Answer: The length of all three sides of the reflecting pool are 8 feet , 17 feet and 16 feet.
Step-by-step explanation:
Let sides along the building be 'x', then the measure of hypotenuse = x+9 and the measure of third side = 7+x
Since , the reflecting pool is shaped like a right triangle.
Then , by using Pythagoras theorem , we have
[tex](x+9)^2=x^2+(x+7)^2\\\\\Rightarrow\ x^2+81+18x=x^2+x^2+49+14x\ \ [\text{Using }(a+b)^2=a^2+b^2+2ab ]]\\\\\Rightarrow\ x^2+81+18x=2x^2+49+14x\\\\\Rightarrow\ x^2-4x-32=0\\\\\Rightarrow\ x^2-8x+4x-32=0\\\\\Rigtarrow\ x(x-8)+4(x-8)=(x-8)(x+4)\\\\\Rightarrow\ x=8\ or -4[/tex]
But length cannot be negative , it means x= 8
Now, the length of side along building = 8 feet
Length of hypotenuse = 9+8 =17 feet
Length of third side = 8+7= 16 feet
Final answer:
Using the Pythagorean Theorem and setting the length of the side along the building as x, we solve the quadratic equation to find that the side along the building is 8 feet, the third side is 15 feet, and the hypotenuse is 17 feet.
Explanation:
To solve for the lengths of all three sides of the reflecting pool, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two legs (a and b). Let's denote the length of the side along the building as x. Therefore, the hypotenuse will be x + 9 feet and the third side will be x + 7 feet. The equation can be set up as follows:
x² + (x + 7)² = (x + 9)²
Expanding the squares and solving for x gives us:
x² + x² + 14x + 49 = x² + 18x + 81
Combine like terms and move everything to one side:
x² + 14x + 49 - 18x - 81 = 0
x² - 4x - 32 = 0
Factoring the quadratic equation:
(x - 8)(x + 4) = 0
Since a length cannot be negative, we take the positive solution x = 8 feet. Now we can find the lengths of each side:
Side along the building: 8 feet
Third side (7 feet longer than the side along the building): 8 + 7 = 15 feet
Hypotenuse (9 feet longer than the side along the building): 8 + 9 = 17 feet
Two blocks of water shape does right rectangular prism a width of 2 cm and a height of 7 cm the dimensions are the larger blocked are doubled the dimensions of the smaller block what is the volume of the larger block of wood into your answer in the box
Answer:
1512 cm³
Step-by-step explanation:
l of larger block 2x bigger than smaller 1
= 2 × 9
= 18 cm
The breadth of the larger block is 2x bigger than the breadth for smaller 1
= 2 × 3
= 6 cm
Height of larger block is two times bigger than the smaller block
= 2 × 7
= 14 cm
Formula:
= 18 × 6 × 14
= 1512 cm³
Tada! :)
Need Help ASAP!!!!!!!!!!!!!!!!!!!!
Answer:
Area = 52 cm2
Step-by-step explanation:
First you have to extend the line. It gave you two rectangles.
To find out the area you have to add this two surfaces.
A1 = 2*10 = 20
A2 = 8*4 = 32
Whole area = A1 + A2 = 20 + 32 = 52 square cm.
You can do this other way around and you get the same answer.
First you have to extend the line. It gave you two rectangles.
To find out the area you have to add this two surfaces.
A1 = 4*10 = 40
A2 = 2*6 = 12
Whole area = A1 + A2 = 40 + 12 = 52 square cm.
A group of 55 pupils were asked if they owned a phone or a tablet.
11 people are known to own both
18 said they only owned a tablet
34 said they owned at least a phone
A student is picked a random, what is the probability that the student doesn’t have a phone or tablet? Give your answer as a fraction in its simplest form.
Select your answer from the list below:
A: 3/63
B: 3/55
C: 11/55
D: 18/55
Answer:
it's B
Step-by-step explanation:
USE The venn diagram
11 said they own both devices so it will be in the middle
34 said they owned at least a phone
34-11 =23
Help! its division pretty easy now do it!
Solve the following:
8,106 ÷ 114
A) 71 R12
B) 75 R67
C) 82 R26
D) 87 R43
The answer is A) 71 R12
The answer would be A) 71 R12
Roses are $2.50 each and lilies are $1.25 each. Ellis spent $28.75 for 15 of the flowers. How many of each type of flower did he buy?
Answer:
8 roses, 7 lilies
Step-by-step explanation:
8 roses = 20$
7 lilies = 8.25$
Added together they equal 28.75 $
Simplify (−2)∙(2a−b)+3(a+b) PLz and Thanks
Answer:
-a+5b
Step-by-step explanation:
(-2)x(2a-b)+3(a+b)
Multiply
Remove Parenthesis
-2(2a-b)+3a+3b
Multiply parenthesis by -2
-4a+2b+3a+3b
collect like terms
-a+5b
Can anyone help me with this fraction?
Answer:
1/6
Step-by-step explanation:
2/12 simplified is 1/6
Answer:
1/6
Step-by-step explanation:
The fraction is the colored parts over the total number of parts
colored 2
----------- = -----------
total 12
This can be simplified by dividing the top and bottom by 2
2/2 =1
12/2 = 6
The fraction becomes 1/6
Is this graph a parabola? Plz someone help!! 20pts
Yes the graph is a parabola
Step-by-step explanation:In mathematics, a parabola is a plane curve that is mirror-symmetrical and is approximately U-shaped. The trajectory of a projectile always shows parabolic path. The shape of car headlights, mirrors in reflecting telescopes and television and radio antennae are examples of the applications of parabolas.
Chad hopes to save more than $450 dollars this year. He expects to be able to save $9 each week. There are 52 weeks in a year, so Chad thinks he will be able to save $468 in one year. Is Chad's answer reasonable? Use rounding to make an estimate and tell whether $468 could be a correct result. Explain your answer.
Answer: yes
Step-by-step explanation:
If you round, then $9 will round up to $10 and 52 will round down to 50. Then, you multiply 10 and 50, which equals 500, so it is a reasonable guess.
I tried, hope it helps!
It took 5 people to clean a classroom in 4 hours. How long would it take 4 people? Please help
Answer:
3 hours
Step-by-step explanation:
Ann, Jim, and Miguel sent a total of 115
text messages during the weekend. Jim sent 10
more messages than Ann. Miguel sent 3
times as many messages as Ann. How many messages did they each send?
Ann sent a total of 21 texts.
Jim sent a total of 31 texts.
Miguel sent a total of 63 texts.
Point A is located at (-2, 4). After it is transformed, point A' is located at (2, 4). What could the transformation be?
A translation 4 units to the right
A rotation of 90° around the origin
A reflection in the y-axis
A translation 4 units up
I wrote zones but then noticed that we actually don't need :p
The answer is "a reflection in the y-axis"
Hope it helps!
Find the area of equilateral triangle (regular 3 gon) with 9 in perimeter
Answer:
Area = 3.897
Step-by-step explanation:
Remark
What you are subtly being told is the side of an equalateral triangle = P/n.
n = the number of sides
n = 3
P = 9
side = 9/3 = 3
The area of an equalateral triangle given 1 side is
Area = sqr(3) * s^2 /4
Area = 3.897
Find an equation for the nth term of the arithmetic sequence. -17, -13, -9, -5, ...
Answer:
The nth term is [tex]a_n=4n-21[/tex]
Step-by-step explanation:
The given arithmetic sequence is -17, -13, -9, -5, ...
The first term of this sequence is [tex]a_1=-17[/tex].
The common difference can be found using any two consecutive terms.
The common difference is [tex]d=-5--9=4[/tex]
The nth term of arithmetic sequence is given by the formula:
[tex]a_n=a_1+d(n-1)[/tex]
We plug in the values to obtain:
[tex]a_n=-17+4(n-1)[/tex]
Expand
[tex]a_n=-17+4n-4[/tex]
Simplify:
[tex]a_n=4n-21[/tex]
Is that right?
7x3=21
21+5=26
Answer:
yes
Step-by-step explanation:
the correct answer is 2 after rounding it off to the nearest number
The figure is made up of 2 hemispheres and a cylinder.
What is the exact volume of this figure?
The volume of the given figure is: 126π cubic inches.
What is the volume of the composite figure?A volume is defined as a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the attached figure will be the sum of the volume of the cylinder and twice the volume of the hemisphere. Therefore, the volume will be:
Volume = Volume of cylinder + 2(Volume of hemisphere)
Volume = (π × R² × H) + 2[²/₃π×R³]
Volume = (π×3²×10) + 2[(2/3)×π×3³]
Volume = 90π +36π
Volume = 126π in³
Read more about Volume of Composite Figure at: https://brainly.com/question/12693294
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Help on this Please!!!!! Will give brainliest!!!!
Check the three attached images.
The first exercise is quite self-explanatory. We have to draw two lines that pass through P and are tangent to the circle.
As for the second, since the circle is tangent to all three side of the triangle, we can conclude that the circle is inscribed in the triangle.
Finally, to draw the common tangent, you have to find the point of intersection between the two circles, and draw a line perpendicular to AB.
When rounding 72.631 to the hundredths place, Jack rounded to 72.64 and Tamar rounded to 72.63. Who is correct? EXPLAIN YOUR ANSWER
Answer:
Tamar
Step-by-step explanation:
Since we're rounding to the hundredths place, we need to see if the thousandths place is greater or equal to 5. Since it is less than 5, we round down to 72.63.
Answer: Tamar
Step-by-step explanation:
Since the number before the 3 is a 1, the number will stay the same and not be rounded up. If the number was 5 or above, it would be rounded up to a 4.
Given that y varies directly with x and that y = 60 when x = 20, find y when x = 12.
1.y varies directly with x
2.substitute the value of x and y in the equation below
y=kx
where k is the constant term
60=20k
k=60\20
k=30
:y=30x.....is the law
To find y when x is 12
You reinstate the law which is y=30x
Then substitutes the value of x to determine y
y=30*12
y=36.
Need help ASAP. What are the coordinates?
Answer:
A'(-5,3) A"(-2,5)
Step-by-step explanation:
First, reflecting across the x axis makes the points (x,-y).
So we get A prime = (-5,3)
Then, we add 3 to the x value and 2 to the y value to get A"
So A" = (-2,5)
Answer:
A. (-5,-3)
B. (-6,-1)
C. (-3,-1)
D. (-2,-3)
Which of the following is an arithmetic sequence?
Answer:
0,2,4,6
Step-by-step explanation:
This sequence is arithmetic because the same number is being added each time: 2. With the others, the number being added changes every time.
ANSWER
[tex]0,2,4,6,8,...[/tex]
EXPLANATION
An arithmetic has a constant difference .
We check to see which of the given sequences has a constant difference.
0,2,4,6,8,... has a constant difference of
[tex]d=2-0=4-2=6-4=8-6=2[/tex]
hence it is an arithmetic sequence.
1,2,4,8,... is not an arithmetic sequence because there is no constant difference.
[tex]2-1 \ne4-2.[/tex]
1,4,8,13,... is also not an arithmetic sequence because there no constant difference.
[tex]4 - 1 \ne8 - 4[/tex]
The first option is correct.
Whar is 4x-2 (x-3)=8
Answer:
x = 1
Step-by-step explanation:
distribute parenthesis on left side and simplify
4x - 2x + 6 = 8
2x + 6 = 8 ( subtract 6 from both sides )
2x = 2 ( divide both sides by 2 )
x = 1
A cylindrical oil drum has a diameter of 2 feet and a height of 3 feet. What is the volume of the oil drum?
Final answer:
The volume of the cylindrical oil drum is 9.426 cubic feet.
Explanation:
The volume of a cylindrical oil drum can be calculated using the formula V = πr²h, where r is the radius of the drum and h is the height. In this case, the diameter of the drum is given as 2 feet, so the radius is 1 foot (since the radius is half the diameter). The height of the drum is given as 3 feet. Therefore, the volume of the oil drum can be calculated as follows:
V = 3.142 × (1 foot)² × 3 feet
Calculating this, we get:
V = 3.142 × 1 foot × 1 foot × 3 feet = 9.426 cubic feet
So, the volume of the oil drum is 9.426 cubic feet.
HURRY!!!! GIVING BRAINLIEST AND 99 POINTS!!!!! What was one invention of the Tang or Song dynasty, and how did it affect China?
The use of gunpowder. Specifically military use, this helped fight wars and win wars because they were able to use the gunpowder. (Not 100% sure)
One important invention that was created in the Song dynasty was the invention of paper money.
Before paper money, people in China used metal and stone coins, which were bulky and could get really heavy at times. However, the paper money made it much easier to carry currency over long distances for trading without the large weight that metal coins had.
This invention affects the whole world today, as many countries have adopted the concept of paper money and still use it. Let me know if you need any clarifications or extra info, thanks!
~ Padoru
Find the lateral surface area of the prism
Answe
255=222-22209/33
=6868
The lateral surface area of the prism with dimensions 4 ft, 3 ft, and 1.5 ft is 21 square feet.
To find the lateral surface area of a prism, you need to add the areas of all the lateral faces of the prism.
For a rectangular prism, the lateral surface area can be calculated by finding the perimeter of the base and multiplying it by the height of the prism.
In this case, with dimensions of 4 ft, 3 ft, and 1.5 ft for the rectangular prism:
Calculate the perimeter of the base: Perimeter = 2(length + width)
Perimeter = 2(4 ft + 3 ft) = 2(7 ft) = 14 ft
Then, multiply the perimeter by the height of the prism to get the lateral surface area:
Lateral Surface Area = Perimeter x Height
Lateral Surface Area = 14 ft x 1.5 ft = 21 square feet
The complete question is: Find the lateral surface area of the prism
frank is a time-share brokers. his earnings are based on a graduated commission. he receives 3% on any time-share sale up to $10,000 and 5% for any amount over the $10,000. last saturday he sold a time-share for $10,500. how much did he make selling the time-share?
Answer:
$325
Step-by-step explanation:
Time-share = $10 500
On first $10 000 ,
Commission at 3 % = 0.03 × 10 000 = $300
On remaining $500,
Commission at 5 % = 0.05 × 500 = 25
Total commission = $325
Frank made $325 selling the time-share.
NEED HELP ASAPP!!!!!!!!!!!!!!!!
The answers might be B and C.
Answer:
B and C
Step-by-step explanation:
B has 4 equal parts easy. C is a more reasonable answer because a has NO equal parts.
he midpoint of segment AB is (5, 3). The coordinates of point A are (1, 5). Find the coordinates of point B.
Answer:
B: (9, 1)
Step-by-step explanation:
The mid point is (5, 3). Compare the x and y values to point A: (1,5)
We can see that the 'x' coordinate is 4 units higher than point A, so the x value for point B will be 4 points higher than the x value of the mid point.
5 + 4 = 9
We can see that the 'y' coordinate is 2 units less than point A, so the y value for point B will be 2 points less than the y value of the mid point.
3 - 2 = 1
Answer:
B coordinate is ( 9 ,1).
Step-by-step explanation:
Given : The midpoint of segment AB is (5, 3). The coordinates of point A are (1, 5).
To find : Find the coordinates of point B.
Solution : We have given
Midpoint of segment AB = (5, 3).
The coordinates of point A = (1, 5).
Mid point : [tex]\frac{(x_{1}+x_{2}}{2} ,\frac{(y_{1}+y_{2}}{2})[/tex].
On plugging the values.
(5,3) = [tex]+\frac{1+x_{2}}{2} ,\frac{(5+y_{2}}{2})[/tex].
Now on comparing x coordinates
[tex](\frac{(1+x_{2}}{2})[/tex] = 5
On multiplying both number by 2
1 +[tex]x_{2}[/tex] = 10.
On subtracting both sides by 1.
[tex]x_{2}[/tex] = 9
Now on comparing y coordinates
[tex]\frac{(5+y_{2}}{2})[/tex] = 3
On multiplying both number by 2
5 +[tex]y_{2}[/tex] = 6
On subtracting both sides by 5.
[tex]y_{2}[/tex] = 1
Then B coordinate is ( 9 ,1).
Therefore, B coordinate is ( 9 ,1).
Therefore, B coordinate is ( 9 ,1).
2z-18-4z=-8 what is the value of z
Answer- z is equal to -5
[tex]\bold{Hey\ there!} \\ \bold{Simply\ both\ sides\ of\ your\ equation\downarrow} \\ \bold{2z+(-4z)+(-18)=-8} \\ \bold{Now, \ you \ have\ to \underline{Combine\ your\ like\ terms}\downarrow} \\ \bold{\bullet \ 2z\ \& \ -4z}\\ \\ \bold{2z+(-4z)=-2z}\\ \bold{-2z-18=-8}\\ \bold{Nextly,\ you\ have\ to\ \underline{add}\ by\ 18\ on\ your\ sides\downarrow} \\ \bold{-2z-18+18=-8+18} \\ \bold{Cancel:-18+18} \\ \bold{Keep:-8+18} \\ \bold{\underline{Divide}\ by\ -2\ on\ your\ sides\downarrow}\\ \bold{\frac{-2z}{-2}}[/tex] [tex]\bold{= \frac{10}{-2}} \\ \bold{Cancel: \frac{-2z}{-2}} \\ \bold{Keep:\frac{10}{-2}} \\ \\ \boxed{\boxed{\bold{Answer: z=-5}}}\checkmark \\ \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}\\ \\ \frak{LoveYourselfFirst:)}[/tex]
Ivan is painting 3 walls in his living room. Each wall measures 9 3/4 feet tall by 14 1/4 feet wide. Ivan needs to estimate the total area he will paint in order to determine the amount of paint to purchase. Which expression best represents the estimated area in square feet that Ivan will paint?
Answer:
The estimated area is [tex]416\frac{13}{16}\ ft^{2}[/tex]
Step-by-step explanation:
we know that
To estimate the area that Ivan will paint , calculate the area of one wall and then multiply by 3
step 1
Convert the dimensions to an improper fractions
[tex]9\frac{3}{4}\ ft=\frac{9*4+3}{4}=\frac{39}{4}\ ft[/tex]
[tex]14\frac{1}{4}\ ft=\frac{14*4+1}{4}=\frac{57}{4}\ ft[/tex]
step 2
Find the area of one wall
[tex](\frac{39}{4})*(\frac{57}{4})=\frac{2,223}{16}\ ft^{2}[/tex]
step 3
Multiply the area of one wall by 3
[tex](3)*\frac{2,223}{16}=\frac{6,669}{16}\ ft^{2}[/tex]
step 4
Convert to mixed number
[tex]\frac{6,669}{16}=\frac{6,656}{16}+\frac{13}{16}=416\frac{13}{16}\ ft^{2}[/tex]
Answer: 3(10 x 14)
Step-by-step explanation: it said in the question or it's more like a hint: "Ivan needs to estimate the total area" and "estimated area in square feet that Ivan will paint?" those are hints to multiple then numbers kinda like adding but adding more into it.
Sorry if it didn't make sense but 3(10 x 14) is what I got in my information which I had written on a paper to figure out what the answer was to the question!
Have a wonderful day! God loves you.