Answers
Case 1: The linear equations has infinite solutions.
Case 2: The linear equations has no solution.
How to find the solution of a system of linear equations graphically
In this problem we find two cases of systems of two linear equations with two variables, which are described by a system of the form:
a · x + b · y = c
d · x + e · y = f
Where:
a, b, d, e - Dependent variable.c, f - Independent variable.The solution of this kind of systems can be found graphically on Cartesian plane, whose procedure is described briefly:
Determine x-intercept on each line.Determine y-intercept on each line.Mark the intercepts on Cartesian plane.Construct the resulting lines. Mark the point of intersection of the two lines.Now we proceed to find the solution for each case:
Case 1
Line 1: y = 0.5 · x + 1
y-Intercept
y = 0.5 · 0 + 1
y = 1
(x, y) = (0, 1)
x-Intercept
0 = 0.5 · x + 1
0.5 · x = - 1
x = - 2
(x, y) = (- 2, 0)
Line 2: - 2 · x + 4 · y = 4
y-Intercept
- 2 · 0 + 4 · y = 4
4 · y = 4
y = 1
(x, y) = (0, 1)
x-Intercept
- 2 · x + 4 · 0 = 4
- 2 · x = 4
x = - 2
(x, y) = (- 2, 0)
Since the two lines have the same intercepts, then there are infinite solutions.
Case 2
Line 1: y = - x - 3
y-Intercept
y = - 0 - 3
y = - 3
(x, y) = (0, - 3)
x-Intercept
0 = - x - 3
x = - 3
(x, y) = (- 3, 0)
Line 2: y + x = 2
y-Intercept
y + 0 = 2
y = 2
(x, y) = (0, 2)
x-Intercept
0 + x = 2
x = 2
(x, y) = (2, 0)
The system of linear equations has no solution as both lines are parallel.
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Related Questions
Find the number of 4 digit numbers that contain at least 3 even digits
Answers
Answer:
2625 different numbers
Step-by-step explanation:
General outlineCombinatoricsSpecial circumstancesPartitioning the situationConclusionPart 1. CombinatoricsThis type of problem is classified as a "Combinatorics" problem: Counting up the number of ways something can happen.
Many times when attempting to count a large number of items, patterns are recognized and shortcuts to count are developed so that one doesn't need to physically count all of the items. Perhaps the trickiest part of counting with these shortcuts is to ensure that one does not over-count (counting a scenario more than once), although it is equally important that we don't under-count (fail to count a situation that applies).
Part 2. Special circumstancesIt should be noted that for a number to be a 4 digit number, it must have 4 digits, and thus the first digit must not be zero (despite that that would be an even digit, the number itself would not be a 4 digit number).
Part 3. Partitioning the situationThere are 2 main scenarios:
1. All 4 digits are even
2. Exactly 3 digits are even (meaning that exactly one digit is odd).
There are two sub-cases to Scenario 2:
2.1. The first digit is odd, and all three of the other digits are even.
2.2. The first digit is even, and exactly two of the other digits are even (meaning that exactly one of the last three digits is odd).
None of scenarios 1, 2.1, and 2.2 overlap, so we're not over-counting:
If all 4 digits are even, then there can't be exactly 3 even digits. If the first digit is odd, then not all 4 digits are even nor is the first digit even. If exactly two of the last three digits are even, then not all 4 digits are even, nor are all three of the last digits even.Further, this is all of the possibilities for a 4 digit number with least three even digits, so we're not under-counting.
Scenario 1 -- All 4 digits are even.
If all 4 digits are even, then the first digit has fours choices (2,4,6,8), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.1 -- The first digit is odd, and all three of the other digits are even
If the first digit is odd, there are 5 choices for the first digit (1,3,5,7,9), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]5*5*5*5=625\text{ choices}[/tex]
Scenario 2.2 -- The first digit is even, and exactly two of the other digits are even
If the first digit is even, there are 4 choices for the first digit (2,4,6,8), and if exactly two of the next 3 digits are even, then there are 5 choices for each of the two even digits (2,4,6,8,0), and 5 choices for the odd digit (1,3,5,7,9), and there are "3 permuted by 2" ways of ordering those three digits.
[tex]4* \left [(5*5*5) * {}_3 \! P_2 \right ]=\\\\=4*\left [5*5*5 * \dfrac{3!}{2!} \right ]\\\\=4*\left [ 5*5*5 * \dfrac{3*2*1}{2*1} \right ] \\\\=4*\left [5*5*5 * 3 \right ] \\\\=1500\text{ choices}[/tex]
Scenario 2.2 broken down (calculated without using the permutation operation) -- The first digit is even, and exactly two of the other digits are even
Then either the second digit is odd (scenario 2.2.1), the third digit is odd (scenario 2.2.2), or the fourth digit is odd (scenario 2.2.3).
Scenario 2.2.1. The second digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second digit is odd: 5 choices for the odd digit (1,3,5,7,9)
The third and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.2. The third digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
The third digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.3. The last digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and third digits are even: 5 choices for each even digit (2,4,6,8,0).
The last digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenarios 2.2.1, 2.2.2, and 2.2.3 comprise all of Scenario 2.2, so [tex]500+500+500=1500\text{ choices}[/tex]
Part 4. ConclusionHow many ways can a 4 digit number be formed where at least 4 of the digits are even?
This is the sum of the choices from Scenario 1, Scenario 2.1, and Scenario 2.2, so [tex]500+625+1500=2625\text{ choices}[/tex].
find the value for the following
Answers
[tex]\sqrt{3-2\sqrt{2} }[/tex] = 0.06
(2x)ˣ = 25√5
How to solve an expression?[tex]\sqrt{3-2\sqrt{2} }[/tex] = [tex]\sqrt{3}-\sqrt{2\sqrt{2} }[/tex] = 1.73205080757 - 1.67428223427 = 0.06
4ˣ . 4ˣ⁻¹ = 24
4ˣ . 4ˣ / 4 = 24
4ˣ(1 - 1 / 4) = 24
4ˣ(3 / 4) = 24
multiply both sides by 4 / 3
4ˣ = 32
2²ˣ = 2⁵
2x = 5
x = 5 / 2 = 2.5
Therefore,
(2x)ˣ = 25√5
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The population of a bacteria culture are tripling. after 6 days, the population has quadrupled. what is the tripling time? find the answer to the nearest thousandth. b) how long did it take for the population to double in size?
Answers
The tripling time of population is 6 days and the population will be doubled in 3.5 days.
Given that the population of a bacteria is tripling in 6 days.
We have to find the tripling time of population and the time when the population will be doubled.
Suppose the population of bacteria in beginning be x.
The population of bacteria seems like arithmetic progression in which a =x, nth term =3x and n=6.
Aritmetic progression is a sequence which is having common difference.
nth term=a+(n-1)d
3x=x+(6-1)*d
3x-x=5d
2x=5d
d=2x/5
d=0.4x
So now we have to find the value of n where population will be 2x.
nth term=a+(n-1)d
put nth term=2x, a=x,d=0.4x
2x=x+(n-1)*0.4x
2x-x=(n-1)*0.4x
x/0.4x=n-1
2.5=n-1
n=2.5+1
n=3.5
Hence the population of bacteria willbe doubled after 3.5 days.
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What is the simplified form of startroot startfraction 2,160 x superscript 8 baseline over 60 x squared endfraction endroot? assume x ≠ 0.
Answers
The simplified form is [tex]6x^{3}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The equation is -
[tex]\sqrt{\frac{2160x^{3} }{60x^{2} } }[/tex]
We can rewrite this using property of multiplication to obtain
[tex]\sqrt{\frac{2160}{60} * \frac{x^{8} }{x^{2} } }[/tex]
We simplify variable expression in the radicand using
[tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
[tex]\sqrt{36 * x^{8 - 2} }[/tex]
[tex]\sqrt{36 * x^{6} }[/tex]
[tex]\sqrt{36 * (x^{3})^{2} }[/tex]
[tex]\sqrt{36} * \sqrt{(x^{3})^{2} }[/tex]
[tex]6 * x^{3}[/tex]
Therefore, the simplified form is [tex]6x^{3}[/tex]
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Let a and b be positive integers such that the product of all positive divisors of a equals the product of all positive divisors of b. Prove that a
Answers
The property A*B = (A' + A") * ( B'+B") is equal to each other.
According to the statement
We have given that the a and b is the positive integers and we have to prove that the product of all positive divisors of a equals the product of all positive divisors of b.
And in this statement
Now we use Distributive property
Here A and B is the positive integer and
A' and A" are the divisors of A and B' and B" are the divisors of B.
Now,
A = A' + A" and B = B'+B"
Now, Multiply both with each other then
A*B = (A' + A") * ( B'+B")
then
A*B = (A' B'+ A'B") + ( A"B'+A'B")
by this way it is equal to each other
Hence proved.
So, The property A*B = (A' + A") * ( B'+B") is equal to each other.
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You use generally accepted facts (such as: there are approximately 6 billion people on the planet. ) without citing them is it plagiarism?
Answers
No, this not plagiarism .You can use generally accepted facts without citing them.
What defines self-plagiarism?
Self-plagiarism is defined as a type of plagiarism in which the writer republishes a work in its entirety or reuses portions of a previously written text while authoring a new work.
What is considered general knowledge in plagiarism?
Common knowledge is typically defined as facts that are unsupported by at least five reliable sources. In the discipline of composition studies, for instance, the statement "Writing is difficult" is taken for granted because at least five reliable sources may support it.How to Avoid plagiarism common knowledge?
Quoting correctly, paraphrasing and summarizing correctly, and documenting (citing) correctly are the keys to providing credit and avoiding plagiarism; you can go to page 3 of this handout for more information. Almost all of the information you discover in outside sources needs to be documented.Learn more about plagiarism
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Drag each tile to the correct box.
Graph the functions as transformations of f(x) = x^(2).
Arrange the parabolas with respect to the position of their vertices from left to right.
Answers
Answer:
Step-by-step explanation:
fit the model, part a, to the data using simple linear regression. give the least squares prediction equation
Answers
Answer:
fitting a simple linear regression first select the cell in data set second on the analyse it ribbon tap in statistical analysis group click fit model and then click the simple degradation model 3rd the wild drop down list select the response variable 4th in the X drop down let's select the predicated
Complete the following conversions. i) 1 m2 = a cm2 ii) 1 cm2 = b mm2 iii) 1 km2 = c m2
Answers
The values that complete the conversions are
a = 10000
b = 100
c = 1000000
Conversion of unitsFrom the question, we are to complete the given conversions
i)
1 m² = a cm²
NOTE: 1 m² = 10000 cm²
∴ a = 10000
ii)
1 cm² = b mm²
NOTE: 1 cm² = 100 mm²
∴ b = 100
iii)
1 km² = c m²
NOTE: 1 km² = 1000000 m²
∴ c = 1000000
Hence, the values that complete the conversions are
a = 10000
b = 100
c = 1000000
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Larry has 6 shirts and 4 pairs of jeans. How many different combinations of one shirt and one pair of jeans can Larry make
Answers
Answer:
24 combinations
Step-by-step explanation:
To get to this answer, I multiplied 6 x 4, since there are 6 shirts and 4 pairs of jeans, there will be a total of 24 combinations. For combinations of two different things, you can just multiply the amount of each item by the other item. hope this helps :)
Write the algebraic expression for the difference between the squares of two numbers.
Answers
The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is
a² - b² = (a + b)(a - b).
An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).
The terms are combinations of numerals and variables.
Variables are represented alphanumerically, which can hold any value as per the expression they are used in.
In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.
We assume the two numbers to be a and b respectively.
Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².
We know that a² - b² is an identity, which can be shown as (a + b)(a - b).
Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).
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Select the correct answer.
A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.
What is the volume of the container, to the nearest cubic centimeter?
A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³
Answers
The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
Calculating VolumeFrom the question, we are to determine the volume of the container
Volume of the container = Volume of the cone - Volume of the small cone
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
For the small cone,
Diameter = 10 cm
∴ Radius, r = 10cm/ 2 = 5 cm
h = 6 cm
For the big cone
diameter = diameter of the container = 30 cm
∴ Radius = 30cm/ 2
Radius = 15cm
h = height of small cone + height of container
h = 6 cm + 20 cm
h = 26 cm
Putting the parameters into
Volume of the container = Volume of the cone - Volume of the small cone
We get,
Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6
Volume of the container = 1/3π (15² ×26 - 5² × 6)
Volume of the container = 1/3π (5850 - 150)
Volume of the container = 1/3π (5700)
Volume of the container = 1/3 × π × 5700
Volume of the container = 5969.026 cm³
Volume of the container ≈ 5969 cm³
Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
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please help me it is easy
I just dont understand
Answers
Answer:
13%
15%
41%
31%
Step-by-step explanation:
To find the percentage one amount is out of another amount, divide the smaller amount by the bigger amount. You will end up with a decimal (0.xy where x is the 10% place and y is the 1% place).
For example: to find the percentage that 39 is out of 300 students, we divide 39 by 300. This gives us the decimal 0.13. Written as a percentage, that is 13%.
We can do this for all of them.
Here is the math for each one:
39 ÷ 300 = 0.13 → 13%
45 ÷ 300 = 0.15 → 15%
123 ÷ 300 = 0.41 → 41%
93 ÷ 300 = 0.31 → 31%
Once you have all these decimals, you might choose to check your work by adding them up. They should at up to 1.00, or 100%. In this case, they do, so we know these answers are correct.
I hope this helps. Please let me know if you have questions.
calculate 20% of rs 250000
Answers
Answer:
50,000
Step-by-step explanation:
20% can be rewritten as 0.2 times 250000: 0.2*250000 = 50,000
Expand the expression / brackets: 2y (3y + 9)=
Answers
Answer:
6y^2 + 18y
Step-by-step explanation:
2y (3y + 9)=
6y^2 + 18y
[2y (3y becomes 6y^2]
[2x( + 9) becomes 18y]
Add them to obtain 6y^2 + 18y
[tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex]
Answers
The solution to the expression [tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex] is [tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]
How to solve the expression?The expression is given as:
[tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex]
Take the LCM of the expression
[tex]\frac{8x^3 * 27x^3 - 4x * 27x^3 + 2 * 9x^2 - 1}{27x^3}[/tex]
Evaluate the products
[tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]
Hence, the solution to the expression [tex]8x^3-4x+\frac{2}{3x}-\frac{1}{27x^3}[/tex] is [tex]\frac{216x^6 - 108x^4 + 18x^2 - 1}{27x^3}[/tex]
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HELPPPPPPPPPPPPP99 n
Answers
Answer:
555 meters
Step-by-step explanation:
toymaker = height/shadow
= 0.9/0.2
CN tower = height/shadow
= x/123.3
solve for x:
;[tex]\frac{0.9}{0.2} = \frac{x}{123.3} \\\\0.2(x) = (0.9)(123.3)\\0.2x = 110.97\\(\frac{10}{2} )\frac{2}{10}x = 110.97(\frac{10}{2})\\ x = 554.85[/tex]
They are all in meters, so we don't need to convert anything so rounded to the nearest meter, the answer is 555 meters
Answer: 555 m
Step-by-step explanation:
We will set up a proportion to solve.
[tex]\displaystyle \frac{\text{vertical side}}{\text{horizontal side}} \;\;\;\;\;\;\;\frac{0.9\;m}{0.2\;m} =\frac{x\;m}{123.3 \;m}[/tex]
Now we will cross multiply.
0.9 * 123.3 = 0.2 * x
110.97 = 0.2x
554.85 = x
x = 554.85
Lastly, we will round the nearest m.
554.85 ➜ 555 m
Transform the given equation into a system of first order equations. (Let x1 = u, x2 = u', x3 = u'', and x4 = u'''. Enter your answers in terms of x1, x2, x3, and x4.) u(4) − u = 0
a) x1' =
b) x2' =
c) x3' =
d) x4' =
Answers
Given the 4th order linear ODE
[tex]u^{(4)} - u = 0[/tex]
we substitute
[tex]x_1 = u[/tex]
[tex]x_2 = {x_1}' = u'[/tex]
[tex]x_3 = {x_2}' = {x_1}'' = u''[/tex]
[tex]x_4 = {x_3}' = {x_2}'' = {x_1}''' = u'''[/tex]
Then the given equation transforms to
[tex]{x_4}' - x_1 = 0[/tex]
but we also need to relate this to the other derivative substitutions. This gives the system of differential equations
[tex]\begin{cases} {x_1}' = x_2 \\ {x_2}' = x_3 \\ {x_3}' = x_4 \\ {x_4}' = x_1 \end{cases}[/tex]
In matrix form,
[tex]\begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}' = \begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}[/tex]
Let [tex]sin\beta =\frac{2\sqrt[]{2} }{5} \\[/tex] and [tex]\frac{\pi }{2} \leq\beta \leq \pi \\[/tex].
Determine the exact value of [tex]sin(\frac{\beta }{2} )[/tex]
Answers
Since beta is in the first quadrant, the final answer will be positive.
To find cos(beta) so we can use the half angle identity, we can substitute into the Pythagorean identity. Doing so gives us that
[tex] \sin( \beta ) = \frac{ \sqrt{17} }{5} [/tex]
So, this means that
[tex] \sin( \frac{ \beta }{2} ) = \sqrt{ \frac{1 - \frac{ \sqrt{17} }{2} }{2} } = \sqrt{ \frac{2 - \sqrt{17} }{4} } = \frac{ \sqrt{2 - \sqrt{17} } }{2} [/tex]
pls HELP Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles?
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side
5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answers
Answer:
The first choice
Step-by-step explanation:
You are setting up as you read it. The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles. On the the right you are setting up 4 positive x tiles and 3 negative unit tiles. It is not asking you to solve with the algebra tiles, just to set it up.
1. Prove the following identities
Answers
Answer:
Step-by-step explanation:
[tex]\sf 1.1)\dfrac{Sin \ \theta-Cos \ \theta}{Sin \ \theta + Cos \ \theta}=\dfrac{(Sin \ \theta-Cos \ \theta)}{((Sin \ \theta + Cos \ \theta)}*\dfrac{(Sin \ \theta-Cos \ \theta)}{(Sin \ \theta-Cos \ \theta)}[/tex]
[tex]\sf = \dfrac{(Sin \ \theta-Cos \ \theta)^2}{Sin^2 \ \theta-Cos^2 \ \theta}\\\\=\dfrac{Sin^2 \ \theta+Cos^2 \ \theta-2Sin \ \theta \ Cos\ \theta}{(Sin \ \theta-Cos \ \theta)}\\\\\\\bf Identity: \ (a +b)^2= a^2 + b^2 - 2ab\\\\\\=\dfrac{1-2Sin \ \theta \ Cos \ \theta}{(Sin \ \theta-Cos \ \theta)} = LHS[/tex]
[tex]\sf 1.2) LHS = tan^2 \ x - Sin^2 \ x = \dfrac{Sin^2 \ x}{Cos^2 \ x}-Sin^2 \ x[/tex]
[tex]\sf =\dfrac{Sin^2 \ x}{Cos^2 \ x}-\dfrac{Sin^2 \ x*Cos^2 \ x}{1*Cos^2 \ x}\\\\\\ = \dfrac{Sin^2 \ x - Sin^2 \ x*Cos^2 \ x}{Cos^2 \ x}\\\\\\= \dfrac{Sin^2 \ x *(1 -Cos^2 \ x)}{Cos^2 \ x}\\\\=\dfrac{Sin^2 \ x*Sin^2 \ x}{Cos^2 \ x} \\\\ \bf 1 - Cos^2 \ x = Sin^2 \ x\\\\= \dfrac{Sin^2 \ x}{Cos^2 \ x}*Sin^2 \ x\\\\=tan^2 \ x * Sin^2 \ x = RHS[/tex]
[tex]\sf 1.3) LHS = \dfrac{1-Cos \ x}{Sin \ x}-\dfrac{Sin \ x}{1+Cos \ x} =\dfrac{(1-Cos \ x)(1+Cos \ x)}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin \ x*Sin \ x}{(1+Cos \ x)*Sin \ x}\\[/tex]
[tex]\sf =\dfrac{1 - Cos^2 \ x}{Sin \ x*(1+Cos \ x)}-\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)} - \dfrac{Sin^2 \ x}{Sin \ x*(1+Cos \ x)}\\\\=\dfrac{Sin^2 x - Sin^2 \ x}{Sin \ x*(1+Cos \ x)} \\\\= 0 = RHS[/tex]
[tex]\sf 1.4) LHS = Sin x - \dfrac{1}{Sin \ x + Cos \ x}+Cos \ x \\[/tex]
[tex]\sf = \dfrac{Sin \ x *(Sin \ x + Cos \ x) - 1 + Cos \ x * (Sin \ x + Cos \ x)}{Sin \ x + Cos \ x }\\\\\\= \dfrac{Sin \ x * Sin \ x + Sin \ x*Cos \ x -1 + Cos \ x*Sin \ x + Cos \ x*Cos \ x}{Sin \ x + Cos \ x}\\\\\\=\dfrac{Sin^2 \x + Sin \ x \ Cos \ x - 1 + Cos \ x \ Sin \ x + Cos^2 \x}{Sin \ x + Cos \ x}\\\\=\dfrac{Sin^2 \ x + Cos^2 \ x - 1 + Sin \ xCos \x +Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{1 - 1 +2Sin \ x Cos \ x}{Sin \ x + Cos \ x}\\\\= \dfrac{2Sin \ x Cos \ x}{Sin \ x + Cos \ x}[/tex]
7 cm
D
What is the sum of the areas of circle C and circle D?
O7ft units²
O 14 units²
O 49 units²
O98 units²
Answers
The sum of areas of circle C and circle D exists 98 square units.
How to estimate the sum of the areas of circle C and circle D?Given: Radius of circle = 7 units
Area of circle [tex]=\pi r^2[/tex] ..............(1)
Where, r be the radius of circle
The radius of circle C, r = 7 units
(1) becomes
Area of circle, C [tex]= \pi 7^2[/tex] square units
[tex]= 49\pi[/tex] units²
Area of circle, D [tex]= \pi 7^2[/tex] square units
[tex]= 49\pi[/tex] units²
Sum of areas of circles C and D,
= Area of circle C + Area of circle D
= 49 + 49
= 98 units²
The sum of areas of circles C and D exist 98 units².
Therefore, the correct answer is option d) 98 units².
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A man mows his 100 ft by 200 ft rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break, he is 40.5% done. How wide of a strip has he mowed around the outside edge
Answers
Based on the length and width of the rectangular lawn, and the percentage the man has mowed, the strip width would be 40.5 m.
what is the width of the strip mowed already?first, find the area of the lawn:
= 100 x 200
= 20,000 ft²
the area mowed is:
= 40.5% x 20,000
= 8,100 ft²
the width is therefore:
= 8,100 / 200
= 40.5 m
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c) tan²0 - cot²0 = sec²0 (1- cot²0)
Prove that LHS = RHS So that LHS will be the sec²0 (1- cot²0)
Answers
Answer:
Maybe this could help?
The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers
Answers
Answer:
56
Step-by-step explanation:
small brain :(
A parabola, with its vertex at the origin, has a directrix at y = 3. which statements about the parabola are true? select two options.
Answers
The correct options about parabola are:
The focus is located at (0,–3).
The parabola can be represented by the equation x^2 = –12y.
According to the statement
we have given that the vertex is at the origin and directrix at y = 3.
and from these given information and we have to find the all abot the parabola like its focus point etc.
So,
We know that the equation of parabola is
(x-h)^2 = 4p(y-k)
Here The vertex is (h,k). and the focus is at (h,k+p). and the directrix is y(k - p.)
So, From the given information
Vertex at the origin means that h=0 and k=0
Directrix at y = 3 means that p=-3
Directrix at the y-axis means the parabola opens upwards.
Thus, the focus is: (0,-3)
And The p-value becomes
: 4(-3) = -12.
And from all these the equation of the parabola is becomes
(x)^2 = -12y
So, The correct options about parabola are:
The focus is located at (0,–3).
The parabola can be represented by the equation x^2 = –12y.
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Disclaimer: The question was incomplete. Please find the full content Below.
Question:
A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two options.
The focus is located at (0,–3).
The parabola opens to the left.
The p value can be determined by computing 4(3).
The parabola can be represented by the equation x2 = –12y.
The parabola can be represented by the equation y2 = 12x.
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Which of the following best describes the slope of the line below?
A. Positive
B. Zero
C. Negative
D. Undefined
Answers
Answer:
Zero
Step-by-step explanation:
Since the line is a horizontal line, the slope does not change. The slope is zero.
Answer:
Zero
Step-by-step explanation:
A zero slope is when the line is horizontal and when the slope equals to zero
I hope it helps! Have a great day!
bren~
Which is the best estimate of negative 14 and startfraction 1 over 9 endfraction (negative 2 and startfraction 9 over 10 endfraction)
Answers
The best estimation is 42.
EstimationFinding the most accurate estimate for:
[tex]-14\frac{1}{9}[/tex] x [tex]-2\frac{9}{10}[/tex]
To obtain, we round each integer to the next full number:
-14 x -3
Remember that adding two negatives produces positive results.
So, 14 x 3
Finally, this provides
42
Therefore, the final answer is 42.
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Answer: its 42
Step-by-step explanation:
Scores for a civil service exam are normally distributed with a mean of 75 and a standard deviation of 6.5. what score marks the difference between the bottom 10% and the top 90%?
Answers
The lowest score you can earn and still be eligible for employment is 85.6925.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
Top 5%.
At least the 100-5 = 95th percentile.
The 95th percentile is X when Z has a pvalue of 0.95. So X when Z = 1.645.
x-75 = 1.645*6.5
x = 85.692
Thus the lowest score you can earn and still be eligible for employment is 85.6925.
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Billy goes on the teacup ride at the local carnival. He is seated 16 inches from the center of his teacup, which is spinning at a rate of 4 revolutions per minute. What is Billy’s angular velocity, in radians per second? Round your answer to the nearest hundredth.
Answers
Answer:
0.42
Step-by-step explanation: