the roof on a shed is a square base pyramid.if one bundle of shingles covers 40ft^2 find the minium number of bundles of shingles needed to cover the roof


slant height is 8.2
Base is 9ft

Triangles are said to be congruent if their two angles and corresponding non-included sides are congruent with each other according to the AAS (Angle-Angle-Side) formula. thus proven.

Consider two triangles from figures ABC and DEF, where,

[Corresponding Angles] B = E The corresponding angles are C = F. And

AC = DF [Side by side]

Triangle's property of angle sum allows us to know this;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

Equations 1 and 2 allow us to state;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

thus in the triangle formed by ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

As a result, according to ASA,

Δ ABC ≅ Δ DEF

The proof of the AAS (Angle-Angle-Side) congruence rule follows.

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Triangles are said to be congruent if their two angles and corresponding non-included sides are congruent with each other according to the AAS (Angle-Angle-Side) formula. thus proven.

Consider two triangles from figures ABC and DEF, where,

[Corresponding Angles] B = E The corresponding angles are C = F. And

AC = DF [Side by side]

Triangle's property of angle sum allows us to know this;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

Equations 1 and 2 allow us to state;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

thus in the triangle formed by ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

As a result, according to ASA,

Δ ABC ≅ Δ DEF

The proof of the AAS (Angle-Angle-Side) congruence rule follows.

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There are 6 four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 that are greater than 3400.

To determine the number of four-digit numbers that can be formed using the digits 2, 5, and 3, we can use the formula nPr, where n is the number of digits we are working with (in this case, 3) and r is the number of digits we want in each combination (in this case, 4).

Therefore, the number of four-digit numbers that can be formed using the digits 2, 5, and 3 is 3P4 = 3! / (3 - 4)! = 3! / (3 - 4)! = 3! / -1! = 3! / 1 = 3 x 2 x 1 = 6.

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Answer:

76.16kg

Step-by-step explanation:

68kg x (1+0.12)

the x (1+0.12) shows we are increasing by 12%

can also be written as

(68kg x 1) + (68kg x 0.12)

The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.

We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.

Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.

Use the distance , in speed/rate formula ,

Rate × Time = Distance

Upstream : (B-S)6 = 258

=> B - S = 43 --(1)

Downstream: (B+S)6 = 330

=> B + S = 55 --(2)

Solve the linear equations by elimination method. Add the two equations.

=> 2B = 98

=> B = 49 km/hr

Substitute this value of B in equation(2) and solve for S, B+S = 55

=> 49+S = 55

=> S = 6 km/hr

So, the rate of the current is 6 km/hr.

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Complete question:

A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.

Answer:

108/11*sqrt*3

Step-by-step explanation:

CB=sqrt 108, DBC=90; DCB=35. CAB=60; ACD=65.

The greatest number of students that can attend the party is 16.

A factor defines a number that divides another number, leaving no remainder, which is equal to zero.

And if we multiply two whole numbers to give us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division.

Now, let us know factors 48 and 64

factors of 48 are 1,2,3,4,6,8,12,16,24,48.

factors of 64 are 1,2,4,8,16,32,64.

so the common factors of 48 and 64 are: 1,2,4,8, and 16

In the common factors of 48 and 64, 16 is the greatest number.

Therefore, the greatest number of students that can attend the party is 16.

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The two values on the number line are of opposite values, and have a distance of three halves units to zero. Thus option B.

A number line is a system in which the position of a directed number is located. It extends from negative infinity to positive infinity, thus all numbers can be located on a number line.

A directed number is any type of number which has either a negative or positive sign i.e its direction.

Considering the values given in the question, it can be deduced that;

i. Both values are opposite of each other because of the negative and positive signs (i.e their directions)

ii. The two values are at a distance of one and a halve to the zero point. So that;

one and a halve = 1 1/2

                           = 3/2

Thus both values are at a distance of three halves to zero.

Therefore, the correct option is B. The values are opposites of each other, and their distance to zero is three halves units.

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If it continues to fall at the rate of 3°C per hour, the temperature will be:

The temperature is currently 0°C and is falling at the constant rate of  3°C per hour which means that in 2 hours, the temperature would be:

= 0 - 3 - 3

= - 6 °C

In 5 hours the temperature would be :

= Current temperature + ( Change in temperature x number of hours )

= 0 + ( - 3 x 5 )

= - 15 °C

In half an hour:

= 0 - ( 3 x 0.5 )

= - 1. 5 °C

3 hours ago:

= Current temperature - ( Change in temperature x number of hours )

= 0 - ( - 3 x 3 )

= 0 + 9

= 9 °C

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Answer:

4

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

9^2 + b^2 = (sqrt(97) )^2

81 + b^2 = 97

Subtract 81 from each side

b^2 = 97-81

b^2 = 16

Take the square root of each side

sqrt(b^2) = sqrt(16)

b = 4

[tex] \longmapsto \: 9^2+b^2 = (\sqrt(97))^2[/tex]

[tex]\longmapsto \: 81+b^2=97[/tex]

[tex] \longmapsto \: b^2 = 97-81[/tex]

[tex] \longmapsto \: b^2 = 16[/tex]

[tex] \longmapsto \: b = 4[/tex]

Answer:

answers is 78 because if 6x45 that 87

The p-value is less than a chosen significance level (alpha), such as 0.05, we reject the null hypothesis and conclude that there is evidence that the proportion of adults who would respond "yes" to the question changed from December 2007 to December 2008. Otherwise, we fail to reject the null hypothesis.

It is important to note that the sample size and the significance level used to calculate the p-value can affect the result of the test. Additionally, it's important to consider other factors that may have affected the results, such as economic conditions or media coverage.

To determine if the proportion of adults in the United States who would respond "yes" to the question changed from December 2007 to December 2008, we need to perform a hypothesis test. The null hypothesis is that the proportion of adults who would respond "yes" to the question did not change from December 2007 to December 2008, and the alternative hypothesis is that the proportion of adults who would respond "yes" to the question did change.

One way to perform the hypothesis test is by using a two-sample proportion test. The test statistic is calculated as:

(p1 - p2) = (676/1009 - 622/1020) = 0.0548

where p1 is the proportion of adults who responded "yes" in December 2008 and p2 is the proportion of adults who responded "yes" in December 2007.

Then, we need to find the p-value for the test statistic, which represents the probability of observing a test statistic as extreme or more extreme than the one calculated if the null hypothesis is true.

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Realism is the faithful representation of reality in literature, and it presents life as it actually is. Option (c) is correct.

Reality is the state of things as they actually are, as opposed to how we would like them to be.

While "Naturalism is a manner and style of writing by which the author portrays 'life as it is' in accordance with the philosophic idea of determinism," "Realism is a manner and method of composition by which the author describes normal, average life, in an exact, truthful way."

Realism is a literary approach used by various schools of writing and is broadly referred to as "the faithful representation of reality" or "verisimilitude."

Therefore, Option (c) is correct. Realism is the faithful representation of reality in literature, and it presents life as it actually.

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For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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The x intercept for 5x - 9 = -8y - 3 is calculated to be  6/5

The term intercept refers to the location where a line or curve crosses a graph's axis.

The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.

At the x-intercept, the value of y is zero, because of this the equation

5x - 9 = -8y - 3 is solved as follows

5x - 9 = -8y - 3 at y = 0

5x - 9 = -8 * 0 - 3

5x - 9 =  - 3

solving for x

5x = -3 + 9

5x = 6

dividing through by 5

5x/5 = 6/5

x = 6/5

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Answer:

The rest would be 39, 48, 57

The perimeter of the triangle is 21

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

The perimeter of the triangle is found by adding all the sides

The vertices of the triangle ABC are (-1,1), (-3, -4), and (5,-2). let A be (-1,1), B be (-3, -4) and C be (5,-2).

The distance between And B = √ (-3-(-1))²+( -4-1)²

Line AB = √ 2²+-5²

AB = √ 4+25

AB =√29 = 5.4

line AC = √5-(-1)² + (-2-1)²

AC = √ 6²+3²

AC = √ 36+9

AC = √ 45

AC = 6.7

The distance between B and C = √( -3-5)² + (-4-(-2)²

BC = √ 8²+4²

BC =✓64+16

BC = √80

BC = 8.9

Therefore the perimeter of the triangle is AB+ BC + AC = 5.4+6.7+8.9 = 21

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The distance between coordinates is d = 7.1 units.

The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line. The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.

Given coordinates,

(3, 11) and (4, 3)

the distance between coordinates is

d=√((x₂ – x₁)² + (y₂ – y₁)²)

here x₁ = 3, x₂ = 4, y₁ = 11 and y₂ = 3

d=√((x₂ – x₁)² + (y₂ – y₁)²)

d=√((4 – 3)² + (4 – 11)²)

d = √(1 + 49)

d = √50

d = 7.0710 units

d = 7.1 units nearest tenth

Hence the distance is d = 7.1 units nearest tenth.

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The way to write the rule is

(x, y) is  (x – 3, y + 5).

A triangle which is on a coordinated plane is translated to the rule

Two lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line.

The original rule x and y coordinates

that are being moved to the left-hand side of the equation by

decreased by 3 units and rise up by 5 units.

Based on the information given,

we can come to the conclusion that other way to

write the given rule is

(x, y) is (x – 3, y + 5).

Hence, the other rule which are given are incorrect.

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(x, y) → (x – 3, y + 5)

The given rule is t–3, 5(x, y). This means that the triangle plane is translated 3 units to the left, and 5 units up. This can be written in another way as (x, y) → (x – 3, y + 5).

The given rule t–3, 5(x, y) states that the triangle is translated 3 units to the left, and 5 units up on the coordinate plane. This can be rewritten as (x, y) → (x – 3, y + 5). This means that for each point (x, y), the new point after the translation will be (x – 3, y + 5). In other words, the x-coordinate of the new point will be three units less than the original x-coordinate, and the y-coordinate of the new point will be five units more than the original y-coordinate. This translation of the triangle can also be visualized as moving the triangle three units to the left and five units up on the coordinate plane.

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Answer:

0.13 to 0.30 mp

Step-by-step explanation:

The angle marked x in the regular hexagon is 120 degrees, and in the regular pentagon is 108 degrees.

The angle marked x in the regular hexagon is 120 degrees, because the sum of all the angles in a hexagon is 720 degrees (360 x 2). Each of the angles in a regular hexagon is 120 degrees, so the angle marked x must also be 120 degrees. The angle marked x in the regular pentagon is 108 degrees, because the sum of all the angles in a pentagon is 540 degrees (360 x 1.5). Each of the angles in a regular pentagon is 108 degrees, so the angle marked x must also be 108 degrees.

Regular Hexagon:

Sum of angles = 720 degrees

Number of angles = 6

Angle x = 720 ÷ 6 = 120 degrees

Regular Pentagon:

Sum of angles = 540 degrees

Number of angles = 5

Angle x = 540 ÷ 5 = 108 degrees

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Answer: 12, g with exponent 4, h with exponent 5 . (12

g

4

h

5

       Brainliest would be much apprechiated

Answer:

2+3+3=8

3×4=12

Step-by-step explanation:

Answer:

[tex]21[/tex]

Step-by-step explanation:

[tex]\textrm{If y varies directly with x we can write this relationship as}[/tex]

[tex]y = k \cdot x[/tex]

[tex]\textrm{k is referred to as the constant of proportionality.}[/tex]

[tex]\textrm{Substituting these values into the above equation we get}[/tex]

[tex]3 = k \cdot 2[/tex]

[tex]So\; k = \dfrac{3}{2}[/tex]

[tex]\mathrm{When }[/tex] [tex]x = 14,[/tex]

[tex]y = \dfrac{3}{2} \cdot 14[/tex]

[tex]y = 21[/tex]

The functions that are symmetric about the y-axis are;

1) The function in the first option; f(θ) = cos(θ)

2) The function in the third option; f(x) = x²

Definition;

A function is symmetric about the y-axis is also known to be an even function such that the same value of the function is arrived at when x is replaced with -x

Analysis of the graphs;

First Function Graph; The graph represents the graph of cos (θ)

∴ The function is f(θ) = cos(θ)

The value of the function when x = π, f(π) = -1

Similarly, the value of the when x = -π, f(-π) = -1

f(π) = f(-π)

∴ f(x) = f(-x)

Therefore; the first function is an even function

Second Function Graph; The function of the graph is x = y²

∴ y = √(x)

The value of the function when x = 4, y = f(4) = 2

However, the when x = -4, f(-4) does not exist

f(4) ≠ f(-4)

∴ f(x) ≠ f(-x)

Therefore; the second function is not an even function (the function, x =

y², is however symmetric about the x-axis)

Third Function Graph; The function the graph represents is y = x²

The value of the function when x = 2, f(2) = 4

Similarly, the value of the when x = -2, f(-2) = 4

f(2) = f(-2)

∴ f(x) = f(-x)

Therefore; the third function is an even function

From the above, the functions which are symmetric about the y-axis, (even functions) are;

The first and the third functions

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Answer:

1 and 3.

Step-by-step explanation:

edg

A. The result of the iterated integral by converting to polar coordinates is 0.

To evaluate this iterated integral, we will convert it to polar coordinates. First, we need to make the substitution x = rcos(θ) and y = rsin(θ). Then, we will need to find the limits of integration for r and θ. The region of integration is the area between the circles with radii a and 2 and between the x-axis and y-axis.

In polar coordinates, the integral becomes ∫∫r dr dθ from r = a to r = 2, and θ = 0 to θ = π/2.

We can now solve the integral by multiplying the integral of r by the integral of θ.

∫2^2 r dr dθ = ∫π/2^0 (-1/2)r^3 dθ = -1/2 * [(r^2)/2] from r = 2 to r = a = -1/2*(2^2 - a^2) = -1/2*(4-a^2) = -2+a^2/2

So the result of the integral is -2+a^2/2 = -2+4/2 = -2+2 = 0

Note that this is not a common way to solve iterated integrals, but rather a way to check the correctness of the solution. The common way is to find the limits of integration by solving the inequality and graphing the area of integration.

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The solutions to each equality are given as follows:

D) s = -1.

E) n = 10/7.

F) k = 3.

The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.

The solution for item d is given as follows:

3 - 2s + 2 = 13 + 6s -> Distributive property.

8s = 5 - 13 -> Combine the like terms.

8s = -8

s = -8/8

s = -1.

The solution for item e is given as follows:

2(n + 9) = -6(2n - 5) + 8

2n + 18 = -12n + 30 + 8 -> Distributive property.

14n = 20 -> Combine the like terms.

n = 20/14

n = 10/7.

The solution for item f is given as follows:

5(4k - 3) - 5k = 10 + 2(3k + 1)

20k - 15 - 5k = 10 + 6k + 2

15k - 15 = 12 + 6k

9k = 27

k = 27/9

k = 3.

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The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have the following;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Answer:

8

Step-by-step explanation:

This is a right triangle.

Since it's a right triangle with given side lengths,

we can use Pythagoras theorem, a² + b² = c² (a and b legs, c is hypotenuse)

to calculate the missing side.

Let x represent the missing side:

[tex]( {2 \sqrt{41} )}^{2} = {10}^{2} + {x}^{2} [/tex]

[tex]164 = 100 + {x}^{2} [/tex]

[tex]64 = {x}^{2} [/tex]

[tex]8 = x[/tex]

The red flags in the prescription are;

We know that the term prescription would have to do with the drugs that an individual has been asked to take in a  given situation. Usually, when a person is sick, the person would have to go to a doctor to get a prescription.

There may be certain red flags in a prescription and these would have to do with the state of health of the patient that is being given the prescription drugs to taken.

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Non of the above Statement is true.

Standard deviation is a mathematical measure of how spread out a dataset is. It is a measure of the variation or dispersion of a set of values from the mean. It is calculated by taking the square root of the variance. Standard deviation can be used to measure the risk associated with an investment, to compare data sets, or to measure the accuracy of a data set.

The standard deviation is a measure of the dispersion of a set of data from its mean, and it is always a non-negative number. It can sometimes be zero, and it can also be larger than the variance.

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Answer:

plus or minus 11

Step-by-step explanation:

2(1)+7

=9

2(1)-4

=-2

and the difference between the 9 and -2 is -11 but the difference between -2 and 9 is 11 so that why it positive or negative 11