Answer:
110
Step-by-step explanation:
13x - 20 + 7x = 180
20x -20 = 180
20x = 200
x = 10
13(10) - 20
=110
Find the area of the region inside the circle r=4cos(theta) and outside the circle r=2.
Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3
What is the polar curve?A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.
r = 1 − cosθsin3θ
Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.
The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.
The figure attached shows the bounded region of the two graphs. The red curve is r=4cos(θ) and the blue curve is r=2.
The points of intersection of the two curves are
θ = π/3 and 5π/3
The area is calculated as follows:
Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.
A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ
=[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ
= [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]
= 4π/3 + 2√3
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Please Help I Do Not Understand. 20+ Points!
If mPQY = 4x – 7 and mRQY = 2x + 25, solve for x. Show all your work. Please help me. I would appreciate it. Thanks. x s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
The value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
Given that, m∠PQY= 4x-7 and m∠RQY = 2x+25 are linear pairs of angles.
What are linear pairs of angles?Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Now, m∠PQY+m∠RQY=180°
⇒4x-7+2x+25=180°
⇒6x+18=180°
⇒6x=162
⇒x=27°
So, m∠=PQY=4x-7
=101°
and m∠RQY=2x+25
=79°
Therefore, the value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
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Answer:
27
Step-by-step explanation:
What is this called ,
, <--- That is called a comma
Write two ratio that are equivalent to 4:5
Answer:
8:10, 12:15
Step-by-step explanation:
Translate the sentence into an equation.
Four times the sum of a number and 3 is 2.
Use the variable w for the unknown number.
Joe works as a pianist in a local restaurant. He makes $8.50 an hour. He was able to work 45 hours last week. How much money did he make that week?
Answer: $382.50
Step-by-step explanation:
8.50 x 45 = 382.50
Find an equation of the line through (3,4) and parallel to y = 2x + 2: y =____. (Type your answer in slope-intercept form.)
Answer:
y = 2x - 2
Step-by-step explanation:
y = 2x + 2
4 = 2(3) + c
4 = 6 + c
c = -2
y = 2x - 2
The line is parallel so slope remains same but intercept changes.
A bookstore offered mystery bags each containing 12 books. The quantity of each type of book was the same in
each mystery bag. A shopper bought 3 mystery bags and found that 6 books were spy novels.
Based on this information, which prediction can the shopper make about buying mystery bags in the future?
A.There will be 4 more spy novels in 8 bags than in 6 bags
B.There will be 2 more spy novels in 6 bags than in 4 bags.
C.There will be 1 more spy novel in 9 bags than in 8 bags.
D.There will be 6 more spy novels in 10 bags than in 8 bags.
The prediction thay the shopper can make about buying mystery bags in the future is A.There will be 4 more spy novels in 8 bags than in 6 bags.
How to calculate the value?Since the shopper bought 3 mystery bags and found that 6 books were spy novels, it means that there are 6/3 = 2 spy novels in each bag.
There, the prediction thay the shopper can make about buying mystery bags in the future is that there will be 4 more spy novels in 8 bags than in 6 bags.
This is because there's an extra 2 bags which will be equal to 4 spy novels
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A power company calculates a person's monthly bill from the number of
kilowatt-hours (kwh), x, used.
the function b(x)
The bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
The given functions are
b(x) = 0.15x; x ≤ 360
b(x) = 0.10(x - 360) + 54; x > 360
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
For a person who uses 560 kWh, it means that:
x > 360
So, we use the following function to determine the bill
b(x) = 0.10(x - 360) + 54
Substitute 560 for x
b(560) = 0.10(560 - 360) + 54
⇒b(560) = 74
Hence, the bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
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Your question is incomplete, probably the complete question/missing part is:
A power company calculates a person's monthly bill from the number of kilowatt-hours ( Nh), x, used. The function b(x)= 0.15x, and x≤360. 0.10(x-360)+54, and x>360 determines the bill. How much is the bill for a person who uses 560 kWh in a month? A. $84 B. $54. $64 D. $74.
help!!! 50 points!!!!
Answer:
Less than and -97
Step-by-step explanation:
Answer: -17
Step-by-step explanation:
find the value by using the systematic of expressions then exponent it then factorize it by using prime numbers
Find the slope of the lines containing the following points
(-2, 1) & (-5,5)
The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].
As per the question statement, two points lie (-2, 1) & (-5,5) on a line.
We are supposed to find the slope of the line.
To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].
Using these values into above mentioned formula, we get,
Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].
Slope of a line: In mathematics, the slope or gradient of a line is a value that describes both, direction and the steepness of the line.To learn more about Slope of lines, click on the link below.
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424 divided by 3243.6
∠A and \angle B∠B are complementary angles. If m\angle A=(x-19)^{\circ}∠A=(x−19) ∘ and m\angle B=(3x+1)^{\circ}∠B=(3x+1) ∘ , then find the measure of \angle B∠B.
Answer:
∠ B = 82°
Step-by-step explanation:
complementary angles sum to 90° , then
∠ A + ∠ B = 90 , that is
x - 19 + 3x + 1 = 90
4x - 18 = 90 ( add 18 to both sides )
4x = 108 ( divide both sides by 4 )
x = 27
Then
∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°
Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbl
Which number sentence tells the story of how many marbles he had left ?
The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form
Total number of marbles Tran bought=25 marbles
Total number of marble Tran has before buying new marbles=10 marbles
Total number of marbles after buying new marbles=35 marbles
Given that he lost 6 marbles because of the hole in his pocket
Therefore, the Total number of marbles left=35-6
The total number of marbles left=29 marbles.
Therefore, The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
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You want to make 20 plates and have 30 bags of shredded cheese. How can you determine how much cheese to put on each plate so that each plate has the same amount of shredded cheese?
The amount of cheese in each plate = 1.5x
There are 30 bags of shredded cheese.
Let 'x' be the quantity of cheese in each bag. Then,
The total quantity of cheese in 30 bags = 30x
Number of plates = 20 plates
We need to determine the quantity of cheese put on each plate so that each plate has the same amount of shredded cheese.
For this we just need to divide the total amount of shredded cheese by the number of plates.
The equal amount of cheese in each of 20 plates = 30x/20
= 3x/2
= 1.5x
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The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?
The water level after the rainfall is 1.75 below average.
How to calculate the difference?From the information, the water level in Colorado river is 2.55 m below average. a large rainfall caused and the water level to rise 0.8 m.
The water level after the rainfall will be:
= -2.55 + 0.8
= -1.75
Therefore, the water level after the rainfall is 1.75 below average.
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Help i am so confused and I need this asap!!
Answer:
25 tickets were purchased ahead of time
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1)
25
× 11
------
275
2)
625
-275
--------
350
3)
350 ÷ 14 = 25
Check:
350 (dollars from purchased ahead of time)
+275 (dollars from purchased at the door)
--------
$ 625 (total ticket sales stated in the word problem)
which of the following expressions has a coefficient of 10 and a constact of 5
Answer:
2
Step-by-step explanation:
millimeters
Equal 15 centimeters 4 millimeters
154mm
we know that 1cm = 10 mm
therefore 15cm= 10*15 mm
= 150 mm
and 4 mm
we get total mm= 15cm +4mm
= 150mm+4mm
= 154 mm
mm stands for millimeters and cm stand for centimeters
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can someone answer this and fast please and thank youuu!
Answer:
Step-by-step explanation:
Which of the following is not a rational number?
A) The product of 14 and 0.833333...
B) The sum of 27 and 43
C) The product of 12 and 17−−√
D) The sum of 5+5√ and 14−5√
The product of 12 and √17 is not a rational number.
Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number.
In other words, p/q, where p and q are both integers and q ≠ 0, can be used to represent a rational number.Irrational numbers are real numbers that cannot be represented as simple fractions. An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.The product of ant two rational numbers is always a rational number , but product of a irrational number and a rational number is not a rational number.
Hence only the third option is correct.
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What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light i_0i 0 ?
The maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀ is given as -
When unpolarized light is polarized with 2 polarizers, this same intensity I = I₀cos2(Ф) (Malus' law) is obtained. When unpolarized light is polarized with just one polarizer, its intensity is reduced to half that of unpolarized light.What is polarization?Polarization is the property of wave oscillations having a definite direction relative to the wave's propagation direction. Transverse waves that can be polarized are EM waves. The polarization direction is defined as the direction parallel to the EM wave's electric field.
The effect of a polariser on polarised light is described by Malus' law, which states that-
One starts with unpolarized light.The first polariser suppresses the unaligned component of the unpolarised light and produces polarised light (at half the intensity of the input). In your notation, the intensity of this polarised output is I₀.The second polariser lets through a fraction (cos)²Ф of the polarised output from the first polariser, where is the angle between the polarisers' axes. So, once again,I₀ is the intensity of the polarised input to the second polariser, not the intensity of the unpolarised input to the two-polariser system. The output intensity is limited by this provision; I = I₀cos2(Ф)To know more about the polarization, here
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The correct question is -
What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀.
A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.
the five prime number are 19,29,29,37,41
mean =sum of observations / total number of observation
= 19+29+29+37+41 /5
= 155/5
=31
median = (n+1) / 2 th term n is number of term and n is odd
= (5+1) /2 th term
= 3 rd term
= 29
mode = the value that appears most in the data
= 29
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The ages of three friends are represented by three consecutive odd integers. If the youngest of
the three is represented by m, express the sum of the ages of the three friends.
Solving the Question
We're given:
m is the smallest age.This means that the consecutive odd integers will be m + 2 and m + 4.
If we add all their ages, it will look like this:
[tex]m+(m+2)+(m+4)\\= m+m+2+m+4\\= 3m+2+4\\= 3m+6[/tex]
Answer[tex]3m+6[/tex]
Which table represents an exponential function?
Answer: Where are the tables?
a car dealer claims that buying a new car sam will pay 20% less for gas than for the car he currently owns. the car sam currently drives cost 15% less to gas than dons car. don pays 800$ per year for gas car. assume all cars will be traveling the same distance. how much does he pay for his current car?
Help pls and pls give explanation!
Sam pays 680$ per year for his current car and will pay 544$ per year if he buys the new car as per dealer's claim.
According to the question statement, A car dealer claims that buying a new car Sam will have to pay 20% less for gas than for the car he currently owns. The car Sam currently drives costs 15% less to gas than Don's car. Don pays 800$ per year for gas car. It is assumed that all cars will be travelling the same distance.
We are supposed to find out how much will Sam pay for his current car.
To solve this question, we need to know about the concept of percentage of any number.
Don currently pays 800$ per year on gas.
Sam pays 15% less than what Don pays, Therefore the money Sam is paying currently will be 800$ minus 15% of 800$ i.e.,
= [tex]800 - \frac{15}{100} *800[/tex]
= [tex]800-120[/tex]
= [tex]680[/tex]$
680$ per year is the money Sam is spending currently.
If he buys the new car, according to the claim of dealer, he will pay 20% less than what he is paying currently i.e., 680$ - 20% of 680$
= [tex]680-\frac{20}{100} *680\\[/tex]
= [tex]680 - 136[/tex]
= [tex]544[/tex]$
Therefore, Sam pays 680$ per year on gas on his current car but if he buys the new car he will pay 544$ per year on gas.
Percentage: In math, a percentage is a number or ratio that can be expressed as a fraction of 100 i.e., if we are supposed to find 20% of 80 then [tex]\frac{20}{100} *80=16[/tex]If you wish to learn more about percentage, click the link given below:
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The problem is:
y = -2(x-3)^2
Please help me find the;
Vertex,
X-Intercepts,
and the Axis of Symmetry
Alg 2, Intercept, Vertex form.
The Vertex is at (3, 0)
The Axis of symmetry is; x = 3
The x-intercept is; x = 3
What is the Vertex and Axis of Symmetry?
We are given the quadratic equation as;
y = -2(x - 3)²
Expanding this gives us;
y = -2(x² - 6x + 9)
y = -2x² + 12x - 18
x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
y coordinate of vertex = f(3) = -2(3)² + 12(3) - 18 = 0
Vertex is at (3, 0)
Axis of symmetry is the x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
x-intercepts is gotten by finding the roots which are; x = 3 and 3
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PLEASE HELP ASAP!!!!!!!!!
Use PEMDAS to solve the following problem: 60* 10-8* (3* 2) What is left after completing the first step of PEMDAS
Answer:60*10-8*6
Step-by-step explanation: after you complete the first step which is perenthesis you are left with 60*10-8*6
The first step is the parenthesis. the left after completing the first step of PEMDAS is answer 552.
How to determine the first step?The equation is given as:
60* 10-8* (3* 2)
Using PEMDAS, the first step is to open the brackets by multiplication So, we have:
60* 10-8* (3* 2)
60* 10-8*6
Then multiply the rest and subtract.
600- 48 = 552
Hence, the first step is the parenthesis. the left after completing the first step of PEMDAS is answer 552.
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8 children have to share two thirds of a watermelon equally what part of the whole watermelon would each child get
Each child would get 1/12 th part of the whole watermelon.
For given question,
8 children have to share two thirds of a watermelon equally .
This means we need to equally distribute 2/3 of whole watermelon to 8 children.
To divide 2/3 part of of a watermelon equally into 8 parts, we need to divide 2/3 by 8.
(2/3) ÷ 8
= [tex]\frac{(\frac{2}{3} )}{8}[/tex]
We know that in 8 = 8/1
So, we rewrite the denominator of above fraction as,
[tex]\frac{(\frac{2}{3} )}{8} \\\\= \frac{(\frac{2}{3} )}{(\frac{8}{1} )} \\\\=\frac{2}{3} \times \frac{1}{8} \\\\=\frac{1}{12}[/tex]
This means, each child will get 1/12 part of the whole watermelon.
Therefore, each child would get 1/12 part of the whole watermelon.
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