The pitch of the roof is roughly 35.3 degrees, and the middle height of the roof is 19.3 feet.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Here,
To find the pitch of the roof, we need to use the Pythagorean theorem to determine the height of the roof at the center. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the height of the roof at the center is the hypotenuse, and the two shorter sides are the width of the house (32 feet) and half of the length of the rafter (22 feet / 2 = 11 feet). So, using the Pythagorean theorem, we can set up the following equation:
h² = (32 / 2)² + 11²
h² = 16² + 11²
h² = 256 + 121
h² = 377
h = √377
h = 19.3 feet
Next, we use the tangent function to find the pitch of the roof. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roof (19.3 feet), and the adjacent side is half of the rafter length (11 feet). So, we can set up the following equation:
tan(pitch) = 19.3 / 11
We can use the inverse tangent function (tan^-1) to find the angle, which will give us the pitch of the roof in degrees.
pitch = tan^-1(19.3 / 11)
The pitch of the roof is approximately 35.3 degrees and height of the roof at the center is 19.3 feet.
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Find the value of x in the supplement
The value of 'x' in the linear pair of angles is 126°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
We know the sum of linear pair of angles is 180°.
Therefore, From the given information
(x - 6)° + 60° = 180°.
x + 54° = 180°.
x = 180° - 54°.
x = 126°.
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Given the two concentric circles with center N below, LN = 13.5. Find the area of
the shaded region. Round your answer to the nearest tenth if necessary.
Answer:
371.54 sqr units
Step-by-step explanation:
area of a circle=πr²
area of inner circle=3.142×8×8=201.088 square units.
area of outer circle = 3.142×13.5×13.5=572.6295 square units
572.6295-201.088=371.5415 square units
=371.54 sqr units
4) what number of floors n would make the probability of that specific sequence of customer floors as large as possible?
It depends on the specific sequence of customer floors you're looking for. Without knowing that sequence, it's not possible to determine the number of floors that would make the probability of that sequence as large as possible.
In general, the probability of a specific sequence of customer floors will depend on several factors, such as the number of floors in the building, the number of customers, and the order in which they press the buttons.
To determine the number of floors that would maximize the probability of a specific sequence, you would need to know the details of the scenario and perform a more in-depth analysis.
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If BD =2. 8, What is CP? (Round your answer to the nearest tenth. Write NA if there is not enough Information given. )
By applying the Isosceles trapezoid concept, it can be concluded that the value of CP is 1.1 units.
Isosceles trapezoid has four sides, in which the two opposite sides (bases) are parallel to each other and the other two sides are equal in length but non-parallel to each other. The diagonals of an isosceles trapezoid are congruent.
We have an isosceles trapezoid with:
Length BD = 2.8 = diagonal
Length AP = 1.7 where P is the center
Since the diagonals of an isosceles trapezoid are congruent, so BD = AC = 2.8
Meanwhile AC = AP + CP. If we substitute the value of AC and AP, we got the value of CP:
CP = AC - AP
= 2.8 - 1.7
= 1.1
Thus, the value of CP is 1.1 units.
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Pls hurry I really need to answer tysm
The proportion is 2 : 3 and the scale model is represented by the Black tabletop color
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the scale of the color tabletop be represented as a : b
Now , the proportion will be
The scale model of the tabletop is given by A : B = 4 inches by 6 inches
So , the proportion is 4/6 = 2 : 3
And , the black tabletop has an original size of 32 inches by 48 inches
Substituting the values in the equation , we get
4 inches by 6 inches is proportional to 32 inches by 48 inches
On simplifying the equation , we get
4/6 = 32/48
2/3 = 16/24
2/3 = 8/12
2/3 = 2/3
Hence , the proportion is 2 : 3
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What is 12:4 ratio in simplest form?
Answer:
12:4 ratio simplified is 3:1
Step-by-step explanation:
(in survey done in a group of 500 children, 250 children liked doughnut only and 30% liked bread but not doughnut. If every children likes at least one of them.): (i)Find the number of children who liked both doughnut and bread. (ii)Find the number of children who like bread
Step-by-step explanation:
Come over here
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The population of a certain animal species decreases at a rate of 12.5% per year. In 2021, at the beginning of the study, you counted 97 of the animal species you are studying in their natural habitat. Write a function that models the change in the animal population.
The equation is P(t)= 97(0.875)t, where t is the number of years since 2021 and P(t) is the population at time t.
The animal population's change through time is modelled by the function P(t) = 97(0.875)t, where P(t) is the population at time t and t is the number of years since 2021. The function is based on the assumption that the population declines by 12.5% annually. As a result, starting in 2021, the population will fall by 12.5% year. The initial population in 2021 (97) must be multiplied by 0.875t in order to determine the population at any given year t. You will receive the population at that specific year from this. For instance, 97(0.875)5 = 60.2 will be the population in 2026 if t = 5. Accordingly, the population fell from 97 to 60.2 after five years. We can track and research population changes by using this function to anticipate the animal species' population over time.
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Gloria recently bought a new Pixel phone. One day, she got an alert regarding her screen time for the past week. She decided she was spending too much time on her phone, so she started to keep an eye on her minutes of screen time.
One week after starting to keep an eye on her screen time, Gloria's weekly screen time was down by 15% to 884 minutes.
What was the growth factor from her initial screen time to her screen time one week later?
The growth factor is 0.85.
How did we get the value?Let's call her initial screen time "x". After one week, her screen time was 884 minutes, which is 100% - 15% = 85% of her initial screen time.
So, 884 minutes = 0.85x
Dividing both sides by 0.85, we get:
x = 1040 minutes
So her initial screen time was 1040 minutes.
The growth factor from her initial screen time to her screen time one week later is:
884 minutes / 1040 minutes = 0.85
So, the growth factor is 0.85.
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Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 26 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 180 square feet of carpeting. What dimensions should the rug have? The dimensions of the rug should be 28 ft. (Use a comma to separate answers as needed.) 18 ft 180 ft 26 ft
The length and width will be 18 feet and 10 feet respectively.
How to calculate the dimensionsFrom the information, Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 26 ft long and she wants to leave a uniform strip of floor around the rug and can afford to buy 180 square feet of carpeting.
The dimensions are 28 by 16 feet
The dimensions of the rug will be:
= (26 - 2x)(18 - 2x)
Maximum area = 180 feet²
(26 - 2x)(18 - 2x) = 180
468 - 88x + 4x² = 180
4x² - 88x + 288 = 0
x² - 22x + 72 = 0
x = 4 and 18
The width will be:
= 18 - 2x
= 18 - 2(4)
= 10
The length will be:
= 26 - 8
= 18 feet
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Now you will attempt to copy your original triangle using one of its angles:
Draw a line segment, DE of any length anywhere on the coordinate plane, but not on top of ∆ABC.
Choose one of the angles on ∆ABC. From point D, create an angle of the same size as the angle you chose. Then draw a ray from D through the angle. You should now have an angle that is congruent to the angle you chose on ∆ABC.
Create a point anywhere outside the mouth, or opening, of the angle you created. The point will initially be named F by the tool, but you should rename it point G. Now draw a ray from E through G such that it intersects the first ray. Your creation should be a closed shape resembling a triangle.
Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.
Click on point G, and move it around. By moving point G, you can change
DEF and EFD while keeping FDE fixed.
Take a screenshot of your results for one position of G, save it, and insert the image in the space below.
The construction of similar triangles are given in attached figure.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Similar shapes are shapes whose lengths are in an equivalent ratio. Triangle ABC and triangle DEF are similar because the side lengths of both triangles are in an equivalent ratio (refer to the attachment).
Step 1: Draw a random triangle ABC
The lengths of two sides and an angle are:
AB=10
BC=6
C=90
Step 2: Draw and measure the length of DE
DE=15
Step3: Calculate the ratio
The corresponding line segment to DE is line segment AB.
So, the ratio (k) is:
k= DE/AB
k= 15/10
k=1.5
Step 4: Multiply the ratio by the other line segment in step 1
In (1), we have:
BC=6
So,
EF=k*BC
EF=1.5*6
EF=9
Step 4: Draw a circle with center F and radius EF
The center of the circle is point F and the radius of the circle is 9 units
Step 5: Draw a ray from the center (i.e. point F) to DE
Refer to the attached image for
Triangle ABC
Triangle DEF
Circle with center F and radius 9
Ray from F to DE
Therefore, construction of similar triangles are given in attached figure.
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A cylinder shaped pipe is 24 inches long and has a diameter of 6 inches. Witch measurements is closest to the lateral surface area of the pipe in square inches?
The lateral surface area of the cylinder for the given measurements is equal to 452.16 square inches.
Pipe is in form of cylinder
Diameter of the cylinder = 6 inches
Height of the cylinder 'h' = 24 inches
Radius of the cylinder 'r' = diameter / 2
= 6/ 2
= 3inches
lateral surface area of the cylinder = 2πrh
value of π = 3.14
Substitute the value we get,
⇒lateral surface area of the cylinder = 2 × π × 3 × 24
⇒lateral surface area of the cylinder = 144π square inches
⇒lateral surface area of the cylinder = 144 × 31.4
⇒ lateral surface area of the cylinder = 452.16 square inches
Therefore, the lateral surface area of the cylindrical pipe is equal to 452.16 square inches.
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need help pls
schoology]
Answer:
31⁰
Step-by-step explanation:
[tex]a + 59 = 90[/tex]
[tex]a + 59 - 59 = 90 - 59[/tex]
[tex]a = 31[/tex]
An image of a parallelogram is shown.
What is the area of the parallelogram?
The area of the parallelogram is 416.25 cm²
What Is the Area of Parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm², m², in², etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
Given here: The height = 18.25 ft and base=22.5 ft.
Thus the area of the parallelogram is
A=18.25×22.5
A=416.25 cm²
Thus the area of the parallelogram is 416.25 cm²
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Employee Performance
Adequate
Good
Outstanding
5%
8%
10%
The employee makes 10.60 per hour.
What is the raise amount if the performance is Adequate?
The raise amount if the performance of the employee is adequate, would be $ 0. 53
How to find the raise amount ?To find the raise amount when the performance by an employee for the period is adequate, the formula is:
= Current pay per hour x Raise percentage for adequate work
Current pay per hour = $ 10. 60 per hour
Raise percentage for adequate work = 5 %
The raise amount is therefore :
= 10. 60 x 5 %
= 10. 60 x 0. 05
= $ 0. 53
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(-2/3) (4/5) + (-2/3) (-2/5)
Answer: -0.26666666666
Step-by-step explanation:
need helpppp
SCHOOLOGY
The missing angle measures are given as follows:
b = c = 137º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex in crossing segments, and these angles are congruent.
The vertical angles in this problem are:
b and c.
Additionally, these angles form a linear pair with the angle of 43º, meaning that they are supplementary, with a sum of their measures of 180º, hence their measures are given as follows:
b + 43º = 180º
b = 180º - 43º
b = 137º.
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What is the slope of a line containing the points 5,5 and -9,0
The slope of a line containing the points 5,5 and -9,0 is 5/14.
What is the slope of a line which passes through points ( p,q) and (x,y)?If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
Given;
The two points 5,5 and -9,0
m= 0-5/-9-5
m=-5/-14
m=5/14
Therefore, the slope will be 5/14.
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NEED HELP ASAP WILL GIVEE BRAINALIST TO THE CORRECT ANSWER DUE IN 20 MIN
Answer:
Below
Step-by-step explanation:
4/ 9 z - 5/9 z + 2 - 3/9 z - 9
(4-5-3)/9 z +2 - 9
-4/9 z +2-9
-4/9 z - 7
find the first second third and fourth derivative of y is equals to 10x raise to Power 9 + 25 x raise to power 4 + 68 + 6 + 12x raise to power 4
Answer:
Step-by-step explanation:
The first derivative of the given function y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:
dy/dx = 90x^8 + 100x^3 + 48x^3
= 90x^8 + 148x^3
The second derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:
d^2y/dx^2 = 720x^7 + 444x^2
The third derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:
d^3y/dx^3 = 5040x^6 + 888x
The fourth derivative of y = 10x^9 + 25x^4 + 68 + 6 + 12x^4 is:
d^4y/dx^4 = 30240x^5 + 888
randomly cut a rod into 3 pieces, what is the probability that you can form a triangle with the resulting 3 pieces?
The probability of a random rod forming a triangle if it is divided into 3 parts is 1.
Here we are asked the probability of a random rod forming a triangle if it is divided into 3 parts.
Now a point to be noted here is that we are not asked whether it forms a perfect triangle. A perfect triangle would have been the case when while making a triangle, no extra length is left out.
A triangle has three vertices and three edges. Hence we can safely say if there are 3 pieces of rod, it will ultimately form a triangle.
There might be some spare length on the side, but nonetheless, a triangle will be formed.
Hence the probability to form a triangle is 1
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One equation of a pair of dependent linear equations is 2x + 5y = 3. The second
equation will be
The local grocery store is having a sale on sports drinks. For a particular brand of sports drink, a 6-pack of 20-ounce bottles costs $4.96. What is the unit price (per ounce) for the sports drink? Round your answer to the nearest cent.
Answer:
0.24
Step-by-step explanation:
4.96÷20=0.248
Round to the nearest cent: 0.24
puja limbu did 8 out of 10 math problem and raju lama did
11 out of 15 similar math problem express the number of problem solved by each of the them in fraction and identify who did better performance
The equivalent fractions for their ratios are given as follows:
Puja Limbu: 24/30.Raju Lama: 22/30.Hence, due to the higher numerator, Puja Limbu had the better performance.
What are equivalent fractions?Equivalent fractions are fractions that have the same denominator.
The fractions for this problem are given as follows:
Puja Limbu: 8/10.Raju Lama: 11/15.The common denominator is the least common multiple of 10 and 15, which is of 30, hence the equivalent fractions are given as follows:
Puja Limbu: 24/30. -> multiply numerator and denominator by 3, as 30/10 = 3.Raju Lama: 22/30. -> multiply numerator and denominator by 2, as 30/15 = 2.More can be learned about equivalent fractions at https://brainly.com/question/24372153
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(8^x/4+4)=(8^-19x/4)
Answer:x = 1/60
Step-by-step explanation:
(8^x/4+4)=(8^-19x/4)
Apply fraction cross multiply: a/b = c/d then a*d = c*b
8^x * 4 = (4+4) * 8^-19x
simplify
8^x * 4 = 8 * 8^-19x
Apply exponet rules
xln(8) + ln(4) = (-19x +1) ln(8)
then just solve
x= 1/60
while y = -1/8
lamar is customizing his next pair of basketball shoes. the following table shows the design components and how many options he has for each. * how many different shoe combinations can lamar create?
By applying Fundamental counting principle, it can be concluded that there are 2560 different shoe combinations that can be created.
Fundamental counting principle states that if the first event can be done in k₁ different ways, the second event can be done in k₂ different ways, and so on until the [tex]n^{th}[/tex] event, then the number of different ways of all these events is K, where:
K = k₁ x k₂x . . . x kₙ
The following table shows the design components and how many options Lamar has for each:
Design component Number of options
Primary color 8
Secondary color 8
Sole color 8
Lace color 5
Then we can calculate the number of different combinations that can be created as follows:
Number of combinations = number of option₁ x number of option₂ x
number of option₃ x number of option₄
= 8 x 8 x 8 x 5
= 2560
Thus there are 2560 different shoe combinations that can be created.
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Rajiv travels from Calais to Paris.He travels 185 miles.Find out how far he travels in kilometers.
He travels a total distance of 296 Kilometers.
What is distance?The amount of space between two locations is defined as distance. It is often measured in metres, kilometres, or miles. Distance may also refer to the length of time it takes to go from one location to another. The length of a path or the size of an item may be measured using distance. Distance may also be used to calculate an object's speed or the time it takes to go a specific distance.
Given :
miles = 185
Since , 5 miles = 8 kilometers
Therefore, on converting , 185 miles into kilometers , we get
185/5 = 37 kilometers
Also , it has given that 37 Km is exactly 8 times , thus
total distance = 37 * 8 = 296
Hence , he travels a total distance of 296 Kilometers.
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What are the statements and reasons to prove that a kite is a kite
The statements and reasons to prove that a kite is a kite are:
Has two pairs of equal sides, AB=BC and AD=CD Angle A = angle C The diagonal of AC is not the same length as BDAbout kite shapeA kite is a flat figure that has 2 pairs of equal sides and 2 diagonals that are perpendicular and intersect.
In terms of shape, the kite is similar to a rhombus, but the difference is that in a rhombus, all four sides are the same length.
The nature of a kite's flat wake is that it consists of 4 sides with 2 pairs of sides of the same length.
Characteristics of KitesThe properties of a kite's flat wake are as follows:
• Has 4 sides consisting of 2 pairs of equal sides, namely AB = AD and BC = CD
• Has 4 corners consisting of 2 pairs of opposite angles
• Has 2 opposite angles that are equal in size, namely ∠ABC = ∠CDA
• Has 2 diagonals that intersect and are perpendicular
• 2 Diagonals that intersect each other with different lengths
• Has 1 axis of symmetry
• Has 1 fold symmetry
• Has 1 rotational symmetry
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p to view steps... 9 p 2 − 1 p q − 2 q ÷ 1 − 3 p 3 p − 6 9 p 2 - 1 p q - 2 q ÷ 1 - 3 p 3 p - 6
By applying Algebraic fractions simplifying concept, it can conclude that the simplified expression is - (9p + 3) / q.
Algebraic fractions simplifying can be done by factoring the quantifier and denominator, then dividing by the common factors of the quantifier and denominator.
We have the following algebraic fraction:
((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)
To simplify this expression, we will do the following steps:
First, we apply the division rule: (a/b) / (c/d) = ad / bc:
((9p² - 1) / (pq - 2q)) / (1 - 3p) / (3p - 6)
⇔ ((9p² - 1) (3p - 6)) / ((pq - 2q) (1 - 3p))
Then we find the factors of (9p² - 1), that are (3p - 1) (3p + 1):
⇔ ((3p - 1) (3p + 1) (3p - 6)) / ((pq - 2q) (1 - 3p))
Factor other expressions that are not already factored in:
⇔ ((3p - 1) (3p + 1) 3 (p - 2)) / (q (p - 2) (1 - 3p))
Now we cancel the common factor (p - 2), so we have:
⇔ (3 (3p - 1) (3p + 1)) / (-q (3p - 1))
Then we cancel the common factor (3p -1), so we have:
⇔ (3 (3p + 1)) / -q
Finally, we expand the expression:
⇔ - (9p + 3) / q
Thus the simplified expression is - (9p + 3) / q.
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70 POINTS !!!! please help and show work !!
Find the equation of the line passing through (1,5) and parallel to y = 3x - 1.
The equation of the line passing through (1,5) and parallel to y = 3x - 1 is f(x) = 3x + 2
What is the equation of a line?The equation of a line can be formed with the help of the slope of the line and a point on the line.
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.
Parallel lines have the SAME SLOPE. Since the formula is in the form y=mx+b, the slope. m. is 3.
The line is y = 3x + b and goes through (1,5), so, let's determine b:
5 = 3(1) + b
2 = b
Hence, the equation of the line is f(x) = 3x + 2
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