Answers
Ok so the general form of a circle is given by;
(x-a)²+(y-b)²=r²
where a and b are the coordinates of the center
and r is the radius of the circle
For this case we know that the center is (5,-7)
So the general equation of the circle would be;
[tex](x - 5) {}^{2} + (y - ( - 7)) {}^{2} = r {}^{2} [/tex]
[tex](x - 5 {}^{2} + (y + 7) {}^{2} = r {}^{2} [/tex]
Since we know that (-3,-1) is a point on that circle, we can say that it satisfies the equation of the circle;
[tex]( - 3 - 5) {}^{2} + ( - 1 + 7) {}^{2} = r {}^{2} [/tex]
[tex]r {}^{2} = ( - 8) {}^{2} + ( 6) {}^{2} [/tex]
[tex]r {}^{2} = 64 + 36 = 100[/tex]
So now,
[tex](x - 5) {}^{2} + ( {y + 7)}^{2} = 100[/tex]
Related Questions
Write the equation of the line that passes through the given point and has the given slope. (-12,5)
slope = 1/3
Answers
Answer: y= 1/3x + 41
Answer:
[tex]_{\text{point-slope form}}[/tex]
[tex]\huge\boxed{y-5=\dfrac{1}{3}(x+12)}[/tex]
[tex]_{\text{slope-intercept form}}[/tex]
[tex]\huge\boxed{y=\dfrac{1}{3}x+9}[/tex]
[tex]_{\text{standard form}}[/tex]
[tex]\huge\boxed{x-3y=-27}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] - slope
[tex](x_1;\ y_1)[/tex] - a point on a line
We have
[tex]m=\dfrac{1}{3};\ (-12;\ 5)\to x_1=-12;\ y_1=5[/tex]
Substitute:
[tex]y-5=\dfrac{1}{3}(x-(-12))\\\\y-5=\dfrac{1}{3}(x+12)\\==================[/tex]
[tex]y-5=\dfrac{1}{3}(x+12)\qquad|\text{use the distributive property}\ a(b+c)=ab+ac\\\\y-5=\dfrac{1}{3}x+4\qquad|\text{add 5 to both sides}\\\\y=\dfrac{1}{3}x+9\\=======================[/tex]
[tex]y=\dfrac{1}{3}x+9\qquad|\text{multiply both sides by 3}\\\\3y=x+27\qquad|\text{subtract}\ x\ \text{from both sides}\\\\-x+3y=27\qquad|\text{change the signs}\\\\x-3y=-27[/tex]
Write an equation of a line that passes through the point Z (6, – 2) and is perpendicular to the line y=-1/3x + 2
Answers
Answer:
y = 3x - 20
Step-by-step explanation:
First, we have to find the slope of the equation. We can do by taking the opposite reciprocal of the slope of the original line.
The opposite reciprocal of-1/3 is 3/1 or 3.
So, the slope of our equation will be 3. Our equation so far is:
y = 3x + b.
To find b, or the y-intercept of the line, we can simply substitute the given coordinates into the equation. If we replace x with 6 and y with -2 and solve the equation, we can find the value of b.
-2 = 3(6) + b
-2 = 18 + b
-2 - 18 = b
b = -20
So the equation is,
y = 3x -20.
To check our equation, we can again substitute the coordinates into the equation and solve. If both sides are equal, then the equation is correct.
-2 = 6(3) - 20
-2 = 18 - 20
-2 = -2
The two lines are perpendicular if a 90° angle is formed when they
intersect.
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is ; y = 3·x - 20
Reason:
The equation of the required line is, y = 3·x - 20
The given point is Z(6, -2)
Perpendicular to the line, [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex]
Solution:
The slope of a line perpendicular to another line having a slope, m, is [tex]-\dfrac{1}{m}[/tex]
The slope of the given line is [tex]-\dfrac{1}{3}[/tex]
The slope of the perpendicular line is therefore;
[tex]m = -\dfrac{1}{\left(-\dfrac{1}{3}\right)} = \dfrac{3}{1} = 3[/tex]
The point and slope form of the equation of the given line is therefore;
y - (-2) = 3·(x - 6)
y + 2 = 3·x - 3×6 = 3·x - 18
y = 3·x - 18 - 2 = 3·x - 20
y = 3·x - 20
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is therefore;
y = 3·x - 20
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Please Answers these
AND NO LINKS PLEASE
Answers
Answer:
10: 112.5
12: 84
13: T F T
14: F T T
15: T F T
What is the cost, in dollars, for 1 box of pasta
Answers
Answer:
.99 cents. i think but for a pAck two dollars
Step-by-step explanation:
internet
Answer:
.99 cents. i think but for a pack two dollars
Step-by-step explanation:
100 yards
40 yards
40 yards
100 yards
1.
What is the area of one of the blue half circles? HINT: Remember, Area = pi x radius squared.
So you will need to use the 40 (this is the diameter so make sure you find the radius). Then
since you only want a half circle, you will need to divide it by 2. SHOW ALL WORK!
Answers
Answer:
Depends on how the teacher wants the answer:
400π (in terms of pi) or 1256.6 (rounded to tenths place)
Step-by-step explanation:
40/2 = 20, the radius of one of the blue circles
Use the formula: πr², but divide it by 2 because it is a semicircle
π20² = 400π = 1256.63706
Let me know if you need help rounding it if the question asks you to.
Estimate the percent of apartment residents who pay less than $700 per month.
A. 60%
B. 75%
C. 50%
D. 55%
Answers
According to the graph, it is found that the percent of apartment residents who pay less than $700 per month is given by:
B. 75%
What does the graph states?It states that:
Around 5% of the respondents pay less than $600 in rent.25% pay between $600 and $649.45% pay between $650 and $699.25% pay between $700 and $749.5% of the respondents pay more than $749 in rent.Hence, for less than $700, we have that:
5% + 25% + 45% = 75%.
Thus option B is correct.
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2:3 = %
2:3 is in ratio change to percentage
Answers
Answer:
2:3 = 66%
Step-by-step explanation:
⇒ Convert the fraction 2/3 into decimal
⇒ 2/3 = 0.666
⇒ Multiply the decimal by 100: 0.66 × 100 = 66%
Therefore, the solution is 66%.
Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.
2x2 – 9x
x2 + 6x – 24
x2 – 2x – 9
–4x2 + 8x + 36
Answers
The expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.
To use synthetic division, we first need to set up the divisor in the correct form. Since we are looking for the expression for the area of the base of the rectangular prism, we know that the volume of the prism is given by:
volume = (area of base) × (height)
We are given that the height is x + 4, and the volume is x³ + 2x² – 17x – 36. Therefore, we can write:
x³ + 2x² – 17x – 36 = (area of base) × (x + 4)
Now we can use synthetic division to find the expression for the area of the base. The divisor is x + 4, so we write:
-4 | 1 2 -17 -36
| -4 8 36
|-----------------
1 -2 -9 0
The last number in the bottom row is 0, which means that x + 4 is a factor of the polynomial. The other numbers in the bottom row give us the coefficients of the quotient polynomial. Therefore, we can write:
x³ + 2x² – 17x – 36 = (x + 4)(x² – 2x – 9)
So the expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.
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Altogether a torch and battery cost £2. 50
torch costs £2 more than battery how much does battery cost in the simplest for fraction
Answers
The answer is 1/2
The graph below shows a company's profit f(x), in dollars, depending on the price of goods x, in dollars, being sold by the
company:
f(x)
150
120 +
90
60
30
х
2
3
4
5
7
-
-3 -2 -1
-30
8
11
Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and
profit for the company in the situation described?
Part C: What is an approximate average rate of change of the graph from x = 1 to x = 3, and what does this rate represent in
context of the described situation?
Answers
what are the missing numbers?
Answers
Answer:
30
19.5
16
Step-by-step explanation:
you need to find the rule, so divide 12 by 8 and see the factor is 1.5, so just multiply all the numbers by 1.5 to get the second column, and for the last one divide the number by the factor
Answer:
20 honey = 30 flour
13 honey = 19.5 flour
16 honey = 24 flour
Step-by-step explanation:
CROSS MULTIPLYING:
12x20=240, 240/8=30
13x12=156, 156/8= 19.5
8x24=192, 192/12=16
A merchant offers a large group of items at 32% off. Later, the merchant takes 16% off these sale prices and claims that the final price of these items is 186 off the original price. What is the total percent discount?
Answers
The total percent discount offered by the merchant is 57.12%.
What is the total percent discount?A discount is when the price of an items is reduced. It makes a good cheaper when a discount is applied.
The percent change in price after the first discount = 100% - 32% = 68%
The final price after the second discount = (100 - 16%) x 68%
= 57.12%
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A father is 34 years of age. At present his son is 8 years old. In how many years will the father be three times as old as his son ? (11 6 years (3) 4 years (2) 5 years (4) 3 years
Answers
5yrs
Step-by-step explanation:
Father's age = 34yrs
Sons age = 8yrs
In how many yrs will the father be 3× as old as his son?
Let their ages be X
(x + 34) 3(x + 8)
x + 34 = 3x + 24
CLT
x-3x = 24 - 34
-2x/2 -10/2
X = 5
The diameter of a circle is 28 millimeters. What is the circle's area
Use 3.14 for .
Answers
Answer:
615.44 mm²
Step-by-step explanation:
Before finding the area of the circle, first, let us find the radius of the circle.
Given that,
diameter ⇒ 28 mm
Therefore,
d = 2r28 = 2r
Divide both sides by 2.
14mm = radius
And now, let us find the area.
The formula to find the area of the circle is :
Area = π r²Let us solve now.
Area = π r²
= 3.14 × 14 × 14
= 43.96 × 14
= 615.44 mm²
can someone give me formulas to calculate area
Answers
Answer:
Step-by-step explanation:
Triangle
Area = ½ × b × h
b = base
h = vertical height
Square
Area = a2
a = length of side
Rectangle
Area = w × h
w = width
h = height
Parallelogram
Area = b × h
b = base
h = vertical height
Trapezoid (US)
Trapezium (UK)
Area = ½(a+b) × h
h = vertical height
Circle
Area = π × r2
Circumference = 2 × π × r
r = radius
Ellipse
Area = πab
Sector
Area = ½ × r2 × θ
r = radius
θ = angle in radians
3(x+5)+10
Please help
Answers
Answer:
3x+15+10
3x + 25
Step-by-step explanation:
Answer:
3x + 25
Step-by-step explanation:
Please help
45−3x=18x
Answers
Answer:
Your answer is: x = 15/7
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Hope this helped : )
Where in the bible is there an indication of the value of pi.
Answers
Answer:
No where
Step-by-step explanation:
What should i pick?!!
Answers
Answer:125x^6y^6 (Red)
Step-by-step explanation: To find the answer we need to do first 5^3 which is 125. Then according to exponent rule, we multiply the exponents inside by the exponent outside, so it would be x^6 and y^6.
It would be 125x^6y^6.
Hope this helps you!
Ye Samantha left home with $42.51. The subway fare was $1.20. At the sta-
tion she bought a magazine for $1.95. Lunch cost $4.36. After work she
bought a skirt on sale for $26.00. Her subway fare home was also $1.20.
At the station Shelly gave Samantha $5 to pay back a loan. How much
money did Samantha have at the end of the day?
Answers
how many inches are in 10 yards? Please show all work and if i have to divide or multiply.
Answers
Answer:
1 yard is 3 feet. There is 36 inches in a yard. There is 12 inches in a foot. Multiply 36 by 10 to get 360. There is 360 inches in 10 yards.
Step-by-step explanation:
Hope this helps! :)
have a blessed day and remember to keep smiling! :)
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Sue jarred 30 ounces
of jam in 3 days.
How many ounces
of jam can Sue jar
in 5 days?
It’s one of those 2.
Answers
Answer:
50 ounces
Step-by-step explanation:
hope it helps you
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thanks
Will give brainliest
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario.
What number will complete the point-slope equation that models this scenario?
y−50,000=[_______](x−10)
−3,000
−2,000
2,000
3,000
Answers
Answer:
- 3000 is the answer
Step-by-step explanation:
just took the test on edu
The slope of the given equation is -3000.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
We are aware that the Havertown newspaper had 80,000 readers in the year 2000 (when x=0) and 50,000 readers in the year 2010 (when x=10). With this knowledge, we can determine the slope of the line that depicts this situation:
slope = (change in y) / (change in x) = (50,000 - 80,000) / (10 - 0) = -3,000
So the slope of the line is -3,000.
We also have a point on the line: (10, 50,000). Using the point-slope form of the equation of a line, we can write:
y - 50,000 = -3,000(x - 10)
Now we just need to find the value that goes in the blank to complete the equation.
Because the line's slope is -3,000, y reduces by 3,000 for every unit increase in x.
We can see that a one-unit increase in x corresponds to a one-year increase in the time since x indicates the number of years from the year 2000. As a result, we might conclude that 3,000 fewer copies of the newspaper were distributed annually.
The point-slope equation is complete when:
y - 50,000 = -3,000(x - 10)
So the answer is -3,000.
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tell whether the relationship is a proportional relationship ( explain why or why not)PLEASE, PLEASE HELP ME ANSWER IT RN IT IS DUE TODAY!!!
Answers
a = −b
b = −c
a + b + c = 8
Answers
Answer:
8
Step-by-step explanation:
if a = -b, then -a = b.
plug that into the (b = -c) problem, and you get -a = -c, or a = c
if a and c ar equal, then and b = -c, b also equals -a.
the problem then becomes a - b +c, where a = 8, c = 8, and b = -8
a = -b -> 8 = -(-8)
b = -c -> -8 = -(8)
a = c -> 8 = 8
Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to know how many quarts q of cranberry juice he should mix with 4 quarts of apple juice to make cranberry-apple juice. He also wants to sell the juice at cost for $4.50 per quart. Which equation below represents the situation?
A. 3.60(q – 4) + 25.20 = 4.50q
B. 3.60q + 25.20 = 4.50(q + 4)
C. 6.30(q – 4) + 14.40 = 4.50q
D. 6.30q + 14.40 = 4.50(q + 4)
Answers
Answer:
The correct answer is D
Step-by-step explanation:
Cost of q quarts of Cranberry juice will be: $ 6.30q and cost of 4 quarts of apple juice will be $ (3.60×4)= $ 14.40. Total quarts of items would be q+4 , and he also wants to sell the juice at cost for $4.50 per quart. That means that the total cost to sell the juices will be $4.50(q+4) . Also, Total cost= Cost of q quarts of cranberry juice+cost of 4 quarts of apple juice.
Is 7 a solution to the compound inequality
Answers
Answer:
yes
Step-by-step explanation:
any number more than 5 works, even 5.01
I need help on number 4 please help!*Will mark Brainlest*
Answers
Answer:
i guess 3 rd option is correct. ........hope it helps u ♥♥♥♥
how do i do objective function
Answers
Answer:
Find the appropriate form for your objective function Then you will describe which solvers can handle complex then, you pass the extra Parameters finally, the function argument details.
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
3x - 4y + 8 = 0
Step-by-step explanation:
In figure,
When x = 0, y = 2
x = 4, y = 5
Two points on the line are (0, 2) & (4,5).
Slope = (5 - 2)/(4 - 0)= 3/4
Equation is:
=> y - 2 = (3/4)(x - 0)
=> y - 2 = 3x/4
=> 4y - 8 = 3x
=> 3x - 4y + 8 = 0