Answer:
40000×1×9%=3 600 this is for year
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]
complete the table for the equation
Answer:
(2,5)
(3,-4)
(4,-7)
(5,-4)
(6,5)
The function g is given in three equivalent forms.
Which form most quickly reveals the y-intercept?
Choose 1 answer:
g(x) = 3x² + 6x - 9
g(x) = 3(x + 1)² – 12
-
g(x) = 3(x+3)(x - 1)
What is the y-intercept?
y-intercept = (0,
▸
The form of the function that most quickly reveals the y-intercept is the second form:
[tex]g(x)=[/tex] [tex]3(x+1)^{2} - 12[/tex]
To find the y-intercept, we need to determine the value of g(x) when x is equal to 0. By substituting x = 0 into the function, we have:
[tex]g(0)=3(0+1)^{2} -12[/tex]
[tex]=3(1)^{2} -12[/tex]
[tex]=3-12[/tex]
[tex]=-9.[/tex]
Therefore, the y-intercept is -9. This means that the graph of the function intersects the y-axis at the point (0, -9), where the x-coordinate is 0 and the y-coordinate represents the y-intercept value.
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4.
A restaurant offers seven kinds of main
courses, nine types of drinks, and four types of
desserts. How many different meals
consisting of a main course, a drink, and a
dessert does the restaurant offer? |
Answer:
252
Step-by-step explanation:
Types of main courses available = 9
Types of drinks offered = 7
Types of deserts = 4
Number of different meals consisting of a main course, a drink and a desert offered
Using the combination rule :
9C1 * 7C1 * 4C1
nCr = n! ÷ (n-r)!r!
So using calculator we obtain :
9 * 7 * 4 = 252
Please help
here the question
Rosalina just started a new job. She has $500 in her bank account. Every week, she deposits $40 into her bank account.
A)
Write an expression to represent how much Rosalina has in her account at any given time using x to represent the number of weeks.
I ALREADY SOLVED A BUT I NEED HELP WITH B!!
B) Rosalina wants to save $700 for the new smart tv write and equation to determine how many weeks (x) it will take for rosalina to have enough money to purchase her new tv
HELP ME PLEASE WITH B I ALREADY SOLVED A
THANK YOU!!
Answer:x=18
Step-by-step explanation:
if she deposites 40 every week 40 times 18 is 720 so in 18 weeks she can have a t.V
Select the correct comparison
Answer:
b
Step-by-step explanation:
The mathematics faculty at a college consists of 7 professors, 4 associate professors, 4 assistant professors, and 6 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor.
Answer:
0.619 = 61.9% probability of choosing a professor or an instructor.
Step-by-step explanation:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
7 + 4 + 4 + 6 = 21 members
7 + 6 = 13 professors or instructors.
Find the probability of choosing a professor or an instructor.
p = 13/21 = 0.619
0.619 = 61.9% probability of choosing a professor or an instructor.
Sinx-sin3x /sin^2x -cos^2x
The answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x). To simplify the given expression, we can use the identity sin 2x = 2sin x cos x.
Substitute the numerator with sin x - sin 3x. Substitute the denominator with sin² x - cos² x to get a common factor.
Substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - cos² x - cos² x).Then substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - 2 cos² x).
Now, use the identity sin 2x = 2sin x cos x to simplify the numerator. sin x - sin 3x can be written as sin x - sin (x + 2x) which equals sin x - [sin x cos 2x + cos x sin 2x].
Now, simplify the expression: sin x (1 - cos² x - cos² x) - sin x cos 2x - cos x sin 2x. We will simplify this expression further, leading us to get sin x (1 - 2 cos² x) - sin 2x cos x.
Finally, the expression becomes sin x (1 - 2 cos² x) - sin 2x cos x / (1 - 2 cos² x). Therefore, the answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x).
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LOOK AT THE IMAGE!!!
DO NOT JUST ANSWER FOR POINTS
Answer:
C) (-3,-1)
Step-by-step explanation:
C) (-3,-1)
GUYS HELP ME PLS. Tina is standing at the bottom of a hill. Matt is standing on the hill so that when Tina's line of sight is
perpendicular to her body, she is looking at Matt's shoes.
a. If Tina's eyes are 5 feet from the ground and 14.5 feet from Matt's shoes, what is the angle of elevation of
the hill to the nearest degree?
Answer:
71°
Step-by-step explanation:
The angle of elevation of the hill can be obtiaed using trigonometry :
Given
the opposite length = 14.5 feets
Adjacent = 5 feets
The angle of elevation vabnbe obtained using :
Tan θ = opposite / Adjacent
Where θ = angle of elevation
Tan θ = 14.5 / 5
Tan θ = 2.9
θ = tan^-1(2.9)
θ = 70.97 = 71°
20141
ID
NJ008306927
10
Name
Manuel Negron
Tune Remaining
00:24:41
A toy manufacturer is using
this design to package its
latest toy, What is the volume
of the box?
4.5 in.
6.5 in.
-6.5 in.
DinO-BO
315.5 cubic in
389 cubic in
4.5
435.8 cubic in
650.5 cubic in
-10.4 in.
with y width x height)
Answer:
315.5cubic in
10.4 x 4.5 x 6.5=
Step-by-step explanation:
Determine whether the function is periodic. If it is periodic, find the period. f(x)=7sin^3x a. 2pi b. 4pi c. Not periodic d. pi
A car and a truck left Washington, DC traveling in opposite directions. The car traveled 19 miles per hour faster than the truck, and at the end of 8 hours they were 1048 miles apart. What was the average speed of each vehicle?
100 POINTS
Answer:
Step-by-step explanation:xmccc
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
A scale of 3
Step-by-step explanation:
dd2d2de2f3f
For the following set of data, find the mean, median and mode.
age of children Danielle babysits:
6,9,2,4,3,6,5
(3 Points)
Mean = 4 years old
Mean = 5 year old
Mean = 9 years old
Mode = 2 years old
Mode = 6 years old
Mode = 9 years old
Median = 4 years old
Median = 4.5 years old
Median = 5 years old
Pyramid A has a height of 10 feet and a volume of 120 cubic feet. The base of Pyramid B has the same dimensions as Pyramid A but is twice as tall. How is the volume affected by the change in the dimensions? (PLEASE HELP!)
A volume of a pyramid=base area×height/3
both the bases have same dimensions
pyramid B is twice the height of A
therefore the volume is doubled
Answer:
Pyramid B = 240 cubic feet, the volume doubled
Step-by-step explanation:
Pyramid A: 120/10 =12, 12 x 3 = 36 ft² base
Pyramid B: 36 ft² base x 20 ft tall x 1/3 = 240 cubic feet
Daria rolls a number cube. What is the probability that it will land on a 1?
Answer:
1 out of 6 or 16.7%
Step-by-step explanation:
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent.
The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3
To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:
Since for all x > 0, we have:
Thus, by the limit comparison test:
converges if and only if converges.
We can evaluate using the power rule of integration:
where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:
∫(1/x^4) dx from 1 to infinity = lim as b → infinity
=>
=> 0 - (-1/3)
=> 1/3
Since the integral dx converges by comparison to a convergent integral, and its value is 1/3.
To learn more about Convergent integral :
Note: The full question is
Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1
The line passes through the points (3, 7) and (4, 9)
Answer:
I'm confused as to what your asking?
Answer:
y= 2x +1
Step-by-step explanation:
slope 9-7/4-3 = 2/1= 2
y-7 = 2(x -3)
y-7 = 2x -6
y = 2x +1
606 divided by 49 in long division
Answer:
12 <----
Step-by-step explanation:
the remainder is 18 but the answer is 12 and the full thing would be
------> 6.18367346939
olve the Following Inequality Select the possible range of solution to make the Statement True.
-6m < -24
Group of answer choices {Select All That Apply}
1, 2, 3
-1, -2, -3
4, 5, 6
-, 4, -5, -6
Answer:
We have ,
=> -6m < -24
=> m < -24/-6
=> m < 4
Therefore ,
m € (4,-∞)
hi can I send a screenshot?
Answer:
Yeah
Step-by-step explanation:
☁️ Answer ☁️
Yes! Send a screenshot and ask ur question
determine if the work for each problem is correct correct only errors and explain your thinking
Answer:
v= BH
the second part is wrong the base is 7.5 not 9.5
so the base look like this
v = 7.5(13)
v = 97.5
Step-by-step explanation:
How much Hundreds equal 28?
Answer:
0.28
Step-by-step explanation:
0.28*100=28
A savings account starts with $181.25. After 7 years of continuous compounding at an interest rate, r, the account has $1450.
What is the interest rate percentage?
Round the answer to the nearest hundredth
Enter your answer in the box.
Answer:
29.71%
Step-by-step explanation:
The interest rate of the savings account is = 114.3%
Calculation of interest rate percentage of an accountThe start up or principal amount (P) = $181.25
Simple interest after 7 years (SI) = $1450
Time or duration (T) = 7 years
To calculate the rate percentage of interest;
R = SI × 100/P×T
R = 1450 × 100/ 181.25 × 7
R = 145000/1268.75
R = 114.3%
Therefore, the interest rate percentage of the savings account is = 114.3%
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Which describes the correlation shown in the scatterplot?
Answer:2,4
Step-by-step explanation:
According to a NY Times article in 2009, the average selling price of an LCD TV was $700. What would be the cost of that same TV in 2016 dollars?
The prices of products usually fall due to depreciation and the appearance of new technological objects. In this case, the value of the television would lower its price due to the appearance of other technologies such as LED.
How to calculate LCD TV depreciation?To calculate the depreciation of the LCD TV, the year of manufacture, the useful life, the prices of new products (generally better), among others, must be taken into account.
A ballpark figure of 15% is generally used to calculate the depreciation of a television per year. In this case, following this pattern, the television would have a value of:
700 - 105 = 595595 - 89.25 = 505.75505.75 - 75.86 = 429.88429.88 - 64.48 = 365.39365.39 - 54.80 = 310.58310.58 - 46.58 = 263.99263.99 - 39.59 = 224.39Learn more about depreciation in: https://brainly.com/question/15085226
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Lodging is $75.00 per night. Find the cost of three nights and 7% sales tax.
Answer: $240.75
Step-by-step explanation:
-9b+2n-4+2b
Solve please
Answer:
-9b+2n-4+2b
-7b+2n-4 is your answer
PLS HELP DO NOT TRIY THE FAKE I CANT UPLOAD STUFF
The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m.
Write a question that could be answered by solving the equation 10−0.035d=4.
Answer:
By solving this equation for the variable ' d ', you learn how many days after you fill the tank you'll have to send somebody back to fill it again.
Step-by-step explanation: