Answer:
[tex]\dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
Step-by-step explanation:
The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ the angle which the which the radius makes relative to the x=axis
The following equations are used to convert from cartesian coordinate to polar coordinates
[tex]r = \sqrt{x^2 + y^2}\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\[/tex]
Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives
[tex]2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = \dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
63 > 7y solve the inequality for y and simplify your answer as much as possible
Answer:
y < 9
Step-by-step explanation:
Hello!
We can solve the inequality for y by dividing both sides by 7.
Remember, when dividing or multiplying both sides of an inequality with a negative number, make sure to flip the sign. Since 7 is positive, we don't have to flip the sign.
Solve the Inequality63 > 7y63/7 = 7y/79 > ySo the inequality is true for all y values less than 9.
Hey there!
63 > 7y
7y < 63
DIVIDE 7 to BOTH SIDES
7y/7 < 63/7
SIMPLIFY IT
y < 63/7
y < 9
You have an open circle starting at 9 and going down to left side of the number line.
Therefore, your answer should beD
y < 9
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model. Unfortunately I can’t show the model because “it hurts their feelings”
Answer: The answer to the division problem is 21
Answer: I know 273 divided by 13 is 21 but without the model I don't know what else you need. sorry!
Step-by-step explanation:
-6+ (-3) how to find answer?
Answer:
-9
Step-by-step explanation:
−6 − 3
= −6 + −3
= -9
Answer:
-9!
Step-by-step explanation:
When you add negatives, it becomes more negative. Think of -6 getting 3 smaller.
How is a number squared?Select one:a. Multiplying a number by 4. b. Multiplying a number by itself. c. Dividing a number by 4. d. Dividing a number by itself.
A number is squared when it is multiplied by itself.
Hence, the correct option is Option B
HELP ME PLSS OMLLL IMA CRY
Answer:
Remember, ratios are just fractions, and fractions are just division problems.
Step-by-step explanation:
Step-by-step explanation:
25%of 20 is 5
subtract from the total of the whole candy.
WRITE AN EQUATION TO DESCRIBE THE RELATIONSHIP BETWEEN J AND Mj | 4 | 12 | 20m | 3 | 9 | 15
First, we can use the points (4,3) and (20,15) to find the slope of the line:
[tex]\begin{gathered} s=\frac{m_2─m_1}{j_2─j_1}=\frac{15─3}{20─4}=\frac{12}{16}=\frac{3}{4} \\ s=\frac{3}{4} \end{gathered}[/tex]Now we can find the relation function using the point (4,3) and the slope s=3/4
[tex]\begin{gathered} m─m_1=s(j─j_1) \\ \Rightarrow m─3=\frac{3}{4}(j─4)=\frac{3}{4}j─(\frac{12}{4})=\frac{3}{4}j─3 \\ m=\frac{3}{4}j \end{gathered}[/tex]therefore, the equation to describe the relationship between J and M is m=3/4j
Select the correct answer. A chart shows a stock price model graph labeled the price of the stock in dollars along the y-axis and time in a day along the x-axis. Based on the stock price model, what is the best prediction of what the price will do next? A. hold value B. keep increasing C. start decreasing D. no way to predict
Answer:B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Pls help solve all 3 questions
Thank you :)
Answer:
Q18: x = 21, y = 15
Q19: x = 16, y = 10
Q20: x = 24, y = 19
Step-by-step explanation:
Q18:
(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)
9x - 9 = 180
9x = 189
x = 21
11y - 32 = 6x + 7 (vertically opposite angles)
11y - 32 = 6(21) + 7
11y - 32 = 133
11y = 165
y = 15
Q19:
8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)
3x = 48
x = 16
(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)
8(16)-14 + (5y + 16) = 180
114 + 5y + 16 = 180
5y + 130 = 180
5y = 50
y = 10
Q20:
47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)
5x + 60 = 180
5x = 120
x = 24
5y - 23 = 3x (corresponding angles)
5y - 23 = 3(24)
5y - 23 = 72
5y = 95
y = 19
Write in words the meaning of P^2 - 7P.
Answer:
P squared minus 7 times P
Step-by-step explanation:
Factor completely... Please help me with this
Answer: (5x - 1)(x + 9)
Step-by-step explanation:
Please note the method of factoring may differ per class, but this is how I was taught.
First, we will multiply the coefficient of x² by the constant.
5 * -9 = -45
Next, we will find two numbers that add up to 44 (coefficient of x) and multiply to -45 (the number we got above).
-1 * 45 = 45
-1 + 45 = 44
-1 and 45 ✓
Now, we can start to factor. First, we will rewrite 44x.
5x² + 45x - 1x - 9
Then, we will factor by grouping.
5x(x + 9) -1(x + 9) ➜ (5x - 1)(x + 9)
The completely factored form is:
(5x - 1)(x + 9)
Is 5^x a polynomial?
yes, 5^x a polynomial. a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
What is Polynomial?a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
In the given expression 5^x x is a variable and 5 is a real number.
5^x is a finite polynomial or infinite polynomial. It depends upon the value of x. If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
Hence If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
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(b)The graph of y = g(x) is shown. Draw the graph of g(2x). Will award 100 Brainly points
The points of the graph is (0,0) (2,-4) and (4,-2)
Using the stated transformation, the graph of g(2x) is given at the end of the answer.
Horizontal stretch and compressionAn horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
If a > 1, it is a compression by a factor of 1/a.If a < 1, it is a stretch by a factor of 1/a.In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
(0,0).(1,-4).(2,-2).That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
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P(x) = -0.3x² + 75x - 2000, where x represents the selling price.
1. At what price should the stands be sold to earn the maximum profit?
2. According to the function given, what is the maximum profit that the company can make?
3. What are the break-even points (the selling prices for which the profit is 0)? Give the answer to the nearest cent.
Answer:
Below in bold.
Step-by-step explanation:
P(x) = -0.3x² + 75x - 2000
Convert this to vertex form:
p(x) = -0.3(x^2 - 250)^2 - 2000
= -0.3[(x - 125)^2 - 125^2] - 2000
= -0.3[(x - 125)^2 - 15625] - 2000
= -0.3(x - 125)^2 + 4687.5 - 2000
= -0.3(x - 125)^2 + 2687.5
2687.5 is the maximum value of the profit.
1. This corresponds to a selling price of $125 for the stands.
2. Maximum profit is $2687.5.
3. At the breaking points P(x) = 0:
-0.3(x - 125)^2 + 2687.5 = 0
(x - 125)^2 = 2687.5 / -0.3 = 8958.33
x - 125 = +/- sqrt( 8958.33)
x = 125 +/- sqrt( 8958.33)
x = 30.352, 219.648,
So, the breaking even points are $30.35 and $219.65 to nearest cent.
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 6 or 10 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your answer asa percent. If necessary, round your answer to the nearest tenth.O 1.2%O 13.9%O 77.8%O 22.2%
When rolling two dice the possible outcomes are:
Probability is calculated as follows:
[tex]\text{probability = }\frac{\text{ number of favorable outcomes}}{total\text{ number of outcomes}}[/tex]There is a total of 6x6 = 36 possible outcomes. From the table, we can see that 5 of them are a 6 and 3 of them are a 10. Then, the number of favorable outcomes is 5 + 3 = 8. Therefore, the probability of winning on your next turn is:
[tex]\begin{gathered} \text{probability = }\frac{8}{36} \\ \text{probability = }0.222 \\ \text{ Expressed as a percent, that is,} \\ \text{probability = }0.222\cdot100=22.2\text{ \%} \end{gathered}[/tex]Kennedy has $0.81 worth of pennies and nickels. she has 9 more nickels than pennies. write a system of equations that could be used to determine the number of pennies and the number of nickels that kennedy has. define the variables that you use to write the system.
Variable used to write the equation are x, Number of pennies and y, Number of nickels and the system of equations used is x+y=0.81 and x+9=y.
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Let the variables defined to form the system of equation are as follows:
x= Number of pennies
y= Number of nickels
Total worth of pennies and nickels is 0.81
mathematically, x+y=0.81
Given condition, she has 9 more nickels than pennies
mathematically, x+9=y
So, the system of equation which can be used to determine the number of pennies and the number of nickels that Kennedy has are x+y=0.81 and x+9=y, where variables used are x and y.
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a rectangle has a length that is twice the size of its width. if the perimeter of the rectangle is 48 inches, what is the area of the rectangle in square inches?
The area of the rectangle is, 128 square inches.
What is perimeter, area?
The area of a shape or figure is the area it occupies, whereas the perimeter of a shape is the distance it encircles on all sides.
The square unit or unit2 is used as the unit of area, and the unit is also used for the perimeter.
Given: A rectangle has a length that is twice the size of its width. The perimeter of the rectangle is 48 inches.
Suppose the width of the rectangle is x.
So, the length is 2x.
As perimeter is 48 inches.
So, x + x + 2x + 2x = 48
6x = 48
x = 8 inch.
The width of the rectangle is 8 inches.
Therefore, the length of the rectangle is 2x = 2(8) = 16 inches.
Now to find area of the rectangle,
Since,
Area of rectangle = length x width
= 16 x 8
Area of rectangle = 128 inch^2.
Therefore, the area of the rectangle is 128 square inches.
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What’s the answer plss
Answer: 18.1 cm, ( i think you can use a ruler)
Step-by-step explanation:
Cassie baked 24 cookies with 4 scoops of flour. How many scoops of flour does Cassie need in order to bake 42 cookies?
Answer:
7
Step-by-step explanation:
24 with four scoops is 6 with one scoop and 6 times 7 is 42 so 1 times 7 is 7 so the answer is 7 scoops
a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min; the well-mixed solution is pumped out at the same rate. find the number a(t) of grams of salt in the tank at time t.
The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).
Initially, the tank has A(0) = 50 g of salt.
The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min
And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,
As an outcome, the quantity of salt in the tank modifications as
A'(t) = (5 - A(t)) ÷ 40.
Solve ODE for A(t):
A'(t) + (A(t) ÷ 40) = 4
[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]
([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]
[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C
A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]
Given A(0) = 30, conclude that
30 = 160 + C
C = -130,
This denotes that the quantity of salt in the tank at period t equivalents
A(t) = 200 - 130 e(-t ÷ 40).
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A number was tripled, then decreased by 10, then doubled, and then increased by 2. The result was 5 times the original number.
If the original number was x, the equation will be
x=
Answer:
x = 18
The number is 18.
Step-by-step explanation:
Convert the words into an equation.
let x;
( 3x - 10 )( 2 ) + 2 = 5x;
6x - 20 + 2 = 5x;
6x - 18 = 5x;
Subtract both sides by 5x.
6x - 5x - 18 = 5x - 5x;
x - 18 = 0;
Add 18 to both sides.
x - 18 + 18 = 18;
x = 18;
1.39 to 1 decimal point
Answer: 1.4 or just 1
Step-by-step explanation:
But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)
Answer: 1.4
Step-by-step explanation:
I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4
Suppose that g(x) = f(x) + 2. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 2 units to the left.
B. The graph of g(x) is the graph of f(x) shifted 2 units up.
C. The graph of g(x) is the graph of f(x) shifted 2 units to the right.
D. The graph of g(x) is the graph of f(x) shifted 2 units down.
The graph of g(x) with the graph of f(x): Option D, which is a shift of 2 units to the left, is correct.
What is Function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
We are aware that the graph of the modified function is:
for every parent function f(x).
g(x) = f(x + a)
is a left- or right-shift of the parent function f(x), depending on the value of a.
The shift is 'a' units to the left if a>0.
The shift is 'a' units to the right if a0.
Here, G(x) has been changed as follows:
G(x) = F(x + 2)
i.e. a=2>0.
2 units up: G(x) = F(x) + 2.
2 units down: G(x) = F(x) - 2.
2 units to the left: G(x) = F(x + 2).
2 units to the right: G(x) = F(x - 2).
Hence, Option D, which is a shift of 2 units to the left, is correct.
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What’s 4/6 - 1/3 simplified
Answer:
1/3
Step-by-step explanation:
(4/6) - (1/3)
The denominators need to be the same, so let's convert the second term to (2/6), which is the same as (1/3)
(1/3)*(2/2) = (2/6)
Now we can wite:
(4/6) - (2/6)
This is equal to 2/6 or 1/3
Hello!
The equation [tex]\frac{4}{6} - \frac{1}{3}[/tex] simplified is [tex]\frac{1}{3}[/tex].
Step-by-step explanation:
Begin by giving both equations common denominators in this case we will use 18.
For the first set of fractions we multiply 4 by 3 to get 12 and for the second set of fractions we multiply 1 by 6 to get 6.
Our new set of fractions will look like this [tex]\frac{12}{18}[/tex][tex]- \frac{6}{18}[/tex]
Now we can subtract the numerators since our denominators match.
[tex]12-6=6[/tex] so the new answer will be [tex]\frac{6}{18}[/tex]
It's time to simplify both sets of fractions before we can completely solve the equation. (divide by 2, then 3)
[tex]\frac{6}{18}[/tex] ÷ [tex]2=\frac{3}{9}[/tex] ÷ [tex]3=\frac{1}{3}[/tex]
Since 3 is larger than 1 we are done reducing, time to solve for the final answer.
[tex]\frac{4}{6} -\frac{1}{3} =\frac{1}{3}[/tex]
Hope this helps!
twenty-five percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. (round your answers to three decimal places.) among 15 randomly selected cars, what is the probability that at most 5 fail the inspection?
The required probability is 0.852
Here, n=15
P(X ≤5) = P(X = 1)+...+ P(X = 5)
= [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]
= 0.01336+...+0.16515
= 0.85163
= 0.852 (Round to 3 decimal place)
Hence, the required probability is 0.852
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The width of a rectangle is 3 units less than the length. The area of the rectangle is 18
units. What is the length, in units, of the rectangle?
Answer:
First let the length be a variable (eg: x) so that we can form an expression and solve.
Let the length of the rectangle be x units.
Form an expression for the width of the rectangle using the information given.
Width = (x - 3) units
Area of rectangle = length x width
Using the formula, form an equation.
x(x - 3) = 18
Simplify and solve for x.
x² - 3x = 18
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
x - 6 = 0 or x + 3 = 0
x = 6 or x = - 3 (reject)
The length cannot have a negative value so reject - 3.
Hence, the length of the rectangle is 6 units.
A group of friends wants to go to the amusement park. They have no more than $760 to spend on parking and admission. Parking is $17.75, and tickets cost $33.50 per person, including tax. Which inequality can be used to determine x x, the maximum number of people who can go to the amusement park?
what is the first step that contains an error
7+8x=0
first step -Subtract 7 from both sides.
7+8x-7=0-7
Step 2
8x=-7
Step 3
Divide both side by 8
[tex]\frac{8x}{8}=\frac{-7}{8}[/tex]Instead of dividing the right hand side of equation in step 2 by 8, the right hand side is multiplied by 8 in step 3.
So, the error is in step 3.
Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model.
Using the model Carter will find parts A, B and C b to be
Part A = 26 tens
Part B = 13
Part C = 13 ones
What is a model?A model is a representation in form of shape used for to achieve a desired aim. Models are choose with respect to the importance
How to determine parts A. part B, and part C using the modelThe given model is a rectangle
Subtracting 13 from 273 to give 260. This can be arranged in tens by doing
= 260 / 10
= 26
Hence, A is 26 tens
Representing the C part in place value we have 13 ones
Since B = C, we have B = 13
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what do you divide by 15 to get to 9
Answer:
aproamitly 1.66666666667
Step-by-step explanation: 15/9=1.66666666667 thus
15/1.66666666667=9
Answer: it's 135 the other dude used a calculator probs
only fill in the missing ones pls
The input and output is follows,
4 4 * 20 + 40
17 18 * 20 + `70
t t+1 * 20 + (t * 10)
What is patterns in math?The arithmetic pattern is also known as the algebraic pattern.A numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule.Pattern rules can use one or more mathematical operations to describe the relationship between consecutive numbers in the pattern.How to Recognize Patterns :
Actively Look for PatternsOrganize the PiecesQuestion the DataVisualize the DataImagine New PossibilitiesTherefore,
From given question the first no is just next number of input that is input +1i.e.. input number is 2 then the first number of output is 2+1 = 3
Second number of output is constant 20.Third number of output is input value * 10i.e. . input number is 2 then the third number of output is 2 * 10 = 20
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