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).
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What is correct A, B or C
Answer:
A is the correct solution
Step-by-step explanation:
3x³ + 4x² + 0x - 1 / x - 2
3 10 20
-2 | 3 4 0 -1
- (3 -6)
10 0
- (10 -20)
20 -1
- (20 -40)
39
3x² + 10x + 20 + 39/(x - 2)
In an economics class, 4 students earned an A, 6 earned a B, 5 earned a C, 5 earned a D, and 3 earned an F. If a single student is picked at random, what is the probability that they earned an B or C?
Provide your answer as a simplified fraction.
Answer:
11/23
Step-by-step explanation:
B = 6
C = 5
6+5=11
11/23
discuss the criteria of a good test
How do you solve this
Answer:
x > 3
Step-by-step explanation:
And then, I believe you just need to solve that answer. But I'm not sure tho
Identify an equation in point-slope form for the line parallel to y = -
2/3x+8 that passes through (4, -5).
A. y-4=(x+5)
B. y+5=2/3 (x-4)
C. y+5 = 3/2(x-4)
D. y-5=-2/3(x + 4)
Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point. You must show all your work
3x + y = -2
y = 2x +3
The substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
A system of linear equation is a group of one or more linear equations which can be solved by using a simultaneous equation or elimination method.
From the information given;
3x + y = -2 ----- (1)
y = 2x +3 ----- (2)
By using substitution method, we will replace the value of equation (2) into equation (1), by doing so, we have:
3x + (2x + 3) = -2
3x + 2x + 3 = -2
5x + 3 = -2
5x = -2 - 3
5x = - 5
x = -5/5
x = -1
From equation (2), let's replace the value of x = - 1 into equation (2);
y = 2x + 3
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
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What is the 7th term in the sequence below?
-19, -7, 5, 17, .....
Select one:
a.65
b.29
c.101
d.53
Answer:
53
Step-by-step explanation:
—19 + 12 = —7
—7 + 12 = 5
5 + 12 = 17
.
.
.
so the n term of the sequence will be: 12n — 31
so 7th term will be: 12 × 7 — 31 = 53
Answer:
d. 53
Step-by-step explanation:
increases 12 units at each step:
17 + 12 = 29
29 +12 = 41
41 + 12 = 53 (7th term)
Hope this helps
Please help me! Im a little bit stumped!
Answer:
2x+34=4x+20
14=2x
x=7
Step-by-step explanation:
So the answer is 7
Answer:
some bedmas laws you have to use
first do the 4(x+5) since its distubutive
you get 2x + 34 = 4x + 20 normally i like to keep x positive so i dont have to divide by -1 at the end so subtract 5 to the other side qnd subtract 2x to the other side and you get
2x= 14
x = 7 is the answer
How much must you deposit in an account that pays 6.25% interest, compounded annually, to have a balance of $700 after two years?
= $
The compound interest is applied to the remaining balance in the account
each subsequent year.
The amount that must be deposited is approximately $620.07Reasons:
The given compound interest rate, r = 6.25% = 0.0625
The balance in the account after 2 years, A = $700
Required:
The required deposit, P, that gives the given account balance after 2 years.
Solution:
The following is the compound interest formula to use;
[tex]A = \mathbf{P \times \left(1+r \right)^{ t}}[/tex]Where;
t = 2 years
We get;
[tex]\displaystyle P = \mathbf{ \frac{A}{(1 + r)^t}}[/tex]
Which gives;
[tex]\displaystyle P = \frac{700}{(1 + 0.0625)^2} \approx \mathbf{620.07}[/tex]
The amount that must be deposited to give $700 after 2 years is P ≈ $620.07Learn more about compound interest here:
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In the typing World 120 words in 3 minutes is average how many words could they type in 2 hours
Answer:
7,200 words
Step-by-step explanation:
Answer: 4,800
I multiplied 120 by 20 because 60 divided by 3 is 20. Then I multiplied my answer by 2 because the question is asking how many words could they type in 2 hours
is it true that George Washington LOVED political parties?
Answer:
No, It's false.
Step-by-step explanation:
In the long history of the United States, only one president, George Washington, did not represent a political party.
Are the ratios 2:1 and 17:7 equivalent?
Answer:
no
Step-by-step explanation:
1 x 7 = 7 but 2 x 7 does not equal 17
PLEASE HELP
If you help You’ll automatically be my favorite person ever
Answer:
Put one point on -4 on the Y-axis (bottom middle) and one at (-2,2)
A random variables X and Y are distributed according to the joint PDF. The value of constant a = _______.f(x,y)=ax if 1<=1x<=y<=2 and 0 otherwise
======================================================
Explanation:
PDF = probability density function
The given joint PDF is
[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]
Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.
So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7 leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.
As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.
-----------------
Based on that, we'll have a double integral that looks like this:
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]
The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.
On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]
To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.
-----------------
Let's simplify the double integral.
We'll start by computing the inner integral with respect to y.
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]
Then we'll finish it off by integrating with respect to x.
[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]
[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]
Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.
Recall that V = 1. So,
[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]
a = 3/2 is the final answer.
13. This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers.
35 40
42 ?
? ?
The missing numbers in the multiplication table are 49, 48 and 56 respectively
Given:
35
42
?
35 = 7 × 5
42 = 7 × 6
? = 7 × 7 = 49
40
?
?
40 = 8 × 5
? = 8 × 6 = 48
? = 8 × 7 = 56
Multiplication table is a mathematical table showing the products of each of integers such as 7 and 5, 1 and 10, 13 and 12 etcTherefore, the missing numbers in the multiplication table are 49, 48 and 56 respectively
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i need help with this problem ;-;
Fid the value of the expression
Answer:
2
Step-by-step explanation:
The question askes what is k divided by m (k/m) when k is equal to 8 and m is equal to 4. So, plug the values into the original questions 8÷4. This means that the number 8 is being split into 4 groups. When 8 is divided into 4 groups each group is left with 2. Therefore, the answer is 2.
Another way to solve this is to make a fraction. 8÷4 is the same as 8/4. If you simplify that fraction you also get 2.
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
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At Pizza Pi, 68% of the pizzas made last week had extra cheese. If 17 pizzas had extra cheese, how many pizzas in all were made last week?
Answer: 50
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
Factor each product-
0.7√300
-0.125√192
Answer:
1. 7 to the square root of 3
2. negative square root of 3
Step-by-step explanation:
1. simplify 0.7 x 10 square of 3
2. Calculate: you get 7 to the square root of 3
1. simplify -0.125 x 8 to the square root of 3
2. Calcaute: you get negative square root of 3
The factors of the expression 0.7√300 and -0.125√192 will be 7 x √3 and - 1 x √3, respectively.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
0.7√300 and -0.125√192
Simplify the expressions, then we have
0.7√300 and -0.125√192
7√3 and - √3
Factorize the expression, then we have
7 x √3 and - 1 x √3
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What is nx25=5x60 and how did you get the answer?
Hey there!
n * 25 = 5 * 60
25n = 5 * 60
25n = 300
DIVIDE 25 to BOTH SIDES
25n/25 = 300/25
CANCEL out: 25/25 because it gives you 1
KEEP: 300/25 because it helps solve for the n-value
NEW EQUATION: n = 300/25
SIMPLIFY IT!
n = 12
Therefore, your answer is: n = 12
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
-2(4x-6)=6-6x help me
Answer:
x=3
Step-by-step explanation:
you have to move the terms collect like terms and divide both sides and down load photo math that helps alot with giving answersCan anyone help! me 30 points
Answer:
the first one and the last one
Step-by-step explanation:
Hope it will helps you ❤️❤️❤️
Please mark me as a brainliest
My mom walks 1 mile in 14
minutes. If she walked for 56
minutes, how far did she walk?
Answer:
4 miles
Step-by-step explanation
If your mom can walk 1 mile in 14 minutes then 2 miles would take her 28 minutes 3 miles would take her 42 minutes and finally if she walked 4 miles it would take her 56 minutes.
14 + 14 + 14 + 14 = 56
14 x 4 = 56
A nature preserve worker calculates there are 6,000 deer in Sharon Woods Park. She also estimates that 75 more deer die than are born each year.
a. Write a linear function to estimate how many deer will be in the park in x years.
b. Use the linear function to predict how many deer will be in the park in 3 years.
c. In how many years will there be 5,325 deer left in Sharon Woods Park?
The linear equation used to represent this situation is y = -75x + 6000
A linear equation is in the form:
y = mx + b;
where y, x are variable, m is the slope of the line and b is the y intercept.
Let y represent the amount of deer present in x years. There are 6000 deer presently, hence a = 6000. Also 75 more deer die than are born each year. Hence m = -75.
The linear equation is given by:
y = -75x + 6000
In 3 years:
y = -75(3) + 6000
y = 5775
For there to be 5325 deer:
5325 = -75x + 6000
x = 9 years
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Does (–1, 2) make the equation y = x + 9 true?
Answer:
(-1, 2) does not make the equation y=x+9 true.
Step-by-step explanation:
y=x+9
(-1, 2)=(x, y)
2=(-1)+9,
-1+9=8,
2 does not equal to 8.
Answer: No.
ALGEBRA Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%. During the monthly billing cycle, Ben charged $238.75, made a payment of $300.00, and had a finance charge of $7.99. Find his unpaid balance, previous balance, and new balance.
The new balance is a credit of $ 48.78.
Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:
Finance charge + new purchases + previous balance - payments = X 238.75 x 1.01875 + 7.99 - 300 = X 243.22 + 7.99 - 300 = X 251.21 - 300 = X -48.78 = X
Therefore, the new balance is a credit of $ 48.78.
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on what interval (s) are f(x) = x3 2x²+x+6 decreasing?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
please help will brain list if correct no links please
Answer:
C
Step-by-step explanation:
the angle opposite of it is 30
Find the slope of the line passing through the points (-7,8) and (-7,-6)
Find the slope of the line passing through the points (-9,-8) and (3,-8)
Answer:
1) undefined
2) 0
Step-by-step explanation:
Slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Problem 1:
(x1, y1) = (-7, 8)
(x2, y2) = (-7, -6)
Plug those 2 points into the slope formula and solve:
[tex]m=\frac{-6-8}{-7--7}\\\\m=\frac{-14}{0}[/tex]
Here, you can't divide by 0, so this slope is undefined. An undefined slope would make a completely vertical line on a graph. In this case, the equation of the line would be just:
[tex]x=-7[/tex]
Problem 2:
(x1, y1) = (-9, -8)
(x2, y2) = (3, -8)
[tex]m=\frac{-8--8}{3--9}\\\\m=\frac{0}{12}\\\\m=0[/tex]
The slope is 0, and that would make a horizontal line on a graph. The equation would be:
[tex]y=-8[/tex]
You don't actually need to fully work out the slope that way. If you ever have 2 points with the same x-coordinate, the slope has to be undefined. If you ever have 2 points with the same y-coordinate, then the slope has to be 0, assuming it's linear of course. You can see that in the points given, the first 2 have the same x and the second 2 have the same y.