y=-3/2x+1
-6x-4y=-4
Solve and graph
Answers
The two equations graph to the same line. In standard form, it is
3x +2y = 2
There are infinite solutions. Any (x, y) pair that satisfies this equation is a solution of the "system."
Related Questions
Use the alternating series estimation theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. check your answer graphically. (round your answers to three decimal places.) sin(x) ≈ x − x3 6 |error| < 0.000001
Answers
[tex]sin(x)=x/1!-x^3/3!+x^5/5!-x^7/7!+x^9/9!-...[/tex] ...............(1)
Using the given approximation S(x)=x-x^3/3! ................(2)
Therefore the error term for the approximation is
error=(2)-(1)
[tex]=-(+x^5/5!-x^7/7!+x^9/9!-..)[/tex]
[tex]=-x^5/5!+x^7/7!-x^9/9!-..[/tex]
The alternative series theorem says we need only to ensure that the absolute value of the first term dropped (x^5/5!) is less than the error limit, in order to ensure that the sum will be below the error limit
This means that
|x^5/5!| < 0.000001
Solving for x:
x^5=5!*0.000001=0.000120
x=(0.000120)^(1/5)=0.164375
Thus the approximation of sin(x) ≈ x-x^3/3! has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].
Check:
sin(0.164375)-(0.164375)^3/3!=9.993513*10^(-7) < 0.000001
The approximation sin (x) = x - x^3/6 has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].
What is alternating series?In mathematics, the alternating series is an infinite series of a term in the form of
[tex]{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} \\{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}[/tex]
The expansion series of sin(x)
[tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!} +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +..[/tex] (a)
the given approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] (b)
So, the approximation error term =(b)-(a)
[tex]\rm = -[ +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +\frac{x^{9} }{9!}-....]\\\rm = -\frac{x^{5} }{5!} +\frac{x^{7} }{7!} -\frac{x^{9} }{9!}+....[/tex]
The alternative series theorem states that we need to ensure that the absolute value of the first term [tex]\rm \frac{x^{5} }{5!}[/tex]less than the error limit, For that the sum will be below the error limit, which means
[tex]\rm \frac{x^{5} }{5!}[/tex] < 0.000001
Solving for x, we get
x [tex]\rm x^{5} = 5! \times 0.000001\\ = 0.000120\\\rm = 0.000120^{1/5} \\ = 0.164375[/tex]
Therefore, the approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].
by checking
[tex]\rm sin(0.164375)-(0.164375)^{3/3!} \\= 9.993513\times10^{-7} < 0.000001[/tex]
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Express the work in terms of l, f, and θ. remember to use radians, not degrees, for any angles that appear in your answer.
Answers
Then work done is
W=FLcos(theta)
(Read assumptions above due to lack of diagram)
A ___________ is a line segment that has endpoints on a circle and passes through the center of the circle.
Question options:
radius
diameter
an obtuse angle
a regular polygon
Answers
A line segment that has points on the circle that passes through the center of the circle is the diameter.
The radius goes from a point on a circle to the center of the circle; it is half of the diameter.
An obtuse angle is an angle that measures more than 90 degrees.
A regular polygon is a polygon that is equiangular and equilateral.
A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. The correct option is: diameter
A diameter is a line segment that has endpoints on a circle and passes through the center of the circle. It is a crucial geometric element in the study of circles and plays a fundamental role in various geometric properties.
Key points about the diameter:
Definition: As mentioned, a diameter is a line segment that connects any two points on the circle's circumference and passes through the center of the circle. It is the longest chord of the circle.
Length: The length of the diameter is exactly twice the length of the radius. If "r" represents the radius, then the length of the diameter is "2r."
Properties: The diameter divides the circle into two equal halves, each known as a semicircle. It is also the largest possible chord of a circle.
In summary, a diameter is a significant geometric concept related to circles, and it is characterized by its property of passing through the center of the circle and being twice the length of the radius.
The correct option is: diameter
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the area of a circle is 78.5 square meters. what is the radius ?
Answers
a collection of nickels and dimes is worth $2.95 there are 47 coins and all how many nickels are there
Answers
D= dimes
N=nickels
Determine if the columns of the matrix form a linearly independent set. justify your answer. left bracket start 4 by 3 matrix 1st row 1st column negative 2 2nd column negative 1 3rd column 0 2nd row 1st column 0 2nd column negative 1 3rd column 3 3rd row 1st column 1 2nd column 1 3rd column negative 6 4st row 1st column 2 2nd column 1 3rd column negative 12 endmatrix right bracket −2 −1 0 0 −1 3 1 1 −6 2 1 −12
Answers
[tex] A= \left[\begin{array}{ccc}-2&-1&0\\0&1&3\\1&1&6\\2&1&-12\end{array}\right][/tex]
then here is an outline of how to determine whether the columns form a linearly independent set.
12. Which one of the following is a geometric sequence?
A. −7, 10, 23, 36, . . .
B. 8, 4, 2, 1, 1/2, 1/4, . . .
C. 2, −3, 9/2, −18/4
D. 0, 1, 2, 3, . . .
Answers
Answer:
B. 8, 4, 2, 1, 1/2, 1/4, . . .Step-by-step explanation:
A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.
So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.
By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it
[tex]8\times \frac{1}{2}= 4 (second \ term)\\4 \times \frac{1}{2}=2 (third \ term)\\ 2 \times \frac{1}{2}= 1 (fourth \ term)\\ 1 \times \frac{1}{2}= \frac{1}{2} (fiftg \ term)\\ \frac{1}{2} \times \frac{1}{2}= \frac{1}{4} (sixth \ term)[/tex]
As you can observe, we perfectly built the sequence is its ratio or factor.
Therefore, choice B is a geometric sequence.
passes thru ( 7, -5) and has m=0
Answers
hope this helps
A bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph. Find the distance from the village to the railroad station, if it’s known that it took 1 more hour for the bicyclist to get back to the village.
Answers
Which expressions are polynomials? Select each correct answer. y x2−x√+2 2 + s 4x³ + y
Answers
Answer:
Answers are
Y
2+s
4x^3+y
Step-by-step explanation:
I did the quiz
The first, second, and third are the polynomials.
PolynomialPolynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable
Given
1. y
2. x² - x +√2
3. 2 + s
4. 4x³ + y
To find
Which expressions are polynomials?
How to get Which expressions are polynomials?1. y is a polynomial with variable y.
2. x² - x +√2 is a polynomial with variable x.
3. 2 + s is a polynomial with variable s.
4. 4x³ + y is not a polynomial because the polynomial has only one variable in it.
Thus, the first, second, and third are the polynomials.
More about the polynomial link is given below.
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According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to TWO decimal places.)
Answers
Explanation:
Let x = hourly wage for a social worker. Then, the z-score for x is given by
[tex]\text{z - score} = \frac{x - \mu}{\sigma} [/tex]
where
[tex]\mu = \text{ mean hourly wage of a social worker }= \$ 28.08 \\ \sigma = \text{ standard deviation of the wage of the social worker }= \$ 1.97[/tex]
Since Jeronica's salary is $31.60, the z-score of Jeronica's is given by
[tex]\text{z - score} = \frac{x - \mu}{\sigma} \\ \\ \text{z - score} = \frac{31.60 - 28.08}{1.97} \\ \\ \boxed{\text{z - score} = 1.79}[/tex]
simplify x + 2/ x^2 - 6x - 16 divided by 1/9x
Answers
Simplify the expression
9/x(x - 8)
Hope this helps! :)
~Zain
Using Cramer’s Rule, what is the value of x in the system of linear equations below? x+3y=16 3x+y=8
Answers
Using Cramer's Rule, the value of x in the given system of linear equations is 1.
Explanation:We can solve the given system of equations using Cramer's Rule. Cramer's Rule states that in a system of linear equations, if the determinant of the coefficient matrix is non-zero, then the system has a unique solution.
First, let's find the determinant of the coefficient matrix:
| 1 3 |
| 3 1 |
Det = (1*1) - (3*3) = -8
Since the determinant is non-zero (-8 ≠ 0), the system has a unique solution.
Next, let's find the determinant of the x-column matrix:
| 16 3 |
| 8 1 |
Det(x) = (16*1) - (3*8) = -8
Finally, we can find the value of x by dividing the determinant of the x-column matrix by the determinant of the coefficient matrix: x = Det(x) / Det = (-8) / (-8) = 1.
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 10 and its height is 6?
Answers
B=k/H
B is the base of the triangle (B=10).
H is the height of the triangle (H=6).
k is the constant of variation.
2. When you clear "k", you obtain:
B=k/H
k=BxH
k=10x6
k=60
3. Now, you have:
B=60/H
4. You can give any value to "H" and you will obtain the base of the second triangle.
5. If H=12, then:
B=60/H
B=60/12
B=5
6. Therefore, the possible base and height of a second triangle is:
B=5
H=12
Answer:
12 and 5
Step-by-step explanation:
The Orlando eye in Orlando, Florida is a regular polygon with 30 sides. Which of the following is the measure of each interior angle of the polygon?
Answers
Answer:
The measure of each interior angle of the polygon is [tex]168\°[/tex]
Step-by-step explanation:
we know that
The sum of the internal angles in a polygon is equal to
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have
[tex]n=30\ sides[/tex]
substitute
[tex]S=(30-2)180\°=5,040\°[/tex]
To find the measure of each internal angle divide the total sum of internal angles by the number of sides
so
[tex]5,040\°/30=168\°[/tex]
Answer:168
Step-by-step explanation:
N is the number of sides. Formula is (n-2)×180/n. So (30-2)= 28×180=5040÷30= 168
Which is the measure of AB? 10 feet 15 feet 20 feet 100 feet
Answers
A paperweight in the shape of a rectangular pyramid is shown:If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex,which shape describes the cross section
Answers
A triangle has 3 vertices. In this case one vertex will be located at the same position as is the vertex of the pyramid. The other two vertex will be located on the sides of the rectangular base of the pyramid.
None of the angle will be a Right Angle so the triangle will be an Oblique Triangle. To determine if the triangle is equilateral, isosceles or scalene we need to know the side lengths of the pyramid.
Answer:
The correct answer is a triangle will be formed.
Step-by-step explanation:
If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex, the resulting figure will have 3 sides or vertices. Hence, this shape will be a triangle. The triangle only forms if it does pass through the top vertex.
So, triangle is the answer.
Which of the following are linear factors of p(x) = x 3 - 2x 2 - 5x + 6 ?
Answers
.. (x +2)
.. (x -1)
.. (x -3)
_____
Obviously, you don't mind using "technology" (Brainly) to tell you the answer. You might find it useful in the future to learn to use your graphing calculator. It can make short work of these questions.
J is the midpoint of KL. The coordinates of J are (-8,7) and the coordinates of K are (3,4) find the coordinates of L. (show work) (please don't reply if you don't know the answer).
Answers
if k is at (3,4) and j is at (-8,7)
set. (y1,x1) and(y2,x2)
[(y2-y1),(x2-x1)]
[(-8-3),(7-4)]
distance from k to j is (-11,3)
now take coordinates of j and distance from. k->j and add them to get coordinate for L
[(-11+(-8)),(7+3)]= (-19,10)=L
Explain how to compare 43 and 35
Answers
The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons have the symbols ^79Br and ^81Br, respectively, with the mass numbers derived from adding the number of neutrons to the atomic number 35.
Explanation:To address Exercise 1.8.2, we first need to identify the element with 35 protons. In the periodic table, the element with 35 protons is bromine (Br). This element is defined by the number of protons in its nucleus, which is also known as its atomic number. Therefore, bromine is the element we are looking for.
Next, we need to write the symbols for bromine's isotopes with 44 and 46 neutrons. The total number of nucleons (protons plus neutrons) gives us the mass number of an isotope. For bromine with 44 neutrons, the mass number is 35 (protons) + 44 (neutrons) = 79. Therefore, the symbol for this isotope of bromine is ^79Br.
For the isotope with 46 neutrons, the mass number is 35 (protons) + 46 (neutrons) = 81. So, the symbol for this isotope of bromine is ^81Br. Each isotope differs in the number of neutrons, and therefore, in the mass number, while the number of protons (the atomic number) remains constant.
The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons are written as ^79Br and ^81Br, respectively, where the numbers represent the mass numbers of each isotope.
Explanation:To answer Exercise 1.8.2, we must first identify the element with 35 protons. The element with 35 protons is bromine, which is represented by the chemical symbol Br. To write the symbols for its isotopes with 44 and 46 neutrons, we must add the atomic number (protons) and the number of neutrons to get the mass number for each isotope.
For the isotope with 44 neutrons:
Mass number = Number of protons + Number of neutronsMass number = 35 + 44Mass number = 79Therefore, the symbol for this isotope is ^79Br.For the isotope with 46 neutrons:
Mass number = 35 + 46Mass number = 81Therefore, the symbol for this isotope is ^81Br.Isotopes of an element have the same number of protons but different numbers of neutrons, hence different mass numbers. The isotopes of bromine are thus ^79Br and ^81Br, referring to the atomic mass which is composed of the protons and neutrons together.
If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is
Answers
[tex]\sigma^2=npq=np(1-p)=10*0.7*0.3=2.1 [/tex]
[tex]\sigma=standard\,deviation=\sqrt{2.1}=1.449[/tex] (to 3 decimal places)
The standard deviation for the given binomial distribution is 1.449.
What is binomial distribution?A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.
Formula for the calculation of standard deviationσ = [tex]\sqrt{nP(1 -P)}[/tex]
where,
σ is the standard deviation
n is the number of trials in the binomial experiment.
P is the probability of success on an individual.
According to the given question we have,
The number of trials in the binomial experiment, n = 10
The probability of success on an individual, p = 0.70
Therefore, the standard deviation is given by
σ = [tex]\sqrt{10(0.70)(1 -0.70)} = \sqrt{7(0.3)}=\sqrt{2.1} =1.449[/tex]
Hence, the standard deviation for the given binomial distribution is 1.449.
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G find z such that 9.0% of the standard normal curve lies to the right of z. (round your answer to two decimal places.)
Answers
Please help meeeeeee!
Answers
(4x)+(5x+9)=180------------->supplementary angles
therefore
9x+9=180---------> 9x=180-9
x=171/9=19
x=19°
the answer is the option E
x=19°
Suppose that 44% of all Americans approve of the job the president is doing. The most recent Gallup poll consisted of a random sample of 1400 American adults.
A) What is the mean of the sampling distribution?
B) What is the standard deviation of the sampling distribution?
C) Describe the normal approximation for this sampling distribution.
D) What is the probability that the Gallup poll will come up with a proportion within 3 percentage points of the true 44%?
Answers
n = population = 1400
p = probability of positive answer = 0.44
A) The mean of a binomial distribution is
μ = np
= 1400 × 0.44
= 616
Hence, μ = 616
B) The standard deviation of a binomial distribution is
σ = √[np(1 - p)]
= √[1400×0.44×(1-0.44)]
= √(1400×0.44×0.56)
= 18.6
Hence, σ = 18.6
C) A binomial distribution B(n, p) can be approximated by a normal distribution N(μ, σ) only when:
np ≥ 10 (we have 616 > 10)
np(1 - p) ≥ 10 (we have 344.96 > 10)
Hence, the normal approximation is N(616, 18.6)
D) We need to calculate the probability of the sample population to be within 3% of the true mean.
In order to do so, as a first thing, we need to calculate the sample standard deviation, which will be given by the formula:
[tex]\sigma = \sqrt{ \frac{p(1-p)}{n} } [/tex]
= √[0.44 × (1 - 0.44) ÷ 1400]
= √0.000176
= 0.013
Now, we need to calculate the z-score associated with the values we want: since we want 3% from the mean, it means between 41% and 47%.
The z-score can be calculated by the formula:
z = (Y - p) / σ
z₁ = (0.41 - 0.44) / 0.013 = -2.31
z₂ = (0.47 - 0.44) / 0.013 = 2.31
Therefore, we can write
P(0.41 ≤ Y ≤ 0.47) = P(-2.31 ≤ z ≤ 2.31)
= P(z ≤ 2.31) - P(z ≤ -2.31)
= P(z ≤ 2.31) - [1 - P(z ≤ 2.31)]
= 2×P(z ≤ 2.31) - 1
From a standard normal distribution table, we find:
P(z ≤ 2.31) = 0.9896
Therefore:
2×P(z ≤ 2.31) - 1 = 2 × 0.9896 - 1
= 0.9792
Hence, the probability to find a proportion within 3% of the real mean is 97.92%
Eight soccer players share 7 oranges. How would this be as a fraction?
Answers
The seven oranges would be the numerator of the fraction, and the eight soccer players would be the denominator. So, the fraction would look like:
7/8
Regina scored 84% on a test. She answered 63 items correctly. How many items did Regina answer incorrectly?
Answers
Divide both sides by 84% to normalize:
84%/84% = 63/84%
1 = 75
This means that 100% would be equivalent to 75 questions correct
From here, subtract 75-63=12
Find total number of questions on the test. The percent (84%) is out of 100%. So set up a proportion. 84% out of 100% is 63 out of x (total number of questions on the test).
x= total # questions on test
63/x= 84%/100%
cross multiply
(63*100)= (x*84)
6300= 84x
divide both sides by 84
75= x (total # on test)
STEP 2:
Subtract number correct from total number of questions to equal number incorrect.
x= number incorrect on test
x= 75 - 63
x= 12 incorrect answers
ANSWER: 12 incorrect answers
Hope this helps! :)
A rectangle prism has length of 20 inches, a width of 2 inches and height of 3 1/4 inches. The prism is filled with cubes that have edge lengths of 1/4 inches. How many cubes are needed to fill the rectangle?
Answers
Vtotal = (20) * (2) * (3 1/4)
Votal = 130 in ^ 3
We now look for the volume of each individual cube:
Vcube = (1/4) ^ 3
Vcube = 1/64 in ^ 3
The number of cubes will be:
N = (Vtotal) / (Vcube)
N = (130) / (1/64)
N = 8320
Answer:
to fill the rectangle are needed 8320 cubes
At Jim's Juice Box Factory, his machine can fill 300 juice boxed an hour. Each juice box holds 0.8 cups. How many gallons of juice does Jim's factory need per hour?
Answers
.. = 15 gal/h
Jim's factory needs 15 gallons of juice per hour.
Winners of the georgia lotto drawing are given the choice of receiving the winning amount divided equally over 2222 years or as a lump-sum cash option amount. the cash option amount is determined by discounting the annual winning payment at 44% over 2222 years. this week the lottery is worth $33 million to a single winner. what would the cash option payout be?
Answers
To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.
Explanation:To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:
PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)
where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:
PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)
Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.
Find an equation for the plane that contains the line v = (−1, 1, 2) + t(7, 6, 2) and is perpendicular to the plane 8x + 5y − 7z + 8 = 0.
Answers
The equation for the plane that contains the given line and is perpendicular to the provided plane is 8x + 5y - 7z + 17 = 0.
Explanation:To find an equation for the plane that contains the line given by v = (−1, 1, 2) + t(7, 6, 2) and is perpendicular to the plane described by 8x + 5y − 7z + 8 = 0, we first need to understand that the normal vector of this plane will be parallel to the normal vector (8, 5, -7) of the given plane since both planes are perpendicular to each other.
Knowing that the line lies on the required plane, we can use the point (−1, 1, 2) that the line passes through, along with the parallel normal vector, to write the equation of our plane. The general form of the equation of a plane is Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane. Substituting our point into the equation, we calculate the constant D.
Thus, the equation of our plane will be 8x + 5y − 7z + D = 0. Inserting the point (−1, 1, 2) into this equation gives us 8(-1) + 5(1) - 7(2) + D = 0, which simplifies to -8 + 5 - 14 + D = 0. Solving for D yields D = 17. Hence, the final equation of the plane is 8x + 5y − 7z + 17 = 0.