Answers
Answer:
[tex]\sqrt{122}\approx{11.05}[/tex]
Step-by-step explanation:
In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation [tex]a^2+b^2=c^2[/tex].
In the triangle on the left:
[tex]a^2+b^2=c^2[/tex]
[tex]5^2+9^2=c^2[/tex]
[tex]25+81=c^2[/tex]
[tex]106=c^2[/tex]
[tex]\sqrt{106}=c[/tex]
The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:
[tex]a^2+b^2=c^2[/tex]
[tex]4^2+(\sqrt{106})^2=c^2[/tex]
[tex]16+106=c^2[/tex]
[tex]122=c^2[/tex]
[tex]\sqrt{122}=c[/tex]
[tex]c\approx{11.05}[/tex]
Related Questions
1+1 I dont know what's the answer
Answers
We are given the following operation
[tex]1+1[/tex]The result of this operation is the addition of one and another one that is by definition 2, we represent it like thio
What is the value of the expression below? 64 + 16 A. 4 C. - 4 B. 1 D. 8
Answers
We want to find the value of the expression:
[tex]\frac{64}{16}[/tex]Since 2 is a common factor of both numerator and denominator, we divide by 2s:
[tex]\frac{64}{16}=\frac{32}{8}=\frac{16}{4}=\frac{8}{2}=\frac{4}{1}=\text{ 4}[/tex]The answer is 4. (Option A)
DO ev ew 1 A local business is installing a ramp to the back door of t the ramp is 80 inches while the vertical height of the ran What is the approximate degree measure of the angle of 2
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Using the given information, let's make a diagram
To find x, we just have to use the sine function which is equivalent to the ratio between the opposite leg and the hypotenuse.
[tex]\begin{gathered} \sin x=\frac{20}{80}=\frac{1}{4} \\ x=\sin ^{-1}(\frac{1}{4}) \\ x\approx14 \end{gathered}[/tex]Hence, the angle of elevation is 14°.A pet store has 8 cats, 12 dogs, and 3 rabbits. The ratio 8:23 compares Irby Pets 1 dogs to cats 2 cats to dogs 3 rabbits to cats 4 cats to all animals
Answers
The ratio for each animal between the stores is the divition of pet store with Irby Pets so:
For cats is going to be:
[tex]\frac{8}{2}=4[/tex]So the ratio is 4:1
for dogs is going to be:
[tex]\frac{12}{3}=4[/tex]So the ratio is again 4:1
So the total ratio will be 4:1
if you walk 200 meters in 1 minute, 400 meters in 4 minutes and 800 meters in 10 minutes find your average velocity for the whole walk
Answers
First, calculate each velocity:
[tex]v=\frac{distance}{time}[/tex]so:
[tex]v1=\frac{200m}{1min}[/tex][tex]v2=\frac{400m}{4min}=\frac{100m}{min}[/tex][tex]v3=\frac{800m}{10min}=\frac{80m}{min}[/tex]Now calculate the average between the 3 velocities:
[tex]av\text{ }v=\frac{200+100+80}{3}=\frac{126.67m}{min}[/tex]The answer is 126.67 m per minute.
ze space below the questo8. Each of the 10 floors in the largebuildings has 8 windows on the front andon the back and 4 windows on each ofthe 2 sides. A cleaning contractor willwash the windows for $6 each. What isthe cost of washing all the windows inthe 22 large buildings?
Answers
Step 1
Find the number of windows on each floor
In a large building, there are 10 floors, each floor has the following;
[tex]\begin{gathered} 8\text{ windows }in\text{ the front} \\ 8\text{ windows in the back} \\ 4\text{ windows on the side to the right} \\ \text{and} \\ 4\text{ windows to the side on the left} \\ \text{Therefore, each floor has 24 windows} \end{gathered}[/tex]Step 2
Find the number of windows in a large building
[tex]\begin{gathered} \text{There are 10 floors,} \\ \text{Number of windows in each large building = 10 }\times24\text{ = 240 windows} \end{gathered}[/tex]Step 3
Find the cost the cleaning contractor will take to clean the windows in each building.
[tex]\text{\$}6\text{ }\times240\text{ = \$}1440[/tex]Step 4
Find the cost of cleaning all the windows in 22 large buildings
[tex]22\times\text{ \$}1440=\text{ \$}31,680[/tex]Hence, the cost of washing all windows in the 22 large buildings = $31,680
Two-thirds of the people on a hike are adults. If there are 36 adults, what isthe total number of people on the hike?
Answers
You have the following information:
- Two-thirds (which means 2/3) of the people on a hike are adults.
- There are 36 adults
In order to calculate the number of people, you consider that 36 is 2/3 of the total people. If you name x as the total people, the number of adults is 2/3x. Thus, you can write the following algebriac expression:
2/3 x = 36
you solve the previoues equation for x. First, you multiply both sides by 3 and you divide both sides by 2.
x = 36(3/2) = 108/2 = 54
Hence, the number of people on the hike is 54
The length of a rectangle is 2 meters less than 3 times the width. The perimeter is 60 meters. Find the width.The width ismeters.
Answers
Step 1
Let x= the width
[tex]3x-2=length[/tex](because the length is 2 meters less than 3 times the width)
Step 2
The perimeter of a rectangle is given as;
[tex]\begin{gathered} P=2length+2width \\ P=2(3x-2)+2x \\ P=60 \end{gathered}[/tex][tex]\begin{gathered} 60=6x-4+2x \\ 60=8x-4 \\ 60+4=8x \\ x=8m \end{gathered}[/tex]Answer;
[tex]Width=8m[/tex]What is the value of x?
Answers
SOLUTION
The principle behind the Exterior Angle Theorem is that:
the sum of two interior angles is equal to one exterior angle.
In this question, we have that :
X + ( X - 48 ) = X + 50
Collecting like terms, we have that:
2 X - 48 = X + 50
2X - X = 50 + 48
X = 98 Degrees.
CONCLUSION: The value of X = 98 Degrees.
Mr.Foltz has a box for gym class. In the box are 5 basketballs, 9 softballs, 12 volleyballs, and 23 soccer balls. what is the ratio of the vollyballs to basketballs?
Answers
5. What is the order of magnitude for the total weight of 5 cars that weigh 3,000 pounds each?6. 20,000 people voted in each county, and there are 7 counties. What is the order of magnitude for the total number of people who voted?
Answers
An order of magnitude is the class of scale of any amount in which each class contains values of a fixed ratio to the class preceding it. Usually, the amount scaled is 10, and the scale is the exponent applied to this amount.
Question 5
The weight of each car is 3,000 pounds. There are 5 cars in total. Therefore, the total weight is given to be:
[tex]\Rightarrow3000\times5=15000\text{ pounds}[/tex]Writing the calculated weight in standard form, scaling to 10, we have:
[tex]15000=1.5\times10^4[/tex]Therefore, the order of magnitude is 4.
Question 6
The number of people that voted per county is 20,000. There are 7 counties in total. Therefore, the total number of people that voted is:
[tex]\Rightarrow20000\times7=140000[/tex]Writing the calculated number in standard form, scaling to 10, we have:
[tex]140000=1.4\times10^5[/tex]Therefore, the order of magnitude is 5.
Hello, is it possible to help me understand this question a little better?
Answers
1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:
As we can see in each step the aim is to cancel the leading coefficient.
2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:
[tex]\frac{3x^3-4x^2+5x-2}{3x+2}=\quad x^2-2x+3-\frac{8}{3x+2}[/tex]Note that the remainder is written above the divisor on the final answer.
In how many ways can a committee of three men and two women be formed from a group of eight men and seven women?
Answers
By counting principle rule, we have
[tex]\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}[/tex]Then the ways a committee of three men and two women can be formed is
[tex]\binom{8}{3}\cdot\binom{7}{2}=1176[/tex]Therefore, there are 1176 possible ways.
13. Michael found that the difference
between two numbers is 259.
What could the two numbers be?
How did you find the numbers?
Answers
The numbers whose difference are calculated could be 300 and 41
How to determine the two numbers?From the question, we have the following statement that can be used in our computation:
The difference between two numbers is 259
Represent the two numbers with x and y
So, we have the following representation
x - y = 259
Make x the subject of the formula
This gives
x = 259 + y
Assume y is 41
So, we have
x = 259 + 41
Evaluate the sum
x = 300
Hence, the numbers are 300 and 41
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Find the surface areaDo not round pleaseFormula: SA= 2 * 3.14 * r * h + 2 * 3.14 * r^2
Answers
Given:
The radius of cylinder is r = 2 yd.
The height of cylinder is h = 7.
Explanation:
The formula for the surface area of cylinder is,
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values in the formula to determine the surface area.
[tex]\begin{gathered} S=2\cdot3.14\cdot2\cdot7+2\cdot3.14\cdot(2)^2_{} \\ =87.92+25.12 \\ =113.04 \end{gathered}[/tex]Answer: 113.04
Name Samantha cebolos Date 3/8/202 Kuta Software - Infinite Algebra 2 Absolute Value Inequalities Solse each inequality and graph its solution. 2) Ip+4158 1 onls 18 -12 -10 - - - belzaalila -8LPtube -2 -1 0 1 2 8 -BHL PLO
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} |5x|\le10 \\ \Rightarrow5x\le10 \\ =\frac{5}{5}x\le\frac{10}{5} \\ =x\le2 \\ \\ OR \\ |5x|\le10 \\ \Rightarrow-5x\le10 \\ =\frac{-5}{-5}x\le\frac{10}{-5} \\ =x\le-2 \\ \\ \therefore x\le\pm2 \end{gathered}[/tex]x is lesser than or equal to plus or minus 2
We will proceed to plot the graph
15. Which of the following is the equation of the graph below? (2 points) y - - 3 2 -10 1 2 3 4 5 (A) y = -2x + 4 (B) y = 2x + 4 (C) y = -x - 2 (D y = -2x - 2
Answers
How would I solve this. Since I’m not sure what formula I could be using to solve this or how?
Answers
Answer:
[tex]\begin{gathered} a)\text{ 23 \%} \\ b)\text{ w\lparen t\rparen= 90e}^{0.23t} \end{gathered}[/tex]Explanation:
a)We have the general representation as follows:
[tex]w(t)\text{ = ae}^{kt}[/tex]when t = 3, we have the value doubling
Thus: w(t) = 2 * 90 thousand = 180 thousand megawatts
Thus:
[tex]\begin{gathered} 180\text{ = 90e}^{3k} \\ e^{3k}\text{ = 2} \\ k\text{ = }\frac{ln\text{ 2}}{3}\text{ = 0.231} \end{gathered}[/tex]This means we have the continuous growth rate at 23%
b) Writing w as a function of t, we have it that:
[tex]w(t)\text{ = 90e}^{0.23t}[/tex]Jessica was just offered a position as the Head Makeup Consultant. As a manager she will not earncommission or overtime. Her starting salary will be $38,500 per year and is based on a 40 hour workweek paid biweeklyDetermine Jessica's hourly rate. Will Jessica earn more as an hourly paid employee or manager?How much more or less? Show work for credit.
Answers
Assuming there are 52 woking weeks in a year (Since it is the standard used by companies). And in week Jessica can have a maximum of 40 hours, we can conclude that;
[tex]\begin{gathered} \text{Hourly rate (H) =}\frac{38,500\text{ per year}}{52\text{ we}eks\text{ per year (40 hours per we}ek\text{)}} \\ \text{Hourly rate (H) = }\frac{38,500}{52(40)} \\ H\text{ = 18.51} \end{gathered}[/tex]Therefore Jessica's hourly rate is $18.51.
And by calculating her salary per year if she is paid hourly, let us again assume that there are 52 working weeks in a year and she works 8 hours per day 5 times a week as the standard working hours. We get;
[tex]\begin{gathered} \text{Yearly Salary (paid by hour) = 18.51/hour x 52 w}eeks\text{ x 8 hours/day x 5 days/w}eek \\ \text{Yearly Salary (paid by hour) = 18.51 x 52 x 8 x 5} \\ \text{Yearly Salar (paid by hour) = 38,500.80} \end{gathered}[/tex]Therefore Jessica's salary per year if she is paid hourly is $38,500.80, so there is a $0.80 difference between her initial salary.
A shirt retails for $22.40. A 10% tax is then applied to the original. What is the final price after tax? $20.16 $24.64 $22.50 $32.40 $22.30
Answers
To solve this question, follow the steps below.
Step 01: Find the value of the tax.
If a tax of 10% is applied, then the tax is:
[tex]\begin{gathered} tax=\frac{10}{100}*22.40 \\ tax=2.24 \end{gathered}[/tex]Step 02: Find the final price.
The final price is the original price + tax.
Then, the final price is:
[tex]\begin{gathered} final\text{ }price=22.40+2.24 \\ final\text{ }price=24.64 \end{gathered}[/tex]Answer: $24.64.
There are 15 pieces of the same size candy in a bag. Four are banana flavored, three strawberry flavored, and two orange flavored. What would be the probability of picking an orange or a cherry flavored candy from the bag? Write your answer as percent rounded to the nearest tenth.
Answers
Given:
Total number of candy in a bag is 15.
Number of orange flavored candy is 2
Number of cherry flavored candy is 6
Let A be the event of picking an orange or a cherry flavored candy from the bag.
[tex]\begin{gathered} n(A)=2+6 \\ n(A)=8 \end{gathered}[/tex][tex]P(A)=\frac{8}{15}[/tex][tex]\begin{gathered} \text{Percentage}=\frac{8}{15}\times100 \\ \text{Percentage}=53.3\text{ \%} \end{gathered}[/tex]the first square is 3 cm by blank centimeters in the other square 13 .5 them by 9 cm what is the scale factor going from the smallest rectangle to the largest one. ans what is the missing side.
Answers
Answer:
Step-by-step explanation:
I need to do the “use vocabulary in writing part” But if I can get help with all that would be much appreciated
Answers
• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.
And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.
1) As congruent triangles have three congruent angles and sides in order, then we state that, using this specific vocabulary:
2) Δ ABC is congruent to ΔDEF, because
• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.
And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.
3) Hence, that's the answer.
The area of the triangle below is 24.75 square centimeters. What is the length of the base?
Answers
Okay, here we have this:
Considering the provided figure and information, we are going to calculate the requested measure, so we obtain the following:
So to calculate the length of the base, we will solve in the formula for the area of the triangle, we have:
Triangle Area=(Base*height)/2
Triangle Area*2=Base*height
Base=(Triangle Area*2)/height
Let's replace:
[tex]\begin{gathered} Base=(24.75cm^2\cdot2)\frac{\placeholder{⬚}}{5.5cm} \\ =\frac{49.5cm^2}{5.5cm} \\ =9cm \end{gathered}[/tex]Finally we obtain that the length of the base of triangle is 9 cm.
What are the domain and range of the function f(x)=2x+1?domain: (0.00)range: (-0.00domain: (-0.00)range: (0.co)domain: (-0.00)range: (2.00)domain: (0.00)range: (2.0)
Answers
The given function is expressed as
f(x) = 2^(x + 1)
The domain of a function is the set of all the possible values of x that would satisfy the function.
The range of a function is the set of all the possible values of y that would satisfy the function.
Since the fuction has no denominator or even root, the values of can be all real numbers. This means that the domain would be between - infinity and infinity
For the range, no matter how small the value of x that we input into the function, the value of f(x) or y would never be lesser than zero. Also, there is no limit to the value of f(x) even if we input very large values of x. Thus, the range is between 0 and infinity. Thus,
the correct option is the second one
Of 100 students in a club,23 are freshman. What percent of the students are freshman ?
Answers
Answer
Percentage of students that are freshman = 23%
Explanation
Total number of students in a club = 100
Number of freshman = 23
Percentage of students that are freshman = [(Number of freshman)/(Total number of students in a club)] x 100
Percentage of students that are freshman = (23/100) x 100
Percentage of students that are freshman = 23%
how to determine maximum or maximum point without using a graph
Answers
you could calculate the derivative and equalize it to zero,then you can evaluate the function in the boundary points of the domainand compare them to the ones found in the last step to find the maximum of a given function.
Rewrite the expression using the distributed Property and for the final answer cant have Double signs/operations
Answers
Distributive Property
The distributive property of the product with respect to the sum states that if a product and a sum are to be operated like follows:
x* ( y + z )
Then the result is the product of x by each term separately:
x* ( y + z ) = x*y + x*z
Now, we have the expression:
8 ( 2m + 1 )
Applying the distributive property:
8 * 2m + 8 * 1
16m + 8
Question 10How many area codes of the form (XYZ)are possible if the digit 'X' and 'Y' can beany number 1 through 9 and the digit 'Z'can be any number 2 through 9?
Answers
1 14 แ li ! 14 badute Value ineguanten NM แจls แทนเจ 1 ปี 58 หมอยอด | |44| |14 นางอ 24.122 (Mitr 5.1 \\\\\ย - 5 \\
Answers
This implies that
[tex]\begin{gathered} 10b\text{ +7 }>\text{ 37} \\ or \\ 10b\text{ +7 <-37} \end{gathered}[/tex][tex]\begin{gathered} \text{if 10b + 7>37} \\ \text{then 10b >37-7} \\ 10b\text{ >30} \\ b\text{ >}\frac{30}{10} \\ b\text{ >3} \end{gathered}[/tex][tex]\begin{gathered} \text{if 10b + 7<-37} \\ 10b\text{ <-37-7} \\ 10b<-44 \\ b<\frac{-44}{10} \\ b<-4.4 \end{gathered}[/tex]Combining them we have
-4.4
Now to the graph