Answers
A.= [tex]$\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)[/tex], B = [tex]$\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)[/tex],
C=[tex]$\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)[/tex], D = [tex]$\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)[/tex]
[tex]$\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)[/tex]
[tex]$\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)[/tex]
[tex]$\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)[/tex]
[tex]$\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)[/tex]
How to convert any given polar coordinates into standard polar coordinates.When [tex]r\geq 0[/tex] and [tex]0\leq \theta < 2\pi[/tex], we call the polar coordinates [tex](r,\theta)[/tex] standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and [tex]\theta[/tex] with [tex]\theta + \pi[/tex]. 2. Now if [tex]\theta < 0 \textrm{ or }\theta\geq 2\pi[/tex], we add a suitable multiple of [tex]2\pi \textrm{ to }\theta[/tex] to bring it inside [0,[tex]2\pi[/tex]) interval.
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Related Questions
Find the unit vector in the same direction as v = -5i - 9j
Answers
According to the given data the unit vector in the same direction as v is
u = (-5/ sqrt(106))i - (9/ sqrt(106))j.
What is meant by unit vector?A unit vector is a vector that has a length or magnitude of 1. In other words, a unit vector is a vector that has been normalized, or scaled down to have a length of 1 while still pointing in the same direction as the original vector.
According to the given information:To find the unit vector in the same direction as v = -5i - 9j, we first need to calculate its magnitude.
The magnitude of v is given by:
|v| = sqrt((-5)^2 + (-9)^2) = sqrt(25 + 81) = sqrt(106)
Now we can find the unit vector in the same direction as v by dividing v by its magnitude:
u = v / |v| = (-5i - 9j) / sqrt(106)
Therefore, the unit vector in the same direction as v is:
u = (-5/sqrt(106))i - (9/sqrt(106))j
Note that the unit vector has a magnitude of 1 and points in the same direction as v.
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Expand & simplify
(x + 3) (x+ 1)
Answers
evaluate by polynomial long division:
(6x^3-6x^2-24x+24)/(3x-3)
Answers
The quotient results from the division is 2x²-8.
We have,
(6x³ - 6x² -24x + 24) / (3x-3)
Performing the division as
3x-3 | 6x³ - 6x² -24x + 24 | 2x² - 8
6x³ - 6x²
_____________
0 -24x + 24
-24x + 24
____________
0
Thus, the quotient is 2x²-8.
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A random sample of 10 fields of corn has a mean yield of 37.1 bushels per acre and standard deviation of 5.91 bushels per acre. Determine the 98% confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
The critical value of that used in constructing the confidence interval is (42.512 , 31.688)
We have the following information from the question:
Sample mean, x(bar) = 37.1 bushels per acre
Sample size, n = 10
Alpha, α = 0.05
Sample standard deviation, s = 5.91 bushels per acre
Degree of freedom = n - 1 = 9
We have to determine the 98% confidence interval for the true mean yield.
We use the formula:
x(bar) ± [tex]t_c_r_i_t_i_c_a_l[/tex][tex]\frac{s}{\sqrt{n} }[/tex]
Plug all the values in above formula:
37.1 ± 2.896[tex](\frac{5.91}{\sqrt{10} } )[/tex]
37.1 ± 5.412 = (42.512 , 31.688)
Hence, The critical value of that used in constructing the confidence interval is (42.512 , 31.688).
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Find the quotient and remainder using long division for
x³ + 3x² + 6x + 10
x + 2
The quotient is
The remainder is
Answers
The quotient of the long division of the polynomial is x² + x + 4 and the remainder is 2.
What is the quotient and remainder?The quotient and remainder of the polynomial using long division is calculated as follows;
x² + x + 4
-------------------------
x + 2 √ x³ + 3x² + 6x + 10
- (x³ + 2x²)
-------------------------------
x² + 6x + 10
- ( x² + 2x)
--------------------------------------
4x + 10
- (4x + 8)
------------------------------------
2
Thus, the quotient of the long division of the polynomial is x² + x + 4 and the remainder of the long division of the polynomial is 2.
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solve using zero product property to solve for the roots
show your work please
Y = x^2 - 6x + 8
Answers
Answer: {2, 4}
Step-by-step explanation:
You need to find 2 numbers that multply to +8(last number) and add to -6(middle number)
-4 and -2 satisfy this rule
place in parentheses
(x-4)(x-2) set both = 0 and solve
x-4 = 0 x-2 = 0
x=4 x=2
The number of bats in a colony is growing exponentially. After 1 year, there were 130 bats. After 4 years, there were 1040 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 7 years? Do not include units in your answer.
Answers
Answer:
1,040 ÷ 130 = 8
After 7 years: 1,040 × 8 = 8,320
Find the area of the picture below
Answers
ERROR ANALYSIS Describe and correct the error in finding the circumference of OC. X 9 in. с C= 2 Tr = 2π(9) =18ain.
Please show work.
Answers
The correct calculation after correcting the error in finding the circumference is 9π
Describing and correct the error in finding the circumferenceGiven that we have a circle of diameter 9 inches
The circumference iis the product of the diameter and pi
So, the step in the question is incorrect because the diameter is taken as the radius
Having mentioned that, the correct solution is
C = π(9)
So, we have
C = 9π
So, the circumference is 9π
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A school principal surveys 175 students to determine which language they speak at home. She determines that 24% speak Spanish and 12% speak Haitian Creole. How many of the students surveyed speak Spanish or Haitian Creole at home?
A 21
B 42
C 63
D 84
Answers
The number of students surveyed speak Spanish or Haitian Creole at home are 42.
What is percentage?
Percentage is a part of a whole.
Let the number of students who speak Spanish be S and the number of students who speak Haitian Creole be H. We can set up the following equations based on the given information:
24% of 175 students speak Spanish
So, S = 0.24 x 175
And 12% of 175 students speak Haitian Creole
So, H = 0.12 x 175
We need to obtain the number of students who speak either Spanish or Haitian Creole,
So, S + H - (number of students who speak both languages).
percentage who speak both languages = 100% - (24% + 12%) = 64%
So, the number of students who speak both languages is 0.64 x 175 = 112
Now, we are obtaining the number of students who speak either Spanish or Haitian Creole:
S + H - (number of students who speak both languages) = (0.24 x 175) + (0.12 x 175) - 112
= 42
Therefore, the answer is B) 42, which represents the number of students who speak Spanish or Haitian Creole at home.
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Consider the following function.
[tex]k(x)=x^{2} +5x+6[/tex]
Step 3 of 3 : Find two points on the graph of the parabola other than the vertex and x-intercepts.
Answers
1. The cost of the three lightest packages is ($8.80 / $9.60 / $10.45 / $11.40)
2. The cost of the remaining packages is ($20.35 / $22.20 / $30.80 / $33.60)
Answers
The cost of the three lightest packages is $8.80.
The cost of the remaining packages is $33.60.
The total cost of all packages is $42.40.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
By critically observing the line plot that represents the weight of meat, we have the following weights:
Three lightest weights = 5/8 pounds + 5/8 pounds + 6/8 pounds
Cost of three lightest weights = (5/8 + 5/8 + 6/8) × $4.40
Cost of three lightest weights = $8.80.
Cost of remaining package = (1 + 1 1/8 + 1 1/8 + 1 1/8 + 1 2/8 + 1 3/8) × $4.80
Cost of remaining package = $33.60
Total cost of all packages = $8.80 + $33.60 = $42.40.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Hector is in the 32% tax bracket. He acquired 10,000 shares of stock in Eclipse Corporation three years ago at a cost of $100 per share. In the current year, Hector received a payment of $225,000 from Eclipse Corporation in exchange for 2,000 of his shares in Eclipse. Eclipse has E & P of $975,000. Hector has a capital loss carryover of $50,000 in the current tax year. Assume that Hector has no capital losses and taxpayers in the 32% tax bracket are subject to the long-term capital gains and qualified dividends tax rate of 15%.
The $225,000 payment from Eclipse Corporation is a qualifying stock redemption for tax purposes.
Hector may use $fill in the blank eb9ae1fb8010fec_1
25,000
of the capital loss carryover to offset the gain on the redemption. His income tax liability is $fill in the blank eb9ae1fb8010fec_2
64,000
.
Answers
the answers are:
Hector may use $25,000 of the capital loss carryover to offset the gain on the redemption.
His income tax liability is $64,000.
what is Hector's tax liability ?
To define means to provide a clear and precise explanation of what something means or refers to. It involves breaking down a concept or term into its key components and providing a thorough understanding of its meaning. A definition can be used to clarify or explain the meaning of a word, idea, or concept to ensure a common understanding between people.
To calculate Hector's tax liability, we need to first determine his gain on the redemption.
Hector received $225,000 in exchange for 2,000 shares, which means he received $112.50 per share (225,000/2,000). His cost basis in the 2,000 shares redeemed is $100 per share, so his gain on the redemption is $12,500 per share ($112.50 - $100 = $12.50).
Hector's total gain on the redemption is therefore $25,000 ($12,500 x 2,000 shares).
Since Hector has a capital loss carryover of $50,000, he can use up to $25,000 of it to offset his gain on the redemption. This will result in a tax liability of 15% on the remaining $25,000 gain, which is $3,750 ($25,000 x 0.15).
Hector's income tax liability will also include the tax on his other income, such as wages or interest income. Assuming he has no other deductions or credits, his total income tax liability will be $64,000.
Therefore, the answers are:
Hector may use $25,000 of the capital loss carryover to offset the gain on the redemption.
His income tax liability is $64,000.
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Andre wants to purchase some onions and tomatoes to make spaghetti for a friend’s birthday dinner. He looks at two different recipes. Recipe A calls for 4 times the number of tomatoes, x, plus 5 times the number of onions, y, which should produce 109 plates of spaghetti. Recipe B calls for 2 times the number of tomatoes used minus the number of onions, which should produce 23 plates of spaghetti.
Create a system of equations
Answers
Answer:
Recipe A: 4x + 5y = 109
Recipe B: 2x - y = 23
Step-by-step explanation:
Answer:
Step-by-step explanation:
Recipe A: 4x+5y=109
Recipe B: 2x-y=23
valuate −8 + 10 × 4 ÷ (−2). Question 25 options: −4 −28 −3 −20
Answers
Answer: its -28
Step-by-step explanation:
i dont know i used a app
Volume of square-base container =3 456 cm³ 2.3.1 Determine the length of the side of the square-base container. Formula: Volume = side2 x height
Answers
Answer:
mark me brilliant
Step-by-step explanation:
We can use the given formula to solve for the length of the side of the square-base container:
Volume = side^2 x height
where side is the length of the side of the square base, and height is the height of the container.
We are given that the volume of the container is 3,456 cm³. However, we do not know the height of the container.
To find the length of the side of the square base, we need to first determine the height of the container. We can do this by rearranging the formula:
height = Volume / (side^2)
Plugging in the values we know:
height = 3456 cm³ / (side^2)
We know that the container has a square base, so the length of each side of the base is the same. Therefore, we can write:
Volume = side^2 x side x height
Substituting the expression we found for height:
Volume = side^2 x side x (3456 cm³ / side^2)
Simplifying:
Volume = 3456 cm³ = side^3
Taking the cube root of both sides:
side = ∛3456 cm = 18 cm
Therefore, the length of the side of the square-base container is 18 cm.
Pls help me (its in the png below)
Answers
The number of pieces of mail that the United States Postal Service delivers in 6 days would be 2 ¹⁶ . 3 ⁴ . 5 ⁴ mail
How to find the number of mail ?The number of mail delivered in 6 days by the United States Postal Service would be:
= Number of mail delivered in a second x Number of seconds in 6 days
= (2⁸ . 5² ) x ( 2⁸.3⁴.5² )
The properties of exponents, which state that when multiplying two powers with the same base, we can add their exponents, allow us to simplify the expression:
= 2⁸ ⁺ ⁸ . 5 ² ⁺ ² x 3 ⁴
= 2 ¹⁶ . 3 ⁴ . 5 ⁴ mail
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Find the domain and range
Answers
The domain is all real numbers and the range is greater than zero. Then the correct option is A.
Given that:
Function, y = 1/2 · (2)ˣ
The domain means all the possible values of x and the range means all the possible values of y.
The function is an exponential function, then the domain of the function will be all real numbers.
The value of the exponential function is always positive. Then the range will be greater than zero.
The domain is all real numbers and the range is greater than zero. Then the correct option is A.
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
Answers
This gives us the third term of (3x-2y)6 as 18x5y.
What is Equation?An equation is a mathematical statement that states that two expressions are equal. It is written with an equals sign and can contain numbers, variables, operations, and other mathematical symbols. Equations are used to solve a wide variety of problems in mathematics, science, and engineering.
The third term of the expression (3x-2y)6 can be found by applying the power rule of algebra. The power rule states that when a variable is raised to a power, that power is distributed to the terms of the expression. Therefore, the third term of (3x-2y)6 can be found by distributing the power 6 to the two terms, 3x and -2y. This gives us the third term of (3x-2y)6 as 18x5y.
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The required equation that represents the relation between two types of wood is 45(x + 3) = 60x
What are equations?An equation is a mathematical statement that contains an equal sign (=) and represents the equality between two expressions.
It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Equations can be solved to determine the value(s) of the variable(s) that make the statement true.
Here we have
A contractor got 45 expensive wood and 60 cheap wood for the same total price. The 45 expensive wood cost $3.00 more than the 60 cheap wood
x = price of the 60 cheap wood
If 'x' is the price of cheap wood then cost of 60 cheap woods = 60x
The 45 expensive wood cost $3.00 more than the 60 cheap wood
Cost of 45 expensive woods = (x + 3)45 = 45(x + 3)
Here both costs are equal
=> 45(x + 3) = 60x
Therefore,
The required equation that represents the relation between two types of wood is 45(x + 3) = 60x
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A patient is given 800mg of ibuprofen. The average half-life of ibuprofen is about 1.8 hr. Write an exponential model of the form P(t)=P0e^kt that represents the amount of ibuprofen in the patients bloodstream in t hours after the medicine is administered. Round the value of k to five decimals. Then use the model to determine how much ibuprofen will be in the patients bloodstream after he is given a second dose of 800 mg in 4 hr after the first dose. Round your answer to two decimals places
Answers
An exponential model of the form that represents the amount of ibuprofen in the patients bloodstream in t hours after the medicine is administered is [tex]P(t) = 800e^{\frac{t}{1.8} }[/tex].
The amount of ibuprofen that would be in the patients bloodstream after he is given a second dose of 800 mg in 4 hr after the first dose is 7382.25 mg.
How to determine the correct statement about the future value?In Mathematics, the future value of a physical substance based on its half-life can be determined or calculated by using this exponential function:
[tex]P(t) = P_{0}e^{\frac{t}{T} }[/tex]
Where:
A(t) represents the future value.P₀ represents the initial value.T represents the half-life.t represents the time measured in years.Based on the information provided above, the required exponential function is given by;
[tex]P(t) = 800e^{\frac{t}{1.8} }[/tex]
After 4 hours, we have;
[tex]P(4) = 800e^{\frac{4}{1.8} }\\\\P(4) = 800e^{2.2222}[/tex]
P(4) = 7382.25 mg
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If these cylinders and prisms were broken into two separate groups, what would be an equivalent ratio to 8/2? i dont have much longer and btw it doesn't have a picture.
100 points?
Answers
The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.
We have,
Cylinder and prism.
Here we have to find the equivalent ratio to 8/2.
First simplifying the given ratio as
8/2
= (4 x 2)/2
= 4 /1
Now, some more ratios equivalent to 8/2.
1. 8/2 x 3/3 = 24/ 6
2. 8/2 x 4/4 = 32/8
3. 8/2 x 6/6= 48/12
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A plane is ascending at an angle of 11° from the horizontal. The plane's current altitude is 5.1 km. See the figure below. (The figure is not drawn to scale.) Find
the plane's new altitude, h, after 0.05 hours if it travels at a constant speed of 500 km/hr along the direction of its flight. Carry your Intermediate computations
to at least four decimal places, and round your answer to the nearest tenth of a kilometer.
5.1 km
h = kilometers
Plane after 0.05 hours -
11°
X
5
h km
Ground
Answers
The plane's new altitude after 0.05 hours is approximately 9.9 kilometers.
How to solvewe'll use the sine function to find the vertical distance of the plane
sin(angle) = vertical_distance / total_distance
vertical_distance = sin(angle) × total_distance
To find the sine of 11°, we need to convert the angle to radians. We know that 180° = π radians:
11° × (π radians / 180°) ≈ 0.191986 radians
Now, we can find the vertical distance:
vertical_distance = sin(0.191986) × 25 km
vertical_distance ≈ 0.190809 × 25 km
vertical_distance ≈ 4.77022 km
Finally, we'll add this vertical distance to the initial altitude to find the new altitude:
h = initial_altitude + vertical_distance
h = 5.1 km + 4.77022 km
h ≈ 9.87022 km
Rounding to the nearest tenth of a kilometer:
h ≈ 9.9 km
So, the plane's new altitude after 0.05 hours is approximately 9.9 kilometers.
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what is the inverse of f if f(x)= 3sqrt(x-4)
Answers
Use a calculator to approximate √13. Round your answer to 4 decimal places.
Answers
Answer:
3.6056
Step-by-step explanation:
Christina’s savings account grows at a rate of 2% compounded quarterly. If her initial deposit is $750, write a function A(t)
that models the balance of the savings account after t years.
Answers
Answer:
Step-by-step explanation:
A = P * (1 + r/n)^(n*t
The function that gives the amount of money in dollars, J(t), in Jamie's account t years after the initial deposit is A = 750(1.0002)^4t. (in dollars)
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
For this case, we're given that:
Initial amount Christina deposits = P = $750
Rate of interest = 2% compounding quarterly
Time = t years
Rate of interest is compounding quarterly.
Each year has 4 quarters.
Quarterly interest rate compounding quarterly = 2%.
t years has 4t quarters = T
Thus, we get the final amount in Christina’s account as
A = P * (1 + r/n)^(n*t)
A = 750(1 + 0.02/100)^4t
A = 750(1.0002)^4t
Thus, the function that gives the amount of money in dollars, J(t), in Christina’s account t years after the initial deposit is A = 750(1.0002)^4t (in dollars)
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Evaluate the expression when b = -2 and c = 4. b - 5c
Answers
Answer:
-22
Step-by-step explanation:
The expression is b - 5c.
when b = -2 and c = 4,
we get:
(−2)−5(4)
＝−2−20
＝−22
Answer:
-22
Step-by-step explanation:
b - 5c b = -2 and c = 4
-2 - 5(4) = -2 - 20 = - 22
So, the answer is -22
what is the difference between -15-9?
Answers
Answer:
Step-by-step explanation:
-15-9 = -24
I would think about it as adding 15 and 9, but just make the answer negative.
Which ordered pair represents the point labeled C?
The x axis starts at negative 3, with tick marks every one unit up to positive 3. The y-axis starts at negative 3, with tick marks every one unit up to three. Point A is left two units and up one unit from the origin. Point B is right two units and up one unit from the origin. Point C is down two units from the origin. Point D is left one unit and down one unit from the origin.
(−2, 1)
(−1, −1)
(0, −2)
(2, 2)
Answers
The ordered pair that represents the point labeled C is (0, -2). Option (C) is the correct answer.
We can start by considering the given information about the coordinate axes. The x-axis starts at negative 3 with tick marks every one unit up to positive 3, and the y-axis starts at negative 3 with tick marks every one unit up to 3. The origin is the point where the x-axis and y-axis intersect, and it has coordinates (0, 0).
Next, we are given information about four points labeled A, B, C, and D. Points A and B are both one unit up and two units to the left or right of the origin, respectively. Point D is one unit to the left and one unit down from the origin.
Finally, we are asked to determine the coordinates of point C. We know that point C is labeled as being two units down from the origin, which means that it has a y-coordinate of -2.
To determine the x-coordinate of point C, we can observe that it lies on the y-axis, which means that it has an x-coordinate of 0 (since the y-axis intersects the x-axis at x = 0). Therefore, the ordered pair that represents point C is (0, -2), which matches option (C).
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solve 732.178+167-542.137
Answers
Answer:
357.041 is the answer first add then subtract
can someone help me on number 2
Answers
Answer:i think for p its 16 and for A is 64
i just did 8 X 8 = 64 for A and for p i did 8 + 8 = 16
Step-by-step explanation:
