \times g)(5) = ( 26)( 3) =7 8[/tex]

Part a) Total Cost

Total Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.

The total cost is ( $65,000 fixed) + (15,000 x $7.5)

=$65,000+$112,500

=$177,500  

Part b) Total Revenue

Revenue from 1 tire = $25

Total tires recapped = 15000

So, Total revenue = 15000 tires x $25/tire

Total Revenue =$375,000  

Part c) Total Profit

Total Profit = Revenue - Cost

Using the above values, we get:

Profit = $375,000 - $177,500

Profit = $197,500  

Part d) Break-even Point

Break-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:

For break-even point

Cost of recapping x tires = Revenue from x tires

65,000 + 7.5 x = 25x

65,000 = 17.5 x

x = 3714 tires

Thus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.

For this case we have that by definition of vertical translations of functions, it is fulfilled:

Assume [tex]k> 0[/tex]:

To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

In the figure it is observed that:

The original function is [tex]G (x) = x ^ 2[/tex], the function was moved 4 units down. So, the new function is:

[tex]F (x) = x ^ 2-4[/tex]

Answer:

Option B

Answer:

Option B is correct.

Step-by-step explanation:

G(x) = x^2

then f(x) = x^2-4

since the graph is shifted 4 units down because when something is subtracted from the function the graph is shifted down.

that's why f(x) = x^2-4.

Hence Option B is correct.

Answer:

No solutions.

Step-by-step explanation:

The value of y cannot be equal to both -3/2x - 3 and -3/2x + 5.

Answer:

a relation and function ⇒ answer C

Step-by-step explanation:

* Lets revise the relation and the function

- The relation is between the x-values and y-values of ordered pairs.

- The set of all values of x is called the domain, and the set of all values

 of y is called the range

- The function is a special type of relation where every x has a unique y

- Every function is a relation but not every relation is a function

* Lets solve the problem

∵ The graph is a parabola

∵ The parabola is a function because every x-coordinates of the

   points on the parabola has only one y-coordinate

- Ex: some ordered pairs are (-5 , -5) , (-2 , 5) , (0 , 7) , (2 , 5) , (5 , -5)

∵ Every x-coordinate has only one y-coordinate

∴ The graph represents a function

∵ Every function is a relation

∴ The set of ordered pairs in the graph below can be described as

   a relation and function

Answer:

The selling price of each bat is $36.98

Step-by-step explanation:

* Lets explain how to solve the problem

- Nolan buys baseball bats to sell in his store

- Each bat costs him $19.99

- He is using a mark up rate of 85%

- The selling price = cost price + markup

* Lets solve the problem

∵ The cost price of each bat is $19.99

∵ The markup is 85%

- To find the markup multiply its percent by the cost price

∴ The markup = 19.99 × 85/100 = $16.9915

∵ The selling price = the cost price + the markup

∴ The selling price = 19.99 + 16.9915 = 36.9815

* The selling price of each bat is $36.98

Answer:

Slope = -1

Step-by-step explanation:

Use the following formula:

slope (m) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (1 , -3)

(x₂ , y₂) = (3 , -5)

Plug in the corresponding numbers to the corresponding variables. Simplify:

m = (-5 - (-3))/(3 - 1)

m = (-5 + 3)/(3 - 1)

m = -2/2

m = -1

The slope of the line is -1.

~

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We have as data the following points:

[tex](x_ {1}, y_ {1}) :( 1, -3)\\(x_ {2}, y_ {2}): (3, -5)[/tex]

Substituting the values:

[tex]m = \frac {-5 - (- 3)} {3-1}\\m = \frac {-5 + 3} {3-1}\\m = \frac {-2} {2}\\m = -1[/tex]

Thus, the slope is -1.

Answer:

The slope is -1

ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)

[tex] \frac{7}{10} = \frac{4}{x} \\ x = \frac{40}{7} [/tex]

The distance the wall should place its base will be 5.71 feet.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between the wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)

The distance will be calculated as below:-

( 7 / 10 ) = ( 4 / x )

x = ( 10 x 4 ) / 7

x = 5.71 feet

Therefore, the distance the wall should place its base will be 5.71 feet.

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Answer:

The vertex of the function is (1 , 2)

The domain is (-∞ , ∞) OR {x : x ∈ R}

The range is [2 , ∞) OR {y : y ≥ 2}

Step-by-step explanation:

* Lets revise the standard form of the quadratic function

- The standard form of the quadratic function is

  f(x) = a(x - h)² + k , where (h , k) is the vertex point

- The domain is the values of x which make the function defined

- The domain of the quadratic function is x ∈ R , where R is the set

 of real numbers

- The range is the set of values that corresponding with the domain

- The range of the quadratic function is y ≥ k if the parabola upward

  and y ≤ k is the parabola is down ward

* Lets solve the problem

∵ f(x) = 3(x - 1)² + 2

∵ f(x) = a(x - h)² + k

∴ a = 3 , h = 1 , k = 2

∵ The vertex of the function is (h , k)

∴ The vertex of the function is (1 , 2)

- The domain is all the real number

∵ The domain of the quadratic function is x ∈ R

∴ The domain is (-∞ , ∞) OR {x : x ∈ R}

- The leading  coefficient of the function is a

∵ a = 3 ⇒ positive value

∴ The parabola is opens upward

∴ The range of the function is y ≥ k

∵ The value of k is 2

∴ The range is [2 , ∞) OR {y : y ≥ 2}

Answer:

20/45 & 21/45

Step-by-step explanation:

Find a common denominator. What you do to the denominator, you do to the numerator. In this case, the smallest denominator is 45.

(4/9)(5/5) = 20/45

(7/15)(3/3) = 21/45

The two fractions you have is:

20/45 for 4/9

21/45 for 7/15

~

Answer:

20/45 for 4/9  and 21/45 for 7/15

Step-by-step explanation:

The least common denominator of 4/9 is 20/45.

The least common denominator of 7/15 is 21/45.

Answer:

A. 15.

Step-by-step explanation:

9^2 + 12^2

= 81 + 144

= 225.

Taking the square root: we get 15.

The Pythagorean theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The missing side length in the given right-angled triangle is 15. Thus, the correct option is A.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Given the two sides of the triangle, therefore, using the Pythagorean theorem, the third side of the triangle can be written as,

x² = 12² + 9²

x² = 144 + 81

x² = 225

x = 15

Hence, the missing side length in the given right-angled triangle is 15. Thus, the correct option is A.

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Answer:

See explanation

Step-by-step explanation:

Some important information is missing in the question, however I will try to help.

Let us assume the theater is located at (-5,6) and the library is located at (4,1), then we can use the distance formula to find the distance from the Theater to the Library.

The distance formula is given by:

[tex]d = \sqrt{(x_2-x_1) ^{2} +(y_2-y_1) ^{2} } [/tex]

We plug in the values to get:

[tex]d = \sqrt{ {(4 - - 5)}^{2} + {(6 - 1)}^{2} } [/tex]

[tex]d = \sqrt{81 + 25} [/tex]

[tex]d = \sqrt{144} = 12[/tex]

You can plug in the points you have to get the required answer

Answer:

D, √74

Step-by-step explanation:

got it right on odyssey ware

Answer: 14 m

Step-by-step explanation:

8 m + 6 m = 14 m

Answer:

10 cm.

Step-by-step explanation:

We have been given a cuboid. We are asked to find the shortest distance from A to B is the given diagram.

We know that shortest distance from A to B will be equal to hypotenuse of right triangle with two legs 8 meters and 6 meters.

[tex]AB^2=8^2+6^2[/tex]

[tex]AB^2=64+36[/tex]

[tex]AB^2=100[/tex]

Now, we will take square root of both sides of our given equation as:

[tex]AB=\sqrt{100}[/tex]

[tex]AB=10[/tex]

Therefore, the shortest distance from A to B is 10 cm.

Answer:

35 books

Step-by-step explanation:

56/8 = 7

7 x 5 = 35

5/8 of 56 = 35

J.K. Rowling will autograph 35 of the 56 books sold, which is calculated by multiplying the total number of books by 5/8.

To find out how many books J.K. Rowling will autograph, we need to calculate 5/8 of the 56 books sold. Here's the step-by-step calculation:

Find out what 5/8 of the total amount is by multiplying the total number of books (56) by 5/8.

To do this, first multiply 56 by 5, which equals 280.

Then divide that number by 8, which equals 35.

Therefore, J.K. Rowling will autograph 35 books.

Answer:

8/5

Step-by-step explanation:

[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].

Start with the inside first: h(-3).

h(-3) means use the function called h and replace the x with -3.  The expression that is called h is 4-x.

4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.

So the value for h(-3) is 7, or h(-3)=7.

Now this is what we thus far:

[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].

g(7) means use the function called g and replace x with 7.   The expression that is called g is (x+1)/(x-2).

(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.

This is our final answer:

[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].

Answer

Both graphs have the same number of x-intercepts. The graph of the function f(t) = t² has one x-intercept, which is the value of t for which f(t) = t² = 0, and that is t = 0. The graph of the function g(t) = (t - 8)² has also one x-intercept, which is the value of t for which g(t) = 0 and that is t = 8.

The function f(t) = t² is the most simple form of a parabola, so it is considered the parent function. The function g(t) = (t - 8)² is a daughter function of f(t); then, the graph of g(t) is a horizontal translation of the graph of f(t),  8 units to the right, so the number of x-intercepts (the points where the x-axis is crossed or touched by the graph) does not change, it is just their position what changes.

Explanation:

The x-intercepts are the points where the graph of the function touches or crosses the x-axis. They are found by doing the function equal to zero. In this case f(t) = 0 and g(t) = 0.

You can solve easily f(t) = t², as, just by simple inspection, the soluton is t = 0.

Then, when you realize that the function g(t) = (t - 8)² is a horizontal translation (8 units to the right) of the parent function f(t), you can conclude quickly that the number of x-intercepts of both graphs is the same. Thus, uisng the transformation of the parent function, 8 units to the right, you conclude that both the graph of f(t) and the graph of g(t) have the same number of x-intercepts: one.

f rests at (0/0) and grows upwards, so there is only a single x-intercept. g is f moved 3 to the left, so it also only has one intercept but at (-3,0).

Answer:

The value of k is -11

Step-by-step explanation:

If (x+2) is a factor of x3 − 6x2 + kx + 10:

Then,

f(x)=x3 − 6x2 + kx + 10

f(-2)=0

f(-2)=(-2)³-6(-2)²+k(-2)+10=0

f(-2)= -8-6(4)-2k+10=0

f(-2)= -8-24-2k+10=0

Solve the like terms:

f(-2)=-2k-22=0

f(-2)=-2k=0+22

-2k=22

k=22/-2

k=-11

Hence the value of k is -11....

Answer:

7

Step-by-step explanation:

You can use the distance formula, but since both points have the same y-coordinate, they lie on a horizontal line. Just find the difference between the x-coordinates and take the absolute value.

distance = |-3 - 4| = |-7| = 7

Answer:

The distance is:

[tex]d=7[/tex]

Step-by-step explanation:

The distance d between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated using the following formula:

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

In this case the points are:

A (4,2), B (-3,2).

Then the distance is:

[tex]d=\sqrt{((-3)-4)^2 + (2-2)^2}[/tex]

[tex]d=\sqrt{((-7)^2 + (0)^2}[/tex]

[tex]d=\sqrt{49}[/tex]

[tex]d=7[/tex]

Answer:

m<SYD = 106.02°. Reason: alternate exterior angles are equal.

Step-by-step explanation:

Answer:

m<SYD = 106.02°. Reason: alternate exterior angles are equal.

Step-by-step explanation:

The principles of circle geometry dictate that: if chords are equal then their corresponding arcs are equal; if arcs are equal then their chords are equal; and diameters perpendicular to chords bisect the chord. However, some of the proposed arguments in the question are not matching these principles.

The three statements highlighted in this question are the principles of circle geometry.

1. If chords are equal, then arcs are equal: This theorem states that if two chords in a circle are equal in length, then their corresponding arcs (the part of the circumference that the chord subtends) are also equal. If BC = DE as stated, then Arc BC = Arc DE.

2. If arcs are equal, then chords are equal: This is the converse of the first theorem. If two arcs of a circle are equal, then the chords subtending these arcs are equal. However, this principle is not relevant for the condition if AX is perpendicular to BC, then BX = XC.

3. Diameters perpendicular to chords bisect the chord: This theorem states that if a diameter of a circle is perpendicular to a chord, then it bisects the chord. Therefore the statement if Arc BC = Arc DE, then BC = DE is not relevant to this theorem.

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Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 : a ≠ 0, then

The nature of it's roots can be determined by the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

For x² - 4x + 4 = 0 ← in standard form

with a = 1, b = - 4, c = 4, then

b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0

Hence roots are real and equal

This can be shown by solving the equation

x² - 4x + 4 = 0

(x - 2)² = 0

(x - 2)(x - 2) = 0, hence

x - 2 = 0 or x - 2 = 0

x = 2 or x = 2 ← roots are real and equal

Answer:

27,0 the distance away from the school​

Step-by-step explanation:

Apply the formula for equation of a straight line;

y=mx+c where c is the y intercept , and m is the gradient

From the graph, the slope is negative where speed decreases with increase in time

Find the gradient by applying the formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Taking y₁=24, y₂=20, x₁=9, x₂=12

Then;

[tex]m=\frac{20-24}{12-9} =\frac{-4}{3}[/tex]

write the equation of the function as ;

y=mx+c, c=36( the y-intercept when x=0) hence the equation is;

[tex]y=mx+c\\\\y=\frac{-4}{3}x+36[/tex]

To get x-intercept, substitute value of y with 0

[tex]y=mx+c\\\\\\y=-\frac{4}{3} +36\\\\\\0=-\frac{4}{3} x+36\\\\\frac{4}{3}x =36\\\\\\4x=36*3\\\\\\x=108/4=27[/tex]

This means that the x-intercept is 27 ,and this means you will require 27 minutes to cover the whole distance to the school.

Answer:

A: 36,0 the distance away from the school

Step-by-step explanation:

At 0 it means you have spent 0 minutes going to school which means you haven't left the starting point yet.

36 is the distance left (in meters) from your current position and school. This means that the school is 36 meters away from the starting point.

Answer:

Step-by-step explanation:

Let 'c' be the number of child bikes  c=20

and 'a' be the number of adult bikes. a=6

According to the problem  

The restriction of building time for a week is 4c+6a≤120 hours.........(1)

and the restriction of testing time for a week is 4c+4a≤100 hours..........(2)

Lets check whether company can build c=20 and a=6 bikes in a week by putting these values in (1) and (2).

4c+6a≤120 hours.........(1)

4(20)+6(6)≤120

80+36≤120

116≤120 (true)

4c+4a≤100 hours..........(2)

4(20)+4(6)≤100

80+24≤100

104≤100 (true)

Hence,  the company can build 20 child bikes and 6 adult bikes in the week....

Answer:

x can be any value

Step-by-step explanation:

(5^0)^x = 1,

5^0 =1

1^x =1

X can be any value

For this case we have the following expression:

[tex](5^{ 0})^{x} = 1[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^{n * m}[/tex]

Then, rewriting the expression:

[tex]5 ^ 0 = 1[/tex]

Thus, the variable "x" can take any value:

Answer:

The variable "x" can take any value

Answer:

n = 19.

Step-by-step explanation:

If there are x guinea pigs then there are 3/2 x and 2/3 x rats.

So n = x + 3/2 x + 2/3 x

n = 19x / 6

19x = 6n

Let x = 6 , then n = 19*6 / 6 = 19.

Now n and x must be whole numbers so x is 6 and n = 19 are the smallest possible values.

Answer:

n=19

Step-by-step explanation:

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Answer:

5 units

Step-by-step explanation:

According to the given statement  Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.

To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs

The square of the required distance = 4^2+3^2 = 16+9 =25

By taking root of 25 we get:

√25 = 5

Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′  is 5 units. ..

[tex]\bf \begin{array}{lll} term&value\\ \cline{1-2} a_1&128\\ a_2&128r\\ a_3&128rr\\ &128r^2 \end{array}~\hspace{5em}\stackrel{a_3}{128r^2}=\stackrel{a_3}{8}\implies r^2=\cfrac{8}{128}\implies r^2=\cfrac{1}{16} \\\\\\ r=\sqrt{\cfrac{1}{16}}\implies r=\cfrac{\sqrt{1}}{\sqrt{16}}\implies r=\cfrac{1}{4}\qquad \leftarrow \textit{common ratio} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=7\\ a_1=128\\ r=\frac{1}{4} \end{cases}\implies a_7=128\left( \frac{1}{4} \right)^{7-1} \\\\\\ a_7=128\left( \frac{1}{4} \right)^6\implies a_7=128\cdot \cfrac{1}{4096}\implies a_7=\cfrac{128}{4096}\implies a_7=\cfrac{1}{32}[/tex]