Answer:
Center (3, -8), radius = [tex]\sqrt{39}[/tex]
Step-by-step explanation:
The Standard Form for the equation of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is the point (h, k) and the radius is r.
Match up the given equation with the standard form.
[tex](x-h)^2=(x-3)^2 \rightarrow h=3\\(y-k)^2=(y+8)^2 \rightarrow k=-8[/tex]
That last bit can be tricky, k = -8, not 8. Watch the signs!
What are the domain and range of the function f(x)=-3(x-5)2 +4?
domain: (-00, 5)
range: (-00,00)
domain: (-0,4]
range: -00,00)
domain: (-0,5]
range:
(-0,4]
O domain: (-0,00)
range: (-0,4]
Answers:
Domain is [tex](-\infty, \infty)[/tex]
Range is [tex](-\infty, 4][/tex]
============================================
Explanation:
We can replace x with any real number we want. We don't have any restrictions to worry about since there are no division by zero issues for instance. Also, there isn't any issues of things like taking the square root of a negative number.
Therefore, the domain is the set of all real numbers which translates to the interval notation of [tex](-\infty, \infty)[/tex]
This interval notation can be thought of as [tex]-\infty < x < \infty[/tex]
----------------------------
The range on the other hand isn't the set of all real numbers. It might help to graph this parabola (see below). You should see that the highest point occurs at the vertex (5, 4). This then tells us that the largest y can get is y = 4.
In other words, y = 4 or y can be smaller than this.
In symbols, we would say the range is [tex]y \le 4[/tex] and that translates to the interval notation of [tex](-\infty, 4][/tex]
The curved parenthesis always goes with either infinity. The square bracket says "include the endpoint 4 as part of the interval".
What is the polar form of Negative 9 StartRoot 3 EndRoot + 9 i?
Answer:
Step-by-step explanation:
In the rectangular complex number -9√3 + 9i, which has a standard form a + bi, the a = -9√3 and the b = 9. We need this in polar form (r, θ) where
[tex]r=\sqrt{a^2+b^2}[/tex] and filling in:
[tex]r=\sqrt{(-9\sqrt{3})^2+(9)^2 }[/tex] (notice we do not put the i in there with the 9).
[tex]r=\sqrt{243+81}[/tex] so
r = 18. Now let's move on to the angle, which is a little more difficult. The angle is found in the inverse tangent ratio:
[tex]tan^{-1}(\frac{b}{a})[/tex] so filling that in, we have:
[tex]tan^{-1}(\frac{9}{-9\sqrt{3} })=\frac{1}{-\sqrt{3} }[/tex] Since tangent is the side opposite over the side adjacent, y is positive and x is negative in the second quadrant. This is a 30 degree angle in QII, which has a reference angle of 150 degrees. This angle in radians is [tex]\frac{5\pi}6}[/tex], so the polar form of that number is (18, [tex]\frac{5\pi}{6}[/tex])
Answer:
its d
Step-by-step explanation:
i guessed lol
can you please find the range of these numbers? 18, 16, 19, 15, 17. I will give 16 points
Answer: Hi the Range is 4
Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:
18, 16, 19, 15, 17
19,18,17,16,15
19-15= 4
What are the coordinates of the point on the directed line segment from (-6, -6)(−6,−6) to (9, -1)(9,−1) that partitions the segment into a ratio of 2 to 3?
Answer:
(0, -4)
Step-by-step explanation:
The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)
The ratio the required point partitions the line = 2 to 3
The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;
[tex]\left(\dfrac{a}{a + b} \times (x_1 - x_2)+ x_1, \ \dfrac{a}{a + b} \times (y_1 - y_2)+ y_1 \right)[/tex]
Therefore, the required point is located as follows;
[tex]\left(\dfrac{2}{2 + 3} \times (9 - (-6))+ (-6), \ \dfrac{2}{2 + 3}\times (-1 - (-6))+ (-6) \right) = (0, -4)[/tex]
The coordinates of the point is (0, -4)
Jomar decides that he needs to study for an average of 1 hour and 30 minutes
a day in order to prepare for his French test this Friday. He studies for 2 hours
each day on Saturday through Monday, but is too busy to study on Tuesday
and Wednesday. How long must Jomar study on Thursday to be prepared for
his test?
Answer:
Jomar needs to study for 3 hours on Thursday to be prepared for his test.
Step-by-step explanation:
If we want to make the average a certain amount of time over a certain number of days, we can first figure out the number of days and total amount needed. Here, we can see that the average is 1 hour and 30 minutes, and there are 6 days (Saturday-Thursday). Therefore, as
average = total / length, we can multiply both sides by length to get
average * length = total
Plugging 1.5 hours in for average and 6 days for length, we get
1.5 * 6 = 9 hours as the total amount needed to get an average of 1.5 hours a day
Our total so far is 2 hours for Saturday, 2 hours for Sunday, and 2 hours for Monday. This adds up to 6 hours, and we need 9. The difference between 9 and 6 is 3, meaning that Jomar needs to study for 3 hours on Thursday to be prepared for his test.
Can someone help me with this, Thx!
Answer:
x = 45
Step-by-step explanation:
x = 20 + 25
as x is vertically opposite to GED
and vertically opposite angles are equal
What is the domain of the function of y=√x+8 -7
Answer:
Step-by-step explanation:
Recall that the argument of the square root function y = √x must always be 0 or greater.
If you meant y=√x+8 -7, the domain is therefore [0, infinity).
But if you meant y=√(x+8) -7, the domain is [-8, infinity).
Those parentheses are important!
If you have $50 in yo ur bank account, deposit a $50 birthday check, and withdraw $20 to buy a shirt, how much is left in your account at the end?
Answer:
80
Step-by-step explanation:
50+50=100-20=80
бр - 5 =13
need help !
Answer:
[tex]p=3[/tex]
Step-by-step explanation:
[tex]6p-5=13[/tex]
[tex]+5[/tex] [tex]+5[/tex]
[tex]6p=18[/tex]
[tex]/6[/tex] [tex]/6[/tex]
[tex]p=3[/tex]
Jennifer can clean the house by herself in 3 hours. Her little brother Andy helps her clean and it takes them 2
hours working together. How long would it have taken Andy to clean the house if he had worked alone?
a. hours
b. 3 hours
c. 6 hours
d. 1 hour
Answer:
c
Step-by-step explanation:
If he could clean the house alone in one hour, then it wouldve taken him and his sister less than that. if he could clean it in 3 hours, it wouldve tkane him and his sister 1.5 hours.
Answer:
Step-by-step explanation:
c. 6 hours
find the volume of a cylinder with radius 5 and surface area 180pi
Answers : either 200pi or 325pi help !
Answer:
The volume of a cylinder is 325π.
Step-by-step explanation:
The volume of a cylinder is given by:
[tex]V = \pi r^{2}h[/tex]
Where:
h: is the height
r: is the radius = 5
We can find "h" from the surface area of the cylinder:
[tex]SA = 2\pi rh + 2\pi r^{2} = 180\pi[/tex]
[tex] h = \frac{180\pi - 2\pi r^{2}}{2\pi r} = \frac{180\pi - 2\pi (5)^{2}}{2\pi*5} = 13 [/tex]
Hence, the volume is:
[tex]V = \pi r^{2}h = \pi*(5)^{2}*13 = 325 \pi[/tex]
Therefore, the volume of a cylinder is 325π.
I hope it helps you!
solve for x and y in the system of equation
y=x²-4x
2x-y=2
I'll mark brainliest
Step-by-step explanation:
[tex]y = {x}^{2} - 4x \\ y = x(x - 4) - - - (a) \\ 2x - y = 2 \\ y = 2x - 2 \\ y = 2(x - 2) - - - (b) \\ (a) = (b) : \\ x(x - 4) = 2(x - 2) \\ {x}^{2} - 4x = 2x - 2 \\ {x}^{2} - 6x + 2 = 0 \\ x = 5.6 \: \: and \: \: 0.4 \\ y = 2(5.6 - 2) \: \: and \: \: 2(0.4 - 2) \\ y = 7.2 \: \: and \: \: - 3.2[/tex]
Given m||n, find the value of x.
(7x-4)
(3x+28)º
Answer:
8
Step-by-step explanation:
7 x 8 = 56 56 - 4 = 52.
3 x 8 = 24 24 + 28 = 52
The ratio of coloured papers to wight papers is 3:8.If there are 48 wight papers, how many coloured papers are there?
Answer: The total number of colored papers is 18.
Step-by-step explanation:
Given: The ratio of coloured papers to wight papers is 3:8.
Let total number of colored papers = 3x
and total number of wight papers = 8x
Since, there are 48 wight papers , then
[tex]8x=48[/tex]
[tex]\Rightarrow\ x=6[/tex]
Now , number of colored papers = 3(6)=18
Hence, the total number of colored papers is 18.
What is the first step in solving the equation 4.2y-5.2=18.5
whats is the answer to 7 x 1781
Answer:
12,467
Step-by-step explanation:
7 · 1781 = 12467
A woman buys 50 eggs for $6.60. Some cost 12 cents each and the rest 14 cents each.
How many of each kind of eggs has she bought?
Answer:
She bought 20 eggs that were 12 cents, and she bought 30 eggs that were 14 cents.
Step-by-step explanation:
Create a system of equations where x is the number of 12 cent eggs and y is the number of 14 cent eggs.
x + y = 50
0.12x + 0.14y = 6.6
Solve by elimination by multiplying the top equation by -0.12:
-0.12x - 0.12y = -6
0.12x + 0.14y = 6.6
Add these together and solve for y:
0.02y = 0.6
y = 30
So, she bought 30 eggs that were 14 cents. Plug in 30 as y into one of the equations, and solve for x:
x + y = 50
x + 30 = 50
x = 20
So, she bought 20 eggs that were 12 cents.
She bought 20 eggs that were 12 cents, and she bought 30 eggs that were 14 cents.
Pls help I don’t get it
Answer:
h = 5/2
Step-by-step explanation:
[tex]\frac{3}{4} *\frac{1}{2} *h=\frac{15}{16} \\\\\frac{3}{8} *h=\frac{15}{16}[/tex]
divide both sides by 3/8
[tex]h=\frac{5}{2}[/tex]
I need help on this please!
Answer: The correct answer is D, also for part B, do you need help with that one too?
Step-by-step explanation:
During a pancake making contest, Team A makes 8 more pancakes than team B. Team C made twice as many pancakes is team B. Together, the three teams made a total of 72 pancakes. How many pancakes did team A make?
Answer:
A = 24
Step-by-step explanation:
Use the problems provided info!
A = B+8
C = 2B
72 = B+8+2B+B
72-8 = 4B
6434 = 4B/4
16 = B
A = 24
B = 16
C = 32
An author published a book which was being sold online. The first month the author sold 14400 books, but the sales were declining steadily at 5% each month. If this trend continues, how many total books would the author have sold over the first 23 months, to the nearest whole number?
Answer:
The author sold a total of 30240 books following this trend.
Step-by-step explanation:
Let's find 5% of 14400 first;
14400 * 5%
14400 * 5/100
144 * 5
720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)
=> aₙ = a₁ + r(n - 1)
=> a₂₃ = 14400 + 720(23 - 1)
=> a₂₃ = 14400 + 720(22)
=> a₂₃ = 14400 + 15840
=> a₂₃ = 30240
Hope this helps!
The author sold a total of 30240 books following this trend.
Let's find 5% of 14400 first;
[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]
What is an arithmetic progression?A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.
So using the arithmetic progression we have:
[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]
See more about arithmetic progression at brainly.com/question/20385181
plz help ill make u brainliest
A manufacturer ships its product in boxes with edges of 4 inches. If 12 boxes are put in a carton and completely fill the carton, what is the volume of the carton?
HELP PLEASE I need an answer ASAP
Answer:
72/97
Step-by-step explanation:
take angle c as reference angle
to find sin c
sin c = opposite / hypotenuse
sin c = 72 / 97
Answer:
i dont know
Step-by-step explanation:
Noah wants to buy a skateboard that usually sells for $79.99. All merchandise is discounted by 12%. What is the total cost of the skateboard if Noah has to pay a state sales tax of 6.75%?
Answer:
$74.36 sorry all i got
Step-by-step explanation:
First, we need to determine the sales price of the skateboard. The formula for find the discounted prices is:
Where:
is the sales price of the item: what we are solving for in this part of the problem.
is the regular price of the item: $79.16 for this problem.
is the discount rate: 12% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 12% can be written as
12
100
Substituting and calculating
gives
79.16
79.16
12
100
79.16
949.92
100
79.16
9.4992
69.6608
69.66
rounded to the nearest cent.
Now we can find the total price of the item with tax included. The formula for this is
#t = p + (p * r)
Where, this time:
is the total price: what we are solving for in this problem.
is the price of the item: it is the sales price of the item for this problem which is $69.66
is the tax rate: 6.75% or, using the same rule as in the formula above:
6.75
100
Substituting and calculating
gives:
69.66
69.66
6.75
100
69.66
470.205
100
69.66
4.70205
74.36205
74.36
rounded to the nearest cent.
Noah would pay a total cost (with the discount and after tax) of $74.36
Find the perimeter of the window to the nearest hundredth perimeter: about ft
Answer:
I would answer but I have no numbers to give the answer
A man earns$140 in 5 day week. What is his pay for 3 days?
please this is ratio and proportion
Answer:
$84
Step-by-step explanation:
Do 3/5*140 which will give you 84 dollars
find the equation of a line that passes through (3 1) and ia parallel to y=1-2x leave your answer in the form of y=mx+c
Answer:
y = -2x+7
Step-by-step explanation:
Parallel lines have the same slope
y = 1-2x has a slope of -2
So the new line has a slope of -2
We have a slope of -2 and a point of (3,1)
y = mx+c
1 = -2(3)+c
1 = -6+c
Add 6 to each side
1+6 =c
7 =c
y = -2x+7
3. Ruby and Sapphire love strawberries. Ruby starts out with 10 strawberries and finds 3 more
every minute. Sapphire starts out with 30 strawberries and eats 2 every minute. How long will it
take for them to have the same number of strawberries?
PLEASE HELP ME. AND SHOW YOUR WORK. PLEASE IM DYING.
Answer:
4 minutes
Step-by-step explanation:
Let the time taken for them to have the same number of strawberries be x minutes.
Initially
Ruby: 10 strawberries
Sapphire: 30 strawberries
After x minutes
Ruby: (10 +3x) strawberries
Sapphire: (30 -2x) strawberries
Since we let x minutes be the amount of time that has passed when they have the same amount of strawberries,
10 +3x= 30 -2x
Bring all x terms to one side, constant to the other:
3x +2x= 30 -10
Simplify:
5x= 20
Divide both sides by 5:
x= 20 ÷5
x= 4
∴ It will take 4 minutes.
Gia is thinking of a number, witch she calls n .she adds 4 to the number and then doubles the sum.
write an expression to represent Gia's number.
Answer:
2(n+4)
good luck
Answer:
n+4=n×2
Step-by-step explanation:
that is the equation
The 12 pair pack of socks includes 4 pairs of Polo, 5 pairs of plain white socks, and a few grey pairs. What is the Possibility of pulling a pair of grey sock two times in a row? The first pair is not to be returned.
Answer:
2/11
Step-by-step explanation:
12-4-5=3
So now we know that we have:
4 pairs of polo socks
5 pairs of plain white socks
3 pairs of grey socks
To pull a grey sock one time is 3/12 since there are 12 total socks and 3 pairs of grey socks but since we remove a sock, in the second time, the probability would be 2/11.
Hope this helps! Brainliest?