Answer:
the correct numbers are 8 and 5
find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0
Answer:
Radius: [tex]r =\frac{\sqrt {21}}{6}[/tex]
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
Step-by-step explanation:
Given
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Solving (a): The radius of the circle
First, we express the equation as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
So, we have:
[tex]9x^2 + 9y^2 + 27x + 12y + 19 = 0[/tex]
Divide through by 9
[tex]x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0[/tex]
Rewrite as:
[tex]x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}[/tex]
Group the expression into 2
[tex][x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
Next, we complete the square on each group.
For [tex][x^2 + 3x][/tex]
1: Divide the [tex]coefficient\ of\ x\ by\ 2[/tex]
2: Take the [tex]square\ of\ the\ division[/tex]
3: Add this [tex]square\ to\ both\ sides\ of\ the\ equation.[/tex]
So, we have:
[tex][x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}[/tex]
[tex][x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Factorize
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2[/tex]
Apply the same to y
[tex][x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}[/tex]
Add the fractions
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}[/tex]
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
By comparison:
[tex]r^2 =\frac{7}{12}[/tex]
Take square roots of both sides
[tex]r =\sqrt{\frac{7}{12}}[/tex]
Split
[tex]r =\frac{\sqrt 7}{\sqrt 12}[/tex]
Rationalize
[tex]r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}[/tex]
[tex]r =\frac{\sqrt {84}}{12}[/tex]
[tex]r =\frac{\sqrt {4*21}}{12}[/tex]
[tex]r =\frac{2\sqrt {21}}{12}[/tex]
[tex]r =\frac{\sqrt {21}}{6}[/tex]
Solving (b): The center
Recall that:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where
[tex]r = radius[/tex]
[tex](h,k) =center[/tex]
From:
[tex][x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}[/tex]
[tex]-h = \frac{3}{2}[/tex] and [tex]-k = \frac{2}{3}[/tex]
Solve for h and k
[tex]h = -\frac{3}{2}[/tex] and [tex]k = -\frac{2}{3}[/tex]
Hence, the center is:
[tex]Center = (-\frac{3}{2}, -\frac{2}{3})[/tex]
Frank has 6 red socks, 8 black socks, and 10 white socks in his sock drawer. If Frank blindly reaches into his sock drawer, what is the probability that he will select a white sock and then another white sock? Round to the nearest percent A. 9% B. 16% C. 41% D. 80%
Answer:
B
Step-by-step explanation:
The first probability is 10/24, and the second is 9/23. If you multiply these two fractoins you get 15/92. 15/92 is approximately equal to 16%.
If ∆SDE ~ ∆SWT, find WT.
Please please please help no link no links no links
Answer:
400
Step-by-step explanation:
V = a² * h/3
Plug in your values:
V = 10² * 12/3
Then solve:
100 * 4 = 400
Factor out the greatest common monomial factor from polynomial. Show your work or explain your reasoning
Answer:
7(1 +3x)
Step-by-step explanation:
The simplest monomial is a constant that is a prime number. That constant is a factor of the coefficient of the only other monomial in the expression, so it can factored from both terms.
= 7 + 7·3x
= 7(1 +3x)
please help me fast thanks
Answer:
1.86/2 = 0.93/2 = 0.465/2 = 0.2325
Step-by-step explanation:
Maria needs to be at the airport terminal at 18:45. It will take 2 3/4 hours to drive to the airport from her home, and a further 40 minutes to park and get to the terminal.
What is the latest time she should leave home?
Give your answer as a time in the 24-hour clock.
Answer:
18:45
Step-by-step explanation:
PLS HELP ME OUT GUYS PLS PLS PLS PLS
the 1st, 2nd, and 3rd are correct
Approximate 218.16 to the nearest tens.
I need help. This is due later today.
Answer:
D is one of them
Step-by-step explanation:
Does (1, 10) make the inequality y > 2x + 7 true?
yes
no
Answer:
Yes.
10 > 9
Step-by-step explanation:
This inequality is true because 10 is greater than 9.
y > 2x + 7
10 > 2(1) + 7
10 > 2 +7
10 > 9
The perimeter of a rectangle is 56mm. Three of the sides have a length of 15mm, 13mm, and 15mm. What is the side length?
convert 2x + y = -1 to slope intercept form
Answer:
y=-2x-1
Step-by-step explanation:
Your goal from Standard form to slope intercept form is to have the x on the right side of the equal sign. All you have to do is subtract 2x from both sides and you end up with y= -2x-1
The graph for y≥-3.
true
false
helpp me
Answer:
I think it's false
Step-by-step explanation
A research company desires to know the mean consumption of meat per week among males over age 43. A sample of 1384 males over age 43 was drawn and the mean meat consumption was 3 pounds. Assume that the population standard deviation is known to be 1.3 pounds. Construct the 99% confidence interval for the mean consumption of meat among males over age 43. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{1.3}{\sqrt{1384}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 3 - 0.1 = 2.9 pounds
The upper end of the interval is the sample mean added to M. So it is 3 + 0.01 = 3.1 pounds
The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.
You want to put a 5 inch thick layer of topsoil for a new 26 ft by 27 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer:
Step-by-step explanation:
he volume of the topsoil is
28 ft by 21 ft by 5/15 ft = 245 cubic feet
There are 27 cubic feet in one cubic yard.
245/27 = 9.074074074.... = 9.074
Need 9.25 = 9 and 1/4 cubic yards
Which graph(s) show an inverse relationship? Check all that apply.
Answer:
can you show the graph please?
Karin has 7 more pieces of candy than Danny. Danny has d pieces of candy. Karin uses the expression 7 + d to figure out how many pieces of candy she has.
How many pieces of candy does Karin have if d = 4?
A. 2
B. 28
C. 3
D. 11
Answer:B
Step-by-step explanation:
If d=4 and Danny has 7 more peices all you have to do is multiply. 7x4 and that equals 28
So the final answer is 28 which is choice B
6x-23+3m in standard form
Answer:
6x-23+3m
6x+3m-27 we can't add them b/c they have d/t
variables so the answer is 6x+3m-27
What is the slope of the line?
Answer:
-7/4
Step-by-step explanation:
Hi,
To find the slope of the line, get two points, and divide the change in y over the change in x. So, let's find two points.
(1,-3) and (-3,4)
Change in y: 4 - (-3) = 7 (Remember when you subtract a negative, you add)
Change in x: -3 - 1 = -4
7/-4 = -7/4
-7/4 is your slope.
I hope this helps :)
Given the definitions of f(x) and g(x) below, find the value of (g o f) (-3)
f(x)=2x^2+6x+9
g(x)=3x-6
Answer:
21
Step-by-step explanation:
(g o f) (-3) = g ( f(-3) )
First, let's find f(-3):
f(x)=2x²+6x+9
f(-3)=2(-3²)+6(-3)+9
f(-3)=18-18+9
f(-3)=9
Now that we know the value of f(-3), we can sub this into g(f(-3)):
g ( f(-3) ) = g(9)
Find g(9):
g(9)=3x-6
g(9)=3(9)-6
g(9)=27-6
g(9)=21
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
I will ONLY give you a brainliest of you answer this questions CORRECTLY!
Answer:
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Step-by-step explanation:
Surface area of a cylinder = 2πrh+2πr² = 2π(rh+r²)
Cylinder A = 2π(rh+r²)
Cylinder B = 2π((2r)(2h)+(2r)²) = 2π(4rh+4r²)=2π(4(rh+r²))
To find how many times greater Cylinder B's surface area is than Cylinder A's surface area, divide:
[tex]\frac{Cylinder B}{Cylinder A}[/tex]
=2π(4(rh+r²))/2π(rh+r²)
(divide top and bottom by 2π)
=4(rh+r²)/(rh+r²)
(divide top and bottom by (rh+r²))
=4
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Which of the following equations have a solution of y = 8
Answer:
B
Step-by-step explanation:
Plug in 8 for y in each equation to see if it's true
6+5(8)=46
6+40=46 ✔️
Please help me
This is analytic geometry
Answer:
The coordinates of point B are (-3,-3).
Step-by-step explanation:
Let [tex]A(x,y) = (6,-6)[/tex], [tex]C(x,y) = (-6,-2)[/tex] and [tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex], then we have the following formula by vectorial definition of a line segment:
[tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex]
[tex]B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)][/tex]
[tex]B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)[/tex]
[tex]B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)[/tex]
[tex]B(x,y) = (-3, -3)[/tex]
Cell phone Plan A costs$70 per month and comes with a free$500 phone. Cell phone Plan Bcosts$50 per month but does not come with a phone. If you buy the$500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?
Please answer WITHEXPLANATION!
Answer:
25
Step-by-step explanation:
A = 70*M
B = 500 + 50*M
Costing the same means equal, so we have the equation:
70M = 500 + 50M
-50M -50M
20M = 500
20M / 20 = 500 / 20
m- 25 months
Given the following information, find the length of the missing side. Leave your answer as a simplified radical.
Answer:
Long = 5√3
Step-by-step explanation:
Hypotenuse = 10
Short = 5
Long = ?
Apply Pythagorean theorem to find Long:
Long² = hyp² - short²
Long² = 10² - 5²
Long² = 100 - 25
Long² = 75
Long = √75
Long = √(25*3)
Long = 5√3
Please help! And don't give me a link, I know it's a scam.
Is a triangle with these measures possible?
52°, 18°, and 110°
Answer:
Yes.
Step-by-step explanation:
Well if the sum of the angles is equal to 180, then it's a triangle. Since [tex]52+18+110=180[/tex], a triangle with the measures 52°, 18°, and 110° is possible. Hope this helps!
what is 6/3 + (- 1/6)
Answer:
The answer to your problem is 1 5/6
Answer:
11/6
Step-by-step explanation:
First you need to get a common denomintor in order to add fractions. Here you can multiply 6/3 by two to get 12/6. Then you can just do 12/6-1/6 since adding a negative number is the same as subtracting, leaving you with 11/6, which cannot be reduced so that is your final answer.
PLS HELPPP GEOMETRY!!!!!!
You are on a fishing boat that leaves its pier and heads east. After traveling for 24 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of S45°W for 13.4 miles.
a. At this time, how far are you from the boat's pier?
b. What bearing could the boat have originally taken to arrive at this spot?
Answer:
a-17.3 miles b-S57 E
Step-by-step explanation:
d^2=30^2+12^2-2(30)(12)
sin45
Pleaseee help is he right or wrong and why!!!
Answer:
No, Andre is not correct.
Step-by-step explanation:
I believe Andre is not correct because each 1 on the left balances with a 1 on the right. So taking away the two 1s on the left only leaves the hanger balanced if two 1s are removed on the right. This leaves on the left and three 1s on the right, so x=3. This is like x+2=5 if you subtract 2 from the x side then you get x=3. Hope this helps!