I’m a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the variable x create an expression that represents the perimeter of the rectangle.

Answer:

  1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

  B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

  V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

Comment on the geometry

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.

Two nontrivial functions f(x) and g(x) that satisfy the equation f(g(x)) = (-6-3x)^6 are f(x) = x^6 and g(x) = -6 - 3x. These functions were found by assigning the inner function to g(x) and the outer function to f(x).

Looking at the expression [tex]f(g(x)) = (-6-3x)^6[/tex], we can see that it is a composition of two functions. A possible way to choose the functions f(x) and g(x) is to let g(x) be the inner function and f(x) be the outer function.

Let's choose g(x) = -6 - 3x. This function linearly transforms the input x. Now, let's choose the function [tex]f(x) = x^6[/tex]. This function takes any input (including results from the g(x) function) and raises it to the power of 6.

So, when we apply g to x (g(x)) and then f to the result (f(g(x))), we get the original equation[tex]f(g(x)) = (-6-3x)^6[/tex]. Therefore, the two nontrivial functions f(x) and g(x) that satisfy the equation are f(x) = x^6 and g(x) = -6 - 3x.

https://brainly.com/question/17348508

#SPJ3

Answer:

The monthly payment, PMT = $450.71

Therefore the correct option is C.) $450.71

Step-by-step explanation:

i) Value of Loan, or Present value, PV = 24000

ii) Annual percentage rate , APR = 0.048

iii) number of periods, n = 12

iv) periodic interest, R = APR / n  = 0.048 / 12 = 0.004

v) number of years, t = 5

v) Monthly Payment, PMT =  [tex]\frac{PV\times R}{1 - (1 + R)^{(-1\times n \times t})} = \frac{24000 \times 0.004}{1 - ( 1 + 0.004)^{-60}}[/tex] = $450.71

Answer:

The novel has 180 pages.

Step-by-step explanation:

108 pages is 60% of the novel.

108 / 3 = 36.

20% of the novel is 36 pages.

36 * 5 = 180 pages

Step-by-step explanation:

[tex](6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1} [/tex]

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

Answer:

[tex]x^3y^6z^3[/tex]

Step-by-step explanation:

we have

[tex](xy^2z)^3[/tex]

Applying the property of exponents

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

[tex](xy^2z)^3=(x^3)(y^2)^3(z^3)=x^3y^{2*3}z^3=x^3y^6z^3[/tex]

The correct simplification of [tex]\((xy^2z)^3\) is \(x^3y^6z^3\).[/tex]

To simplify the expression [tex]\((xy^2z)^3\),[/tex] you need to raise each component within the parentheses to the power of 3.

[tex]\(x^3\)[/tex] represents \(x\) raised to the power of 3, [tex]\(y^{2 \times 3}\)[/tex] represents [tex]\(y^6\)[/tex] (since you multiply the exponents when raising a power to a power), and [tex]\(z^3\)[/tex]represents \(z\) raised to the power of 3.

So, [tex]\((xy^2z)^3\) simplifies to \(x^3y^6z^3\).[/tex]

The given options are:

[tex]a) \(x^3y^3z^3\)\\b) \(x^3y^6z^3\)\\c) \(x^3y^8z^3\)\\d) \(x^4y^5z^4\)[/tex]

Comparing the simplified expression [tex]\(x^3y^6z^3\)[/tex] with the options, the correct answer is option (b) [tex]\(x^3y^6z^3\).[/tex]

For more such questions on simplification

https://brainly.com/question/18139584

#SPJ3

Final answer:

To find the ratio of red to yellow marbles, given the ratios of red to blue and blue to yellow, we equalize the blue part of both ratios and combine them, resulting in a red to yellow ratio of 2:5.

Explanation:

The question concerns finding the ratio of red marbles to yellow marbles given the ratios of red to blue marbles and blue to yellow marbles. To solve this, we use the given ratios: the ratio of red marbles to blue marbles is 1 : 4, and the ratio of blue marbles to yellow marbles is 2 : 5. Firstly, we make the number of blue marbles consistent in both ratios by finding a common value. Multiplying the first ratio by 2 gives us red to blue as 2 : 8, and keeping the second ratio as is (blue to yellow as 2 : 5), we can now combine these to find the ratio of red marbles to yellow marbles. The red to yellow ratio, through the intermediary blue, becomes 2 : 5.

Answer:

132

Step-by-step explanation:

65+67=132 || 180-132=48 || 180-48=132

Answer:

132 Degrees.

Step-by-step explanation:

The interior of any triangle is 180 degrees.

Solve for angle DBC

65 + 67 = 132

180 - 132 = 48 degrees

Since the sum of DBA and DBC is 180, and we already know what 180 - 48 is, there you have it.

Answer:

Explanation:

Please, find attached an image with the table that accompanies this question.

1. Pattern

The table is:

Years:               2        4       5       8       9

Height (in.):      34      50   58     82    90

The most simple pattern is a linear pattern. A linear pattern has a constante rate of change.

The rate of change between two points is:

Find the rate of change for the data:

Hence, the heigth and the years since the tree was transplantated show a linear relationship: every year the tree grew 8 inches.

2. Intial height:

You can find the initial height of the tree by using the rate of change of the height.

3. Relationship

You can describe the relationship in terms of the initial height and the numbers of years since the tree was transplantated.

Then, the height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.

You can even write an equation (function):

Answer:

  80%

Step-by-step explanation:

The percentage change between two numbers can be calculated as ...

  percentage change = ((new value)/(old value) -1) × 100%

  = (2700/1500 -1) × 100% = (1.80 -1) × 100% = 80%

Traffic volume increased 80%.

Final answer:

It will take 400 minutes for the temperature to decrease by 5°F, calculated by dividing 5°F by the rate of ¾°F/h, resulting in 6.6667 hours, which is then converted into minutes (6.6667 hours × 60 minutes/hour = 400 minutes).

Explanation:

To calculate the time it will take for the temperature to decrease by 5°F, knowing that the temperature decreases at a rate of ¾ of a degree per hour, we can use the following steps:

Divide the total desired temperature decrease (5°F) by the rate of temperature decrease per hour (¾°F/h).

Calculate the total hours required for a 5°F decrease.

Since we want to find the time in minutes, we multiply the hours by 60 (as there are 60 minutes in an hour).

Step 1: 5°F divided by ¾°F/h = 5 ÷ 0.75 = 6.6667 hours
Step 2: 6.6667 hours are needed.

Step 3: 6.6667 hours × 60 minutes/hour = 400 minutes

Therefore, it will take 400 minutes for the temperature to decrease by 5°F.

No if you simplify 27/8 it equals 3 3/8.

Step-by-step explanation: To graph x < 6 on a number line, we start with an open dot at +6. The reason we use an open dot at +6 is that x is less than +6 but it is not equal to +6. Next we drawn an arrow going to the left to show that all numbers less than +6 are solutions to this inequality.

Image is attached below.

The cost of each stone sphere is $ 36.81

Solution:

Given that,

An architect plans to buy 5 stone spheres and 3 stone cylinders

For the same​ amount, she can buy 2 stone spheres and 6 stone cylinders

Let "x" be that same amount

Let "a" be the cost of each stone sphere

Cost of each stone cylinder = $ 36.81

Therefore,

x = 5 stone spheres and 3 stone cylinders

x = 5a + 3(36.81)

Similarly,

x = 2 stone spheres and 6 stone cylinders

x = 2a + 6(36.81)

Equate both,

[tex]5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81[/tex]

Thus cost of each stone sphere is $ 36.81

By setting up and solving equations based on the given scenarios, we find that the cost of each stone sphere is also $36.81, the same as one stone cylinder.

Let's denote the cost of one stone sphere as S and the cost of one stone cylinder as C. We know one stone cylinder costs $36.81. We are given two scenarios involving the purchase of stone spheres and cylinders with equal total cost. In the first scenario, 5 stone spheres and 3 stone cylinders are bought, and in the second, 2 stone spheres and 6 stone cylinders are purchased.

Formulating these scenarios into equations gives us:

Substituting the value of C into the equation simplifies it to:

5S + 3(36.81) = 2S + 6(36.81)

Simplifying further:

5S + 110.43 = 2S + 220.86

Subtracting 2S and 110.43 from both sides results in:

3S = 110.43

Dividing both sides by 3 gives:

S = $36.81

Therefore, each stone sphere also costs $36.81.

Answer:

  see attached

Step-by-step explanation:

The given function is a vertical expansion of the sine function by a factor of 3 and a translation downward by 5 units.

It will oscillate between -8 and -2, with a midline at y = -5. The multiplier 12 indicates the period of the function will be 2π/12 = π/6 ≈ 0.5233... for the given value of π.

A graphing calculator is a useful tool for creating the graph.

Answer:

Step-by-step explanation:

took the test

Answer:

3.6

Step-by-step explanation:

30%×12= 3.6

30%=0.3

Answer:

There are 12 students in Miss Jacobs class.

Step-by-step explanation:

Divided 10.2 and 0.85

If you check your answer. 0.85 multiplied by 12 is 10.2

Answer:

$1575

Step-by-step explanation:

70 % of his salary is 0.7 X 450 = 315

He gets it for 20 weeks

presuming the salary is monthly.

You do 315 X 5 = 1575   20 /4 = 5 months

Answer:

It's the third one

Guaranteed!!

Hence, the graph second is correct.

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here,

[tex]f(x)=-x\\g(x)=2x[/tex]

So,

[tex]g(x)-f(x)=2x-(-x)\\\\(g-f)(x)=2x+x\\\\(g-f)(x)=3x[/tex]

Draw the graph:-

Hence, the graph second is correct.

To know more about the simplification

https://brainly.com/question/12795317

#SPJ2

Elsa's rate of typing = 1.25 words per sec

Time is taken for typing each word = 0.8 a

It is a method of solving by finding the value of one unit and the calculating the value of given unit by multiplying with the single value.

Numbers of words Elsa can type in 1 minute(the 60s)  = 75

Numbers of words Elsa can type in one second = 75/60

∴ Rate of typing = 1.25 words per sec

Time is taken to type one word = 60/75

                                                = 0.8 sec

Learn more about ut unitary method here: https://brainly.com/question/15300456

#SPJ2

Answer:

175 m

Step-by-step explanation:

We are given;

We are required to determine the new perimeter if the sides of the rectangle are multiplied by 7.

We know that;

Perimeter of a rectangle = 2(L+W)

Therefore, initially;

2(L+W) = 25 m

Hence;

L + W = 12.5 m

if the sides are multiplied by 7, then;

New length = 7L

New Width = 7W

Thus;

New perimeter = 2(7L+7W)

                         = 14 (L + W)

but, L + W = 12.5

Thus;

New perimeter = 14 (12.5)

                         = 175 m

Therefore, the new perimeter will be 175 m

Answer:

The answer to the problem is 175

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + 3y = - 28

y = -5x

x + 3(-5x) = -28

x -15x = -28

-14x=-28

x=2

y = -5(2)

y=-10

Answer:

h=18m, b=2m

Step-by-step explanation:

Let the base be b and height be h

Condition 1:

b=2h ----(1)

Condition 2:

Area=b*h

b*h=648 -----(2)

Putting (1) into (2)

2h*h=648

2h^2=648

Dividing both sides by 2

h^2=324

Taking sq root on both sides

h=18 m

Now

Putting value of h in eq (1)

b=2(18)

b=36 m

Answer:

It is a prime number which is either 2 less or 2 more than another prime number

Step-by-step explanation:

Final answer:

The twin prime conjecture posits the existence of an infinite number of twin prime pairs, which are pairs of prime numbers that are two units apart.

Explanation:

The twin prime conjecture is an unsolved question in mathematics that relates to the distribution of prime numbers. It specifically addresses the existence of pairs of primes that are only two numbers apart, such as (11, 13), (17, 19), and (41, 43), which are known as twin primes. The conjecture proposes that there are an infinite number of these twin prime pairs, even though prime numbers themselves become less frequent as numbers increase. Despite many efforts, a definitive proof of this conjecture has not yet been found.

Yo sup??

by angle sum property we know that the sum of all angles in a triangle is 180

let the unknown angle be x

then,

x+60+90=180

x=180-150

x=30

Hope this helps

The sum of the angles of a triangle is 180°.

The angle measures you know are 60° and 90° (because the box in the top right corner of the triangle means that it is a right angle, which equals 90°). So you can do this to find the missing angle:

60° + 90° + ? = 180°    Add 60 and 90

150° + ? = 180°     Subtract 150 on both sides

? = 30°  The missing angle is 30°

Final answer:

To express 0.230769231 as a fraction, the numerator is 230769231 and the denominator is 10^9.

Explanation:

To express the decimal 0.230769231 as a fraction, we need to determine the numerator and denominator. The numerator is the decimal without the decimal point, which is 230769231. The denominator is based on the number of decimal places, which is 9 because there are 9 digits in the decimal part. Therefore, the fraction is 230769231/10^9.

Answer:

Your answer is 9

Step-by-step explanation:

the answer is nine because if you look at the pattern, every number to the left is times 3 to the right. For example, 4 to 12 is times 3. this would work for n because 9x3 equals 27. the rule is times three.

Answer:

There are  10 pigs and 30 chickens

Step-by-step explanation:

Let the number of pigs be x

let the number of chickens be y

Then there are 40 heads . So the total number of pigs and chickens is 40

x + y = 40-----------------------(1)

We know that pigs have 4 legs and chickens have 2 legs

4x + 2y = 100----------------------(2)

Solving (1) and (2)

multiply  (1) by 2

2x + 2y = 80-------------------------(3)

subtract (3) from (2)

4x + 2y = 100

2x + 2y = 80

----------------------------

2x = 20

----------------------------

[tex]x = \frac{20}{2}[/tex]

x = 10

Now Substituting x in (1), we get

10 + y = 40

y = 40 - 10

y = 30