If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?
The third ordered pair that satisfies the equation of the circle is (123, 369).
The given parameters;
[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)The third ordered pair of the equation can be determined by using general equation of a circle;
[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]
The radius of the circle is calculated as;
[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
[tex]b < r\\\\b < 388.96[/tex]
[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]
Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).
Learn more about equation of circle here: https://brainly.com/question/11711668
Write 6,070,000 in expanded form.
Answer:
6,000,000 + 0 + 70,000 + 0 + 0 + 0 + 0
bonus : word form: six million seventy thousand
Step-by-step explanation:
hope this helps! have a g'day
The total cost for a piece of land is 600000. If the land is 100 meter shorter and each meter costs 1000 more the total cost would remain unchanged. Use a quadratic equation to determine the length of the land.
Answer:
5,00000000
Step-by-step explanation:
6000000000
Hurry!! Answer it please:))
Answer:
Option C.
Domain:
{3, 0, 2, 4}
Step-by-step explanation:
The domain is the set of all the values of x.
Answer:
C is the answer!:)
Step-by-step explanation:
Domain is all numbers on the left and range is on the right
Find the value of sin D rounded to the nearest hundredth, if necessary.
Answer:
0.22
Step-by-step explanation:
So in this problem, we have to find the hypotenuse first, since sine is opposite over hypotenuse.
We can do this using the pythagorean theorem (you can search it if you don't know). Or, we can just remember this as one of our pythagorean triplets (9,40,41). The last side will be 41.
We have to find the value of sin(D)
opposite/hypotenuse = 9/41 = 0.2195 which is about 0.22
A convention center is in the shape of a rectangular pyramid with a height of 332 m. Its base measures 475 m by 571 m. Find the volume of the convention center. If necessary, round your answer to the nearest tenth
Answer:
30,015,566.7 m³ OR 3.0 x 10⁷ m³
Step-by-step explanation:
The formula for finding the volume of a rectangular pyramid is:
V = lwh/3
where l = length
w= width
h = height
(475)(571)(332)/3 = 30,015,566.7 m³ = 3.0 x 10⁷
At Charles Walters Middle School, 25% of the students live more than 8 miles from school, What fraction of the students live more than 8 miles from school? Write your answer as a fraction in simplest form. ?
Answer:
1/4
Step-by-step explanation:
0.25 = 1/4
Answer:
1/4
Step-by-step explanation:
25% is 25/100. 25/100 simplified is 1/4.
classyfying triangles unit 4
Answer:
What do you mean by that?
Step-by-step explanation:
Answer:
Is there more to the question? or a link/ picture you forgot to add?
Step-by-step explanation:
The dimensions of a rectangular garden is 3 m by 10 m. When both dimensions are increased by equal amounts, the area of the garden doubles. What are the dimensions of the new garden?
Answer:
5 by 12 m
Step-by-step explanation:
The area for rectangle is LxW
The original area is 3*10, or 30 meters.
When both dimensions are increased, now the area is 60.
We can now inch up slowly to see what works:
3.5 and 10.5=36.75 X
4 and 11=40 X
5 and 12=60 YES!
The new dimensions of the garden are 5 m by 12 m, increased by 2, and the new area is 60 meters^2.
y’’’’ - y = 0
y(0) = 0
y’(0) = 1
y’’(0) = 0
y’’’(0) = 0
Answer:
bick in my vaogina toes Step-by-step explanation:
A bag contains 6 red tiles and 15 yellow tiles. Lilia removes 2 red tiles. How many
yellow tiles should she remove so that the ratio of red tiles to yellow tiles in the
bag stays equivalent to 6:15? Show your work.
Answer:
I would remove 5 yellow tiles.
Step-by-step explanation:
If the beginning ratio was 6:15, I would start by finding the ratio of 1 red tile to ? yellow tiles. By multiplying 1 by 15, giving you 15, and dividing 15 by 6, I would find out that 1 red tile is equal to 2.5 yellow tiles. I would then set up an equation so there is 1/2.5 = 4/?, the 4 being the remaining red tiles after removing 2. I would then find the yellow tiles by multiplying whatever number the 1st numerator can be multiplied by to equal the 2nd numerator. Basically, I know that 1 multiplied by 4 is equal to 4, so I would multiply 2.5 by 4, which is equal to 10. Now that I know 4 red tiles is equal to 10 yellow tiles, I would remove 5 tiles to keep the ratio equivalent to 6:15
HOPE THIS HELPS :)
Which number is a factor of 15 but no a multiple of 3?
Answer: 5
Step-by-step explanation:
Sam needs a bowl to mix her punch. She has 2-cup bowl, and a 6-cup. What is the smallest bowl sam can use to make her punch?
Answer:
the 2 cup bowl
Step-by-step explanation:
it is literally the smallest bowl she can use at her disposal
what is the exact value of tan(-π/3)?
A. -√3
B. -√3/3
C.√3/3
D. √3
[tex]\tan \left(-\dfrac{\pi}3\right)\\\\=-\tan \left(\dfrac{\pi}3\right)\\\\=-\sqrt 3[/tex]
Can someone help me I will mark u brilliant
Answer: its 45% for sure
Answer:
i believe 45%
Step-by-step explanation:
hope this helps! :D
have a miraculous day, and brainliest is immensely appreciated!! <3
For each right triangle below, find all unknown side lengths and angle measures:
can anyone help for number 8 and 9
Answer:
10.
here,
h=c
b=5
p=12
,we know that,
h²=b²+p²(pythagoras theorum )
c=5²+12²
c=25+144
c=169
hence the value of c is 169.
Opposite rays form a:
O line
O ray
O point
O plane
5
Answer:
ray
Step-by-step explanation:
help i dont know what this means
The youth group is going on a trip to the state fair. The trip costs $64. Included in that price is $12 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer:
12+26x=64
Step-by-step explanation:
64-12=52
52/2=26
$26 per pass
equation 12+26x=64
x=2 in this case x is representing the number of passes
12 is the ticket
and 64 is total cost
Subtract 8 feet from 9 yards, 1 foot.
7 yards, 1 foot
1 yard, 1 foot
6 yards, 2 feet
6 yards, 1 foot
Answer:
6 yards, 2 feet
Step-by-step explanation:
9yards and 1 ft - 8 feet= 6.66666667 yards
6.66666667 yards=6 yards, 2 feet
6 yards, 2 feet
hope it helps
I’ll give brainliest to the person who give me the correct answer and pointsss.
Match them
I think the y=ab^x goes with the first graph and the y=logbc goes with the second
Step-by-step explanation:
pictures
Please help I don’t understand!!
Answer:
[tex] \frac{5(x + y)}{ - 8x} [/tex]
Step-by-step explanation:
quotient means division
numerator is the top
denominator is the bottom
product means multiply
sum means add
A rectangular field is four times as long as it is wide if the perimeter of the field is 420 yards what are the fields dimensions
Answer:
168yards by 42yards
Step-by-step explanation:
Perimeter =2(l+b)
Perimeter =420yards
length=4×breadth
l=4b
P=2(l+b)
P=2(4b+b)
P=2(5b)
P=10b
420=10b
b=420/10
b=42yards
l=4b=4×42yards
l=168yards
hence the dimensions are 168yards by 42yards
Two mechanics worked on a car. The first mechanic charged $75 per hour, and the second mechanic charged $45 per hour. The mechanics worked for a
combined total of 25 hours, and together they charged a total of $1425. How long did each mechanic work?
Answer:
First mechanic 10 hours, Second is 15 hours
Step-by-step explanation:
x + y = 25, so y = 25 - x
75x + 45y = 1425
Substitute in the first equation
75x + 45(25 - x) = 1425
75x + 1125 - 45x = 1425
30x = 300
x = 10
Therefore, y = 15
Answer:
they both worked
8 hours
Explain in your own words the steps to dividing decimals by decimals.
Bill and his 3 friends read 55 books each for the year. Each book had 320 pages, How many pages did they all read in total that year?
Answer:
they all read 52.800 pages in that year
Step-by-step explanation:
320 X 55 = 17.600 pages/person
17.600 X 3 = 52.800 pages
Pls help I’m failing do it on paper and put it in the answer box
Step-by-step explanation:
there is no mathematical problem to solve.
just follow the instructions as given.
this is an exercise for you to get a feeling about what is what. it is imperative that you do it.
there is really nothing to solve.
remember, that a positive slope means the line goes up (from left to right), and a negative slope means the line goes down (again from left to right).
and I am sure you know what vertical and horizontal means.
You decide to reduce the amount you spend eating out by $150 a month and invest the total saved at
the end of each year in your retirement account. How much will the account be worth at 5% in 15
years? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the
nearest cent.)
The type of savings is the saving of uniform amount with interest applied to the sum of the amount in the account.
The amount the account is worth after 15 years is approximately $38,841.1Reasons:
The amount saved per month = $150
Amount saved per year, A = 12 × $150 = $1,800
The interest rate on the account, i = 5%
The amount, F, in the account after 15 years is given as follows;
The uniform series compound amount factor formula is presented as follows;
[tex]\displaystyle F = \mathbf{\frac{A \cdot \left[ \left(1 + i \right)^n - 1 \right]}{i}}[/tex]
Therefore;
[tex]\displaystyle F = \frac{1,800 \times \left[ \left(1 + 0.05 \right)^{15} - 1 \right]}{0.05} \approx \mathbf{38,841.4}[/tex]
The amount the account is worth after 15 years to the nearest cent is approximately $38,841.4.
Learn more about compound interest here:
https://brainly.com/question/9742437
Find X. Enter a number for your answer. Do not type the symbol for degree or the
word "degrees"
Use angle sum property (the 3 angles in a triangle sum up to 180°).
2x + x + 54 = 180
3x + 54 = 180
3x = 180 - 54
3x = 126
x = 126/3
x = 42
_____
Hope it helps ⚜
x = 42
Explanation:-We know that,Angles of a triangle adds to 180°
So,=> 2x + x + 54 = 180
=> 3x = 180 – 54
=> 3x = 126
=> x = 126/3
=> x = 42
(x = 42° ; 2x = 84°)
You plant 9 rows of different bulbs in a garden. For each row, you use the rule, “onion, onion, garlic, flower.” How many garlic and flower bulbs do you plant altogether? How many bulbs do you use in all?
Answer: Who the actual fudge gardens anymore????? like what are you an old lady? ur name edna? ethel? doreen? geez louise u are old.
Step-by-step explanation:
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