A building is 5 feet tall. the base of the ladder is 8 feet from the building. how tall must a ladder be to reach the top of the building? explain your reasoning.show your work. round to the nearest tenth if necessary.
Answers
The ladder must be 9.4 ft to reach the top of the building
Here, we want to get the length of the ladder that will reach the top of the building
Firstly, we need a diagrammatic representation
We have this as;
As we can see, we have a right triangle with the hypotenuse being the length of the ladder
We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides
Thus, we have;
[tex]\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}[/tex]
Related Questions
Find two functions f and g such that (f O g) (x) =h(x) [tex]h(x) = (9x + 7)^{2} [/tex]
Answers
f(x) = x² and g(x) = 9x + 7
Explanation:(fog) (x) = h(x)
h(x) = (9x + 7)²
To get the two functions, we need to understand that the function g(x) will be inserted in function f(x) to get (fog)(x)
g(x) = 9x + 7
This is the function that will be inserted into f(x)
Since we have a square, the function of f(x) will have a square
f(x) = x²
Putting both together, replace x with (9x + 7) in f(x)
(fog)(x) = (9x + 7)²
Hence, f(x) = x² and g(x) = 9x + 7
Use the pythagorean theorem to find the distance between (2,8) and (-8,2) A. 16.0 B. 4.0 C. 12.3 D. 11.7
Answers
Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:
[tex]\begin{gathered} d^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ \text{Thus:} \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Since we have the two coordinates: (2, 8) and (-8, 2)
where:
(x1, y1)= (2, 8)
(x2, y2) = (-8, 2)
Therefore, the distance between them is:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{((-8)_{}-2_{})^2+(2-8)^2} \\ d=\sqrt[]{((-10_{})^2+(-6)^2} \\ d=\sqrt[]{100+36} \\ d=\sqrt[]{136} \\ d=11.66 \\ d=11.7\text{ (to one decimal place)} \end{gathered}[/tex]Therefore, the distance between the two p is: 11.7
Correct option is: Option D
The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= 0.2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012, where x = 0 corresponds to 2003, x = 1to 2004, and so on, and y is in millions of students.(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is millions.(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
In order to find the projected enrollment for 2008, we need to use the value of x equal to 5, because x represents the number of years after 2003.
Then, using the linear model with x = 5, we have:
[tex]\begin{gathered} y=0.2145\cdot5+15.79\\ \\ y=1.0725+15.79\\ \\ y=16.8625 \end{gathered}[/tex]Rounding to the nearest tenth, we have y = 16.9.
Isolate one radical on one side of the equation.Raise each side of the equation to a power equal to the index of the radical and simplify. Check all proposed solutions in the original equation.
Answers
The given equation is
[tex]\sqrt[]{3\text{ - 2x}}\text{ - 4x = 0}[/tex]The first step is to add 4x to both sides of the equation. We have
[tex]\begin{gathered} \sqrt[]{3\text{ - 2x}}\text{ - 4x + 4x = 0 + 4x} \\ \sqrt[]{3\text{ - 2x}}\text{ = 4x} \\ \text{Squaring both sides of the equation, we have} \\ (\sqrt[]{3-2x)}^2=(4x)^2 \\ 3-2x=16x^2 \end{gathered}[/tex]3 - 2x = 16x^2
Adding 2x to both sides of the equation, we have
3 - 2x + 2x = 16x^2 + 2x
3 = 16x^2 + 2x
Subtracting 3 from both sides of the equation, we have
3 - 3 = 16x^2 + 2x - 3
0 = 16x^2 + 2x - 3
16x^2 + 2x - 3 = 0
This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have
16x^2 + 8x - 6x - 3 = 0
By factorising, we have
8x(2x + 1) - 3(2x + 1) = 0
Since 2x + 1 is common, we have
(2x + 1)(8x - 3) = 0
2x + 1 = 0 or 8x - 3 = 0
2x = - 1 or 8x = 3
x = - 1/2 or x = 3/8
We would substitute these values in the original equation to check. We have
[tex]\begin{gathered} For\text{ x = }-\text{ }\frac{1}{2} \\ \sqrt[]{3\text{ - 2}\times-\frac{1}{2}}\text{ - 4}\times-\text{ }\frac{1}{2}\text{ = 0} \\ \sqrt[]{3\text{ - - 1}}\text{ + 2 = 0} \\ \sqrt[]{4}\text{ + 2 = 0} \\ 2\text{ + 2 }\ne0 \end{gathered}[/tex][tex]\begin{gathered} \text{For x = }\frac{3}{8} \\ \sqrt[]{3\text{ - 2}\times\frac{3}{8}}\text{ - 4}\times\frac{3}{8}\text{ = 0} \\ \sqrt[]{3\text{ - }\frac{3}{4}}\text{ - }\frac{3}{2}=\text{ 0} \\ \sqrt[]{\frac{9}{4}}\text{ - }\frac{3}{2}\text{ = 0} \\ \frac{3}{2}\text{ - }\frac{3}{2}\text{ = 0} \end{gathered}[/tex]The solution is x = 3/8
11-3x75-1 what is the answer?
Answers
Answer:
Step-by-step explanation:
-215
Answer:
-215
Step-by-step explanation:
the answer to 11-3x75-1 is -215
I need help simplify each expression look for the terms first
Answers
8k + 3 +4k
________________
First, add the k
8k + 4k = (8+4) k = 12 k
________________
you add if there are other variables or numbers
3
________________
12k + 3
Do you have any questions regarding the solution?
Expected FrequencyA fair five sided spinner is spun 40 times.a) How many times would it be expectedto land on red?P(Red) = 15It would be expected to land on redItimes.1-5Hint:Set up and solve a proportion.
Answers
It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.
[tex]\frac{1}{5}\cdot\frac{8}{8}=\frac{8}{40}[/tex]So, it is expected to land 8 times on the red colour.
So answer is,
[tex]\frac{1}{5}=\frac{8}{40}[/tex]and It would be expected to land on red 8 times.
Assume that 5 cards are drawn from a standard deck of 52 cards. How many ways can I get 3 sevens, 1 six and 1 five?
Answers
Answer
64 ways
Explanation
In a standard deck of 52 cards, there are four 'sevens', four 'sixes' and four 'fives'.
Using Combination formula, the number of ways to pick 3 sevens, 1 six and 1 five is given as
⁴C₃ × ⁴C₁ × ⁴C₁
= 4 × 4 × 4
= 64
Hope this Helps!!!
i need help solving -12=3-2K-3K
Answers
Solve
[tex]\begin{gathered} -12=3-2k-3k \\ \text{Collect like terms} \\ -12-3=-2k-3k \\ \text{Note that when a positive value crosses the equality sign, it becomes negative} \\ \text{Similarly when a negative value crosses the equality sign it becomes positive} \\ \text{Hence, 3 crosses over and becomes negative} \\ -12-3=-2k-3k \\ -15=-5k \\ \text{Divide both sides by -5} \\ \frac{-15}{-5}=\frac{-5k}{-5} \\ 3=k \end{gathered}[/tex]1 B 0 A C If the distance from point A to point C is 7.5 units and O=40°, find the distance from point A to point B to the nearest tenth. (1 Point) a. 8.9 b. 4.7 C. 6.3 d. 2.5
Answers
Answer
Option C is correct.
AB = 6.3 units
Explanation
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using trignometric relations, we can see that TOA wil work for this
Tan θ = (Opp/Adj)
θ = 40°
Opp = AB = ?
Adj = AC = 7.5 units
Tan 40° = (Opp/7.5)
Opp = AB = 7.5 (Tan 40°) = 6.3 units
Hope this Helps!!!
Factor 9x^4-18x^3+36x^2
Answers
Given the expression:
[tex]9x^4-18x^3+36x^2[/tex]You can factor it by following these steps:
1. Find the Greatest Common Factors (GCF) of the terms:
- The Greatest Common Factor (GCF) of the coefficients can be found by decomposing each coefficient into their Prime Factors:
[tex]\begin{gathered} 9=3\cdot3 \\ 18=2\cdot3\cdot3 \\ 36=2\cdot2\cdot3\cdot3 \end{gathered}[/tex]Notice that all the coefficients have:
[tex]3\cdot3=9[/tex]Therefore, that is the Greatest Common Factor (GCF) of the coefficients.
- The Greatest Common Factor (GCF) of the variables is the variable with the lowest exponent:
[tex]x^2[/tex]Hence:
[tex]GCF=9x^2[/tex]2. Now you can factor it out:
[tex]=9x^2(x^2-2x+4)[/tex]Hence, the answer is:
[tex]9x^2(x^2-2x+4)[/tex]make a table of values then graph the following quadratic functions, label atleast 5 points
Answers
Given the function below:
[tex]f(x)=\frac{-4(x-3)^2}{9}+4[/tex]Substituting each value of x in the table in the function above, we get
[tex]\begin{gathered} f(0)=\frac{-4(0-3)^2}{9}+4\text{ = }\frac{-4(-3)^2}{9}+4 \\ \\ f(0)=\frac{-4\times9}{9}+4\text{ =-4+4 = 0} \end{gathered}[/tex][tex]f(1)=\frac{-4(1-3)^2}{9}+4\text{ =}\frac{-4\times4}{9}+4=\frac{-16}{9}+4=\frac{20}{9}[/tex][tex]f(6)=\frac{-4(6-3)^2}{9}+4\text{ = }\frac{-4(3^2)}{9}+4\text{ =-4+4 = 0}[/tex]the sum of billiard balls was arranged in an equilateral triangle and 7 balls were extra. Then the same set of billiard balls was arranged into a triangle where each side has one more ball than in the first arrangement but now the new arrangement cannot be completed because there is a shortage of three balls. How many balls are in the set?
Answers
There were 52 billiard balls in the set.
Assume that billiard balls are arranged in rows to form an equilateral triangle, then the first row consists of 1 ball, second row consists of 2 balls, and third row consists of 3 balls, and so on. So there must be n balls in the nth row.
So, the total number of billiard balls that forms the equilateral triangle with n rows is:
1 + 2 + 3 + ... + n = n(n + 1)/2
Let x1 and x2 be the total number of balls in the first and second arrangements respectively.
Then,
x1 = n(n + 1)/2 + 7
It has been said that there were 3 lesser balls in the second arrangement:
x2 = (1 + (n + 1))/2 × (n + 1) - 3
x2 = (n + 1) × (n + 2)/2 - 3
Since x1 = x2,
n(n + 1)/2 + 7 = (n + 1) × (n + 2)/2 - 3
We solve above equation to find the value of n,
multiplying both the sides by 2
n(n + 1) + 14 = (n + 1)(n + 2) - 6
n² + n + 14 = n² + 3n + 2 - 6
n - 3n = -4 - 14
-2n = -18
n = 9
So, x1 = 9(9 + 1)/2 + 7
= 9(5) + 7
= 45 + 7
= 52
Therefore, there were 52 billiard balls in the set.
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please help me work through this homework problem! thank you!
Answers
Given:
Given the function
[tex]y=3+\frac{3}{x}+\frac{2}{x^2}[/tex]and a point x = 3.
Required: Equation of the line tangent to y at x = 3.
Explanation:
The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.
[tex]y^{\prime}=-\frac{3}{x^2}-\frac{4}{x^3}[/tex]Substitute 3 for x into the derivative.
[tex]\begin{gathered} y^{\prime}|_{x=3}=-\frac{3}{3^2}-\frac{4}{3^3} \\ =-\frac{31}{27} \end{gathered}[/tex]Therefore, the slope of the tangent line is -31/27.
Substitute 3 for x into y.
[tex]\begin{gathered} y|_{x=3}=3+\frac{3}{3}+\frac{2}{3^2} \\ =3+1+\frac{2}{9} \\ =4+\frac{2}{9} \\ =\frac{38}{9} \end{gathered}[/tex](3, 38/9) is the only point on the tangent line where it intersects the original graph.
Plug these coordinates along with slope into the general point-slope form to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-\frac{38}{9}=-\frac{31}{27}(x-3) \end{gathered}[/tex]Solving for y will give the equation in slope-intercept form.
[tex]\begin{gathered} y=-\frac{31}{27}(x-3)+\frac{38}{9} \\ =-\frac{31}{27}x+\frac{69}{9} \end{gathered}[/tex]Final Answer: The equation of the tangent line is
[tex]y=-\frac{31}{27}x+\frac{69}{9}[/tex]
State whether the given information is enough to prove that ABCD is a parallelogram.
Answers
From the image given, the data shows that
[tex]\begin{gathered} <1\cong<3 \\ \text{and} \\ AD\cong BC \end{gathered}[/tex]We can observe that
[tex]\begin{gathered} \Delta BDA\cong\Delta DBC\text{ (SAS)} \\ \text{ Reasons:} \\ AD\cong BC\Rightarrow side \\ \measuredangle1\cong\measuredangle3\Rightarrow\text{angle} \\ BD\cong DB(common\text{ sides or reflexive)}\Rightarrow\text{side} \end{gathered}[/tex]Thus, from the above we can say that;
[tex]\begin{gathered} AB\cong DC\text{ (corresponding parts of congruent triangles are congruent)} \\ \text{Therefore, } \\ \measuredangle2\cong\measuredangle4 \end{gathered}[/tex]Hence
Yes, the given information is enough to prove that ABCD is a parallelogram.
Given the formula for the perimeter of a rectangle, p=2l+2wwhich answer would you get if you solve for l? p−2w 2 p/w-2 p/2−2w p−2l/2
Answers
If we have:
[tex]p=2w+2l[/tex]To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:
[tex]\begin{gathered} p=2w+2l \\ 2w+2l=p \\ 2w-2w+2l=p-2w \\ 2l=p-2w \end{gathered}[/tex]Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:
[tex]\begin{gathered} 2l=p-2w \\ \frac{2l}{2}=\frac{p-2w}{2} \\ l=\frac{p-2w}{2} \end{gathered}[/tex]So, the answer we would get is
[tex]\frac{p-2w}{2}[/tex]Convert 255 to base 2
Answers
We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.
Convert 255 to base 2?
255 = 8 bits
255 in Binary: 255₁₀ = 11111111₂
Binary is a system used in mathematics and computer science where values and numbers are stated as 0 or 1.Binary is base-2, which means that there are just two digits or bits used.For computers, 1 denotes truth or "on," while 0 denotes falsehood or "off." Computers communicate and represent information using binary code.Everything you see on a computer, including letters, numbers, and pictures—basically everything—is made up of multiple 0s and 1s combinations. One of the four different kinds of number systems is the binary number system.When used in computer programs, binary numbers are solely represented by the digits 0 (zero) and 1. (one).Here, the base-2 numeral system is used to represent the binary numbers.One binary number is (101)2, for instance. The modern binary number system was first suggested and refined by Gottfried Leibniz in the 17th century in his article Explication de l'Arithmétique Binaire [1].The system was created by Leibniz about 1679, although it wasn't published until 1703.He had already used 0 and 1.To learn more about binary refer
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Consider the non-right triangle below.Suppose that m∠CAB=62∘, and that x=35 cm and y=17 cm. What is the area of this triangle? cm^2
Answers
Given that:
x=35 cm and y=17 cm
and angle CAB= 62 degree
[tex]\begin{gathered} A=\frac{1}{2}\times x\times y\times\sin (\angle CAB) \\ A=\frac{1}{2}(35)(17)\sin (62) \\ A=297.5\times\sin (62) \\ A=262.67cm^2 \end{gathered}[/tex]Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
Which data display would you use to represent this data?
O Histogram
Scatter plot
O Line graph
O Line plot
Answers
To represent the data, histogram would have been used.
Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 8 10 16
Total Pages 25 38 85 76 180
In a histogram, a graphical representation of the distribution of data is done. The histogram is represented by a set of rectangles, adjacent to each other and each bar represent a kind of data.
Here the number of chapters can be kept in x axis and the total number of pages can be kept in the y axis.
Therefore, histogram would be used to display the data.
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what is a unit rate for meter per second if a car travels 274 m in 17 seconds
Answers
The rate is 274m/17s = 16.1176m/s
Find the surface area Formula: SA= p * h + 2 * B
Answers
Given:
For the given figure,
[tex]h=2ft,w=3ft,l=8ft[/tex]The surface area is calculated as,
[tex]\begin{gathered} S=2lh+2wh+2wl \\ S=2\cdot8\cdot2+2\cdot3\cdot2+2\cdot3\cdot8 \\ S=32+12+48 \\ S=92 \end{gathered}[/tex]Answer: surface area is 92 square ft.
What is the sum of the exterior angles of a polygon with 30 sides a) 180°b) 30°c) 90°d) 360°
Answers
Note that:
The sum of the exterior angles of a polygon does not depend on the number of sides of the polygon
The sum of the exterior angles of a polygon is 360°
Therefore, the correct option is 360°
Jenna bought a package of 2 chicken drumsticks. If the package weighed 0.232 kg, what is the average weight of
each drumstick?
Answers
Answer:
0.116
Step-by-step explanation:
[tex]\frac{0.232}{2}[/tex] = 0.116
The pie chart below shows the percentage of total revenue that a publisher receives from publications.A) which category accounts for approximately 1/5 of publishers total revenue type in which one (textbooks, cookbooks, magazines, paperbacks,poetry, nonfiction B)Approximately percentage total revenue from paperbacks poetry combined C) if revenue from nonfiction 10% total revenue approximately percentage total comes from poetry
Answers
a) To determine which category represents approximately one-fifth of the publisher's revenue, you can compare the given pie chart with a pie chart divided into 5 parts.
The category that is approximately one-fifth of the revenue, that is, 20% of the total revenue, is textbooks.
To solve parts b and c you can use the following pie chart to compare with the given chart for the publisher's revenue:
b) Looking at the pie charts, the categories "paperback" and "poetry" are approximately 20% of the total revenue.
c) The category "Nonfiction" is 10% of the total revenue, the category "poetry" is approximately half of the size of the category "nonfiction" so you can say that it corresponds to 5% of the total revenue.
Kayla has $37.99 in her checking account. she uses her debit card to make purchases of $26.29 and $22.98 which overdraws her account. her bank charges her account an overdraft fee of $25.00. She then deposits her paycheck for $55.07 from her part time job. what is the balance in her account?
Answers
Aye itz just me, this is the solution:
Initial balance = $ 37.99
Purchase 1 = ($ 26.29)
Purchase 2 = ($ 22.98)
Overdraft fee = ($ 25.00)
Deposit = $ 55.07
______________________
New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07
New balance = $ 18.82
An example of an experiment that leads to a uniform probability distribution is...Choose one answer. 1. the sum of rolling two dice 2. measuring the heights of all the students in a school 3. tossing a coin ten times and recording the number of heads 4. selecting a card from a deck of 52 cards
Answers
Solution
A probability distribution in which all of the values of the random variable occur with equal probability is called a uniform probability distribution. Describe an example of an experiment that would produce a uniform distribution. Then find the theoretical probabilities that would result from this experiment. Include a table and graph of the distribution.
Answer:
The theoretical probability experiment of rolling a die would result in a uniform distribution because the probabilities of rolling a 1,2,3,4,5,6 are all equally likely to occur.
Therefore the sum of rolling two dice is an option
Hence the correct answer is
Option 1
What is the area of the blue shape?
Answers
In rectangle , 38.5 sq units is the area of the blue shape.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.We can split the shape into two rectangles.
The small rectangle at the top has an area of 14 sq units (2 * 7).
The middle rectangle has an area of 49 sq units ( 7*7).
Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.
Adding that to 14 sq units will give us 38.5 sq units.
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Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/
Answers
Prob 22
7 + | 6v + 7| ≤ 60
then
| 6v + 7| ≤ 53
now eliminate lines ||
6v + 7 ≤ 53
and
6v + 7 ≤ - 53,. 6v ≤ -60
Now solve for x
6v ≤ 47,. v≤ 46/6
also
6v ≥ -47,. v≥ -46/6
Then answer is
-10 ≤ v ≤ -46/6
Graph for problem 22
The confidence interval on estimating the heights of the students is given as (5.5, 6.5). Find the sample proportion of the confidence interval.
Answers
Answer:
Step-by-step explanation:
Sample SpaceFind the number of outcomes in the following experiments. 1. Selecting a letter from the English alphabet
Answers
The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.
S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}