Answer:
The equation of the circle is x² + y² + 12x - 14y - 165 = 0 , its center is (-6, 7) and its radius is 5√10 units.
Step-by-step explanation:
a. The center of the circle
Since the equation of the tangent of the circle is 3x - y = 15, we write it in standard form. So y = -3x - 15. Its gradient is -3. The perpendicular line tot he tangent is the radius and it passes through the center of the circle and the point (9, 12). For two perpendicular lines of gradient m₁ and m₂, m₁m₂ = -1. If m₁ = -3, then m₂ the gradient of our radius line is gotten from m₁m₂ = -1
m₂ = -1/m₁ = -1/-3 = 1/3
Since the radius also passes through the point (9, 12), its equation is gotten from
(y - y₁)/(x - x₁) = m₂ where (x₁, y₁) = (9, 12)
Substituting the value of the variables into the equation, we have
So, (y - 12)/(x - 9) = 1/3
cross-multiplying, we have
3(y - 12) = (x - 9)
expanding the brackets, we have
3y - 36 = x - 9
collecting like terms, we have
3y = x - 9 + 36
3y = x + 27
So, the equation of the radius line is
3y - x = 27.
Now, since the center of the circle lies on the line 2y + x = 8, the radius line and this line intersect at the center of the circle. So, we solve both equations simultaneously to find the center of the circle.
So, 3y - x = 27 (1)
2y + x = 8 (2)
adding (1) and (2), we have
5y = 35
y = 35/5
y = 7
Substituting y = 7 into (2), we have
2y + x = 8
2(7) + x = 8
14 + x = 8
x = 8 - 14
x = -6
So, the center of the circle is at (-6, 7)
b. The radius of the circle
The radius of the circle is the length of the line from the tangent point to the center of the circle. So, r = √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) = (-6, 7) and (x₂, y₂) = (9, 12).
Substituting these into r, we have
r = √[(9 - (-6))² + (12 - 7)²]
= √[(9 + 6)² + (12 - 7)²]
= √[15² + 5²]
= √[225 + 25]
= √250
= √25 × √10
= 5√10 units
c. The equation of the circle
Now, the equation of a circle with center (h,k) and radius, r is
(x - h)² + (y - k)² = r² where (h. k) = (-6,7)
Substituting the variables into the equation, we have
(x - (-6))² + (y - 7)² = (√250)²
(x + 6)² + (y - 7)² = 250
expanding the brackets, we have
x² + 12x + 36 + y² - 14y + 49 = 250
collecting like terms, we have
x² + y² + 12x - 14y + 36 + 49 - 250 = 0
x² + y² + 12x - 14y - 165 = 0
So, the equation of the circle is x² + y² + 12x - 14y - 165 = 0 , its center is (-6, 7) and its radius is 5√10 units.
What is 1 2/3 - 2 1/3
Answer:
-1 1/3
Step-by-step explanation:
1 2/3 - 2 1/3
1-2 is -1
2/3 -1/3 is 1/3
-1 1/3
What is the x intercept for the following equation? Enter your answer in the format (x,y)
-1/4x-1/3y=13
Copland competes in 27 swimming events this
season. He wins either first place or second
place in each event. Copland has 3 more first-
place wins than second-place wins. In how
many events did he win first place, and in how
many did he win second place?
Answer:
15 wins 12 2nd because subtract 3 from 27 that's 24 divide that by 2 its 12 so you add the extra 3 to 12 and that's 17
Explain the Error Tina says that 6 :8 is equivalent to 36 :64. What did Tina
do wrong?
Answer:
she multiplied the numbers to itself
ILL MARK U BRAINLIEST!!!
Answer:
Step-by-step explanation:
B
A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper A 95% confidence interval that results from examining 771 customers in one fast-food chain's drive-through has a lower bound of 175.2 seconds and an upper bound of 178.2 seconds. What does this mean?
Answer:
Step-by-step explanation:
The confidence interval is an interval that determines an unknown population parameter. It showcases the probability that a particular population parameter will fall within this interval. As the sample size reduces, the width of the confidence interval usually increases.
What the given question mean is that one can still be 95% confident that the mean drive-through service times of this fast-food chain is between 175.2 seconds and 178.2 seconds.
Find the value of x. geometry
Answer:
21 or 26
Step-by-step explanation:
The point A (−5,4) is reflected over the point (−2,5) and its image is point B. What are the coordinates of point B?
Answer:
The coordinates of B are (1,6)
Step-by-step explanation:
Point Reflection
Given the point P(x,y) and its reflection P'(x',y') with respect to the point C(xc,yc), C is the midpoint of the segment PP'.
This means the coordinates of C are:
[tex]\displaystyle x_c=\frac{x+x'}{2}[/tex]
[tex]\displaystyle y_c=\frac{y+y'}{2}[/tex]
If the coordinates of the midpoint are given, then the endpoint P' can be found solving for x' and y':
[tex]x'=2x_c-x[/tex]
[tex]y'=2y_c-y[/tex]
The point P' is the reflection of P over C.
We are given the coordinates of A(-5,4) and the point (-2,5). We need to find the coordinates of point B(x',y'). Let's use the formulas as if A was point P and C=(-2,5):
[tex]x'=2(-2)-(-5)=-4+5=1[/tex]
[tex]y'=2(5)-4=10-4=6[/tex]
The coordinates of B are (1,6)
Egg noodles: Package A is 12 oz. for $0.99. Package B is 2 lbs. for $2.56
Which is the better deal
Answer:
Package A
Step-by-step explanation:
$0.99 ÷ 12oz = 0.0825
2lb = 32oz
$2.56 ÷ 32oz = 0.0800
therefore the package a is a better deal
What is the slope of a line that passes through the points (-8, 14) and (4,-4)?
Answer:
the answer is -3/2
Step-by-step explanation:
Trust me its correct
pls mark me as brainliest
Can someone please help me on this, this is really confusing
Answer:
my educated guess would be B. i hope i dont get u the wrong answer
Step-by-step explanation:
Answer:
I think A
Step-by-step explanation:
I am not sure but if u multiply 7x7 u get 49 and when u do 9x7 it gets u close to 65 that is my guess
Find the slope of the line.Enter your answer in simplist form (4,2) (1, -4)
Answer:
2Step-by-step explanation:
-4 - 2
1 - 4
-6
-3
2 hope that helps!!!! don´t forget to thank and Brainliest
Graph 3x + y = -1
The graph only takes whole numbers.
Luke's turkey chili recipe calls for 2.5 pounds of ground turkey for every 5 servings. How many servings can he make if he has 6 pounds of ground turkey? Complete the explanation. When entering the equation, use y to represent how many servings he can make and x to represent how many pounds of ground turkey he has.
Answer:
12 servings
Step-by-step explanation:
Luke's turkey chili recipe calls for 2.5 pounds of ground turkey for every 5 servings. How many servings can he make if he has 6 pounds of ground turkey?
From above question:
2.5 pounds of ground turkey = 5 servings
6 pounds of ground turkey = x
Cross Multiply
2.5 × x = 6 × 5
x = 6 × 5/2.5
x = 12 servings
Hence, 6 pounds of ground turkey can make 12 servings.
Completing the explanation.
The equation is
5x = 2.5y
where:
x = represent how many pounds of ground turkey he has = 6 pounds
y = to represent how many servings he can make
Hence,
5 × 6 = 2.5y
y = 5 × 6/2.5
y = 12 servings
What does a positive exponent show?
repeated multiplication by the base
The school carnival committee sold a total of 200 tickets for the grand prize drawing. Sue bought enough tickets so that she had a 20 percent chance of winning the grand prize. How many tickets did Sue buy?
Answer:
40 tickets
Step-by-step explanation:
Given that:
Total tickets sold = 200
Sue's chances of winning = 20% = 0.2
Number of tickets bought by Sue :
P(winning) = 20%
P(winning) = required outcome / Total possible outcomes
Required outcome = number of tickets bought by Sue
Total possible outcomes = total number of tickets sold
0.2 = x / 200
x = 0.2 * 200
x = 40
Vince borrows $900 to buy a couch. He will pay off the loan by paying 1.5% simple interest for 2 years. Vince incorrectly calculates the amount he will pay back using the expression below. 900 + 900(1.015 • 2) What is the correct amount Vince will pay back altogether? Explain the error in Vince's expression. A. 00:00 $903; Vince should have subtracted the first 900 from the amount he will pay. B. 00:00 $913.50; Vince multiplied by the wrong number of years. C. 00:00 $927; Vince wrote the wrong number to represent the interest rate. D. 00:00 $1,813.50; Vince forgot to add the initial $900 to the amount he will pay.
Answer: C. 00:00 $927; Vince wrote the wrong number to represent the interest rate.
Step-by-step explanation:
Given that:
Amount borrowed (p) = 900
Simple interest (r) = 1.5% = 0.015
Time (t) = 2 years
Amount he'll pay back (A) :
A = P(1 + rt)
A = 900(1 + 0.015(2))
A = 900(1 + 0.03)
A = 900(1.03)
A = $927
Find the slope!! Please
Answer: The slope is undefined
Step-by-step explanation:
Answer:
undefined
Step-by-step explanation:
slope equation is y2-y1/x2-x1
use points (-2,2) and (-2,-2)
insert values into equation: -2-2/-2+2
simplify: -4/0
if the zero is on top of the fraction, then the slope is zero but since the zero is on the bottom, the slope has to be undefined
Help plzzzz plzzz plzzzzz plzzzzzzzz
Answer:
1 + X
Step-by-step explanation:
You just write whats there
Answer: I think it might be 1 + x or x = 1
Step-by-step explanation:
I NEED HELP!!!!!!! due in 10 min PLZZZZZ!!!!
Answer:
-3, 6, 7
Step-by-step explanation:
Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large
cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each
type did she sell?
Answer:
3.75
Step-by-step explanation:
HELPPPPP!! A juggler tosses a ball into the air. The ball leaves the juggler's hand 5 feet above the ground and has an initial velocity of 30 feet per second. The juggler catches the ball when it falls back to a height of 2 feet. How long is the ball in the air? Use the model h(t)=−16t2 +v0t +h0, where v0 is the initial velocity (in feet per second), h is the height (in feet), t is the time in motion (in seconds) and h0 is the initial height (in feet).
Remember to round your answer to the nearest hundredth.
Answer:
t = 2.525 seconds
Step-by-step explanation:
h(t) = -16t^2 + v*t + h0 h(t) = the height above the ground after t seconds v = 40 ft/s initial velocity h0 = 4 ft the initial height of the object (the ball) t = the time of the motion h(t) = -16t^2 + 40*t + 4 we need to find t such that h(t) = 3 ft 3 = -16t^2 + 40*t + 4 -16t^2 + 40*t + 4 = 3 by solving we find
t = 2.525 seconds
You can round on your own.
Solving the quadratic equation, it is found that the ball was in the air for 1.97 seconds.
The height of the ball, in feet, after t seconds is given by:
[tex]h(t) = -16t^2 + v(0)t + h(0)[/tex]
In this problem:
The initial velocity is [tex]v(0) = 30[/tex].The initial height is [tex]h(0) = 5[/tex].Thus, the equation is:
[tex]h(t) = -16t^2 + 30t + 5[/tex]
The juggler catches the ball when it falls back to a height of 2 feet, thus it stays in the air until t for which:
[tex]h(t) = 2[/tex]
Then:
[tex]2 = -16t^2 + 30t + 5[/tex]
[tex]-16t^2 + 30t + 3 = 0[/tex]
[tex]16t^2 - 30t - 3 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 16, b = -30,c = -3[/tex]. Then:
[tex]\Delta = b^2 - 4ac = (-30)^2 - 4(16)(-3) = 1092[/tex]
[tex]x_{1} = \frac{30 + \sqrt{1092}}{2(16)} = 1.97[/tex]
[tex]x_{2} = \frac{30 - \sqrt{1092}}{2(16)} = -0.1[/tex]
The ball stays in the air for 1.97 seconds.
A similar problem is given at https://brainly.com/question/21846193
What is 1/4 x (20) 1/3= ???
In the first quadrant you start at (5,6) and move 4 units down what point will you end up on
Answer:
archon warm school exp all P words RCM TCL yxotx8txotd9td0ydotdotdotxotdtodotngtmttgm5gj9rfk5h teen
Please Help!!!!! I will give brainliest!!!
Answer:
d.2x=16;X=8
Step-by-step explanation:
2*8=16
ok
HELPPP ASAP WILL MARK BRAINLEST!!!
Answer:
B
Step-by-step explanation:
Eagles | Frequency
0-4 4
5-9 5
10-14 3
15-19 2
Find the distance between (8,-2) and (-2,6)
find the answer to this question
4.2÷0.07
Answer:
60
Step-by-step explanation:
Make 4.20 to 420
Make 0.07 to 7
We do this so they can be whole numbers not decimals. (also because it is easier)
420÷7=60
60
I hope this helped! :)
what is the missing number ___(7x + 3) = 14x + 6
Answer: 2
Step-by-step explanation:
?(7x+3)=14x+6
2*7=14, 2*3=6
2(7x+3)=14x+6
Answer:
2
Step-by-step explanation:
You find a number that when multiplied by 7 would give you 14 and when multiplied by 3 would give you 6. That number is two
marias mother told her to go to the health food store and buy 10 pounds of apples each bag weighed 5 pounds and contained 15 apples how many apples would she have if she bought the 10 pounds her mother instructed her to buy
Answer:
30 apples
Step-by-step explanation:
10 pounds of apples is 2 bags
5 + 5 = 10 lbs
15 apples per bag x 2 bags = 30 apples
Hope this helps :)
