Answers
8² + 15² = 17²
64 + 225 = 289
This is true, so the triangle is a right triangle.
2)
4² + 12² = 13²
16 + 144 = 169
This is false, so the triangle is not a right triangle.
3)
20² + 21² = 27²
400 + 441 = 729
This is false, so the triangle is not a right triangle.
4)
28² + 45² = 53²
784 + 2,025 = 2,809
This is true, so the triangle is a right triangle.
Related Questions
Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?
Answers
If the second constructor works alone for one day he will do (1/(x+5)) part of work.
If they work together, they will do for one day
[tex] \frac{1}{x} + \frac{1}{x+5} part of work. Also, if they work together, for one day they will do 1/6 part of work. So, [/tex]
[tex] \frac{1}{x} + \frac{1}{x+5} = \frac{1}{6} , \frac{x+5+x}{x(x+5)} = \frac{1}{6} , \frac{2x+5}{ x^{2} +5x} = \frac{1}{6} , 6(2x+5)=x^{2} + 5x 12x+30 =x^{2}+5x x^{2} -7x-30=0 (x-10)(x+3)=0 x_{1}= 10, x_{2}=-3 For our problem we can use only positive value, x=10 days will work the first worker. The second worker will work x+5=10+5= 15 days. First worker alone will work 10 days, second worker alone will work 15 days. Check, (1/10)+(1/15)=(1/6) (3+2)/30=(1/6) 1/6=1/6 True [/tex]
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's call the faster constructor "A" and the slower constructor "B".
We know that B takes 5 more days than A to complete the job.
Let's call the number of days it takes A to build the room "x".
Then the number of days it takes B to build the room is "x+5".
Now,
We also know that if they work together, they can finish the room in 6 days.
Let's call the fraction of the job that A can do in one day "a"
(which means that B can do "a - 1/6" of the job in one day).
We can use the following equation to solve for "a":
1 = (a + a - 1/6) x 6
Simplifying this equation, we get:
1 = (2a - 1/6) x 6
1 = 12a - 1
12a = 2
a = 1/6
So A can do 1/6 of the job in one day.
We can use this information to solve for "x" and "x+5":
1/x + (1/(x+5)) = 1/6
Multiplying both sides by the least common multiple of the denominators (6x (x+5) ), we get:
6 (x+5) + 6x = x (x+5)
Expanding and simplifying, we get:
x² - 7x - 30 = 0
Solving for x using the quadratic formula, we get:
x = 10 or x = -3
Since x has to be a positive number (because it represents the number of days it takes A to build the room), we can ignore the negative solution.
Now,
It takes A 10 days to build the room, and it takes B 15 days to build the room (since B takes 5 more days than A).
Therefore,
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
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the fifth grade classes at sunshine School you six identical buses to go on the field trip there were a total of 30 seats on each bus all the seats on 5 buses were filled the 6 bus had 4/6 of the seats filled 1/5 of all the passengers were adults how many adults went on the field trip with the fifth grade class
Answers
Frank wants to know how many people live in each household in his town. He conducts a random survey of 10 people and asks how many people live in their household. His results are shown in the table.
Number of People per Household
1 6 2 4 4 3 5 5 2 8
Calculate the mean absolute deviation of the number of people per household
Answers
The mean absolute deviation is 1.6.
Given that the number of People per Household
1 6 2 4 4 3 5 5 2 8
We have to determine the mean absolute deviation
What is the mean deviation?The mean absolute deviation is found by finding the mean, then finding how far each number is to the mean, then finding the mean of that.
The mean is: (1 + 6 + 2 + 4 + 4 + 3 + 5 + 5 + 2 + 8)/10 = 40/10 = 4
The distances of all of the numbers are
(absolute value of the difference between 3.5 and the number)
3,2, 2, 0, 0, 1, 1, 1, 2, 4
The mean of those is: 3+2+2+ 0+ 0+1+1+ 1+ 2+ 4 /10 = 16/10 = 1.6
Therefore the mean absolute deviation is 1.6.
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Algebra help ASAP :))))
Answers
Place points at:
(-2, 2)
(-1, 0.5)
(0, 0)
(1, 0.5)
(2, 2)
The parabola should look something like this.
(07.06)Number line with open circle on 9 and shading to the left. Which of the following inequalities best represents the graph above? x < 9 x > 9 x ≤ 9 x ≥ 9
Answers
Inequality representing the relation of 07.06 number line with open circle on 9 and shading to the left is given by x < 9.
What is inequality?" Inequality is defined as the algebraic expression which relates the given variables as per the condition with the sign of inequality <,> , ≤, ≥."
According to the question,
Given,
Number on the number line = 07.06
Number on number line with open circle = 9
Inequality shown on the number line drawn we get,
Condition : shaded to the left
Inequality as per the condition: x < 9
Hence, inequality representing the relation of 07.06 number line with open circle on 9 and shading to the left is given by x < 9.
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What is the sum of 74.835 and 2.67
Answers
I provided you a picture to help you out a little. ^.^
74.835 + 2.67 = 77.505.
Hope this helps!! :)
m∠HGF = 16 x + 4, m∠EGF = 110°, and m∠HGE = 3 x + 11. Find x .
Answers
On a spinner: P(3) = ⅜ and p(4) = ⅓ What is the probability of getting 3 or 4?
Answers
Answer:
3/8. + 1/3
9/24 +8/24
17/24
Is 35 over Pi (35 divided by pi):
Slightly less than 9
Slightly more than 9
Slightly less than 12
OR
Slightly more than 12
Please help and no wrong answers!
Answers
Our calculators record pi as 3.141592654
35/pi = 11.14084602 which is just under 12. <<<<< answer
35/pi is a calculator question. A standard calculator has pi to about 10 digits stored in it's memory. As an educated guess before doing it (according to the bible is just under 12 since pi is recorded as 3 in Kings I think).
Our calculators record pi as 3.141592654
35/pi = 11.14084602 which is just under 12. <<<<< answer
1
Teo has 4 2/3 pitchers of juice. One glass holds 1/6 of a pitcher. How many glasses can Teo fill?
Answers
Change 4 2/3 to 14/3
14/3 / 1/6 = 14/3 x 6/1
84 glasses
Kiesha’s quality-control manager told her she must have 97% of her clocks functioning properly. She found a report that said 6 out of 300 clocks tested were not working properly. Kiesha predicts that she will have enough working clocks to please the manager. Which statements are true about Kiesha’s prediction? Check all that apply.
Kiesha’s experimental probability is 1/30
Kiesha will have more than 97% of the products working.
Kiesha will not meet 97% because more than 3% of her clocks will be broken.
Kiesha’s experimental probability is 1/50
When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
Answers
Kiesha will have more than 97% of the products working. The experimental probability is 0.98, not 1/30 or 1/50. When the inventory is 4000 clocks, the prediction is that 3880 clocks will work.
Explanation:To determine if Kiesha will have enough working clocks to please the manager, we need to calculate the percentage of clocks that are functioning properly. We know that 6 out of 300 clocks tested were not working, which means 300 - 6 = 294 clocks were working properly. The percentage of working clocks is (294/300) x 100% = 98%. This means that Kiesha will have more than 97% of the products working, so the statement 'Kiesha will have more than 97% of the products working' is true. The statement 'Kiesha’s experimental probability is 1/30' is false because the experimental probability is calculated by dividing the number of successful outcomes (294) by the total number of trials (300), giving 294/300 = 0.98. The statement 'Kiesha will not meet 97% because more than 3% of her clocks will be broken' is false because the percentage of working clocks is 98%. The statement 'Kiesha’s experimental probability is 1/50' is false because the experimental probability is 0.98, not 1/50. When the inventory is 4000 clocks, the prediction is that 97% of the clocks will work, which is (0.97 x 4000) = 3880 clocks.
Kiesha's experimental probability of a clock not working is 1/50, and with 98% of her clocks working properly, she will exceed her manager's 97% requirement. When scaled to an inventory of 4000 clocks, Kiesha can expect 3920 to be functioning correctly.
Explanation:When analyzing Kiesha's prediction about her clocks, we find that if 6 out of 300 clocks are not functioning, then 294 clocks are working properly. To determine if Kiesha will have enough working clocks to please her manager (who requires 97% to be in working order), we calculate the percentage of working clocks:
294/300 = 0.98 or 98%
This is higher than the manager's requirement of 97%. Therefore, the following statements about Kiesha's prediction are true:
Kiesha's experimental probability of a clock not working is 6/300, which reduces to 1/50, not 1/30.Kiesha will have more than 97% of the products working, as 98% are functioning properly.If Kiesha has an inventory of 4000 clocks and the same proportion of nonfunctioning clocks, she would expect 3920 clocks to work, because 98% of 4000 is 3920.Thus Kiesha's prediction that she will meet the quality requirements is accurate.
Sarah wants to hang a mirror in her room. The mirror and frame must have an area of 15 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Square with an inner frame with height of 3ft on the left frame and width of 4ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. 3x2 + 14x − 2 = 0 4x2 + 14x − 3 = 0 x2 + 12x − 14 = 0 2x2 + 7x − 14 = 0
Answers
Width of the outer frame:3+2x
Area of the outer out frame"(4+2x)(3+2x)=15
Expand the equation:12+8x+6x+12x^2=15
Combine like terms :4x^2+14x-3=0
Richard and samantha are charting their monthly cash flow. They have some expenses like car repairs and vacations that are not paid each month. How can they account for these non-monthly expenses ?
Answers
This way they can take vacations or if they have car troubles
It would make their life so much easier
Final answer:
Richard and Samantha should estimate yearly costs for non-monthly expenses, divide by 12, and save this amount each month, incorporating it as a fixed expense in their budget.
Explanation:
Richard and Samantha can account for non-monthly expenses in their monthly cash flow by setting aside money each month for these irregular expenses. To do this, they should estimate the total cost of these expenses for the year and divide that amount by 12. This will provide the monthly amount they need to save in order to cover costs such as car repairs and vacations without disrupting their budget. Each month, this amount should be treated like a fixed expense and set aside in a savings or separate account, ensuring that funds are available when these expenses occur.
Example:
Car Repairs: Estimated at $600 per year (divide by 12 = $50 per month)
Vacations: Estimated at $1200 per year (divide by 12 = $100 per month)
By including these estimated expenses in their monthly budget, they can create a more accurate and effective budget that accommodates all their financial activities throughout the year.
a storage container is shaped like a rectangular prism the volume of the container is 1360 cubic feet the area of the base of the container is 160 square feet what is the height of the container
Answers
The volume of a prism is given by:
Volume of a prism = base area * height
From the the problem, we have been given volume of the prism = 1360 feet^3
Base area = 160 feet^2
height = x
1360 =160 * x
x = 1360/160 = 8.5 feet
Height of the container = 8.5 feet
Find the volume of a right prism with height h=10 cm, if:
The base is a trapezoid with height htr = 3 cm and bases of 2 cm and 5cm
Answers
V = Ab * h
Where,
Ab: base area
h: prism height
The area of the base is:
Ab = (1/2) * (B + b) * (htr)
Where,
B: major base
b: minor base
htr: height of the trapeze
Substituting values:
Ab = (1/2) * (5 + 2) * (3)
Ab = 10.5
Then, the volume is:
V = (10.5) * (10)
V = 105 cm ^ 3
Answer:
The volume of the right prism is:
V = 105 cm ^ 3
Answer:105cm to the power of three
Step-by-step explanation:
The area of a circular pool is 314 square feet. Write and solve an equation to find the diameter of the pool cover.
Answers
Use the area of a circle formula to first calculate the radius.
A= πr^2
plug in known numbers
314= (3.14)r^2
divide both sides by 3.14
100= r^2
take square root of both sides
10 feet= r
STEP 2:
find the diameter
Diameter= 2 * radius
D= 2 * 10
D= 20 feet
CHECK:
A= (3.14)(10)^2
A= (3.14)(100)
A= 314 feet squared
ANSWER: The diameter is 20 feet.
Hope this helps! :)
The length of a rectangle is 3 m longer then it’s width the area of the rectangle is 154 m^2 what is the width of the rectangle
Answers
You can get this by setting up an equation that says:
x (x - 3) = 154
Then distribute and use the quadratic equation to solve.
Alternately, the gardener decides to choose the plants in the first row. What is the average number of tomatoes on these plants
Answers
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 3 ft, 6 ft, 9 ft B. 3 ft, 5 ft, 7 ft C. 3 ft, 6 ft, 12 ft D. 3 ft, 9 ft, 27 ft
Answers
B. 3 ft, 5 ft and 7 ft
Explanation:
In any triangle, the sum of any two sides must be greater that the third one.
Therefore, to know if the given sides represent a triangle or not, all what we will do is add the two short sides and compare the result to the largest one.
We would have 3 options:
sum of short sides > longest side ......> It is a triangle
sum of short sides < longest side ......> It is not a triangle
sum of short sides = longest sides ....> It is not a triangle
Now, for the given:
1- Option A:
sum of short sides = 3 + 6 = 9 ft which is equal to the longest side
This option is incorrect
2- Option B:
sum of short sides = 3 + 5 = 8 ft which is greater than the longest side
This option is correct
3- Option C:
sum of short sides = 3 + 6 = 9 ft which is less than the longest side
This option is incorrect
4- Option D:
sum of short sides = 3 + 9 = 12 ft which is less than the longest side
This option is incorrect
Based on the above, the only correct option is B.
Hope this helps :)
Find P(A or B) if the events are disjointed. P(A) = P(B) =
P(A) = 11/25
P(B) = 9/25
A. 4/25
B. 3/5
C. 2/25
D. 4/5
Answers
Simplify 5 √180 (show work)
Answers
= 5 \/4 x \/45
= 5 x 2 \/9 x \/5
= 10 x 3 x \/5
= 30 \/5
I did this a couple of years ago in AS maths and I think this is how it’s done. Hope it’s helpful!
To simplify 5√180, break down 180 into its prime factors, take out the square of the prime factors, and simplify.
Explanation:To simplify 5√180, we can break down 180 into its prime factors which are 2^2 * 3^2 * 5. Then, we can take out the square of the prime factors since we have a square root. This leaves us with 2 * 3 * 5√5. Simplifying further, we get 30√5.
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The tip of a pendulum moves through an angle of 0.38 rad radians. If the radius of the pendulum is 25 centimeters then which of the following is the length of the arc the tip moves through
Answers
circumference=2*pi*r
for r=25 cm
so
circumference=2*pi*25-----> 50*pi cm
if
2*pi radians (full circle) has a length of----------------> 50*pi cm
0.38 radians-------------------> x
x=0.38*50*pi/(2*pi)-----> x=9.5 cm
the answer is
9.5 cm
which of the following is the correct notation for the complex number
[tex] \sqrt{ - 81 - 14} [/tex]
Answers
The complex number √-81-14 is best represented as 9i - √14 (option A)
Why is this correct?
In order to determine the correct notation for the complex number;
The square root of -81 yields the imaginary unit, [tex]\(i\)[/tex], multiplied by 9 (as [tex]\(\sqrt{-81} = 9i\)[/tex]).
The value -14 represents the real part of the complex number.
Hence, the precise notation that combines the imaginary and real parts of this complex number is 9i - √14.
Therefore, in a concise and accurate manner, the complex number √-81-14 is best represented as 9i - √14.
Complete question:
Which of the following is the correct notation for the complex number √-81-14
a) 9i - √14 b) √-81 + √-14 c) √-81 - 14i
Your last five customer interactions lasted 2,3,6,8 and 4minutes how many minutes did i average across the 5
Answers
2 to 3 is 1
3 to 6 is 3
6 to 8 is 2
8 to 4 is 4
adding 1+2+3+4= 10 minutes; the average
You average across 4.6 minutes per customer.
What is average?The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.
Given:
Your last five customer interactions lasted 2,3,6,8 and 4 minutes.
The total number of observation is 5.
The average = the sum of the observations / the number of observations.
The average = (2 + 3 + 4 + 6 + 8)/5
The average = 23/5
The average = 4.6 minutes.
Therefore, 4.6 minutes per customer is the average.
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what does the expression 0.30y represent ?
Answers
Angle P measures 112 degrees, what are the measures of angle N and O?
Answers
in this triangle the lines NP and OP are identical so the 2 unknown angles would be equal
so the 2 unknown angles would be 180 - 112 = 68 / 2 = 34 each
angle N & O are 34 degrees
The measures of angle N and O are: 34°
How to find the angle of the Isosceles triangle?We know that Isosceles triangle has two equal sides and we also know that the sum of angles in a triangle is equal to 180 degrees.
Since an Isosceles triangle has two equal sides, we know that the base angles are equal.
We are given the apex angle as 112 degrees. Thus:
2x + 112 = 180
2x = 180 - 112
2x = 68
x = 34
Thus:
The measures of angle N and O are 34°
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the sum of three numbers is 161 the second number is six times the first and the third is 5 more than the second find the numbers
Answers
If I eaen $500 a year how much do I earn a month?
Answers
The google family built a rectangular swimming pool in their backyard.The floor of the pool has an area of 485 5/8 square feet.If the width of the pool is 18 1/2 feet,what is the length of the pool?
Answers
W= Width= 18 1/2 ft
L= Length= ?
Area= LW
plug in known numbers
485 5/8= (L)(18 1/2)
convert to improper fractions
3885/8= (L)(37/2)
divide both sides by 37/2
3885/8 ÷ 37/2= L
to divide fractions, multiply by the reciprocal/inverse of 37/2
3885/8 * 2/37= L
multiply numerators; multiply denominators
(3885*2)/(8*37)= L
multiply inside parentheses
7770/296= L
simplify
105/4 feet= L
change to mixed number
26 1/4 feet= L
ANSWER: The length is 26 1/4 feet (or 26.25 feet).
Hope this helps! :)
[tex]485 \dfrac{5}{8} = 18 \dfrac{1}{2} \times \text{ Width}[/tex]
Divide both side by 18 1/2:
[tex]\text{ Width} = 485 \dfrac{5}{8} \div 18 \dfrac{1}{2} [/tex]
Convert to improper:
[tex]\text{ Width} = \dfrac{3885}{8} \div \dfrac{37}{2} [/tex]
Change divide fraction to multiplicationf fraction:
[tex]\text{ Width} = \dfrac{3885}{8} \times \dfrac{2}{37} [/tex]
Mutliply and simplify:
[tex]\text{ Width} = \dfrac{104}{4} = 26 \dfrac{1}{4} \text{ feet}[/tex]
Answer: Length = 26 1/4 feet
Find the volume of a right prism with height h=10 cm, if the base is a trapezoid with height htr = 3 cm and bases of 2 cm and 5cm
Answers
Volume =10.5 x 10 = 105 cm³
Answer: 105 cm³
We have been given that the base of the prism is a trapezoid. Hence, first of all we find the area of the trapezoid.
Trapezoid has height 3 cm and bases of 2 cm and 5 cm.
Hence, the area of the trapezoid is given by
[tex]A=\frac{a+b}{2} \times h\\ \\ A=\frac{2+5}{2} \times 3\\ \\ A=\frac{21}{2}[/tex]
Therefore, the volume of the right prism with height h=10 cm is given by
[tex]V=\text{Base area }\times { height}\\ \\ V=\frac{21}{2} \times 10\\ \\ V=105 cm^3[/tex]
Therefore, the volume of the right prism is 105 cubic centimeters.