The third ordered pair that satisfy the given equation 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 satisfy the given equation is (123, 369).
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An elliptical mirror measures 20 inches wide and 24 inches high. The ellipse is centered at (0, 60) on a coordinate plane, where units are in inches. Which equation represents the mirror?
The height and width of the outline (perimeter) of the mirror, as well as the
center in relation to the plane of the edges are given.
[tex]\displaystyle The \ mirror \ can \ be \ \mathbf{ represented} \ by \ the \ equation; \underline{\frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]
Reasons:
Width of the elliptical mirror = 20 inches
Height of the elliptical mirror = 24 inches
Center of the ellipse = (0, 60)
The equation of an ellipse is; [tex]\displaystyle \mathbf{\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2}} = 1[/tex]
Where;
(h, k) = Coordinates of the center;
a = Semi major axis
b = Semi minor axis
In the mirror, we have;
(h, k) = (0, 60)
a = 24 ÷ 2 = 12
b = 20 ÷ 2 = 10
Which gives;
[tex]\displaystyle \frac{(x - 0)^2}{10^2} + \frac{(y - 60)^2}{12^2} = \frac{x ^2}{100} + \frac{(y - 60)^2}{144} = \mathbf{\frac{(y - 60)^2}{144} + \frac{x^2}{100}} = 1[/tex]
Therefore;
[tex]\displaystyle The \ equation \ that \ represent \ the \ mirror \ is; \underline{ \frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}[/tex]
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Find the slope of the line that passes through (6, 8) and (2, 17).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-9/4
Step-by-step explanation:
Slope is equal to the change in y, over the change in x, or rise over run.
x, is the run
y, is the rise
You can substitute the coordinate numbers on the equation to find the slope. which is y2-y1/x2-x1
m= 17-(8)
——
2-(6)
Your answer will be -9/4 (it doesn’t matter where the negative goes, and there’s a negative because 2-6= -4)
Hope this helps.
Gabe has a savings account at the local bank. He deposits $150 in his account every 2 months. Which equation models the relationship between the months that deposits are made, x, and the amount of money deposited in the account, y?
Answer:
y=150(x/2)
Step-by-step explanation:
y = 150(x/2)
y represents the amount of money that is deposited into Gabe's account. x represents the amount of time he is adding money for.
x is divided by 2 because however long gabe has been adding money into his account, he does it every 2 months. This means that if x = 12 (time = 12 months) , then Gabe has only made (12/2) = 6 deposits of $150. If x = 4 (time = 4 months), then Gabe would have only made (4/2) = 2 deposits of $150.
With this being said, 150 is being multiplied by the number of deposits (x/2) to find the total amount of money deposited (y).
A board is 81.28 centimeters long. How long is the board in inches? Use the following conversion: 1 inch is 2.54 centimeters
Cheyenne is on her school swim team.
She has won 6 of her 15 events so far
this year. Which equation can be used
to determine how many events she will
need to win in a row to have an overall
win rate of 75%?
The equation that can be used to determine how many events Cheyenne will need to win in a row to have an overall win rate of 75% is x+6=(3/4)×15.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that there is a total of 15 events. And in order to win 75% of the event, Cheyenne need to win,
The number of matches Cheyenne needs to win = 75% of 15
= 11.25 ≈ 12 events
Since Cheyenne has already won 6 events out of 15, she needs to win 6 more events.
Hence, the equation that can be used to determine how many events Cheyenne will need to win in a row to have an overall win rate of 75% is x+6=(3/4)×15.
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A card is fresh from an ordinary deck. Find the probability that it did a diamond given that it is a jack
Answer:
1/52
Step-by-step explanation:
A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%
If you are looking for the probability of a diamond, it is 1/4, or 25%
2/3+7/15
Help pls
no scam
[tex] \boxed{ \huge \bf \: Solution:—}[/tex]
[tex] \sf \longmapsto \dfrac{2}{3} \ + \dfrac{7}{15} [/tex]
[tex]\sf \longmapsto \: \dfrac{10}{15} + \dfrac{7}{15} [/tex]
[tex]\sf \longmapsto \: \dfrac{10 + 7}{15} [/tex]
[tex]\sf \longmapsto \dfrac{17}{15} [/tex]
Decimal—1.13333[tex]\boxed{\huge\bf{Answer:—}}[/tex]
[tex]\bf \dfrac{17}{15} [/tex]
OR
[tex]\bf{1.13}[/tex]
Answer:
17/15 or 1 2/15Step-by-step explanation:
2/3 + 7/15 = The common denominator is 1510/15 + 7/15 = 17/15 = 1 2/15can someone give me the answers please?
Answer:
6. slope= -4/5 Y-intercept is 3
7.
a.y=-2x
b.y=1x+1
c.5/2x-1
d.y=4x+3
e.y=-3/2x-5
Step-by-step explanation:
The area of a circular cake plate is 1520 cm?. Find the diameter of the plate to the nearest cm
Answer:
Hola
tengo una pregunta
de que país
eres? ._.
Enter the number that belongs in the green box
Answer:
8
Step-by-step explanation:
The diagonals of a parallelogram divide each other into two equal parts.
please help meeeeeeee due in 5 minutessssssssssssss
Answer:
I think it would be 6. But im not 100% sure
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Mean x¯¯¯ 12.875
Median x˜ 11.5
Mode 15
Range 34
Minimum 6
Maximum 40
Count n 16
Sum 206
Quartiles Quartiles:
Q1 --> 8.5
Q2 --> 11.5
Q3 --> 14.5
Interquartile
Range IQR 6
Outliers 40
Arthur is saving money to buy a used car in 8 months. The car costs $2,180. Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car. What is the minimum initial deposit Arthur must make? Round to the nearest whole dollar.
The minimum initial deposit Arthur must make is $ 4.24.
Since Arthur is saving money to buy a used car in 8 months, and the car costs $ 2,180, and Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car, to determine what is the minimum initial deposit Arthur must make the following calculation should be performed:
X x 1.25 x 1.56 x 1.95 x 2.44 x 3.05 x 3.81 x 4.76 = 2180 514.10X = 2180 X = 2180 / 514.10 X = 4.24
Therefore, the minimum initial deposit Arthur must make is $ 4.24.
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Put these numbers in order from least to greatest.
1/2 1/10 0.4?
Answer:
1/10, 0.4, 1/2
Step-by-step explanation:
Answer:
1/10 0.4 1/2
Step-by-step explanation:
1/10 = 0.1
0.4 = 0.4
1/2 = 0.5
therefore 0.1 0.4 0.5
1 divided by 11/2 as a fraction
Answer:
1.375 decimal to fraction.
2/7 Fraction to Decimal
Step-by-step explanation:
PLEASE HURRY! WILL MARK BRAINLIEST IF CORRECT!! (Screenshot)
I will give brainliest to whoever gets the right answer
Answer:
[tex]18[/tex]
Step-by-step explanation:
Step 1: Input the values and solve
[tex]b - 7a[/tex]
[tex](4) - 7(-2)[/tex]
[tex]4 - (-14)[/tex]
[tex]4 + 14[/tex]
[tex]18[/tex]
Answer: [tex]18[/tex]
The lengths two sides of a triangle are 10 cm and 11cm. Between what two measures should the length of the third side fall?
Step-by-step explanation:
a triangle can only be a triangle (all sides connect with each other), if every side is less than the sum of the other 2 sides.
so, the third side must be shorter than 10+11 = 21 and longer than 11-10 = 1, so that the side of 11 cm is shorter than the sum of the other two sides.
Answer:
1 < x < 21
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
11 - 10 < x < 11 + 10
1 < x < 21
PLEASE write an equation in point-slope form for the line that passes through the point with the given slope. (-2,11) m=4/3
Answer:
[tex]y-11=\frac{4}{3}(x+2)[/tex] or y - 11 = (4/3)(x+2)
Step-by-step explanation:
Point-slope equation is: [tex]y-y_1=m(x-x_1)[/tex]
If we replace y1 with 11 and x1 with -2 then this will be our resulting formula:
[tex]y-11=m(x+2)[/tex]
And of course we need to replace m with our slope:
[tex]y-11=\frac{4}{3}(x+2)[/tex]
Find the value of the variable.
Answer:
Step-by-step explanation:
Draw a line from S to T'
T' is where the angle PTQ intersects the circle when SR is extended so that it hits the circumference of the circle.
This line bisects the 50 degree angle (which is given. It also bisects PRS.
y is shown on the diagram.
Your first job is to find y
It's y + 90 + 25 = 180 because all triangles are made up of 180 degrees.
y it turns out is 65 degrees.
Now comes the interesting part. PRT' is supplementary to y. It is labeled as 180 - y
<PRT' + Y = 180
y = 65
<PRT' = 180 - 65 = 115
Since PRT' = 115 and since PR = PT' (They are both radii). x/2 + x/2+ 115 = 180 I'll talk about x/2 down below this.
x + 115 = 180 All triangles = 180
x = 65.
Where did x/2 come? As long as PTQ is situated on the arc that it is on then <PTQ is always going to be x. You will have to piece together the two diagrams to make this work.i
It's a very good application of circles and lines well worth your time to get to know.
help asap!!!! please!!
Answer:
13 blue and 20 yellow
urwelcome
write one equivalent ratio of the given radio
1. 3/9
2.6/7
3.11/12
4.2/8
5.3/6
Solve. 4 + x 7 = 2
pls helpppp
Answer: x=14
Step-by-step explanation:
4+x/7=2
-4 -4
X/7=-2
*7 *7
X=14
Answer:
-14
Step-by-step explanation:
Multiply
(5x+y)(6x-7y)
Answer:
30x2−29xy−7y2
Step-by-step explanation:
=(5x+y)(6x+−7y)
=(5x)(6x)+(5x)(−7y)+(y)(6x)+(y)(−7y)
=30x2−35xy+6xy−7y2
=30x2−29xy−7y2
In 7 hours, Deandre reads 42 chapters of a book.
What is his rate in chapters per hour?
Answer:
6 chapters per hour
Step-by-step explanation:
[tex]\frac{42 (chapters)}{7 (hours)} =6[/tex]
Hope this helps
32. The length of each side of a square wooden box, in inches, is represented by the expression
8m'. The volume of the box, in cubic inches, is (8m").
Which simplified expression represents the volume of the box?
C. 512m
D. 512m
A. 8m
B. 24m
the length of the box is represented by (8m2)
does that mean 8m^2?
in English that would be 8 times m^2 or 8 * m * m.
if that is true, then the volume of the box would be equal to (8*m^2)^3 which is equal to 8^3 * m^6 which is then simplified further to 512 * m^6 which can also be written as 512m^6.
if we assume that m is 3, then the side of the box is equal to 8 * 9 which is equal to 72 and that is cubed to get 373248.
working that out algebraically, it would look like this:
(8*3^2)^3 equals 8^3 * (3^2)^3 which is equal to 8^3 * 3^6 which is equal to 512 * 729 which is equal to 373248
The simplified expression that represents the volume of the box is D. 512m.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.
The volume of a cube or a square box can be calculated by multiplying the length of one side by itself twice since all sides of a cube are equal. Therefore, the volume of the square wooden box in the question is:
Volume = (8m')³
= 8m' * 8m' * 8m'
= 64m' * 8m'
= 512m"³
So the simplified expression that represents the volume of the box is 512m"³. Both options C and D in the original question have the same answer, but there is a typo in option D where it only says "512m" instead of "512m³".
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Gonna be sending in quite a few of these lol thanks
Answer:
A
Step-by-step explanation:
Simply multiply each rows of the firstly stated matrix by the columns of the second and then add each with respect to their location.
A dugout needs to reach at least 54 feet below ground level. This means it needs to be more than 214 times its current depth. This depth is represented by the inequality 214d<−54, where d is the current depth of the dugout.
Select from the drop-down to correctly interpret the solution of this inequality.
The current depth of the dugout is
Choose...
feet below ground level.
Solving the inequality, it is found that:
The current depth of the dugout is of 0.25 feet below ground level.
The current depth of the dugout is of d.
The inequality below represents how much the dugout needs to reach, according to the current depth:
[tex]214d < -54[/tex]
We solve it similarly to an equality, hence:
[tex]d < -\frac{54}{214}[/tex]
[tex]d < -0.25[/tex]
The current depth of the dugout is of 0.25 feet below ground level.
A similar problem is given at https://brainly.com/question/14361489
Answer:
deeper then 24
Step-by-step explanation:
Please make me brainliest
Enter the number that belongs in the green box
Answer:
72°
Step-by-step explanation:
The diagonals of a parallelogram intersect at a point that forms the center of symmetry of the parallelogram.
rico wants to buy a battery operated toy car which caused 580 7.50 he has already save one 50.00 points his ninong give him 200 point zero zero if he saved 12.50 a day from his allowance how long will it take him to save the rest of money to buy the toy car
Answer:
19 days
Step-by-step explanation:
1 - Make an equation with the variables provided.
150 + 200 + 12.50x = 587.50
2 - Simplify both sides.
350 + 12.50x = 587.50
3 - Subtract 350 from both sides.
12.50x = 237.50
4 - Divide by 12.50 to find your x variable.
x = 19 days
Brainliest would be appreaciated! :-)
What is the perimeter of the trapezoid?
10m
8m
10m
18m
Answer:
46 m
Step-by-step explanation:
The perimeter of any figure is the sum of the lengths of its sides.
8m +10m +10m +18m = 46 m
The perimeter of the figure is 46 meters.