Where a is determined by the conditions x2 + y2 ≤ 1 and x + y ≥ 1?
Answers
Related Questions
Jayden has been reading a 275275275-page book for English class. On average, he has read about 101010 pages in 151515 minutes (\text{min})(min)left parenthesis, m, i, n, right parenthesis. With a deadline looming, Jayden realizes that he won't finish in time unless he skims through the rest of the book. If he skims the book, he can cover 151515 pages in 10\,\text{min}10min10, space, m, i, n. If it takes Jayden 555 hours and 50\,\text{min}50min50, space, m, i, n to finish the book (reading and skimming combined), how many pages did Jayden have to skim through?
Answers
r: reading
s: skimming
We write the system of equations that adapts to the problem:
r + s = 275
(15/10) r + (10/15) s = 355
We solve the system of equations:
r = 206
s = 69
Note: see attached image for system solution.
Answer:
Jayden had to skim 69 pages through
12km is equal to how many meters? (show all work)
Answers
12 kilometers is equal to 12,000 meters.
Container A can hold 9 cups of liquid. container B can hold 5 pints of liquid. Container c can hold 2 quarts of liquid. Whice container has the greatest capacity? Explain
Answers
1 cup = 0.5 pints
1 cup = 0.25 quarts
That means that 9 cups are equivalent to 4.5 pints and 2.25 quarts of liquid.
1 pint = 2 cups
1 pint = 0.5 quarts
That means that 5 pints are equivalent to 10 cups and 2.5 quarts of liquid.
1 quart = 4 cups
1 quart = 2 pints
That means that 2 quarts are equivalent to 8 cups and 4 pints of liquid.
FINAL ANSWER:
Judging by our calculations, Container B has the greatest capacity.
The circle is centered at the point (-3,4) and has a radius of length 3. What is its equation?
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Please help:
Solve using logarithms. Round the solution to the nearest hundredth. Show your work.
(you will need to use a calculator at some point)
Answers
So, the first thing we are going to do is take natural logarithm, [tex]ln[/tex], to both sides of our equation:
[tex]ln(5^{x+2} )=ln(9^{2x+3} )[/tex]
Now, by the power rule of logarithms:
[tex](x+2)ln(5)=(2x+3)ln(9)[/tex]
[tex] \frac{(x+2)ln(5)}{2x+3} =ln(9)[/tex]
[tex] \frac{x+2}{2x+3}= \frac{ln(9)}{ln(5)} [/tex]
[tex] \frac{x+2}{2x+3} =1.365[/tex]
[tex]x+2=1.365(2x+3)[/tex]
[tex]x+2=2.73x+4.095[/tex]
[tex]-1.73x=2.095[/tex]
[tex]x=- \frac{2.095}{1.73} [/tex]
[tex]x=-1.211[/tex]
Using our calculator we can conclude that [tex]x[/tex] is approximately -1.211
convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x
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f(x)=a^x
"a" is the base and "x" is the exponent.
2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:
y=ln x
e^y=e^(lnx)
e^y=x
3. Therefore, the answer is:
x=e^y
Answer:
To solve this problem, you need to remember that an exponential function has the following form:
f(x)=a^x
"a" is the base and "x" is the exponent.
2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:
y=ln x
e^y=e^(lnx)
e^y=x
3. Therefore, the answer is:
Step-by-step explanation:
This figure consists of a rectangle and semicircle.
What is the perimeter of this figure?
Use 3.14 for pi.
24.00 ft
30.28 ft
34.28 ft
36.56 ft
HELP ASAP WILL GET BRAINLIEST AND 10 POINTS!! IF CORRECT
Answers
Answer:
30.28
Step-by-step explanation:
just did the k12 test so i thought i would help out:)
Jenna has 8 pairs of jeans. Three of them are blue. What percentage of her jeans is blue?
= 37.5%
But my question is this:
Jenna bought two more pairs of jeans.
If both of them are blue, what percentage of her jeans is blue now?
If both of them are not blue, what percentage of her jeans is blue now?
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b) blue/total = (3)/(8 +2) = 3/10 = 30%
This week laptops are 25 percent off if a laptop cost $340 what is it's sale price
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A roadway repair crew has fixed 42 mi of the roadway. That number of miles is 30% of the total number of miles that need to be repaired
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Answer:
The answer is 140 miles 100x42 is 4200 divide that by 30= 140Step-by-step explanation:
Reciprocal of 1/10 = ?
Reciprocal of 16 = ?
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Use the chain rule to find ∂z/∂s and ∂z/∂t. z = x5y7, x = s cos(t), y = s sin(t)
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Using the Chain Rule of differentiation, we can solve for ∂z/∂s and ∂z/∂t given the functions for z, x, and y. The Chain Rule is fundamental for calculus by finding the derivative of composite functions.
Explanation:To solve for ∂z/∂s and ∂z/∂t with z = x5y7, x = s cos(t), and y = s sin(t), we'll employ the use of the Chain Rule of differentiation. First, we consider ∂z/∂s. As z is x raised to the power of 5 then multiplied by y to the power of 7, we can express ∂z/∂x and ∂z/∂y. Proceeding using the chain rule, which in simpler terms could be stated as 'the derivative of the outside times the derivative of the inside', we get the values of ∂z/∂s and ∂z/∂t. The chain rule in calculus is an important tool when differentiating composite functions.
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A band that will be the opening act for a concert charges a $500.00 flat fee as well as 10% of all profits from ticket sales. If the band earns $1,200, how much was made in total ticket sales for the show?
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Answer:
The answer is 7,000
Your welcome ;)
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
Answers
But first, we should solve for x
Opposite angles add up to 180 degrees.
So we'll use angles B and D
x + 10 + x + 24 = 180
combine like terms
2x + 34 = 180
subtract 34 from both sides
2x = 146
divide both sides by 2
x = 73
Now let's solve for the angles
Angle D: x + 24 = 97
Angle B: x + 10 = 83
Angle A: x + 15 = 88
Opposite angles add up to 180
we know that angle A is 88
C + 88 = 180
subtract 88 from both sides
C = 92
Hope this helps!
Answer:
92 is correct
Step-by-step explanation:
the second of two numbers is 4 more than the first the sum of the numbers is 56 find the numbers
Answers
Answer:
26, 30
Step-by-step explanation:
If you subtract from the sum the excess of the second over the first, you have a sum that is twice the first.
first number = (56 -4)/2 = 26
The second number is 4 more, so is ...
second number = 26 +4 = 30
_____
Check
Their total is 26 +30 = 56, as required.
What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
8
33
45
57
Answers
To find the range of this set, we must subtract the lowest number in the set from the highest number.
In this set, the highest number is 45 and the lowest number is 12. Subtract:
45 - 12 = 33
ANSWER:
The range of this set is B. 33.
You have an equally likely chance of choosing any number from 1 to 10. What is the probability that you choose a number greater than 6?
Answers
(1/10)+(1/10)+(1/10)+(1/10)=4/10=2/5
Answer is 2/5
Answer:
2/5
Step-by-step explanation:
1 to 10, it is 10 numbers
and there are 4 numbers which are 7,8,9,10 are bigger than 6
so P =4/10=2/5
Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thursday and Friday. How long did Leo paint this week
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Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thurday, and friday. Thus, the total time of the week for which he painted is 1.58% of the total time.
What is a fraction?A fraction represents a part of a whole number or, more commonly, any number of equal parts. A fraction can be defined as the parts of a certain size, for example, one-half, eight-fifths, three-quarters, etc.
The time for which Leo painted in this week can be calculated as:
Leo painted 2/3 of an hour each day for monday, tuesday, thursday, and friday
Therefore, the time of painting in an hour = 40 minutes
2/3 × 60 = 120/ 3 = 40 minutes = 40 × 4 = 160 minutes
The number of minutes in a day,
1 day = 60 × 24 = 1,440 minutes
The number of minutes in seven days,
7 days = 1440 × 7 = 10,080 minutes
Therefore, the total time for which Leo painted = time for which he painted in minute divided by total time in minutes
Total time for which Leo painted = 160/ 1440 = 0.0158 or 1.58%
Therefore, total time for which he painted in this week is 0.0158 of total time
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Find the longer diagonal of a parallelogram having sides of 10 and 15 and an angle measure of 120° between them. 13.2 18.0 21.8 23.1
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to get the length of the longest diagonal we use the cosine rule which states that----------> c²=a²+b²-2abCos(C)
where a,b and c are the sides and C is the angle.
therefore
a=15,b=10,C=120,c=?
to solve for the length C we shall substitute the values
c²=15²+10²-2*15*10*cos 120
c²=225+100-300*cos120
c²=325-(300*(-0.5))
c²=325-(-150)c²=475
c=√475
c=21.79-------------> c=21.8 units
since this is the opposite side to the largest angle, we therefore conclude that the longer diagonal of the parallelogram is 21.8 units
the answer is 21.8 units
Answer:
21.8
Step-by-step explanation:
solve the following system using substitution x+4y=21 4x-y=16
Answers
4x-y=16
Isolate one of the variables
x + 4y = 21
subtract 4y from both sides
x = -4y + 21
Plug that into the other equation
4x - y = 16
4(-4y + 21) - y = 16
-16y + 84 - y = 16
combine like terms
-17y + 84 = 16
subtract 84 from both sides
-17y = -68
divide both sides by -17
y = 4
Plug that into the equation
x+4y=21
x + 4(4) = 21
x + 16 = 21
subtract 16 from both sides
x = 5
Hope this helps!
A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10-6 seconds. How much time would the program take to complete 2.5 × 103 mathematical operations?
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x = 1.5 * 10^-6 * 2500
x = 0.00375 or 3.75 * 10^-3 second.
Good question.
You forgot A, B, C, and D but the correct answer is option D, 3.75 x 10 ^ -3 seconds
paul is in charge of the egg toss at the world egg day fair. there are 48 people participating in teams of 8 people. each team needs 1 egg. paul is buying eggs in cartons that each have 6 eggs. how many cartons does paul need?
Answers
Final answer:
Paul needs to buy 1 carton of eggs, as there are 6 teams needing 1 egg each, and one carton contains 6 eggs.
Explanation:
Paul needs to calculate how many cartons of eggs to buy for the egg toss at the world egg day fair.
With 48 people participating in teams of 8, we have a total of 48/8 = 6 teams, and each team needs 1 egg.
Since each carton contains 6 eggs, Paul needs to buy 6/6 = 1 carton to provide one egg for each team.
Please help me with question 22
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-----------------------------------------------------
Erase line A. For the pair of lines B and C, the marked angles are same side exterior angles. They are supplementary
(2x+18) + (6x+26) = 180
8x + 44 = 180
8x = 180-44
8x = 136
x = 136/8
x = 17
Since x = 17,
smaller angle = 2x+18
smaller angle = 2*17+18
smaller angle = 34+18
smaller angle = 52 degrees
2.7 Q9
The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function.
Answers
Answer: [tex](gof)(-1)=-2[/tex]
Step-by-step explanation:
By definition, a composite function is a function formed by substituing one function into another function.
Given the composite function:
[tex](gof)(-1)[/tex]
You can rewrite it in the following form:
[tex]g(f(-1))[/tex]
In order to evaluate it, follow these steps:
- Based on the table of the function f(x), the ouput value for [tex]x=-1[/tex] is [tex]y=3[/tex]. Then:
[tex]f(-1)=3[/tex]
- This will be the input of the function g(x).
- Notice in the table of the function g(x) that the output value when [tex]x=3[/tex] is [tex]y=-2[/tex]:
[tex]g(3)=-2[/tex]
Therefore:
[tex]g(f(-1))=-2[/tex] or [tex](gof)(-1)=-2[/tex]
Answer:
The value of [tex]\rm{gof(-1)}[/tex] is -2.
Step-by-step explanation:
Given,
The table contains the functional value of f(x) and g(x).
To find: [tex]\rm{gof(-1)}[/tex]
[tex]\rm{fog(-1)}[/tex] is a composite function of f(x) and g(x).
[tex]\rm{gof(-1)}=\rm{g[f(-1)}][/tex]
Clearly from the table, the value of f(x) when [tex]x=-1[/tex] is 3.
Therefore,
[tex]f(-1)=3[/tex]
Now,
[tex]\rm{gof(-1)}=\rm{g[f(-1)}]\\\rm{fof(-1)}=\rm{g(3)}[/tex]
Clearly from the table, the value of g(x) when [tex]x=3[/tex] is -2.
Thus,
[tex]\rm{gof(-1)}=-2[/tex]
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Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitude of the triangle Prove: a2 + b2 = c2 Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Answers
This is because since f + e = c,
then a² + b² = c(f + e)
a² + b² = c(c)
a² + b² = c²
This is the correct answer
Answer:
Because f+e=c
Therefore ,[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
Given A right triangle ABC as shown in figure where CD is an altitude of the triangle.
To prove that [tex]a^2+b^2=c^2[/tex]
Proofe: Given [tex]\triangle ABC\; and\; \triangle CBD[/tex] both are right triangle and both triangles have common angle B si same.
Therefore , two angles of two triangles are equal .
Hence, [tex]\triangle ABC \sim\triangle CBD[/tex] by using AA similarity.
Similarity property: when two triangles are similar then their corresponding angles are equal and their corresponding side are in equal proportion.[tex]\frac{a}{f} =\frac{c}{a}[/tex]Similarly , [tex]\triangle ABC \sim \triangle ACD[/tex] by AA similarity property . Because both triangles are right triangles therefore, one angle of both triangles is equal to 90 degree and both triangles have one common angle A is same .
[tex]\therefore[/tex] [tex]\frac{b}{c} =\frac{e}{b}[/tex]
The corresponding parts of two similar triangles are in equal proportion therefore , two proportion can be rewrite as
[tex]a^2=cf[/tex] (I equation)
and [tex]b^2=ce[/tex] (II equation)
Adding [tex]b^2[/tex] to both sides of firs equation
[tex]a^2+b^2=cf+b^2[/tex]
Because [tex]b^2=ce[/tex] and ce can be substituted into the right side of equation wevcan write as
[tex]a^2+b^2=ce+cf[/tex]
Applying the converse of distributive property we can write
[tex]a^2+b^2=c(f+e)[/tex]
Distributive property: a.(b+c)= a.c+a.b
[tex]a^2+b^2=c^2[/tex]
Because f+e=[tex]c^2[/tex]
Hence proved.
Which equation represents a nonlinear function?
x(y – 5) = 2
y – 2(x + 9) = 0
3y + 6(2 – x) = 5
2(y + x) = 0
Answers
_____________________________________________________
Consider:
_____________________________________________________
Choice: [A]: " x(y–5) = 2 " ;
Divide each side by "x" ;
" [x(y – 5)] / x = 2/x " ;
→ y – 5 = 2/x ;
Add "5" to each side of the equation:
y – 5 + 5 = 2/x + 5 ;
→ y = 2/x + 5 ; not a line; since one cannot divide by "zero" ; there would be no "point" on the graph at "x = 0". So, this answer choice: [A] is correct.
_______________________________________________________
Choice [B]:
y -2x -18 = 0
y - 2x = 18
y = 18 + 2x ; y = 2x + 18 ; is a line.
_________________________________________________
Choice C) 3y + 12 - 6x = 5 ;
3y = 5 - 12 + 6x ;
3y = -7 + 6x ; 3y = 6x - 7 ; y = 6x/3 - 7/3 ; y = 2x - 7/3 ; is a line.
_________________________________________________
Choice: [D]:
2(y+x) = 0 ;
[2*(y+x)] / 2 = 0/2 ; y + x = 0 ; y = -x ; is a line.
_________________________________________________
Answer:
The correct answer is: A: x(y – 5) = 2
Step-by-step explanation:
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Keisha's boat has a top speed of 9 miles per hour in still water. While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 20 miles downstream. Find the rate of the river current.
Answers
The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.
9 + c = 2(9 - c)
9 + c = 18 - 2c
3c = 9
c = 3
Answer: The speed of the current is 3 mph.
Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.
Find r(t) if r'(t) = 3t2i + 4t3j + t k and r(1) = i + j.
Answers
Final answer:
To find the position vector r(t) given its derivative and an initial condition, we integrate each component of the derivative and apply the initial condition to solve for constants of integration. The final position function is r(t) = t³i + t⁴j + (0.5t² - 0.5)k.
Explanation:
To find r(t) given that r'(t) = 3t²i + 4t³j + tk and r(1) = i + j, we integrate each component of r'(t) with respect to t. The integral of a derivative returns the original function plus a constant of integration, which we can solve using the initial condition provided.
For the i component: ∑ 3t² dt = t³+ C1
For the j component: ∑ 4t³ dt = t⁴ + C2
For the k component: ∑ t dt = 0.5t² + C3
Applying the initial condition r(1) = i + j, we substitute t = 1 into r(t) to solve for the constants of integration:
(1) + C1 = 1, so C1 = 0
(1) + C2 = 1, so C2 = 0
0.5(1) + C3 = 0, so C3 = -0.5
Therefore, the position function r(t) is given by t³i + t⁴j + (0.5t² - 0.5)k.
r(t) = t^3i + t^4j + ((1/2)t^2 - 1/2)k.
To find r(t) given r'(t) = 3t^2i + 4t^3j + tk and r(1) = i + j, we need to integrate r'(t) with respect to t.
Step 1: Integrate each component of r'(t) separately:
∫3t^2 dt = t^3 + C1 (integration with respect to t)
∫4t^3 dt = t^4 + C2 (integration with respect to t)
∫tk dt = (1/2)t^2k + C3 (integration with respect to t)
Step 2: Combine the results to get r(t):
r(t) = (t^3 + C1)i + (t^4 + C2)j + ((1/2)t^2k + C3)
Step 3: Use the given initial condition r(1) = i + j to find the values of the constants C1, C2, and C3:
r(1) = (1^3 + C1)i + (1^4 + C2)j + ((1/2)(1)^2k + C3)
i + j = i + j + (1/2)k + C3
Comparing the coefficients of k, we get:
(1/2) + C3 = 0
C3 = -1/2
Therefore, r(t) = (t^3 + C1)i + (t^4 + C2)j + ((1/2)t^2 - 1/2)k
The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they've scored the following points.
84, 67, 74, 87, 67, 73
What is the mean of their scores, rounded to the nearest tenth?
Answers
.. (84 +67 +74 +87 +67 +73)/6 = 452/6 ≈ 75.3
Answer:
(84 +67 +74 +87 +67 +73)/6 = 452/6 = 75.3
Step-by-step explanation:
Exactly what you see :]
what is the difference of the rational expressions below? 13x/5 - 4x/5
a. 9x/5
b. 17x/5
c. 52x/5
d. 52x/25
Answers
a. 9x/5
What you must do in this case is a sum of fractions.
Step 1:
Common factor 5 in the denominator
Step 2:
Perform subtraction of numerator
Step 3:
Rewrite the expression.
See attached image.
Answer:
a. 9x/5