Answer:
Option D is correct
Step-by-step explanation:
Given Equations of Circles:
Circle 1 - [tex](x+12)^2+(y+16)^2=(r_1)^2[/tex]
Circle 2 - [tex](x-30)^2+(y-16)^2=(r_2)^2[/tex]
Both circles passes through origin.
To find: Values of [tex]r_1\:,\:r_2[/tex]
Coordinates of origin = ( 0 , 0 )
Circles passes through origin means x = 0 & y = 0 must satisfy the equation of circles.
So, Substituting x = 0 & y = 0 in Eqn of Circle 1
we get
[tex](0+12)^2+(0+16)^2=(r_1)^2[/tex]
[tex](r_1)^2=12^2+16^2[/tex]
[tex](r_1)^2=144+256[/tex]
[tex](r_1)^2=400[/tex]
[tex]r_1=\sqrt{400}[/tex]
[tex]r_1=20[/tex]
Now, Substituting x = 0 & y = 0 in Eqn of Circle 2
we get
[tex](0-30)^2+(0-16)^2=(r_2)^2[/tex]
[tex](r_2)^2=(-30)^2+(-16)^2[/tex]
[tex](r_2)^2=900+256[/tex]
[tex](r_2)^2=1156[/tex]
[tex]r_2=\sqrt{1156}[/tex]
[tex]r_2=34[/tex]
Therefore, Option D is correct .i.e., [tex]r_1=20\:\:,\:\:r_2=34[/tex]
find the simplified form of (-7.4)^0?
A.-1
B.-7.4
C.0
D.1
Final answer:
Any non-zero number raised to the power of 0 is 1, so the simplified form of (-7.4)⁰ is 1 that is option D is correct.
Explanation:
The simplified form of (-7.4)⁰ is determined by one of the fundamental rules of exponents, which states that any non-zero number raised to the power of 0 is 1. This means that regardless of what the base number is, as long as it is not zero, if the exponent is 0, the result will always be 1. It is important to note that 0^0 is an indeterminate form and is not covered by this rule. Therefore, the simplified form of (-7.4)⁰ is:
D. 1
The first term in a geometric sequence is 1/9 and the common ratio is −3. Find the 7th term in the sequence.
The 7th term of the sequence is 81
The nth term of a geometric sequence is expressed as:
[tex]T_n=ar^{n-1}[/tex]
a is the first term = 1/9r is the common ratio = -3n is the number of terms = 7Substitute the given parameters into the formula to have:
[tex]T_7=1/9(-3)^{7-1}\\T_7=1/9(-3)^6\\T_7=1/9(729)\\T_7=81[/tex]
Hence the 7th term of the sequence is 81
learn more on geometric sequence here: https://brainly.com/question/12006112
Suppose you buy a CD for $300 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity?
A. $328.14
B. $309.12
C. $309.10
D. $303.01
help?,
Find the vertex of y = x2 + 14x − 40 by completing the square.
PLEASE HELP ASAP!!! 51 PTS
Plzzz help will give the brainliest for correct answer
Find the complement of an angle whose measure is 74 degrees. Show all work.
Answer:
16⁰
Step-by-step explanation:
Angle = 74⁰
Complement = 90 - 74 = 16⁰
How the bloody hell do I answer these? Please explain how you did it.
1. In the xy plane, line m passes through the points (a,0) and (0,2a), where a>1. What is the slope of line m?
a)-2 b)-1/2 c)2 d)-2a e)2a
2. First, 3 is subtracted from x and the square root of the difference is taken. Then, 5 is added to the result, giving a final result of 9. What is the value of x?
a)3 b)4 c)5 d)16 e)19
3. If S is the set of positive that are multiples of 7, and if T is the set of positive integers that are multiples of 13, how many integers are in the intersection of S and T?
a)none b)one c)seven d)thirteen e)more than thirteen
4. A florist buys roses at $0.50 each and sells them for $1.00 each. If there are no other expenses, how many roses must be sold in order to make a profit of $3.00?
a)100 b)150 c)200 d)300 e)600
If sound travels approximately 1 km in 3 s, and the lightning is striking 10 km from your house, how much time passes between a flash of lightning and the sound of thunder?
The cost of 16 notebooks at store J is $24. The notebooks at store J are all the same price. The cost of notebooks at store J are all the same price. The cost of store K is shown on the graph below.
Which store has the least expensive cost per notebook and how much?
What is the y intercept of the line given by the equation y= 8x + 75
Answer: (0,8)
Step-by-step explanation:
here you go
Use the angle sum identity to find the exact value of cos 105
the point (0,0) is a solution to which of these inequalities?
a.y+7< 2x + 6
b.y- 7< 2x - 6
c.y -6< 2x - 7
d.y + 7< 2x -6
the apex answer to it D. y – 7 < 2x – 6
Answer: The correct option is (B) [tex]y-7<2x-6.[/tex]
Step-by-step explanation: We are given to select the inequalities that has the point (0, 0) as a solution.
Option (A):
The given inequality is
[tex]y+7<2x+6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x+6=2\times0+6=6.[/tex]
Since 7 > 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (B):
The given inequality is
[tex]y-7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-7=0-7=-7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since -7 < - 6, so the point (0, 0) is a solution to this inequality.
This option is correct.
Option (C):
The given inequality is
[tex]y-6<2x-7.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y-6=0-6=-6,\\\\R.H.S.=2x-7=2\times0-7=-7.[/tex]
Since -6 > - 7, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Option (D):
The given inequality is
[tex]y+7<2x-6.[/tex]
At the point (0, 0), we have
[tex]L.H.S.=y+7=0+7=7,\\\\R.H.S.=2x-6=2\times0-6=-6.[/tex]
Since 7 > - 6, so the point (0, 0) is not a solution to this inequality.
This option is NOT correct.
Thus, the point (0, 0) is a solution to the inequality [tex]y-7<2x-6.[/tex]
Option (B) is correct.
2. Rhianna is buying a car for $14,390. She has a $1000 trade-in allowance and will make a $1500 down payment. She will finance the rest with a 4-year auto loan at 2.6% APR.
Answer:
$261.08
Step-by-step explanation:
Worth of Car=$14,390
Trade-in allowance=$1000
Down Payment= $1500
Value of Loan=14390-(1000+1500)
=$11890
The Monthly Payment for a loan P, taken at a Monthly interest rate, r for a number of m months, is gotten using the formula:
[TeX] Monthly\:Payment=\frac{rP}{1-(1+r)^{-m}} [/TeX]
P=$11890
Monthly Interest Rate,r=0.026/12=0.002167
Number of Months, m=4*12=48 Months
[TeX] Monthly\:Payment=\frac{0.002167*11890}{1-(1+0.002167)^{-48}} [/TeX]
=$261.08
The Monthly Payment on the car loan is $261.08.
The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of the area when r = 5 inches and r = 21 inches. (a) r = 5 inches
Final answer:
The rate of change of the area of a circle with a radius increasing at a constant rate can be calculated using the derivative of the area formula. For r = 5 inches, the rate is 30π square inches per minute and for r = 21 inches, the rate is 126π square inches per minute.
Explanation:
The student is asking about the rate of change of the area of a circle when its radius is increasing at a constant rate. This is a calculus problem that involves derivatives and can be solved using the formula for the area of a circle, A = πr² where A is the area and r is the radius. The rate of change of the radius, ℓr/ℓt, is given as 3 inches per minute.
To find the rate of change of the area, denoted as ℓA/ℓt, we take the derivative of A with respect to t, using the chain rule, which gives us ℓA/ℓt = 2πr(ℓr/ℓt). When r = 5 inches, substituting the values, we obtain ℓA/ℓt = 2π(5)(3) = 30π square inches per minute. Similarly, when r = 21 inches, ℓA/ℓt = 2π(21)(3) = 126π square inches per minute.
If, triangle MNO congruent triangle PQR which of the following can you NOT conclude as being true?
A. ray MN congruent ray PR
B. angle M congruent angle P
C. ray NO congruent ray QR
D. angle N congruent angle Q,
Heyo! ;D
So, we can conclude that based on the information given above, the only one we cannot conclude on being true would be Option A) Ray MN ≅ Ray PR
What is the value of x?
Bill had saved $825 from his last 8 paychecks. He saved either 75$ or 150$ a paycheck.for the 8 paychecks,how many times did bill save $75 from his paycheck
Let us assume the number of times Bill saved $75 from his paycheck = x
Let us assume he number of times Bill saved $150 from his paycheck = y
Since he saved 75$ or 150$ for the 8 paychecks.
So, x+y=8
y=8-x (Equation 1)
Since Bill saved $825 from his last 8 paychecks using $75 or $150.
So, 75x+150y=825 (Equation 2)
Substituting the value of 'y' from equation 1 in equation 2,
[tex] 75x+150(8-x)=825 [/tex]
[tex] 75x+1200-150x=825 [/tex]
[tex] 75x-150x=825-1200 [/tex]
[tex] -75x=-375 [/tex]
x = 5
Therefore, Bill saved $75, 5 times from his paycheck.
Answer:
5
Step-by-step explanation:
A car travels at an average speed of 40 miles per hour for the first 100 miles of a 200-mile trip, and at an average speed of 50 miles per hour for the final 100 miles. what is the car's average speed for the entire 200-mile trip?
mittens are marked down 25% the sale price is 3.15 a pair what was the original price of a pair of mittens
What is the value of x?
I WILL GIVE BRAINLIEST!!! I BEG SOMEBODY TO HELP ME PLS!!!
What is the slope of this line?
A) -1/4
B) 1/4
C) -4
D) 4
Express 1.21212121.... as a fraction
To solve such questions we will have to observe the fact that this is a repeating decimal number with the repeating figures being 2 and 1 as 21.
Thus, we can represent 1.21212121... as [tex] 1.\overline{21} [/tex]
Let us represent the original number 1.21212121... by the letter "a". Thus,
a=1.21212121...=[tex] 1.\overline{21} [/tex]
Therefore,[tex] a=1.\overline{21} [/tex]..................(equation 1)
Let us now multiply (equation 1) by 100 to get:
[tex] 100a=100\times 1.212121...=121.\overline{21} [/tex].....(equation 2)
Now, when we subtract (equation 2) from (equation 1), we will get:
[tex] 100a-a=121.\overline{21}-1.\overline{21} [/tex]
[tex] 99a=120 [/tex]
[tex] \therefore a=\frac{120}{99} [/tex]
Thus the given number 1.21212121... can be represented as a fraction as [tex] \frac{120}{9} [/tex].
please help i have 2 questions thank you
The Truth About Antibacterial Soap
According to Discovery Fit & Health, about 75 percent of liquid soaps claim to be antibacterial. While this kind of soap sounds like a good idea, it is really not more effective than regular soap. Soap in general works by binding with dirt and grime and bacteria. This binding action allows the particles to be washed away easily. Antibacterial soap really does no more than regular soap. In fact, to be more effective than regular soap, antibacterial soap should stay on your skin for about two minutes to do what it claims it can do. Most people do not wash their hands that long. In addition, antibacterial soap may do harm. First it kills both beneficial and harmful bacteria. Second, scientists believe bacteria may become resistant to antibacterial agents over time, especially if they are not used correctly. Finally, antibacterial soap does nothing to viruses. Most of the time, we get sick from viruses, not bacteria. In sum, antibacterial soap does not live up to the hype. You are better off just using regular soap.
Works Cited
Is Antibacterial Soap Any Better than Regular Soap?
http://health.howstuffworks.com/skin-care/cleansing/myths/question692.htm
How is "The Truth About Antibacterial Soap" organized?
Fact by fact
Cause and effect
Chronological order
Problem-solution
its actually language arts not math sorry
it is organized in chronological order
Answer:
chronlogical order
the other answer for the other question is they dont wash their hand long enough
A trapezoid has bases that measure 10 centimeters and 14 centimeters and a height that measures 8 centimeters. What is the area?
For which pair of function is (g*f)(a)=|a|-2
1. f(a)=a^2-4 and g(a)= sqaureroot a
2. f(a)= 1/2a-1 and g(a)=2a-2
3. f(a)=5+a^2 and g(a) = sqaureroot (a-5)-2
4.f(a) =3 -3a and g(a)=4a-5
Answer:
The correct pair is 3
Step-by-step explanation:
1.
[tex]f(a)=a^{2}-4 , g(a)=\sqrt{a} \\gof(a)=g(a^{2} -4)\\=\sqrt{a^{2}-4 } \neq |a|-2[/tex]
2.
[tex]f(a)=\frac{1}{2\cdot a-1}, g(a)=2\cdot a -2\\gof(a)=g(\frac{1}{2\cdot a-1} )\\=\frac{2}{2\cdot a-1}-2\\=\frac{4-2\cdot a}{2\cdot a-1}\neq|a|-2[/tex]
3.
[tex]f(a)=5+a^{2} , g(a)=\sqrt{a-5} -2\\gof(a)=g(5+a^{2} )\\=\sqrt{5+a^{2}-5 } -2\\=\sqrt{a^{2} } -2\\=|a|-2[/tex]
4.
[tex]f(a)=3-3\cdot a , g(a)=4\cdot a-5\\gof(a)=g(3-3\cdot a )\\=4(3-3\cdot a)-5\\=7-12\cdot a\neq|a|-2[/tex]
Hence, the Option 3 is correct
Sue can sew a precut dress in 3 hours. helen can sew the same dress in 2 hours. if they work together, how long will it take them to complete sewing that dress? round to one decimal place.
Final answer:
Sue and Helen can sew a dress in 1.2 hours when working together.
Explanation:
Calculating Time to Sew a Dress Together
Sue and Helen are working together to sew a dress and we need to calculate the total time it will take them to complete the sewing when working simultaneously. Sue can sew a precut dress in 3 hours, which means Sue's rate is 1 dress per 3 hours, or
1/3 dress per hour. Helen can sew the same dress in 2 hours, which means Helen's rate is 1 dress per 2 hours, or
1/2 dress per hour. Working together, their combined rate is the sum of their individual rates:
Total rate = 1/3 + 1/2
This results in a combined rate of 5/6 dresses per hour when we find a common denominator and add the fractions. To find the time it takes them to sew one dress together, we take the reciprocal of their combined rate:
Time = 1 / (5/6) hours
This simplifies to 6/5 hours.
Therefore, Sue and Helen will take 1.2 hours to complete the dress when working together.
Please help asap! Match the graph with the correct equation.
What is true about the solutions of a quadratic equation when the radicand in the quadratic formula is negative? No real solutions Two identical rational solutions Two different rational solutions Two irrational solutions
Answer:
If the radicand in the quadratic formula is negative then no real solutions possible.
Step-by-step explanation:
Given that when the radicand in the quadratic formula is negative then we have to find the true statement about the solution of quadratic equation.
Radicand of quadratic formula i.e the discriminant of quadratic formula.
[tex]D=b^2-4ac[/tex]
which comes in the solution under the root.
The solution of general quadratic equation is
[tex]x=\frac{-b\pm \sqrt D}{2a}[/tex]
As discriminant is negative then we can not find any real root for the given equation.
Hence, option 1 is correct.
No real solutions possible.