Rob buys 50 feet of border to place around the ceiling of a room. The ceiling is shaped like a square with sides that are 10.8 feet long. How many feet of border will Rob have left?

Answer:

\(32 {x}^{5} + 240 {x}^{4} + 720 {x}^{3} + 1080 {x}^{2} + 810x + 243\)

Answer:

Hope it will help you a lot.

The volume of the pyramid is approximately 937.5 cubic inches (rounded to the nearest cubic inch).

We can use the following formula to determine the regular square pyramid's volume:

Volume = (1/3) * Base Area * Height

First, let's find the side length of the square base, denoted by "s". We know that the length of a lateral edge is 15 inches, and in a regular pyramid, each lateral edge is equal to the side length of the base. Therefore, we have:

s = 15 inches

Next, we need to find the height of the pyramid, denoted by "h". We are given the measure of angle MDO, which is 38 degrees. In triangle MDO, the height is the side opposite to the given angle. To find the height, we can use the tangent function:

tan(38°) = height / s

Solving for the height, we have:

height = s * tan(38°)

height = 15 inches * tan(38°)

Now, we have the side length "s" and the height "h". Next, let's calculate the base area, denoted by "A". Since the base is a square, the area of a square is given by the formula:

A = s^2

Substituting the value of "s", we have:

A = (15 inches)^2

A = 225 square inches

Finally, we can substitute the values of the base area and height into the volume formula to calculate the volume of the pyramid:

Volume = (1/3) * Base Area * Height

Volume = (1/3) * A * h

Substituting the values, we have:

Volume = (1/3) * 225 square inches * (15 inches * tan(38°))

Using a calculator to perform the calculations, we find that tan(38°) is approximately 0.7813. Substituting this value, we can calculate the volume:

Volume = (1/3) * 225 square inches * (15 inches * 0.7813)

Volume ≈ 937.5 cubic inches

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The equation that represents the given situation is aₙ = -750n + 18250.

It is given that,

Jack bought a car for $17,500

The car losses $750 in value each year.

So, the first term is calculated by the expression,

18250 - 750 = 17500

Thus, for the nth term, we can write

18250 - 750n = aₙ

⇒ aₙ = -750n + 18250

Thus, the required equation that represents the situation is aₙ = -750n + 18250.

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Answer:

y = -750x + 17500

Step-by-step explanation:

Since the car loses a constant amount each year, the situation is linear. The initial amount (b) is 17500 and the slope (m) is -750. PF

The geometry of the hybrid orbitals about a central atom with sp³ hybridization is tetrahedral.

When two atomic orbitals join to generate a hybrid orbital in a molecule, the energy of the individual atoms' orbitals is redistributed to give orbitals of equivalent energy.

The geometry of the hybrid orbitals about a central atom with sp³ hybridization is tetrahedral.

In sp³ hybridization, the central atom's s orbital and three p orbitals combine to form four sp³ hybrid orbitals. These hybrid orbitals are arranged in a tetrahedral geometry around the central atom, with bond angles of approximately 109.5 degrees. This geometry allows for maximum separation between the hybrid orbitals, minimizing electron-electron repulsion and optimizing stability.

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Answer:

The expression 2a^2b^2 + 2b^2c^2 + 2a^2c^2 - a^4 - b^4 - c^4 can be factored as:

(2ab^2 + 2bc^2 + 2ac^2)(a^2 - c^2) - (a^2 - b^2)(a^2 - c^2)

= (a^2 + b^2 + c^2)(2ab^2 + 2bc^2 + 2ac^2) - (a^2 - b^2)(a^2 - c^2)

Vector subtraction is done by arranging head to tail.

Vector subtraction is the process of finding the vector that results from taking away one vector from another. To perform vector subtraction, we arrange the vectors head to tail, with the tail of one vector touching the head of the other vector. We then draw a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the difference between the two vectors. This can be mathematically represented as:

a - b = a + (-b)

where "a" and "b" are vectors, and (-b) is the additive inverse of b, which is the vector with the same magnitude as b but opposite in direction.

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For the a pyramid and its net shape:

a. To find the area of each triangle, first find the length of the slant height. Using the Pythagorean theorem:

l = √(5² + 4.5²) = √(47.25) ≈ 6.87 cm

Now find the area of each triangle using the formula:

A = (1/2)bh

where b is the base and h is the height. Since the triangles are isosceles, the base is 5 cm and the height can be found using the Pythagorean theorem:

h = √(l² - (b/2)²) = √(47.25 - 12.25) ≈ 6.31 cm

Therefore, the area of each triangle is:

A = (1/2)(5 cm)(6.31 cm) ≈ 15.78 cm²

b. The area of the square is simply the length of one side squared:

A = (5 cm)² = 25 cm²

c. The total surface area of the pyramid is the sum of the areas of the four triangles and the square base:

A = 4A_triangle + A_square

= 4(15.78 cm²) + 25 cm²

≈ 86.12 cm²

Therefore, the surface area of the pyramid is approximately 86.12 cm².

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Image transcribed:

Unit 4B TGA - Surface Area and Volume

Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Please make sure that you show all the work to support your

answers.

of 15 points

Total score:

(Score for Question 1: of 7 points)

1. Find the surface area of the pyramid. SHOW YOUR WORK and include the units.

5 cm

9 cm

9 cm

5 cm

5 cm

a. Find the area of all 4 triangles. SHOW YOUR WORK and include the units.

b. Find the area of the square. SHOW YOUR WORK and include the units.

c. Find the total surface area of the pyramid. SHOW YOUR WORK and include the units,

Answer:

2/7 of the pie

Step-by-step explanation:

6/7 / 3 = 2/7

Answer:

D

Step-by-step explanation:

Since James gave Malcolm a head start of 20 feet, Malcolm's line should start at 20 feet. So that rules out A. They were obviously going further so they went more feet, So C is ruled out because it shows them not moving, plus James didn't get a 15 foot head start which is what the C graph shows. Finally it's not B because if you look at the key at the bottom of every graph, it says that Malcolm is the dotted line, and B shows James getting a 20 foot head start, not Malcolm.

Hope this helps!

Answer:

18.75 years

Step-by-step explanation:

first multiply the amount to the rate

5,000 × 8% = 400

second

7,500/ 400 = 18.75

it takes 18.75 to reach 7,500

A. We should purchase approximately 259 units of chemical P (p) and approximately 28 units of chemical R (r).

B. The maximum production of chemical Z under the given budgetary conditions is approximately 1,170,846 units.

A)  We can set up the following equation based on the budget constraint:

500p + 2500r ≤ 200,000

The production of chemical Z is given by the equation:

z = 170 * p * r⁰.⁵⁵

p + 5r ≤ 400

Let's define the Lagrangian function L as follows:

L(p, r, λ) = 170 * p * r⁰.⁵⁵ - λ(p + 5r - 400)

∂L/∂p = 170r^0.55 - λ = 0 ...(1)

∂L/∂r = 93.5p * r^(-0.45) - 5λ = 0 ...(2)

∂L/∂λ = -(p + 5r - 400) = 0 ...(3)

From equation (1), we can solve for λ in terms of p and r:

λ = 170r⁰.⁵⁵ ...(4)

Substituting equation (4) into equation (2), we get:

93.5p * r(⁻⁰.⁴⁵) - 5(170r⁰.⁵⁵) = 0

93.5p = 850r

p = (850r) / 93.5

p ≈ 9.085r

Now, substituting this value of p into equation (3), we get:

9.085r + 5r = 400

14.085r = 400

r ≈ 28.419

Substituting this value of r back into the equation for p, we have:

p ≈ 9.085 * 28.419

≈ 258.844

B) The maximum production of chemical Z can be calculated using the given formula:

z = 170 * p * r⁰.⁵⁵

Substituting the values of p and r we found:

z = 170 * 259 * 28⁰.⁵⁵

z ≈ 1,170,845.76

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Answer:

(see first pic attached)

Step-by-step explanation:

Answer:

16 berries

Step-by-step explanation:

The advertisement campaign to promote Ray and Kelsey's roller coaster will be brand awareness and improved communication.

An advertisement campaign simply means a strategy that's used to achieve a desired results regrading a product.

In this case, the advertisement campaign to promote Ray and Kelsey's roller coaster will be brand awareness and improved communication.

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ANSWER

LJ = 2

EXPLANATION

The scale factor is 6, so each side of triangle J'K'L' has a length that is 6 times the length of each corresponding side from triangle JKL:

Replacing L'J'=12 and solving

Answer:

  a) "common multiplier" is 3

  b) both reduce to 1/2

Step-by-step explanation:

  \(\dfrac{30}{60}=\dfrac{3\cdot10}{3\cdot20}=\dfrac{3}{3}\cdot\dfrac{10}{20}=1\cdot\dfrac{10}{20}=\dfrac{10}{20}\)

Perhaps your "common multiplier" is 3. It multiplies both numerator and denominator in 10/20 to give you 30/60.

__

  \(\dfrac{10}{20}=\dfrac{10}{10}\cdot\dfrac{1}{2}=\dfrac{1}{2}\\\\\dfrac{30}{60}=\dfrac{30}{30}\cdot\dfrac{1}{2}=\dfrac{1}{2}\)

The simplest form of both fractions is 1/2.

Answer:

\(\left[A]\) The ratios \(\frac{10}{20}\) form a proportion by common multiplier 3 to get \(\frac{30}{60}\)

\(\left[B]\) Both ratio are equal to \(\frac{1}{2}\) in simplest form

Step-by-step explanation:

\(\left[A]\) We need to show both fraction of same proportion.

Ratio 1:  \(\frac{10}{20}\)

If we multiply by 3 at numerator and denominator

\(\frac{10*3}{20*3}\)

\(\frac{30}{60}\)

Therefore \(\frac{30}{60}\) is equivalent ratio to second one 30/60

Hence, The ratio 10/20 form a proportion by common multiplier 3 to get 30/60

∴-----------------------------------------------------------------------------------------------------∴

\(\left[B]\) Now we simplify both ration into simplest form

→ \(\frac{10/10}{20/10} =\frac{1}{2}\)

→ \(\frac{30/30}{60/30} =\frac{1}{2}\)

→ \(\frac{1}{2} =\frac{1}{2}\)

Hence, Both ratio are equal to \(\frac{1}{2}\) in simplest form.

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.

Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next term is obtained by adding 13 to the preceding term in the series. To put it another way, a n = a 1 + d (n - 1) This is the arithmetic sequence's formula.

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.

A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An = a + (n - 1)d gives the nth term of an arithmetic series.

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Therefore , the solution of the given problem of surface area comes out to be x cannot equal 24.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.

Here,

The calculation for a square pyramid's surface area is:

=> S = l² + 2lh

where S is the surface area, h is the height of the pyramid, and l is the length of one edge of the square base.

=> l² = 13² = 169

We also know that the pyramid's surface area is 741 square feet, so we can construct the following equation:

=> 741 = 169 + 2(13)(x)

When we condense the right half, we obtain:

=> 741 = 169 + 26x

169 from both parts are subtracted, giving us:

=> 572 = 26x

When we multiply both parts by 26, we get:

=> x = 22

As a result, rather than 24 feet, the pyramid's height is 22 feet.

Thus, x cannot equal 24.

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the weight of the crate is approximately 66.3 lb and the tension in the horizontal rope is approximately 124.6 lb.

We can solve for the weight of the crate and the tension in the horizontal rope by using the principles of vector addition.

Let's call the weight of the crate "W" and the tension in the horizontal rope "T". We know that the tension in the angled rope is 89.6 lb and that the angle between this rope and the horizontal rope is 46° 20′. We can break down the tension force into its vertical and horizontal components using trigonometry:

Vertical component = T * sin(46° 20′)

Horizontal component = T * cos(46° 20′)

The vertical component of the tension force must balance out the weight of the crate, so we have:

W = T * sin(46° 20′)

Now we can substitute this expression for W into the equation for the horizontal component of the tension force:

T * cos(46° 20′) = Tension in the horizontal rope

We can solve for T by dividing both sides by cos(46° 20′):

T = Tension in the horizontal rope / cos(46° 20′)

Plugging in the given value of the tension in the angled rope, we get:

T = 89.6 lb / cos(46° 20′) ≈ 124.6 lb

Finally, we can solve for the weight of the crate by substituting T into the equation we found earlier:

W = T * sin(46° 20′) ≈ 66.3 lb

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Hi! I'm happy to help!

To solve this, we first have to understand the terms and the way they arrange the equation.

First, we have the difference of ____and_____=. (the "is" after 4 refers to equals)

We will write this as:

_______-_______= ,because difference means subtraction.

For our first blank, we have 3 times a number. Because we do not know this number, we will use a variable.(n) 3 times a number is 3 multiplied by a number. We can just write 3n, because it represent multiplication.

3n-______=

Now, we see the part of the equation after the "and". We just see 4, so we can insert that here:

3n-4=

Now, we see what is shown after the "is".

We just have -19, so we can insert that here:

3n-4=-19

Now, let's solve (not sure if I need to):

To solve for n, we have to isolate it on one side of the equation. To do this, let's cancel out the -4 on the left side of the equation by adding 4 to both sides:

3n=-15

From here, we need to get rid of the 3 next to the n by dividing both sides by 3:

n=-5

So, we write it as 3n-4=-19, and n=-5.

I hope this was helpful, keep learning! :D

9514 1404 393

Answer:

  y = -8x +3

Step-by-step explanation:

We don't need the midpoint formula to find the midpoints. We can count grid squares.

B is 2 up from A, and right 4. So, the midpoint of AB is 1 up and right 2 from A, or point (0, 3).

D is down 4 from C, and right 6. So, the midpoint of CD is down 2 and right 3 from C, or point (1, -5).

The vertical difference between the first midpoint and the second is -8. The horizontal difference is +1, so the slope of the line between the midpoints is ...

  m = rise/run = -8/1 = -8

The first midpoint is the y-intercept of the line, so the equation of the line is ...

  y = -8x +3

_____

If you want to use all of the appropriate formulas, you can. The midpoint formula is ...

  M = ((x1, y1) +(x2, y2))/2 = (x1 +x2, y1 +y2)/2

  M = (A +B)/2 = ((-2, 2) +(2, 4))/2 = (0, 6)/2 = (0, 3)

  N = (C +D)/2 = ((-2, -3) +(4, -7))/2 = (2, -10)/2 = (1, -5)

The slope of line MN is ...

  m = (y2 -y1)/(x2 -x1) = (-5 -3)/(1 -0) = -8/1 = -8

The point-slope equation is ...

  y -y1 = m(x -x1)

  y -3 = -8(x -0)

  y = -8x +3 . . . . . .  add 3 to put into slope-intercept form

The basis for addition of whole numbers is the operation of union.

In set theory, the union of two sets A and B, denoted as A ∪ B, is the set that contains all the elements that belong to either A or B, or both. When we think of whole numbers, we can consider each number as a set containing only that number. For example, the set {1} represents the whole number 1.

When we add two whole numbers, we are essentially combining the sets that represent those numbers. The union operation allows us to merge the elements from both sets into a new set, which represents the sum of the two numbers. For instance, if we consider the sets {1} and {2}, their union {1} ∪ {2} gives us the set {1, 2}, which represents the whole number 3.

In summary, the basis for addition of whole numbers is the operation of union. It allows us to combine the sets representing the whole numbers being added by creating a new set that contains all the elements from both sets. This concept of set union provides a foundation for understanding and performing addition operations with whole numbers.

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The base of the original triangle is 25 (option D).

To find the base of the original triangle, we need to reverse the reduction process using the scale factor of 1/5. Since the reduced triangle has a base of 5, we can multiply it by the reciprocal of the scale factor to find the base of the original triangle.

Base of the original triangle = (Base of the reduced triangle) * (Reciprocal of the scale factor)

= 5 * (1/1/5)

= 5 * 5

= 25

Therefore, the base of the original triangle is 25.

The correct option is D. 25.

The complete question is:

If a scale factor of 1/5 is used to make a reduction, what is the base of the original triangle? reduced triangle height 3 base 5 ..original triangle 0 base 0.

A.1

B.10

C.15

D.25

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Answer:

1: x int = (-7,0)

y int = (0,-7)

2: x int = (4,0)

y int = (0,8)

Step-by-step explanation:

Just use a website called desmos. Simply your equation then plug it in.

m=n and C=D, as CD is an nxn matrix and In and Im have dimensions nxn and mxm, respectively.

To prove that m=n, let us consider the dimensions of the matrices involved. The matrix product CD has dimensions nxm times mxn, which gives an nxn matrix. On the other hand, the identity matrices In and Im have dimensions nxn and mxm, respectively. Therefore, for the products CA and AD to be well-defined, we must have m=n.

Now, let us show that C=D. We have:

CA = In (given)

AD = Im (given)

Multiplying both sides of the first equation by D on the right and both sides of the second equation by C on the left, we get:

CAD = D (from CA=In)

CAD = C (from AD=Im)

Since CAD is equal to both D and C, we have D=C. Therefore, the matrices C and D are equal, and we have proved that m=n and C=D.

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Answer:it’s 20

Step-by-step explanation:I’m smart

Answer:

x+y

Step-by-step explanation:

You're adding x and y to get something but that something doesn't matter as you need an expression. (Hope this helps and sorry for the bad explanation.)

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Let's find a.

We are given a right angle which is 90° and an angle marked by "a" next to it. We know that when they are added together, they make a supplementary angle so we can make a equationa and solve.

90 + a = 180

a = 90°

Let's find b.

By looking at the graph, we can tell that the angle "b" and the angle that measures 163° is the same. Thus, b = 163°.

Let's find c.

Using what we did for a, we can solve for c using what we got for b. We can make an equation and solve.

163 + b = 180

c = 27°

Let's find d.

Using the angle that measures 70°, we can solve it like we did with a and c.

70 + d = 180

d = 110°

Let's find e.

Now that we know what d equals, we know that d and e make a supplmentary angle. So, make an equation and solve.

110 + e = 180

e = 70°

Best of Luck!