suppose a 13 foot ladder is leaning against a building. Reaching to the bottom of a second floor window 12 ft above the ground. How far is the base of the ladder from the building? Round your answer to the nearest 10th
5 ft
4ft
3ft
6ft
Answers
Answer: First Choice. 5ft
Step-by-step explanation:
Here we need to know the idea of the Pythagorean theorem.
Since a building is straight, the base angle is a right angle, thus it would be a right triangle.
Pythagorean Theorem: a² + b² = c²
**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)
Solve:
Given information
a = 12 ft
c = 13 ft
b = unknow base length
Given formula for Pythagorean Theorem
a² + b² = c²
Substitute values into the formula
12² + b² = 13²
Simplify exponents
144 + b² = 169
Subtract 144 on both sides
144 + b² - 144= 169 - 144
b² = 25
Square root both sides
√b² = √25
\(\boxed{b=5}\)
Hope this helps!! :)
Please let me know if you have any questions
Related Questions
Kanya is comparing the rate for shipping and handling for two online shopping websites. For the item she has selected, Big Bargain Bonanza charges $8.00 for handling and $1.25 per pound for shipping. Discount Deals Depot charges $9.50 for handling and $0.95 per pound for shipping for the same item. If her item weighs 6 lbs, which website charges less for shipping and handling, and how much does it charge?
A. Big Bargain Bonanza; $15.50
B. Discount Deals Depot; $10.45
C. Big Bargain Bonanza; $9.25
D. Discount Deals Depot; $15.20
Answers
D. Discount Deals Depot; $15.20
Why?
Lets do Big Bargain Bonanza first.
$8.00 would stay the same as it is for handling. The only number that would change is $1.25, it uses the the words PER pound for shipping.
Your equation would look like this with p being how many pounds Kanya is shipping:
$8.00+$1.25p
Now we just plug in the numbers.
$8.00+$1.25(6)=
$8.00+$7.50=
$15.50
The same games for Discount Deals Depot.
$9.50+$0.95(6)=
$9.50+$5.70=
$15.20
So in conclusion Discount Deals Depot; $15.20 is cheaper than Big Bargain Bonanza;$15.50
Which of the following is equivalent to the expression below?
3(5-2i)
Answers
Answer: 15 - 6i
Step-by-step explanation:
3(5-2i)
3×5+3×(−2i)
Do the multiplications.
15−6i
Amy spent $35 on a magazine and seven notepads. If the magazine costs $7, then how much was each notepad?
Answers
Hello :D
To work this out you need to do:
$35 - $7 = $28
$28/7 = $4
Each notebook costed $4
Solve to find the variable 8t+4(20.55-t)=138
Answers
2) Add similar values
3) Subtract
4) Divide
t = 13.95
What is the value of x to the nearest tenth?A.25.7B.43.2C.88.8D.89.7
Answers
(5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9).
Answers
Answer?
Step-by-step explanation:
Ruiz Creek overflows its banks after 12 centimeters of rainfall. One day rain fell at the rate of 4 centimeters every hour. How much time did people living by Ruiz Creek have to get away from danger?
2 hours
3 hours
4 hours
5 hours
Please assist
Answers
Answer:
3 hours
12 (the amount of cm it takes to overflow) divided by 4 (the amount of rainwater that falls in an hour) = 3
what the meaning of the second singular ideal(definition and examples) and what is different between singular ideal Z(R) and singular second ideal??
Answers
In ring theory, an ideal is a subring that has been multiplied on the left or right by the entire ring, or, equivalently, a subset of the ring that is closed under addition and multiplication by arbitrary elements of the ring. A second ideal of a ring R is a nonempty subset of R that is closed under addition and multiplication by all non-units in R.
The definition of a second ideal is therefore similar to that of an ideal, except that it is required that the ideal not contain any units of R, unlike the ideal, which can include units.
Singular ideals are a family of ideals of a commutative ring R that can be used to give information about the intersection of polynomial ideals with the set of singular points of an algebraic set defined by the ideals. The Z(R) singular ideal of a commutative ring R is the second ideal generated by the set of non-regular elements of R.
The difference between the singular ideal and the Z(R) singular ideal is that the singular ideal is the intersection of all ideals of R that vanish on the singular set of a variety defined by the ideal, while the Z(R) singular ideal is the second ideal generated by the set of non-regular elements of R.
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Gretchen's gross annual salary is $97,300. What is the maximum amount of rent she can afford to pay per month? Round answer to the nearest whole number. Do not include units.
Answers
Given:
Gretchen's gross annual salary = $97,300
The maximum amount of rent she can afford to pay per month can be found using the formula:
\(\text{Max amount of rent she can pay}=\frac{\text{\it{Gross annual salary}}}{\text{\it{Number of months in a year}}}\)
Applying the formula:
\(\text{Max amount of rent she can pay}=\dfrac{97300}{12}\)
\(= \ \$811\)
Hence, the maximum amount of rent she can afford to pay per month is $811
Answer: $811
(c) explain what would happen to the length of the interval if the confidence level were... (i) increased to 99% (ii) decreased to 80%
Answers
If the confidence level were increased to 99%, the width of the confidence interval increases, when decreased to 80%, the width of the confidence interval decreases.
What is confidence interval?A confidence interval provides a range of estimated values for a population parameter's real value. A confidence level is connected to confidence intervals. The width of the confidence interval grows as the confidence level increases. The width of the confidence interval reduces as the confidence level goes down.
Since the margin of error grows as the confidence level does as well, the confidence interval will be bigger. Hence it increases for 99% and decreases for 80%.
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Bill bought a table on sale for $630. This price was 72% of the original price.
What was the original price?
Answers
Answer:
The original price was $875.
Step-by-step explanation:
a = p * w
630 = 72% * w
630 / 0.72 = $875
$875 should be the original price, I hope this helps!
. determine whether each of the following statement is true or false: a) x ∈ {x} true b) {x} ⊆{x} c) {x} ∈{x} d) {x} ∈ {{x}}
Answers
The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.
a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.
b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.
c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.
d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.
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True or false Segment TY is congruent to segment BN
Answers
Answer:
true
Step-by-step explanation:
there are two segments between ty and bn
the grade point averages of the gourmet society are uniformly distributed between 2.5 and 3.5. a. find the probability distribution function, f(x) for this scenario. b. using part (a), find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2
Answers
The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.
The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:
f(x) = 1 / (b - a)
where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:
f(x) = 1 / (3.5 - 2.5) = 1
To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.
The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:
Probability = (width of range) / (total width)
= 0.2 / 1
= 0.2
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Guys can you please help. I dont understand. Thank you. :))))
Lines AB and CD intersect at E. If the measure of angle AEC=5x-20 and the measure of angle BED=x+50, find, in degrees, the measure of angle CEB.
Answers
Answer: 112.5
Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.
Consider a scheduling problem, where there are five activities to be scheduled in four time slots. Suppose we represent the activities by the variables A,B,C,D, and E, where the domain of each variable is {1,2,3,4} and the constraints are A>D,D>E,C
=A,C>E,C
=D,B≥A, B
=C, and C
=D+1 [Before you start this, try to find the legal schedule(s) using your own intutions.] (a) Show how backtracking solves this problem. To do this, you should draw the search tree generated to find all answers. Indicate clearly the valid schedule(s). Make sure you choose a reasonable variable ordering. To indicate the search tree, write it in text form with each branch on one line. For example, suppose we had variables X,Y, and Z with domains t,f and constraints X
=Y and Y
=Z. The corresponding search tree is written as:
X=tY=t
Y=f
X=fY=tZ=t failure
Y=f failure
failure
Z=t solution
Z=f failure
Z=f solution
[Hint: It may be easier to write a program to generate such a tree for a particular problem than to do it by hand.] (b) Show how arc consistency solves this problem. To do this you must - draw the constraint graph; - show which elements of a domain are deleted at each step, and which arc is responsible for removing the element; - show explicitly the constraint graph after arc consistency has stopped; and - show how splitting a domain can be used to sove this problem.
Answers
a) The backtracking algorithm starts by assigning a value to the first variable, A. b) The arc consistency algorithm works by iteratively removing elements from the domains of the variables.
a) Backtracking
The backtracking algorithm starts by assigning a value to the first variable, A. There are four possible values that A can take, so the algorithm will explore four branches. For each branch, the algorithm then assigns a value to the second variable, B. There are four possible values that B can take, so the algorithm will explore another four branches. The algorithm continues in this way, assigning values to the variables one at a time.
The backtracking algorithm will eventually find a solution if there is one. However, the algorithm may also explore many branches that do not lead to a solution. This is because the backtracking algorithm does not consider the constraints until it has assigned a value to all of the variables.
The search tree for the scheduling problem is shown below.
A=1B=2C=3D=4E=1
A=1B=2C=3D=4E=2
A=1B=2C=3D=4E=3
A=1B=2C=3D=4E=4
A=1B=3C=2D=4E=1
A=1B=3C=2D=4E=2
A=1B=3C=2D=4E=3
A=1B=3C=2D=4E=4
A=2B=1C=3D=4E=1
A=2B=1C=3D=4E=2
A=2B=1C=3D=4E=3
A=2B=1C=3D=4E=4
A=2B=3C=1D=4E=1
A=2B=3C=1D=4E=2
A=2B=3C=1D=4E=3
A=2B=3C=1D=4E=4
b) Arc Consistency
The arc consistency algorithm works by iteratively removing elements from the domains of the variables. The algorithm starts by considering all of the arcs in the constraint graph. For each arc, the algorithm checks if there is any value in the domain of the first variable that is inconsistent with any value in the domain of the second variable. If there is any such value, the algorithm removes the value from the domain of the first variable.
The arc consistency algorithm continues in this way, iteratively removing elements from the domains of the variables. The algorithm terminates when no more elements can be removed.
The constraint graph for the scheduling problem is shown below.
A-------D
A-------E
B-------A
B-------C
C-------E
The arc consistency algorithm will remove the following elements from the domains of the variables:
A: 1, 4
B: 2, 4
C: 2, 4
D: 1, 3
E: 1, 3
After arc consistency has stopped, the constraint graph will be as follows:
A-------D
B-------C
C-------E
The arc consistency algorithm has reduced the size of the search space by removing 12 elements from the domains of the variables. This means that the backtracking algorithm will only have to explore 24 branches instead of 32 branches.
Splitting a Domain
The arc consistency algorithm can be used to solve the scheduling problem by splitting the domain of the variable D. The domain of D can be split into two sets: {1, 2} and {3, 4}. The arc consistency algorithm will then be able to find a solution to the problem by assigning a value to D from each of the two sets.
The following is the solution to the scheduling problem using splitting a domain:
A=1
B=2
C=3
D=1
E=4
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an pail collects 1/3 of water in 5/6 of a minute. At what rate is the ail collecting water?
Answers
Answer:
You end with 2/5 of and inch per minute
Al released his balloon from the 10-yard line, and it landed at the 16-yard line. If the ball reached a height of 27 yards, what equation represents the path of his toss?
Answers
The equation of the path of the parabola is y = a(x - 13)² + 27
Given data ,
To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola
Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.
The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:
h = (10 + 16) / 2 = 13
Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)
Now, let's substitute the vertex coordinates (h, k) into the general equation:
y = a(x - 13)² + k
Substituting the vertex coordinates (13, 27)
y = a(x - 13)² + 27
To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).
This means that the highest point (13, 27) lies on the parabola
Substituting the vertex coordinates (13, 27) into the equation
27 = a(13 - 13)² + 27
27 = a(0) + 27
27 = 27
Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number
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ASAP pls
The graph shows two accounts with the same principal and annual interest rate. Use the graph to estimate the answer to each question. Show your workAbout how much more compound interest than simple interest is earned after 35 years? Remember to show your work. About how much more compound interest than simple interest is earned after 45 years? Remember to show your work.
Answers
About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
What is a graph ?
A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.
Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.
Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.
To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:
$10,000 - $4,000 = $6,000
To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:
$18,000 - $5,500 = $12,500
Therefore, about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.
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Avery leans a 24-foot ladder against a wall so that it forms an angle of 80
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the wall where the ladder reaches will be 23.6 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.
The height of the wall where the ladder reaches is given as,
\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)
\(\sf h = 24 \times \text{sin 80}^\circ\)
\(\sf = 24 \times \text{0.9848}\)
\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)
The height of the wall where the ladder reaches will be 23.6 feet.
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Prove that, in a right triangle with a 15° angle, the altitude to the hypotenuse is one fourth of the hypotenuse (without using trigonometric functions).
Answers
Answer:
a = b/4
Step-by-step explanation:
Let a be the altitude to the hypotenuse and b be the hypotenuse. The 15° angle faces a and the right angle faces b.
Using the sine rule,
a/sin15 = b/sin90
a = bsin15/sin90
= 0.25b
= 25b/100
= b/4
A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 120 meters from one entrance of the tunnel, at an angle of 42° to the perpendicular. Also according to his equipment, he is 101 meters from the other entrance of the tunnel, at an angle of 28⁰ to the perpendicular. Based on these measurements, find the length of the entire tunnel. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale. 120 meters 42° 28° 101 meters
Answers
The length of the entire tunnel is 127.88 meters by using cosine law or formulae.
Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.
\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)
Let us take surveyor as point A
one end of the tunnel denoted by point B
other end of the tunnel denoted by point C.
The length of AB is 101 meters
length of AC is 120 meters.
Measure of angle at point A = 42° + 28° =70°
Now lets find the length of tunnel
=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)
=\(\sqrt{14400+10201-24240(0.34)}\)
=\(\sqrt{24601-8246}\)
\(\sqrt{16355}\)
=127.88 meters.
Hence the length of the entire tunnel is 127.88 meters.
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(x/5) + 3 = 9
show your work
Answers
Answer:
x=30
Step-by-step explanation:
9 - 3 = (x/5)
6 = x/5
(x/5) = 6
x = 5x6
x = 30
Check
(30/5) + 3 = 9
6 + 3 = 9
Hey love!
Answer:
The answer is x = 30
Step-by-step explanation:
1. Subtract 3 from both sides
2. Simplify
3. Multiply both sides by 5
4. Simplify to 30 :)
Hope this helps you dear! ヽ(‘ ∇‘ )ノSincerely, Kelsey from Brainly.
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value of π =3.14. Find the area and perimeter of a circle of diameter 4cm
Answers
Step-by-step explanation:
If diameter=4cm,then radius=4÷2=2cm
Area of a circle=πr²
=3.14×2²
=3.14×4
=12.56cm²
Per
Which graph is right?
Answers
Answer:
top one
Step-by-step explanation:
You are not including -2 (else it would be a greater or equal sign) so the dot has to be empty. You can rule out the middle options.
At this point you either remember that "greater than" means "to the right of" or you pick a convenient number, ie, 0. see that your inequality is true (zero is greater than -2) and you pick the graph where the solid line includes 0.
Solve the problem and then click on the correct graph.
y = |x|
Answers
Answer:
2.
Step-by-step explanation:
IM smart
PLZ I NEED HELP MEE ASAP:)
Answers
Answer:
Probably have to go with B
Step-by-step explanation:
PRocess of elimination
CD = TU and RS = AB
The rest are incorrect because the lines are not in the same spot
A school purchased sand to fill a sandbox on its playground. The dimensions of the sandbox in meters and the total cost of the sand in dollars are known. Which units would be most appropriate to describe the cost of the sand?
Answers
The most appropriate units to describe the cost of the sandbox would indeed be dollars.
When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.
Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.
Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.
Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.
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i need help finding a solution to this equation: 5 (n-1/10)=1/2
Answers
Answer:
n = 1/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(n− 1 /10 )= 1/ 2
Step 1: Simplify both sides of the equation.
5(n− 1 /10 )= 1 /2
(5)(n)+(5)( −1 /10 )= 1/2
(Distribute)
5n + −1 /2 = 1 /2
Step 2: Add 1/2 to both sides.
5n + −1 /2 + 1 /2 = 1 /2 + 1 /2
5n=1
Step 3: Divide both sides by 5.
5n /5 = 1 /5
n= 1 /5
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. The probability that her trip will take longer than 80 minutes is Group of answer choices 1.00. 0.40. 0.20. 0.80.]
Answers
The probability that her trip will take longer than 80 minutes is 0.20.
The probability that the trip takes longer than 80 minutes is equal to the area of the uniform distribution to the right of 80. Since the distribution is uniform, the area to the right of 80 is equal to the proportion of the total area that is to the right of 80.
The total area under the uniform distribution is equal to the length of the interval, which is (90 - 40) = 50.
The area to the right of 80 is equal to (90 - 80) = 10.
So the probability that the trip takes longer than 80 minutes is:
10 / 50 = 0.2
Therefore, the answer is 0.20.
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