Mathematics High School

HELP!! PLEASE, 19 POINTS!! The equation (X squared + Y squared - 6x + 4y = d) describes a circle.

1. Determine the Y-coordinate of the center of the circle. (Hint.... Complete the square)
2. The radius of the circle is 6 units. What is the value of "d" in the given equation?

Answers

Answer 1
we have  that

x²-6x+y²+4y=d
Group terms that contain the same variable
(x²-6x)+(y²+4y)=d
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-6x+9)+(y²+4y+4)=d+9+4

Rewrite as perfect squares

(x-3)²+(y+2)²=d+13

the center of a circle is (3,-2)
the radius r²=d+13---------> 6²=d+13---------> d=36-13------> d=23

the answer is
the Y-coordinate of the center of the circle is -2
d is equal to 23
Answer 2
Part 1:
 For this case we have the following equation:
 x ^ 2 + y ^ 2 - 6x + 4y = d
 By completing squares we have:
 x ^ 2 + y ^ 2 - 6x + 4y + (-6/2) ^ 2 + (4/2) ^ 2 = d + (-6/2) ^ 2 + (4/2) ^ 2
 Rewriting we have:
 x ^ 2 + y ^ 2 - 6x + 4y + (-3) ^ 2 + (2) ^ 2 = d + (-3) ^ 2 + (2) ^ 2
 x ^ 2 + y ^ 2 - 6x + 4y + 9 + 4 = d + 9 + 4
 (x ^ 2 - 6x + 9) + (y ^ 2 + 4y + 4) = d + 13
 (x-3) ^ 2 + (y + 2) ^ 2 = d + 13
 Answer:
 The y coordinate of the center of the circle is:
 y = -2
 Part 2:
 For the value of d we have:
 d + 13 = 6
 d = 6 - 13
 d = -7
 Answer:
 The value of d is:
 d = -7

Related Questions

A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exactly two correct answers?

Answers

Found a similar question online. Is the attached picture the same one as yours? Are these the choices also?
a. 5%
b. 65%
c. 45%
d. 25%

The answer is Letter D - 25%. Use the table and count the number of guesses that has two correct answers represented by 1. 01010, 10001, 11000, 01001, 00011 = a total of 5 numbers having 2 correct guesses out of 20 questions. Which means that there's twenty-five percent possibility of correctly guessing the answer out of 20 questions. 5/20 = 25%

Probability of correctly guessing at random exactly two correct answers is; 25%

How to find the experimental probability?

The table is missing but from the table shared by the first answer, we can  count the number of guesses that has two correct answers.

Now, the ones that have two number of 1's are referred to as correct answers. Thus, counting them in the question, they are;01010, 10001, 11000, 01001, 00011.

Thus, there are 5 posssible correct answers out of 20. Thus;

Probability of correctly guessing at random exactly two correct answers is; 5/20 = 25%

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A number line contains points Q, R, S, and T. Point Q is on the coordinate 24, R is on the coordinate 28, S is on the coordinate 29, T is on the coordinate 42. Find the probability that a point chosen at random on QT is on ST. Express your answer as a percent.

A. 25%
B. 42.2%
C. 50%
D. 72.2%

Answers

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

A number line contains points Q, R, S, and T

Point Q is on the coordinate 24

Point R is on the coordinate 28

Point S is on the coordinate 29

Point T is on the coordinate 42

So, According to given condition,

QT is on the coordinate is given by

[tex]42-24=18[/tex]

ST is on the coordinate is given by

[tex]42-29=13[/tex]

So, probability that a point chosen at random on QT is on ST is given by

[tex]\frac{13}{18}\times 100\\\\=72.22\%[/tex]

Hence, option 'D' is correct.

The probability that the Cubs win their first game is 1/3. The probability that the Cubs win their second game is 3/7. What is the probability that the Cubs win games?

Answers

We need to multiply these probabilities up. Indeed, we are talking about independent events. Then, the final answer is 1/3 * 3/7=1/7

The correct answer is:


1/7.


Explanation:


The two events, the Cubs winning their first game and the Cubs winning their second game, are independent. This is because the Cubs winning their first game does not affect the probability of the Cubs winning their second game.


Since the events are independent, to find the probability that both events occur, multiply the probabilities:


1/3(3/7) = (1*3)/(3*7) = 3/21 = 1/7

Factor this trinomial.

x2 – 8x + 15

A. (x – 1)(x – 15)
B. (x – 3)(x + 5)
C. (x – 3)(x – 5)
D. (x – 1)(x + 15)

Answers

x^2- 8 x+15=0
x^2-5x- 3x +15=0
x(x-5) -3 (x-5)
(x-5)(x-3)

To factor x^2 -8x + 15, we find two numbers that multiply to get 15 and add to get -8. These two numbers can be -5 and -3. Therefore, this factors as

x^2 - 8x + 15 = (x-5)(x-3)

Sam wants to know how long it will take to fill his baby pool that holds 24 gallons. After 1 minute, there are 2 gallons of water in the pool. He plots the points (0,0) and (1,2) on his coordinate plane. What is the x-value of the point (x, 24)? A) 6 B) 12 C) 23 D) 25

Answers

When doing this on a graph, you can just continue to plot the points until you reach the x-value of the point (x, 24). But there's an easier way to do that.

List what you know about the problem so far:

1 min  =  2 gal

So, now that we know that, we can list what we need to solve:

x min  =  24 gal

Now, you can simply divide 24 by 2 to get the number of minutes it would take to fill up 24 gallons.

24 ÷ 2 = 12

So,

x = 12

So, 

12 min  =  24 gallons

It would take 12 minutes to fill the 24 gallon holding pool. Which mean the coordinate point would be (12, 24).

Your answer should be   B )  12

The unit rate is gallons per minute, which in this case is 2 gallons per minute. Therefore it will take 12 minutes to fill up a 24 gallon pool.

PLEASE HELP!
A circle is centered at (11, −9) and has a radius of 12.

What is the equation of the circle?

Enter the equation in the box using lower case variables x and y.

Answers

Answer:
(x-11)² + (y+9)² = 144

Explanation:
The general form of the equation of the circle is:
(x-h)² + (y-k)² = r²
where:
h is the x-coordinate of the center
k is the y-coordinate of the center
r is the radius of the circle

In the given, we have:
x-coordinate of the center = h = 11
y-coordinate of the center = k = -9
radius of circle = r = 12

Substitute with the givens in the above formula to get the equation as follows:
(x - (11))² + (y - (-9))² = (12)²
(x-11)² + (y+9)² = 144

Hope this helps :)

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°. What are the two different angle measures of the parallelogram-shaped tile? 20° and 160° 50° and 130° 30° and 150° 70° and 110°
URGENT

Answers

Answer:

Step-by-step explanation:Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°.

Answer : 50° and 130°

Final answer:

To find the angle measures of the parallelogram, we set the expressions for opposite angles equal to each other, solve for 'n', and then determine the angle measures, which are 50° and 130° respectively.

Explanation:

The students wants to find the two different angle measures of a parallelogram-shaped tile where two opposite angles are given by the equations (6n − 70)° and (2n + 10)°. Since opposite angles in a parallelogram are equal, we can set these two expressions equal to each other to find the value of 'n':

6n − 70 = 2n + 10

Solving for 'n', we get:

4n = 80

n = 20

Now, we'll plug the value of 'n' back into the expressions to get the angle measures:

6n − 70 = 6(20) − 70 = 120 − 70 = 50°

2n + 10 = 2(20) + 10 = 40 + 10 = 50°

Since opposite angles are equal in a parallelogram, the other two angles must also add up to 180°. Therefore, the other two angles are 180° - 50° = 130°. The angles of the parallelogram are 50° and 130°.

If i = sqrt -1 what is the value of i3

A. -1
B. i
C. 1
D. -i

Answers

i^3  = i * i * i  = i^2 * i  = -1 * i = -i Answer

Its D

Answer:

The value of i3 is equal to D. -i

Step-by-step explanation:

We can find the answer by taking the definition of i :

i = sqrt(-1)        (1)

i ^2 = (sqrt(-1)) ^2 = -1             (2) because square root and squaring are inverse operations

so from (2)

i ^3= i ^2* i = -1*i = -i

So -i is the final answer or  – (sqrt(-1))         which is the same

If an egg is thrown up and off the roof of a 100 foot building with an initial upward velocity of 10 feet per second, how long until it hits the ground?

Answers

The equation of the height as a function of time for this case is given by:
 h (t) = - 16t ^ 2 + 10t + 100
 By the time the egg hits the ground we have:
 -16t ^ 2 + 10t + 100 = 0
 We look for the roots of the polynomial:
 t1 = -2.2069555463432966
 t2 = 2.8319555463432966
 As it is about time, we use the positive root:
 t = 2.83 s
 Answer:
 it hits the ground at:
 t = 2.83 s

Ok My last 2 questions please!!!

Answers

f(x) = (x-4)/(x(x-4)) = 1/x

the asymptote of the function is 0

Find the possible values of the included angle of a triangle with: A) sides of length 5 cm and 8 cm, and area of 15 cm^2
B) sides of length 45 km and 53 km, and area 800 km^2.

Answers

we know that

The area of ​​a triangle can be calculated by applying the law of sines

Area=(1/2)*a*b*sin C-----> sin C=2*A/[a*b]

Part a) sides of length 5 cm and 8 cm, and area of 15 cm^2
a=5 cm
b=8 cm
A=15  cm²
sin C=2*A/[a*b]------> sin C=2*15/[5*8]----> sin C=3/4
C=arc sin (3/4)-----> C=48.59 degrees
the possible values of the included angle are
C1=48.59°
C2=180°-48.59----> C2=131.41°

the answer Part a) is
48.59° and 131.41°

Part b) sides of length 45 km and 53 km, and area 800 km^2
a=45 km
b=53 km
A=800 km²
sin C=2*A/[a*b]-----> sin C=2*800/[45*53]----> sin C=0.6709
C=arc sin (0.6709)-----> C=42.13°
C1=42.13°
C2=180-42.13°----> C2=137.87°

the answer part b) is
42.13° and 137.87°

Kym spends an average of $78 per week on groceries. She can save 10% of her total grocery bill by joining the store's free shopper's club.About how much money will Kym save in a year (52 weeks) if she joins the shopper's club

Answers

Total amount Kym can save in 52 weeks will be given by:
(amount saved per week)×(number of weeks)
amount saved per week:
10/100×78
=$7.8
The total amount saved for 52 weeks will be:
52×7.8
=405.6

a speed camera takes two photographs of a car

Answers

Hello!

First you have to count how many tallies the car went 9 tallies

Multiply the amount of tallies by how far they represent

9 * 0.8 = 7.2 meters

The car when 7.2 meters in half a second so we double this to get how fast it was going a second

7.2 * 2 = 14.4

The answer is 14.4 m/s

Hope this helps!

Answer:The answer is 14.4 m/s

Step-by-step explanation:

A technician is launching fireworks near the event of a show. Of the remaining 11 fireworks, 4 are blue and 7 are red. If she launches 6 of them what’s the probability that 2 of them will be blue

Answers

[tex] \displaystyle
|\Omega|=\binom{11}{6}=\dfrac{11!}{6!5!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\
|A|=\binom{4}{2}=\dfrac{4!}{2!2!}=\dfrac{3\cdot4}{2}=6\\\\
P(A)=\dfrac{6}{462}=\dfrac{1}{77}\approx1\% [/tex]

You and your friend Sam are going to paint your 300 square feet room together.
Sam takes 10 minutes to paint 25 square feet.
You take 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take us 15 minutes to paint 50 square feet!''
Write a EXCEPTIONAL explanation to convince Sam that he is wrong. Thank You.

Answers

Fraction that Sam painted in 1 min is:
10/25=2/5
Fraction that you painted in 1 min:
5/25=1/5

Fraction pained by both in 1 min:
1/5+2/5=3/5 ft²/min
Time taken to paint 50 ft² will be:
time=3/5×50=30 min
Thus we conclude that Sam was wrong.

The sum of the square of a positive number and the square of 44 more than the number is 250250. what is the​ number?

Answers

let p positive number:

p²+44²>250250

p²>250250-44²

p²>248314

take the square root of both sides:

√p²>+√248314

p> 498.3 or 500 is the number

12,349 is what percent of of 278,901

Answers

[tex] \dfrac{12349}{278901} \times 100 = 4.43\% \text { (nearest hundredth)}[/tex]

Answer: 4.43%

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Simplify by using radical. Rationalize denominators. 2a^-1\2

Answers

2a^-1/2 = 2/ a^1/2= 2/SR of a= 2 SR of a/a

SR equals the square root sign

In the year 2000, there were 200,000 cell phone subscribers in a city in New York. The number of subscribers increased by 60 percent per year after 2000. Which equation can be used to model the number of subscribers, y, in the city t years after 2000?
A) y=200,000(1+60)t
B) y=200,000(1+0.6)t
C) y=200,000(1-60)t
D) y=200,000(1-0.6)t

Answers

The first step is to calculate the percentage increase for each year.
If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year. 

(100+60)% = (100/100 + 60/100)
                     (1 + 0.6)

After 2,000, the subscribers will be 200,000×(1+0.6).
For the following years the 200,000×(1+0.6)t

So, the value of y will be given by,

Y=200,000(1+0.6)t

Answer: The answer is B

Step-by-step explanation:

5. A high school has 16 math teachers for 1856 math students. What is the ratio of math teachers to math students?

Answers

The answer is 16:1856

The ratios are calculated to know the quotient of two quantities. In order to find the ratio, the first quantity is written in numerator i.e. the upper part of the fraction and the second quantity is written in denominator i.e. the lower part of the fraction.

Here, it is given that the total number of Maths teachers are = 16

Total number of Maths students are = 1856

The ratio of Maths teachers to Maths students is calulated as -

Ratio of Maths teachers to Maths students = [tex] \frac{Maths Teachers}{Maths Students} [/tex] = [tex] \frac{16}{1856} [/tex]

Ratio of Maths teachers to Maths students = [tex] \frac{1}{116} [/tex] = 1:116

What is the solution of the equation 2 + 3x = 7? round your answer to the nearest ten-thousandth. 0.2218 0.4522 0.6826 1.4650?

Answers

The solution to the equation 2 + 3x = 7 is x = 5/3. When rounded to the nearest ten-thousandth, the answer is 1.6667.

To find the solution to the equation 2 + 3x = 7, you first isolate the variable x by subtracting 2 from both sides of the equation.

This gives you 3x = 5.

Next, you divide both sides of the equation by 3 to solve for x, which yields x = 5/3.

When you divide 5 by 3 using a calculator, you get 1.66666666...

Since we need to round our answer to the nearest ten-thousandth, this becomes 1.6667.

Therefore, the solution to the equation 2 + 3x = 7, rounded to the nearest ten-thousandth, is 1.6667.

Fórmula para sacar el área de un circulo

Answers

Fórmula para sacar el área de un circulo:

[tex] A = \pi r^2 [/tex]

Rearrange the formula m =
x + y / 2
for y.
A) y = 2mx
B) y = 2m - x
C) y = x - 2m
D) y = 2m + x

Answers

we have that
m = (x + y) / 2
x+y=2*m
y=2*m-x

the answer is the option
B) y = 2m - x 

correct answer is 
y=2m-x 

cross multiply then subtract x 
 
hope this helps love

The size of a television is given by the length ofthe diagonal of the screen. the ratio of the height to the width of wide flat-screen tv is 8:15. find expressions for the width and height of a wide-screen tv in terms of the length of its diagonal.\

Answers

The diagonal of the tv screen is given by:
 d = root ((w) ^ 2 + (h) ^ 2)
 Where,
 w: width
 h: height
 In addition we have the following relationship:
 h / w = 8/15
 Thus,
 For the width:
 d = root ((w) ^ 2 + ((8/15) w) ^ 2)
 For the high:
 d = root (((15/8) h) ^ 2 + (h) ^ 2)
 Answer:
 The expressions for the width and height of a wide-screen tv in terms of the length of its diagonal are:
 d = root ((w) ^ 2 + ((8/15) w) ^ 2)
 d = root (((15/8) h) ^ 2 + (h) ^ 2)

A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question. Suppose a student guesses the answer to each question. Assuming the guesses are independent, find the probability that the student will not guess correctly on any one question.

a. 0
b. 1/5
c. 4/5

Answers

Number of choices per question = 5
Number of wrong answers = 4
P(wrong answer) = 4/5

Answer: 4/5

The value of the probability that the student will not guess correctly on any one question is,

⇒ 4 / 5

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question.

Now, Suppose a student guesses the answer to each question.

Hence, we get;

The value of the probability that the student will not guess correctly on any one question is,

⇒ 4 / 5

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Paula caught a tarpon with a weight that was 11 times as great as the weight of a permit fish she caught. The total weight of the two fish was 180 pounds. How much did each fish weigh?

Answers


[tex]11 + 1 = 12 \\ 180 \div 12 = 15 \\ 15 \times 1 = 15 \\ 15 \times 11 = 165[/tex]
Tarpon=165
Permit=15

The weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Assume that the weight of the permit fish is x pounds.

Then the weight of the tarpon would be 11x pounds.

According to the question, we can write equation as -

x + 11x = 180

12x = 180

x = 15

Weight of permit fish = 15 pounds

Weight of tarpon = 11 x 15 = 165 pounds

Therefore, the weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds.

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write the expression in complete factored form, 4c(y+3)+(y+3)

Answers

4c(y+3)+(y+3)
=(y+3)(4c + 1)

answer
(y+3)(4c + 1)

A map is drawn using a scale of 80 mi to 1 cm. On the map , the two cities are 7.5 cm apart. What is the actual distance between the two cities ??

Answers

we know that
scale =measure in the map/measure in the actual
measure in the actual=measure in the map/scale
scale=1 cm/ 80 mi
for
measure in the map=7.5 cm
measure in the actual=?
measure in the actual=7.5 /(1/80)-----> 7.5*80-----> 600 mi

the answer is
the actual distance between the two cities is 600 miles

20 POINTS AND A FOLLOW plus BRAINIEST IF RIGHT 1. What is the area of sector GHJ, given that 0=pi/4 radians ? Express your answer in terms of pi and as a decimal rounded to the nearest tenth. Show your work.

2. Construct the circle that circumscribes triangle DEF . Use a straightedge and a compass.
(show work by step)

Answers

1. To solve this we are going to use the formula for the area of a sector of a circle: [tex]A= \frac{1}{2} r^2 \alpha [/tex]
where
[tex]A[/tex] is the area of the sector 
[tex]r[/tex] is the radius of the circle 
[tex] \alpha [/tex] is the angle in radians

We know from our problem that the radius of the circle is 5 cm and the angle of the sector is [tex] \frac{ \pi }{4} [/tex], so [tex]r=[/tex] and [tex] \alpha = \frac{ \pi }{4} [/tex]. Lets replace those values in our formula:
[tex]A= \frac{1}{2} r^2 \alpha [/tex]
[tex]A= \frac{1}{2} (5)^2( \frac{ \pi }{4} )[/tex]
[tex]A= \frac{25 \pi }{8} [/tex]
[tex]A=9.8[/tex]

We can conclude that the area of sector GHJ in terms of pi is [tex] \frac{25 \pi }{8}[/tex] [tex]cm^2[/tex], and as a decimal rounded to the nearest tenth is 9.8 [tex]cm^2[/tex].

2. To construct the circle that circumscribes triangle DEF, we are going to draw the perpendicular bisectors of triangle DEF, and then we are going to draw the circle with radius at the interception point of the bisectors. Remember that the perpendicular bisector are the lines that passes trough the midpoint of the segment and are perpendicular to the segment.

What is the length of XPY in terms of pi?

Answers

circumference = 2 x PI x r

= 2 x 3.14 x 30 = 60 PI
the area from x to y = 90 degrees
 so XPY would be 360 - 90 = 270 degrees or 3/4 of a full circle

so XPY = 60 x 3/4 = 45 PI meters

The length of arc XPY in the given circle with a radius 30m is in terms of pi is 45π.

It is given that

The radius r of the circle = 30m

Central angle α intended by arc XPY = 360-90 = 270°

α in radians = 270*π/180

α in radians = 3π/2

What is the formula for arc length?

Arc length is the product of the central angle α and radius r of the given circle.

So, length of arc XPY:

l= r*α(in radians)

l =30* 3π/2

l = 45π

Therefore, the length of arc XPY in terms of pi is 45π.

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