Parallel lines has the same slope. In our case, the slope is -5. Then, the searched line has the form:
[tex]y=-5x+b[/tex]where b is the y-intercept.
We can find b by substituting the given point (3,2) into the las equation. Then, we have
[tex]2=-5(3)+b[/tex]which gives
[tex]\begin{gathered} 2=-15+b \\ 2+15=b \\ 17=b \end{gathered}[/tex]Therefore, the parallel lines is given by
[tex]y=-5x+17[/tex]Which of the following equations have no solutions?Choose all answers that apply:-60x + 32 = 32x + 60 -60x + 32 = 32x - 60 -60x + 32 = -60x - 32-60x + 32 = -60x + 60
Answer:
-60x + 32 = -60x - 32
Step-by-step explanation:
The first step to solve this question is combining the like terms in each option.
In those that we end up with:
0x = c
In which c != 0, we have no solution. So
-60x + 32 = 32x + 60
-60x - 32x = 60 - 32
-92x = 28
No 0x, so it has solution
-60x + 32 = 32x - 60
-60x - 32x = -60 - 32
-92x = -92
No 0x, so it has solution
-60x + 32 = -60x - 32
-60x + 60x = -32 - 32
0x = -64
0x equaling a value different of 0, so no solution.
-60x + 32 = -60x + 60
In today's recording, the first example was the function
f(x) = x² + 5x³ + 10x² + 20x + 24
After depressing our function twice and getting a quotient (depressed polynomial), which was the
resulting quadratic equation that we needed to solve?
O x²+4=0
O x²-4=0
O x² + 4x + 4 = 0
O x² + 4x = 0
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
How can you locate a polynomial's root?Set the equation's value to zero to get the polynomial's roots. Completely factor the polynomial expression. Then, in order to find the variable, set each factor equal to zero. The formula isx^4+5x^3-10x^2-20x+24Finding polynomial roots (zeroes) is the focus of this solution.((((x4)+(5•(x3)))-(2•5x2))-20x)+24
((((x4) + 5x3) - (2•5x2)) - 20x) + 24
Find the roots (zeroes) of F(x) = x4 + 5 x 3 x 10 x 2 x 20 + 24.The Polynomial Roots Calculator is a collection of techniques for identifying x values where F(x)=0.One of the tools discussed above is the rational roots test. Only numbers x that can be written as the quotient of two integers would be considered rational roots.According to the Rational Root Theorem, P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient if a polynomial zeroes for a rational integer P/Q.The Leading Coefficient in this situation is 1 and the Trailing Constant is 24.The element(s) are: of the Trailing Constant: 1, 1, 2, 3, 4, 6, 8, 12, and 24 of the Leading Coefficient: 1.According to the Factor Theorem, if P/Q is a polynomial's root, then q*x-p can be used to divide the polynomial. Keep in mind that q and p come from P/Q in its simplest form.In our situation, this means that 4 different polynomials, including x-2, can divide x4+5x3–10x2–20x+24.To Learn more about polynomial refer to:
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A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work? On a graph
The equation in slope intercept form is C(h) = 50h+25 ,the total cost for 8 hours of work is $425 , and for 10 hours of work is $525.
In the question;
it is given that
the fixed charge of plumber = $25
charge for per hour of service = $50
the hours of service be "h"
and the total cost be "C"
according to the question
C(h) = 50h+25
the equation in the slope intercept form is C(h) = 50h+25
to find the total cost for 8 hours of work , put h=8
C(8) = 50(8) + 25
= 400+25
= 425
to find the total cost for 10 hours of work , put h=10
C(10) = 50(10) + 25
= 500+25
= 525
Therefore , total cost for 8 hours of work is $425 , and for 10 hours of work is $525 .
The given question is incomplete , the complete question is
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?
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is the ordered pair (-8 1) a solution to the equation y=1/2x-3
Answer: No.
Step-by-step explanation:
To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.
y = 1/2x - 3
(1) = 1/2(-8) - 3
1 = -4 - 3
1 ≠ -7
This ordered pair is not a solution.
If y varies inversely as x, and y = 22 when x = 6, find x when y = 15.
Step-by-step explanation:
y varies INVERSELY as x.
that means
y = k/x
therefore,
22 = k/6
k = 22×6 = 132
and then, when y = 15
15 = 132/x
15x = 132
x = 132/15 = 8.8
vehicle speed on a particular bridge in china can be modeled as normally distributed. (a) if 5% of all vehicles travel less than 39.18 m/h and 10% travel more than 73.27 m/h, what are the mean and standard deviation of vehicle speed? (round your answers to three decimal places.) mean standard deviation
The mean and standard deviation of the vehicle speed are 58.33 and 11.64 respectively.
The vehicle speed on a particular bridge in china has normal distribution.
5% represents the 5th percentile which is here, 39.18 m/h.
Since 10% travels more than 73.27 m/h, 90% travels less than 73.27 m/h.
So here the 90th percentile is 73.27 m/h.
Also the z-score, z = (x-μ)/σ, where μ is the mean of normal distribution and σ, the standard deviation.
So 39.18 corresponds to the z with p-value 0.05, i.e., z = -1.645 [from the normal tables]
Hence, z = (x-μ)/σ
⇒ -1.645 = (39.18 - μ)/σ
⇒ -1.645σ = 39.18 - μ
⇒ μ = 39.18 + 1.645σ ----------(1)
Also 73.27 corresponds to the z with p-value 0.9,i.e., z = 1.28.
Hence , z = (x-μ)/σ
⇒ 1.28 = (73.27 - μ)/σ
⇒ 1.28σ = 73.27 - μ
⇒ μ = 73.27 - 1.28σ ----------(2)
Equating (1) and (2), we get,
39.18 + 1.645σ = 73.27 - 1.28σ
2.925σ = 34.05
σ = 11.64
hence μ = 39.18 +1.645 x 11.64
⇒ μ = 58.33
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(-4k - 1) - (-6k - 6)
Answer:
2k + 5
Step-by-step explanation:
Since this is a subtraction problem, you need to change it to an addition problem. When you do this, you also need to change the sign of each term in the second set of parentheses.
(-4k - 1) - (-6k - 6)
(-4k - 1) + (6k + 6)
Remove the parentheses and add like terms.
-4k - 1 + 6k + 6
2k +5
Determine if the table below is proportional?
The table represent a direct proportional relation.
How to determine if a table represents a proportional relation
In this question we find a table with four pairs of elements that have to be tested with respect to the direct proportional formula, which is defined below:
y = k · x
Where:
x - Independent variable.y - Dependent variable.k - Constant of proportionality.The table represents a direct proportional relation if and only if there is only one constant of proportionality:
k₁k₁ = 12 / 3
k₁ = 4
k₂k₂ = 20 / 5
k₂ = 4
k₃k₃ = 8 / 2
k₃ = 4
k₄k₄ = 32 / 8
k₄ = 4
As k₁ = k₂ = k₃ = k₄, the table represent a proportional relationship.
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Help help please please help help I need help 30 POINTS
An adult elephant weighs 2 2/5 tons. An adult hippo weighs 1 4/5 tons. How much will the animals weigh together?
Answer: If you want the result as a fraction it should be 3.7/5. but if you want a whole number it's 4.2. if you want a mixed number its 4 1/5
Step-by-step explanation:
The demand for a certain product is given by p+3q=315, and the supply for this
product is given by p-7q = 65, where p is the price and q is the number of
products. Complete parts (a) and (b) below.
a. Find the price at which the quantity demanded equals the quantity supplied.
$
b. Find the equilibrium quantity.
In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260." option (b) is answer.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.a. The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by p-7q = 65 or, q = (p- 65)/7
The price at which the quantity demanded equals the quantity supplied is given by
315 - p/3 = p - 65/7
7( 315 - p ) = 3( p - 65 )
2405 - 7p = 3p - 195
2405 + 195 = 3p + 7p
2600 = 10p
p = 2600/10 = 260
Thus, the required price is $ 260.
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For any integer of n which of the following, n and n+2, n-1 and n+1, 2n and 2n+2, 2n-1 and 2n+1, 2n+ 1 and 2n+2, 2n and 2n+1 are always 2 consecutive even numbers
The number 2n and 2n + 2 will always are 2 consecutive even numbers.
What is termed as the consecutive even numbers?Consecutive numbers are numbers that obey one another in a regular adding up order or pattern. They are written in a series with a fixed difference here between numbers and no numbers skipped in between. We know that even numbers end in 0, 2, 4, 6, and 8. Consider a set of even numbers ranging from 2 to 12 but rather write those in ascending order. When written from smallest to largest, the numbers are organized as 2, 4, 6, 8, 10, 12. The difference between any former leader pair is 2, as we can see. As a result, these numbers comprise the collection of consecutive even numbers.From the given option in the question;
2n and 2n + 2 will always be two consecutive even number.
For, n = 1, the numbers be 2 and 4.
For, n = 2, the numbers be 4 and 6.
For n = 3, the numbers be 6 and 8....and so on.
Thus, the number 2n and 2n + 2 will always are 2 consecutive even numbers.
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Using the information found in these tables which of the following statements is true
Please helpppp
HELP PLS ITS DUE TONIGHT
Answer:
1. 12
2. 4:5
3. 5
4. 30
5. 42
6. 15
7. 36
8. 1120
9. 10 2/3
Step-by-step explanation:
Answer:
In photo
Step-by-step explanation:
what does x =?
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Part 1. A cardboard box, which weighs 0.6 pound when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6 + 15b + 4 = 25.6.
Select all equations that are also equivalent to 0.6 + 15b + 4 = 25.6.
Responses
Equation A: 15b + 4 = 25.6
Equation A: 15b + 4 = 25.6
Equation B: 15b + 4 = 25
Equation B: 15b + 4 = 25
Equation C: 3(0.6 + 15b + 4) = 76.8
Equation C: 3(0.6 + 15b + 4) = 76.8
Equation D: 15b = 25.6
Equation D: 15b = 25.6
Equation E: 15b = 21
Part 2. To solve the equation 7.5d = 2.5d, Lin divides each side by 2.5d, and Elena subtracts 2.5d from each side.
a. Will both moves lead to the solution? Explain your reasoning.
b. What is the solution?
Part 3. The equation 4(x – 2) = 100 is a true equation for a particular value of x. Explain why 2(x – 2) = 50 is also true for the same value of x.
2(x -2) = 50 is also true for the same value of x.
Given,
Part 1:
When a cardboard box is empty, its weight is 0.6 pounds.
It is filled with 15 bags of beans and a 4-pound bag of rice.
The total weight of the box and the contents inside it is 25.6 pounds.
Let the weight of 15 bean bags is 15b. The given scenario can be represented by the equation as follows :
0.6+15b+4=25.6 ....(A)
Taking like terms together,
15b=25.6-0.6-4 ...(1)
15b = 21 ....(2)
Equation (1) or (2) can be the equivalent equation for the equation (A).
Part 2:
Solve the equation:
7.5d = 2.5d, Lin divides each side by 2.5d,
and Elena subtracts 2.5d from each side.
Now, 7.5d/2.5d = 2.5d/2.5d
3 = 1
It is not equal, There is no solution.
a. 7.5d - 2.5d = 2.5d - 2.5d
5d/5 = 0/5
b. What is the solution ?
Solution is d = 0
Part 3:
Given,
The equation 4(x - 2) = 100 is a true equation for a particular value of x.
Explanation: The basic property of the equation is that if you multiply or divide both sides of the equation by the non-zero whole , the equation still holds.
In the Equation : 4 (x - 2) =100 divide by 2 on both sides because 2 is common factor of (4,10)
So, 4(x - 2) =100
1/2 x 4(x-2) = 1/2 x 100
= 2(x-2) = 50
Above all, 2(x -2) = 50 is also true for the same value of x.
Hence, 2(x -2) = 50 is also true for the same value of x.
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My penMath The area of a triangle can be found using the formula: Area = 1/2 · base · height. Find the area of the triangle pictured below, where the measurements are given in meters (m) 2 m 10 m
Answer:
The area of the given triangle is 10 sq meters
Explanation:
The area of a triangle is given by the formula:
Area = 1/2 base . height
Given that the triangle has base = 10m, and height = 2m
Area = 1/2 * 10 * 2
= 10 square meters
what two numbers multiply to be -6 and add up to be -5
Answer: -2 and -3
Step-by-step explanation:
I need help with these problems ASAP.
The following cases are described:
The rational function is (f / g) (x) = x - 6, whose domain is all the real numbers.The rational function is (f / g) (x) = 1 / (x + 2), whose domain is all the real numbers except x = - 2.How to derive a rational function by division of functions and find its domain
Algebraically speaking, rational functions are expressions of the form f(x) = p(x) / q(x), such that q(x) ≠ 0, where p(x) is the numerator and q(x) is the denominator. Rational functions can be found by using the defintion of division between two functions:
(f / g) (x) = f(x) / g(x)
And the domain of (f / g) (x) is every value of x such that g(x) ≠ 0. Now we proceed to find all the required information for each case:
Case 1 - f(x) = x² - 3 · x - 18, g(x) = x + 3
Rule: (f / g) (x) = (x² - 3 · x - 18) / (x + 3)
(f / g) (x) = [(x - 6) · (x + 3)] / (x + 3)
(f / g) (x) = x - 6
Domain: Since the resulting expression is a linear function, then the domain of (f / g) (x) is all the real numbers.
Case 2 - f(x) = x - 3, g(x) = x² - x - 6
Rule: (f / g) (x) = (x - 3) / (x² - x - 6)
(f / g) (x) = (x - 3) / [(x - 3) · (x + 2)]
(f / g) (x) = 1 / (x + 2)
Domain: The domain of the rational function is any real number except x = - 2.
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If a = 3 and b = -5- 2i, then find the value of the a³b in fully simplified form.
The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."
What is complex numbers?Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").
Here,
The value of a³b
=3³(-5-2i)
=27(-5-2i)
=-135-54i
For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.
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Standard Questions
Question Progress
The average mass of a man is 84 kg and of a woman is 70 kg.
A lift can safely carry 720 kg.
Work out the maximum number of people the lift can safely carry.
We need to know simple division to solve the problem. The maximum number of men in the lift is 8 and the maximum number of women in the lift is 10.
We will be using the simple concept of division to find the number of people that the lift can carry. The average weight of a man is given to be 84 kg and the average weight of a woman is given to be 70kg. The lift can carry 720 kg, we will find separately the number of men and women that can be carried in the lift. Inorder to find the maximum number of men we divide the total weight the lift can carry by the average weight of a man, we will similarly calculate the maximum number of women.
number of men= 720/84=8.57 which means that the number of men is 8
number of women =720/70=10.28 which means that number of women is 10.
Therefore the lift can carry at most 8 men and at most 10 women.
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Mrs. McDonald passed out 189 photos that she had taken during the school year. If each of her 21 students received the same number of photos, how many did each receive?
Answer: 9. 189 divided by 21 is 9.
Step-by-step explanation:
Use the graph to write a linear function that relates y to x.
Answer:
y=4/3x+2
Step-by-step explanation:
Sandra recorded the distances that 6 beetles crawled in 10 seconds down a 36 inch track. The fractions represent the distances that Sandra recorded. 7 2 1 11 5 17 18' 3' 9' 36' 18 3 36. Which list shows distances Sandra recorded in order from least to greatest?
Distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.
Given that, the fractions represent the distances that Sandra recorded is 7/18, 2/3, 1/9, 11/36, 5/18, 17/36.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Here, distance is 10/36
So, the equivalent fractions for the given fractions are
7/18 = 14/36
2/3 = 24/36
1/9 = 4/36
11/36
5/18 = 10/36
17/36
So, least to greatest is
4/36 < 10/36 < 11/36 < 14/36 < 17/36 < 24/36
1/9 < 5/18 <11/36 <7/18 <17/36 <2/3
Therefore, distances Sandra recorded in order from least to greatest is 1/9, 5/18, 11/36, 7/18, 17/36, 2/3.
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PLEASE PLEASE PLEASE HELP ME I WILL MARK BRAINLY
Answer:
pretty sure its WZX
Step-by-step explanation:
please help I need help on how to do it also my videos stopped working
20 shares purchased at $30, means that the initial inversion is 20 times 30 = $600
they are sold for $710, so the difference is 710 - 600 = 110
the commision is 6, so the final gain is 110 -6 =104
profit divided by the inversion:
104/600 = 0.1733
the answer is 17.33 %
How did the people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact? They did not come together to create a government. They did not write laws that protected everyone in the colony. They did not create an orderly community within the colony. They did not form a civil body that could preserve the colony.
The people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact as A. They did not come together to create a government.
What was Mayflower Compact?
The Mayflower Compact was the Plymouth colony's first government instrument. The Pilgrim Fathers, the emigrants who crossed the Atlantic on the Mayflower in search of religious freedom, wrote the manifesto. On November 11, 1620, it was signed on the sands of what is now Provincetown, near Cape Cod. The pilgrims knew they were in a land unfamiliar to the London Company when the Mayflower docked in Plymouth.
The strangers claimed that the Virginia Company contract was null and void. They believed that because the Mayflower landed outside of Virginia Company territory, they were no longer bound by the charter of the company. Because there was no official government over them, the stubborn strangers refused to acknowledge any regulations.
Many of the pilgrims were already weak from disease and a lack of food when they arrived in Plymouth. The journey had been lengthy, and they were running low on supplies. During the winter, the colony lost about half of its population owing to disease and famine.
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Answer:its A i did it on edge
Step-by-step explanation:
1
What is the ratio of blue
circles to red circles?
Answer:
1:1 or one red circle to one blue circle
There is one red and one blue circle
Step-by-step explanation:
In a company 80/ of workers are men if 1120 people workfor the company who aren’t men how many workers are there in all
Answer:
if you meant %, the answer is 2016
Step-by-step explanation:
1120 + 80% is 2016
A woman is training for a cycling event. In the first week she cycles 20 km. In each subsequent week, she cycles 5 km more than she cycled the previous week.
How many kilometres has she cycled in total by the end of the 18th week?
The kilometres that she has cycled in total by the end of the 18th week is 105.
How to calculate the number of kilometers?Based on the information, this is an arithmetic sequence and the formula is illustrated as
= a + (n - 1)d
where a = first term = 20
d = common difference = 5
n = numbers = 18
Therefore, the 18th term will be:
= a + (n - 1)d
= 20 + (18 - 1)5
= 20 + (17 × 5)
= 20 + 85
= 105
The number of kilometers is 105 kilometers.
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