Researchers have determined that a hip roof offers the most protection to a
house during a hurricane.
a. The house has a square base with a side length of 50 feet. The house has
a variation of a hip roof in the shape of a regular pyramid with a square
base. The roof extends 1 foot beyond the walls of the house on all sides.
What is the length of each side of the base of the roof?
b. The slant height of the roof is 35 feet. Find the sum of the areas of the
lateral faces of the pyramid.
c. A metal roof covering offers the most protection to a house during a
hurricane. The cost of installing metal roof covering is $350 for every
100 square feet of roof. What is the cost of installing a metal roof
covering on the house?

45 points to first answer (actually)

Answer:

y = (360 - 117 - 75) / 2 = 84 degrees

Step-by-step explanation:

a) The shape shown in the image could be described as a kite.

b) Since the opposite angles in a kite are equal, we can find the measure of angle y by subtracting the measures of angles x and z from 360 degrees and then dividing by 2, since the sum of the interior angles of a quadrilateral is always 360 degrees. Thus, we have:

y = (360 - x - z) / 2

We can see from the figure that angle x has a measure of 117 degrees, since it is opposite to angle y in one of the congruent triangles formed by the diagonal of the kite. Similarly, angle z has a measure of 75 degrees, since it is opposite to angle y in the other congruent triangle. Substituting these values into the above equation, we get:

y = (360 - 117 - 75) / 2 = 84 degrees

Therefore, the measure of angle y is 84 degrees.

We can see that opposite sides of the quadrilateral are parallel and equal in length, which indicates that the shape is a parallelogram.

To find the size of angle y, we can use the fact that opposite angles in a parallelogram are equal. Let's call the angle at the bottom left corner of the parallelogram "x". Then, we know that:

x + y = 180° (because the two angles form a straight line)

We also know that the angle at the top left corner of the parallelogram is equal to x (because opposite angles in a parallelogram are equal). And since the four angles of a quadrilateral add up to 360°, we can write:

2x + 2y = 360°

Simplifying this equation gives:

x + y = 180°

x + y = 180° - x + y

2x = 180° - x

3x = 180°

x = 60°

Now we can substitute x = 60° into the equation x + y = 180° to solve for y:

60° + y = 180°

y = 180° - 60°

y = 120°

Therefore, the size of angle y is 120°.

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Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

The temperature dropped by 4 degrees Fahrenheit per hour during the 6-hour period.

The temperature drop each hour is calculated as follows;

temperature drop per hour = (change in temperature) / (time elapsed)

change in temperature = final temperature - initial temperature

change in temperature = 58 degrees F - 82 degrees F

change in temperature = -24 degrees F

The time elapsed =  6 hours

The change in temperature or drop in temperature is calculated as;

temperature drop per hour = (-24 degrees F) / (6 hours)

temperature drop per hour = -4 degrees F/hour

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Answer:

(c) 6 days

Step-by-step explanation:

First, we need to calculate how many trips the truck can make per day. We will assume that the truck is filled to its maximum capacity on each trip.

The volume of the truck can be calculated by multiplying its dimensions:

8.17 feet x 9.25 feet x 18.5 feet = 1,482.51 cubic feet

We need to convert this to cubic meters:

1,482.51 cubic feet x 0.0283 cubic meters per cubic foot = 42.01 cubic meters

Therefore, each round trip can transport 42.01 cubic meters of construction waste.

To calculate how many trips are required to remove all the waste, we divide the total volume of waste by the volume of waste per trip:

1,425 cubic meters / 42.01 cubic meters per trip = 33.89 trips

Since the driver can make one round trip per hour, it will take approximately 34 hours to transport all the waste to the landfill.

If the driver starts on Monday at 8 am, they will have 8 working hours that day, for a total of 8 trips. On Tuesday and Wednesday, they will have 8 working hours each day, for a total of 16 trips. Therefore, by noon on Wednesday, they will have made 24 trips, leaving 9.89 trips remaining.

Since each day the driver can make 8 trips, they will need approximately 2 more days of work to completely remove the construction waste from the demolition site. Therefore, the answer is (c) 6 days.

Note: This calculation assumes that there are no delays or complications in the transportation process, such as traffic or equipment malfunctions, which could affect the actual time required to remove all the waste.

Factor of polynomial m are 0,   6n⁴.

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

= 30m³n⁴ - 5m⁴

= 5m³(6n⁴ - m )

let 5m³(6n⁴ - m ) = 0

       5m³ = 0

         m = 0

 6n⁴ - m = 0

      m =   6n⁴

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Answer:

y = (x - 2)² + 4

Step-by-step explanation:

y = x² - 4x + 8

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 8

  = (x - 2)² + 4 ← in vertex form

Answer:

x = 57°

Step-by-step explanation:

We are given a triangle, and we know that the angles in the triangle are <A, <B, and <C.

We know that m<A = 78° and  m<B=45°. We want to find the measure of angle C, which we know currently as x.

Recall that all angles in a triangle add up to 180°. This means that m<A + m<B + m<C = 180°.

Substituting what we know into that equation, we get:

78° + 45° + x = 180°

We can add 78 and 45 degrees together.

123° + x = 180°

Subtract 123° from both sides.

x = 57°

So x, or m<C is 57°.

Teuta bought the car for 8545.71 eu.

What is percent in math?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

Let's assume that the initial price of the car is x.

After a 23% drop in price, the new price of the car is: x -0.23x = 0.77x

We know that the new price after the first year is 6575.8 eu: 0.77x = 6575.8

Solving for x, we get: x = 6575.8/0.77 8545.71

Therefore, Teuta bought the car for approximately 8545.71 eu.

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Using trigonometric ratios θ = 26.57°

A trigonometric ratio is the ratio of the sides of a triangle.

To find the value of θ, we notice that in the triangle, we have the hypotenuse side and the adjacent side.

Using the trigonometric ratio cosθ = adjacent/hypotenuse

where

So, substituting the values of the variables into the equation, we have that

cosθ = adjacent/hypotenuse

= 6√5/15

= 2√5/5

= 2 × 2.236/5

= 4.472

= 0.8944

cosθ = 0.8944

θ = cos⁻¹(0.8944)

= 26.57°

So, θ = 26.57°

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As a result, the following is the given function's Fourier transform:

F(ω) = (1/π) * (sin(ω) / ω)

The Fourier transform is a mathematical operation that separates the frequencies that make up a waveform, which is a function of time. The Fourier transform's output is a complex valued function of frequency.

We must assess the integral in order to determine the given function's Fourier transform, f(x):

F() is equal to 1/(2) * [from - to -] F(x) E(-i) X Dx

where the frequency parameter is and i is the fictitious unit.

We can simplify the integral bounds as follows since the function f(x) is non-zero only in the range -1 x 1.

F() is equal to 1/(2)*[from -1 to 1] F(x) E(-i) X Dx

Let's analyse this integral in stages.

The value of the function f(x) is zero for x -1 or x > 1. As a result, we can increase the integral limits to - and + without changing the integral's value:

F(ω) = 1/(2π) * ∫(from - to -) F(x) = E(-ix) dx = 1/(2*) * the range [- to -1] from -1 to 1 + 0 dx 2dxe(-ix)+[from 1 to ] 0 dx = 1/(2π) * 2 * ∫E(-ix) dx [from -1 to 1]

Let's concentrate on the central integral:

∫[in the range of -1 to 1] e(-ix) dx = (-1/i)* [e^(-iωx)](-1/i)* _[from -1 to 1] (e^(-iω) - e^(iω))

Adding this back into the formula for the Fourier transform results in:

F(ω) = 1/(2π) * 2 * (-1/iω) * (e^(-iω) - e^(iω)) = (1/π) * (sin(ω) / ω)

As a result, the following is the given function's Fourier transform:

F(ω) = (1/π) * (sin(ω) / ω).

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The Fourier transform of the given function f(x) is:

F(ω) = 2 [ - sin(ω) / ω ]

What is Fourier Analysis?

Fourier analysis is a branch of mathematics that deals with the study of the decomposition of a complex signal into simpler components, known as harmonics, using a mathematical tool called the Fourier transform.

To find the Fourier transform of the given function f(x), we need to use the following formula:

F(ω) = ∫ f(x) e^(-iωx) dx

where F(ω) denotes the Fourier transform of f(x) and ω is the frequency variable.

Let's apply this formula to the given function f(x):

F(ω) = ∫ f(x) [tex]e^{(-iωx)}[/tex] dx

= ∫[tex]-1^{1}[/tex] 2 [tex]e^{(-iωx)}[/tex] dx + ∫{-∞}^{∞} 0 [tex]e^{(-iωx)}[/tex] dx

= 2 ∫_[tex]{1}^{{1}}[/tex]  [tex]e^{(-iωx)}[/tex] dx + 0

= 2 [ (1/iω)  [tex]e^{(-iωx)}[/tex]  ]_[tex]-1^{1}[/tex]

= 2 [  [tex]e^{(-iωx)}[/tex]  - [tex]e^{(iω)}[/tex] / iω ]

Simplifying this expression, we get:

F(ω) = 2 [ (cos(ω) - i sin(ω)) / iω - (cos(-ω) - i sin(-ω)) / iω ]

= 2 [ (cos(ω) - i sin(ω)) / iω - (cos(ω) + i sin(ω)) / iω ]

= 2 [ -2i sin(ω) / (2iω) ]

= 2 [ - sin(ω) / ω ]

Therefore, the Fourier transform of the given function f(x) is:

F(ω) = 2 [ - sin(ω) / ω ]

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The part of the foot will the photo collage cover is 1/5 square foot

Recall that an area of a lawn is an area of soil-covered land planted with grasses and other durable plants such as clover which are maintained at a short height with a lawnmower (or sometimes grazing animals) and used for aesthetic and/or recreational purposes

The given parameters are

Area of the Poster =1 sq.ft.

The collage will cover a part of the poster that is

1/5ft wide and 3/5ft long

Area of the Photo Collage Section

=Length X Width

= 1/3 * 3/5

= 3/15 ft = 1/5foot

In conclusion,  the photo cover will cover 1/5  of a square foot

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Answer:

D)

Step-by-step explanation:

The numbers 0, 1, and -1 are zeros of multiplicity 1.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

To find the zeros of the function [tex]y=7x^3-7x[/tex], we can set y equal to zero and solve for x:

[tex]7x^3 - 7x = 0[/tex]

Factor out 7x:

[tex]7x(x^2 - 1) = 0[/tex]

Factor the quadratic expression:

7x(x - 1)(x + 1) = 0

The zeros of the function are the values of x that make y equal to zero. From the factored expression, we see that the zeros are:

x = 0 (with multiplicity 1)

x = 1 (with multiplicity 1)

x = -1 (with multiplicity 1)

Therefore, the correct choice is: The numbers 0, 1, and -1 are zeros of multiplicity 1.

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(x - 3)(x + 6) can be written in vertex form as y = (x - (-3/2))² - 20.25

What is the vertex form?

The vertex form of a quadratic function is a way of writing a quadratic function in form f(x) = a(x - h)² + k where (h, k) is the vertex of the parabola, a is a coefficient that determines the shape and direction of the parabola, and x is the input variable.

Expanding (x - 3)(x + 6), we get:

x² + 6x - 3x - 18 = x² + 3x - 18

To write this expression in vertex form, we need to complete the square. To do this, we add and subtract (3/2)² = 2.25 inside the parentheses:

x² + 3x - 18 + 2.25 - 2.25 = (x² + 3x + 2.25) - 20.25

Now, we can write the expression in vertex form:

y = (x - (-3/2))² - 20.25

Therefore, (x - 3)(x + 6) can be written in vertex form as:

y = (x - (-3/2))² - 20.25

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Answer:

there is somthing wrong of what you ask

because it is impossible to be thet a>0 and b>0 and x<0 and still ax>1 or bx>1

The volume of the model of Saturn is approximately 4,845.6 cm³.

To solve this problem, we can use the combination formula, which is:

n C r = n! / (r! * (n-r)!)

where n is the total number of students eligible for the committee, r is the number of students we want to choose, and ! denotes the factorial function.

In this case, we want to choose a committee of 8 students from a pool of 8 freshmen, 9 sophomores, 8 juniors, and 10 seniors. So, the total number of students eligible for the committee is:

n = 8 + 9 + 8 + 10 = 35

We want to choose a committee of 8 students, so r = 8. Therefore, the number of ways we can choose a committee of 8 students is:

35 C 8 = 35! / (8! * (35-8)!) = 35! / (8! * 27!) ≈ 1,121,112 ways

So there are approximately 1,121,112 ways to choose a dance committee of 8 students from the eligible pool.

The inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.

It appears there's some confusion regarding the expression you supplied. To better interpret it, please consider making further explanations visible.

Nonetheless, an attempt to interpret is provided below:

40 divided by [(2=3)(17=15)]

Essentially, the intention is to multiply the results of each step in this expression. Let us begin assessing the individual components:

The first, 2=3 proves false as a statement; thus, we can grant it a value of zero.

Likewise, 17=15 sets out to be incorrect which, rightfully so, can also assume a figure of nothingness.

Let us now multiply the outcomes of both statements:

(0)(0) = 0

Finally, we divide 40 - the stated number - by the result from before:

40 ÷ 0

Conclusively, the inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.

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Evaluate the following:

40 divided by [2=3 (17=15)]

To solve for the value of x, x is 2.

What is a simple equation?

A given equation which has one unknown variable whose value is to be determined is called a simple equation. This requires the applications of some mathematical principles to know the value of the unknown.

In the given question, the common factor is 25. so divide by 25 to have;

125x - 150 = 100

divide by the common factor, we have;

125x/25 - 150/25 = 100/25

5x - 6 = 4

So that, solve in the usual manner;

5x = 4 + 6

    = 10

5x = 10

x = 10/5

 = 2

x = 2

After solving the equation, the value of x is 2.

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Answer:

144

Step-by-step explanation:

we can use subtraction to solve this, subtracting 220 from 76 ends up with 144

Answer:

A

Step-by-step explanation:

Self explanatory

Answer: b

Step-by-step explanation: i just did this one on a algebra 1b assignment lol

Answer: Probability: 1.3%

Totals, 51, 155. 0 Accounts: 18. 1 Account: 24. 2 Accounts:18. 3 or more: 42.

Statements which  are always true regarding the diagram are

1. m∠5 + m∠6 = 180° ...........Parallel Pair

2. External angle of a triangle is equal to 2+3 = 6.

3. Triangle Sum Property: m2 + m3 + m5 = 180°

Think of ABC as having outside angles.

∠ 1, ∠ 4 , and ∠ 6

Triangle's exterior angle property:

A triangle's exterior angle equals the sum of its internal angles.

Exterior 1 has the following

The exterior angle of a triangle is given by the formula: 1 = 5 + 3.

Similarly,

Exterior 4 consists of

∠ 4 = ∠ 5 + ∠ 2.................Triangle's Exterior Angle

Similarly,

Exterior 6 consists of

The exterior angle of a triangle is given by the formula: 6 = 2 + 3

Property Triangle Sum:

The total of the angles in a triangle equals 180°.

∴ m∠2 + m∠3 + m∠5 = 180° .....Sum Triangle Property

Linear Pair:

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

∴ m∠5 + m∠6 = 180°  ...........Linear Pair

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Answer:

2 Batch Of Cakes

Step-by-step explanation:

See:

Recipe Requirements for 1 Batch:

2 cups of Flour

1/2 cup of Butter

3/4 cup of Sugar

She Has:

8 Cups of Flour

2 Cups of Butter

2 Cups of Sugar

1 batch:

Ingredient : Required - Present

Flour : 2 Cups - 8 Cups

Butter : 50% of 1 Cup - 2 Cups

Sugar : 75% of 1 Cup - 2Cups

Left ingredients:

Flour : 6 Cups

Butter : 1.5 Cups

Sugar : 1.25 Cups

2 batch:

Ingredient : Required - Present

Flour : 2 Cups - 6 Cups

Butter : 50% of 1 Cup - 1.5 Cups

Sugar : 75% of 1 Cup - 1.25 Cups

Left ingredients:

Flour : 4 Cups

Butter : 1 Cup

Sugar : 0.5 ( 1/2 ) Cups

3 Batch:

We Cannot Make The 3rd Batch as There is no sufficient Sugar

Answer: y = -|x| - 3

Step-by-step explanation:

It's an absolute value function that has been shifted down 3 and has been reflected

y = -|x| - 3

Answer:

To find the location of point L, we need to use the fact that point K lies on the perpendicular bisector of segment JL.

The perpendicular bisector of a segment is a line that passes through the midpoint of the segment and is perpendicular to the segment.

First, we can find the midpoint of segment JL:

Midpoint of JL = ((-5 + x)/2, (-8 + y)/2)

where (x, y) is the location of point L.

Since point K lies on the perpendicular bisector of JL, the line passing through K and the midpoint of JL will be perpendicular to JL.

The slope of the line passing through K and the midpoint of JL is:

m = (2 - (-8))/(-9 - (-5 + x)/2) = 10/(-9 - (5 - x)/2) = -4/(x - 7)

where we have used the fact that the line passing through K and the midpoint of JL is perpendicular to JL, so its slope is the negative reciprocal of the slope of JL.

Now, we can use the fact that the line passing through K and the midpoint of JL contains point K(-9, 2) to write the equation of the line:

y - 2 = m(x + 9)

Substituting the expression we found for m, we get:

y - 2 = (-4/(x - 7))(x + 9)

Simplifying this equation, we get:

y = -4x/ (x - 7) - 2

Now, we can substitute the x-coordinates of the answer choices to see which one gives us a valid y-coordinate:

A. (1, -2): y = -4(1)/(-6) - 2 = -1 --> Incorrect

B. (-1, -12): y = -4(-1)/(-8) - 2 = 1/2 --> Incorrect

C. (-3, -2): y = -4(-3)/(-10) - 2 = 6/5 --> Incorrect

D. (-3, -12): y = -4(-3)/(-10 - 4) - 2 = -26/7 --> Correct

Therefore, the location of point L is (-3, -12), which is answer choice D.

Simple interest =  $12,9600

Compounded quarterly = $12,9600

and compounded continuously = $21,686.49

What is simple interest?

Simple interest, often known as the yearly interest rate, is an annual payment based on a percentage of borrowed or saved money.

Here, we have

Given:

Investment = $5,400 at 5.6% interest.

t = 25 years

Final amount at simple interest: F = P(1+rt)

F = 5400(1+0.056×25)

F = 5400(2.4)

F = $12,9600

Final amount at compound interest: F= P(1+r/n)ⁿˣ

compounded quarterly(n=4)

F = P(1+r/n)ⁿˣ

F = 5400(1+0.056/4)⁴⁽²⁵⁾

F = 5400(1.014)¹⁰⁰

F = $21,686.49

Final amount at continuously compound interest: F= Peⁿˣ

F = 5400 e¹°⁴

F = $21,898

Hence,

simple interest =  $12,9600

compounded quarterly = $12,9600

and compounded continuously = $21,686.49

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Answer:

a. km

b.350 ml

c.60 gr

Step-by-step explanation:

the units may be bigger though to whats the options is

Answer:

To find the LCM of the two expressions, we need to factor each expression completely and then take the product of the highest powers of each factor.

So, let's factor each expression:

6(x – 1)2(x + 2)(x – 3) = 2 × 3 × (x – 1) × (x – 1) × (x + 2) × (x – 3)

9(x – 1)(x + 2)2(x – 3) = 3 × 3 × (x – 1) × (x + 2) × (x + 2) × (x – 3)

Now, we can identify the highest powers of each factor.

The LCM will be the product of those highest powers:

LCM = 2 × 3 × 3 × (x – 1)2 × (x + 2)2 × (x – 3)

Therefore, the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3) is 54(x – 1)2(x + 2)2(x – 3).