Answers
Given center of the circle at (-10,6) and radius 4,
(x + 10)² + (y - 6)² = 4²
(x + 10)² + (y - 6)² = 16
Answer: (x + 10)² + (y - 6)² = 16
Center of circle: (-10, 6)
Radius: 4
(x - -10)² + (y - 6)² = 4²
Equation: (x + 10)² + (y - 6)² = 16
Related Questions
Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?
Answers
120n=180*(n-2)
120n=180n-360
180n-120n=360
60n =360
n=6
It is hexagon.
The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.
A.26.5cm3
B.44.2cm3
C.79.5cm3
D.132.5cm3
Answers
1of the first figure in the image attached, is:
a ^ 2 = b ^ 2 + c ^ 2
c =
c=√(6 cm)^2-(4.8 cm)^2
c=3.6 cm
2. The area of the base of the first figure is:
A=BxH/2
A=3.6x4.8/2
A=8.64 cm^2
3. Therefore, the volume of the cone is:
V=(8.64 cm^2)(9.2 cm)
V=79.5 cm^3
Therefore, the answer is: C. 79.5 cm^3
Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?
Answers
562.432-500= 62.432
62.432 / 3= 20.8106
At noon joyce drove to the lake at 30 mph, but she made the long walk back home at 4 mph. how many hours did she walk if she was gone for 17 hours
Answers
t = d / v
Where,
t: time
d: distance
v: speed
For this case we have:
d / 30 + d / 4 = 17
Rewriting we have:
2d + 15d = 17 (60)
17d = 17 (60)
d = 60 mi
Then, the walking time is
t = d / v
t = 60/4
t = 15 hours
Answer:
She walked
t = 15 hours
Answer:
i just did this on a quiz the answer was 15 hours
Step-by-step explanation:
Can someone help me in this trig question, please? thanks
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12
Answers
[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ -------------------------------\\\\ cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=cos\left( \frac{\pi }{6}\right)cos\left(\frac{\pi }{4} \right)-sin\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]
[tex]\bf cos\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}-\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{6}}{4}-\cfrac{\sqrt{2}}{4}\implies \boxed{\cfrac{\sqrt{6}-\sqrt{2}}{4}} \\\\\\ sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=sin\left( \frac{\pi }{6}\right)cos\left( \frac{\pi }{4} \right)+cos\left( \frac{\pi }{6}\right)sin\left(\frac{\pi }{4} \right)[/tex]
[tex]\bf sin\left( \frac{\pi }{6}+\frac{\pi }{4} \right)=\cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}+\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}+\cfrac{\sqrt{6}}{4}\implies \boxed{\cfrac{\sqrt{2}+\sqrt{6}}{4}}\\\\ -------------------------------\\\\ 20\left( \cfrac{\sqrt{6}-\sqrt{2}}{4} \right)\implies 5(-\sqrt{2}+\sqrt{6}) \\\\\\ 20\left( \cfrac{\sqrt{2}+\sqrt{6}}{4} \right)\implies 5(\sqrt{2}+\sqrt{6})[/tex]
The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
The positionSince the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°
So, substituting the value of θ into the positions, we have
(20cos75°, 20sin75°)
The value of 20cos75°
20cos75° = 20cos(45 + 30)
Using the compound angle formula
cos(A + B) = cosAcosB - sinAsinB
With A = 45 and B = 30
cos(45 + 30) = cos45cos30 - sin45sin30
= 1/√2 × √3/2 - 1/√2 × 1/2
= 1/2√2(√3 - 1)
= 1/2√2(√3 - 1) × √2/√2
= √2(√3 - 1)/4
= (√6 - √2)/4
= (-√2 + √6)/4
So, 20cos75° = 20 × (-√2 + √6)/4
= 5 (-√2 + √6)
The value of 20sin75°
20sin75° = sin(45 + 30)
Using the compound angle formula
sin(A + B) = sinAcosB + cosAsinB
With A = 45 and B = 30
sin(45 + 30) = sin45cos30 + cos45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= 1/2√2(√3 + 1)
= 1/2√2(√3 + 1) × √2/√2
= √2(√3 + 1)/4
= (√6 + √2)/4
= (√2 + √6)/4
So, 20sin75° = 20 × (√2 + √6)/4
= 5(√2 + √6)
Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).
So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
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what is 3√27x^9
3x^6
3x^3
9x^3
9x^6
Answers
[tex] \sqrt[3]{27} \sqrt[3]{ x^{9} } [/tex]
Write the number in the first square root in exponential form with a base of 3.
[tex] \sqrt[3]{ 3^{3} } \sqrt[3]{ x^{9} } [/tex]
Now reduce the index of the radical and exponent in the second square root with 3.
[tex] \sqrt[3]{ 3^{3} } [/tex] x³
Lastly,, reduce the index of the radical and exponent with 3 to get your final answer.
3x³
This means that the correct answer to your question will be option B.
Let me know if you have any further questions.
:)
The value of the expression ∛27x⁹ is 9x³.
The given expression is ∛27x⁹.
Cube root of twenty seven times of x power nine.
We can split the terms inside the cube root.
27=3×3×3
∛x⁹ = x³
Now let us plug in the above expression.
= 3√3³ × x⁹
= 3√3³ × √ x⁹
= 3 × 3 × x³
= 9x³.
Hence, the value of the expression ∛27x⁹ is 9x³.
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Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?
Answers
The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
How to calculate EMI?The EMI formula is :
[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]
Where r = 5.5/12/100 = 0.00425
p = 37,796.89
and n = 20 x 12 = 240
Putting the values in formula we get'
= (37,796.89x 0.00425 x 2.767)/1.767
= $350
Hence,
The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
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Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.
Step-by-step explanation:
Determine whether quantities vary directly or inversely and find the constant of variation. If 5 bushels of wheat weigh 136 kg, how much do 3.5 bushels of wheat weigh?
Answers
Let the bushels of wheat is b and weight of the wheat is w.
We can say that more the bushels of wheat more will be the weight of the wheat.
Hence, the quantities vary directly.
Therefore, we have
[tex]b=kw[/tex], where k is the constant of variation.
Now, we have been given that 5 bushels of wheat weigh 136 kg. Thus, we have
[tex]5=136k\\ \\ k=\frac{5}{136}[/tex]
Thus, the constant of variation is [tex]\frac{5}{136}[/tex]
Now, we have been given 3.5 bushels of wheat. Hence, we have
[tex]3.5=\frac{5}{136} w\\ \\ w=\frac{136\times 3.5}{5} \\ \\ w=95.2[/tex]
Therefore, 3.5 bushels of wheat weigh 95.2 kg
Which equation in point-slope form contains the point (4, –1) and has slope 3? y – 1 = 3(x + 4) y – 4 = 3(x + 1) y + 1 = 3(x – 4)
Answers
The equation for point-slope form is
y - b = m(x - a)
m is the slope
(a, b) is a point the line goes through
Put in the values into the equation
y - -1 = 3(x - 4)
Simplify
y + 1 = 3(x - 4)
The answer is C) y + 1 = 3(x - 4)
Hope this helps!
Answer:
the answer is option d y+1 =3 (x-4)
What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.
To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
Answers
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere
if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere
if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere
example
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area
2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area
3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area
sketch one cycle of the cosine function y=-cos 3 theta
Answers
Answer with explanation:
The given cosine function is
y= - cos 3 (theta)= -3 cos A, where , theta =A.
→→Domain of Cos A
= All Real number
= Period is from (-π , π)
Range of Cos A=[-1, 1]
→Domain of Cos 3 A,will be also, all real number.
Period is from,
[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]
But range of Cos 3A,will be same as ,Cos A which is equal to ,[-1,1].
→Plotted the graph of ,y=-cos 3 A, having cycle ,
[tex][\frac{-\pi}{3},\frac{\pi}{3}][/tex]
what is 3 ^9? how to solve?
Answers
3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
What I would do it is narrow it down piece by piece.
3 * 3 * 3 = 27. Do that 3 times, now you are left with:
27 * 27 * 27
27 * 27 or 27² = 729.
That leaves you with:
729 * 27
You can multiply by hand or use a calculator to get your answer of 19683.
To check your answer, plug 3⁹ into a calculator. Your answer should match this.
Which graph would help solve the equation 5log(x+3)=5
Answers
The value of x is 7 for the given equation.
What is logarithm?Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.
For the given situation,
The equation is 5log(x+3)=5.
On solving this equation, we can get value of x.
⇒ [tex]5log(x+3)=5[/tex]
⇒ [tex]log(x+3)=1[/tex]
We know that, log 10 = 1
Then,
⇒ [tex]log(x+3)=log10[/tex]
⇒ [tex]x+3=10[/tex]
⇒ [tex]x=7[/tex]
Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.
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can someone help me on trigonometry ?
Answers
So tan is opposite/adjacent
sin: opposite/hypotenuse
cos: adjacent/hypotenuse
Take theta and do: adjacent/hypotenuse which is cosine
cos theta = adjacent/hypotenuse
cos theta = 1.5/9
inverse cos = 1.5/9 and the answer is: 80.4 degrees
fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?
Answers
1+cot ²∅=csc² ∅
cot ∅=4/7
so
1+(4/7)²=csc² ∅
csc² ∅=1+(16/49)
csc² ∅=(65/49)
csc ∅=(√65)/7
remember that
csc ∅=1/sin ∅
sin ∅=1/csc ∅------> sin ∅=7/√65-----> sin ∅=(7√65)/65
the answer is
the best identity to find sin ∅ is
1+cot ²∅=csc² ∅
Answer:
D edge
Step-by-step explanation:
the probability of winning the game is 7/10. What is the probability that they will lose?
Answers
The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.
If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.
how do you do 27?????
Answers
To start, the equation needed to represent this problem would be an equation:
y= ab^x
a represents the initial amount. In this case, the initial amount would be 4 billion. It would be represented as 4 since each 1= one billion.
b represents the rate. Because the problem discusses a growth, convert the rate, 1.9% to a decimal and add 1 to it (add one if it is a growth, subtract one if it is a decay). b would be 1.019.
x represents the time in which the population grows or t.
When you piece this together, your equation should look like:
y=4(1.019)^t
or
Choice A.
Hope this helps and have a nice day! Feel free to ask any questions about my work. :)
_______________________________________________________
Explanation:
______________________________________________________
Use the formula for "exponential growth" :
______________________________________________________
→ " y = A * (1 + r)^t " ;
______________________________________________________
in which:
______________________________________________________
A = the "beginning population" ;
→ (in number representing "billions of people") ;
→ given the "beginning population" is "4 billion" ;
→ " A = 4 " ;
______________________________________________________
r = rate (of change) = 1.9% ; expressed as a decimal:
→ "r = rate = 1.9% = { 1.9 ÷ 100 } ;
→ {Take the "1.9" ; & move the decimal point 2 (two) spaces backward }:
→ 1.9% = 1.9 ÷ 100 = 0.019 ;
→ " r = 0.019 " ;
→ " t = time" ; (usually in "years" ; however, all the answer choices provided leave the "t" as it is; so we shall do so, too.
________________________________________________________
→ Replace "y" with: " P(t) " ;
→ And rewrite the equation of the function with our known values:
→ " y = A * (1 + r)^t " ;
____________________________________________________
→ becomes:
→ " P(t) = 4* (1 + 0.019)^t " ;
→ " P(t) = 4 * (1 .019)^t " ;
____________________________________________________
→ which is: Answer choice: [A]: " P(t) = 4 * (1 .019)^t " .
____________________________________________________
help! I will give thanks!
Answers
Reason: 60 appeared 4 times.
A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)
Answers
A car is traveling at 48 miles per hour. What is the speed of the car in centimeters per second? (1 mile = 5,280 feet, 1 foot = 12 inches, 1 centimeter = 0.39 inch)
Solution:
We have 48 [tex] \frac{miles}{hour} [/tex]
To convert, miles to centimeters.
Let us convert miles to feet and then inches and then centimeters.
1miles=5280feet
And, 1 foot=12inches
So, 5280 feet or 1 miles =12*5280inches
So, 1miles=63360inches
Now, Let us convert inches to centimeters
1centimeter=0.39inches
Or, 1 inch= [tex] \frac{1}{0.39} [/tex] centimeter
So, 63360inches (or 1 mile)= [tex] \frac{63360}{0.39} [/tex] centimeter
1mile or 63360inches=162461.54centimeter
1mile=162461.54 centimeter
We have, 48 [tex] \frac{miles}{hour} [/tex]
We have, 48 *[tex] \frac{162461.54 centimeter}{60minutes} [/tex]
We have, 48* [tex] \frac{162461.54 centimeter}{60*60seconds} [/tex]
So, We have, 48* [tex] \frac{162461.54 centimeter}{3600seconds} [/tex]
=48*[tex] \frac{162461.54}{3600} [/tex][tex] \frac{centimeters}{second} [/tex]
=48*45.13[tex] \frac{centimeters}{second} [/tex]
=2166.15[tex] \frac{centimeters}{second} [/tex]
Answer:= Speed of the car in centimeters per second is 2166.15 centimeters/second
Please someone help Me with this problem. I really need help.
Answers
HELP!! Drag values to complete each equation.
Answers
12^7 x 12^-5 / 12² which equals 1.
Hope this Helps!!
Answer:
a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
Step-by-step explanation:
We have to complete each equation
We are given that
[tex]((12)^2)^3\cdot (12)^{-4}[/tex]
[tex](12)^6\cdot (12)^{-4}[/tex]
Using identity
[tex](a^x)^y=a^{xy}[/tex]
[tex](12)^{6-4}=(12)^2[/tex]
Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]
[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]
[tex]\frac{(12)^2}{(12)^2}[/tex]
[tex](12)^{2-2}=(12)^0=1[/tex]
Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]
[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch
Answers
square root (25 + 25) =
square root (50) =
7.07106781 =
7.1 (rounded to nearest 10th of an inch.
Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.
Answers
9, 9, 10, 10, 12, 12, 14, 15, 15, 15, 17
1. To find the mean, add all the number together and divide the summation by 11[ which is the total number of the figures given]
Mean = [9 + 9 + 10 + 10 + 12 + 12 + 14+ 15 + 15 + 15 + 17] / 11 = 138 / 11
Mean = 12.5
Therefore, the mean is approximately equal to 13.
2. The median of a number refers to the number in the middle of a sorted set of number.
To find the median of a set of numbers, the numbers have to be arranged first in the correct increasing order and the number that falls in the middle will be the median. If two numbers fall in the middle, add the two together and find the average. For the set of number given above, the number that falls in the middle is 12.
Therefore, the median = 12.
3. The mode of a set of number refers to the number in the set, which has the highest frequency of occurrence, that is, it is the number that occur most. Looking at the set of number given above, 15 occurred three different times. Therefore, the mode of the set of number given above is 15.
Mode = 15.
4. The range of a set of number refers to the difference between the highest and the lowest numbers in the set of a given number. It represents the spread of the data. In the set of numbers given above the range is determined thus:
Range = 17 - 9 = 8.
Therefore, Range = 8.
Mean: 12.545454545455
Median: 12
Range: 8
Mode: 15, appeared 3 times
Largest: 17
Smallest: 9
Sum: 138
Count: 11
An equiangular triangle can be scalene. A. True B. False
Answers
Because equiangular triangle is not to be scalene.
Hope it helped you.
-Charlie
:)
NEED HELP ASAP!
Subtract.
(4x^2+8x−2)−(2x^2−4x+3)
Answer in standard form
Answers
The measure of an angle is 8 times the measure of its complement. tina writes an equation and finds the correct measure of each angle. which shows the equation tina could have written and the angle measures she could have found?
Answers
With all this information, you should have the equation:
n + 8n = 90
To solve, combine like terms to get:
9n = 90
Divide by 9 on both sides to isolate the variable n.
n = 10
Now we plug back in to find our angle measurements. The first angle, n, is 10 degrees. The second angle, 8n, is 8 * 10 which is 80; the second angle is 80 degrees.
The measure of angles are 10 and 80 degree.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
We have,
let the complementary angle = x
and, the another angle is = 8x
We know the complementary angle sum to 90 degree.
So, x + 8x = 90
9x = 90
x =10
Thus, the measure of angles are 10 and 80 degree.
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Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. What is the speed of the train, if it is 5 km/h greater than the speed of the car?
Answers
Speed of the train = 63.75 + 5 = 68.75 km/h
Answer: 68.75 km/h
[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]
The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.
The speed of the train is given by 25 km/hr.
what expression is equivalent to the division expression 3/4 divided by 4/5
Answers
3/4 times 5/4 =
15/16 = .9375
Answer:
3/4 ÷ 4/5 = .75 ÷ .80
Step-by-step explanation:
3/4 ÷ 4/5
= .75 ÷ .80
= 0.9375
If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)
Answers
P(x)/(x-5)
=(2x^3-3x+5)/(x-5)
=(2x^2+10x+47)+240/(x-5)
thus the remainder is:
240
Final answer:
Using the Remainder Theorem, after substituting 5 into the polynomial p(x), we find that the remainder when p(x) is divided by (x - 5) is 240.
Explanation:
To find the remainder of p(x) divided by (x - 5), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial p(x) divided by (x - a) is p(a). Thus, we need to evaluate p(5).
Let's substitute x with 5 in the polynomial p(x):
p(5) = 2(5)^3 - 3(5) + 5
= 2(125) - 15 + 5
= 250 - 15 + 5
= 240.
Therefore, the remainder when p(x) is divided by (x - 5) is 240.
Subtract.
(x + 1) − (−2x − 5)
Answers
Answer:
3x+6
Step-by-step explanation:
you have to distribute the negative to get the parentheses away and simplify