The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
What is the distance between two parallel lines?Let the two lines be ax + by + c₁ = 0 and ax + by + c₂ = 0. Then the distance between the lines is given as,
d = |c₂ - c₁| / √(a² + b²)
Let the distance between Line AB and A'B' be d and the equation of the line AB be ax + by + c₁ = 0. Then the value of c₂ is given as,
d = |c₂ - c₁| / √(a² + b²)
d√(a² + b²) = c₂ - c₁
c₂ = d√(a² + b²) + c₁
Then the equation of the line A'B' is given as,
ax + by + c₂ = 0
ax + by + d√(a² + b²) + c₁ = 0
The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
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A taxi company charges a base fee of $3.00 plus $0.75 per mile. Write an equation to represent the cost of a taxi ride Y for the distance of X miles.
0.75 times the amount of miles+the base fee
Answer:
Y=0.75X+3
What is the value of 150kg in pounds
Answer:
Step-by-step explanation:330.693 lbs
Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides of 6 cm, as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining grey hexagon. What is the side length of the small triangles?
The side length of the small equilateral triangles is 3 cm.
What is the side length of the small triangleLet's call the side length of the small equilateral triangles "x". Since there are three small triangles, the total perimeter of the small triangles is 3x.
The side length of the large equilateral triangle is 6 cm, so each side of the small triangles is a portion of 6 cm. Specifically, each side of the small triangles is (1/2) of a side of the large triangle.
Therefore, the perimeter of each small triangle is 3x, which is made up of three sides of length (1/2)6 cm or 3 cm. So we have:
3x = 3(3 cm) = 9 cm
Solving for x, we get:
x = 3 cm
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Each marble bag sold by Omar's Marble Company contains 4 green marbles for every 3 yellow marbles. If a bag has 28 green marbles, how many yellow
marbles does it contain?
Answer: it contains 21 yellow marbles
Step-by-step explanation:
x = 28 x 3/4
canceling method
x = 7 x 3
x = 21
A gym teacher has a large canvas bag that contains 8 tennis balls, 2 volleyballs, 1 basketball, 3 baseballs, and 5 footballs. If you reach into the bag at random, what is the probability that you select a tennis ball?
8/19 or 42.1%
add all values up to a total, then find the percentage from that total.
8 + 2 + 1 + 3 + 5 = 19 balls total
8 tennis valls to 19 total.
8/19 or 42.1%
PLEASE HELP!!
Write an equation that can used to find the height of the water after x number of minutes. Use the equation to find the height of the water after 10 minutes.
The height of the water after 10 minutes would be ___ centimeters.
The equation to find the height of the water after x minutes is height = = 3 x + 50.
The height of the water after 10 minutes would be 80 centimeters.
How to find the heights of the water ?To find the height of the water, the formula that can be used is :
= rate of change x number of minutes + starting height
Rate of change :
= Change in height / Change in minutes
= ( 53 - 50 ) / ( 1 - 0 )
= 3 / 1
= 3
The equation is therefore:
= 3 x + 50 ( this is the height at 0 minutes)
At 10 minutes, the height would be:
= 3 ( 10 ) + 50
= 30 + 50
= 80 minutes
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Guys please help it’s urgent
Use the associative property to simplify the expression 59 + 40 + 80
A. 59+80+40=139+40=179
B.59+(40+80)=59+120=179
C.59+40+80=99+80=179
D.59+10(4+8)=59+10(12)=59+120=179
59+(40+80)=59+120=179 is implify the expression by Associative property .
What is the associative property?
A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.
The associative quality of addition The amount remains unchanged when the order of the addends is changed. By way of illustration, (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4) 2. plus, left parenthesis, 3. plus, 4. right parenthesis = 2. plus. left parenthesis, 3. plus. right parenthesis.
Associative property
(59 + 40) + 80 = 59 + (40 + 80)
(99) + 80 = 59 + (120)
179 = 179
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A group of people were asked if Marilyn Monroe had a thing with John F Kennedy. 110 responded "yes", and 163 responded "no". Find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John.
Probability = ______ (Please enter a reduced fraction.)
The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%
How to find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John
We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:
Probability of "no" = Number of "no" responses / Total number of responses
Total number of responses = Number of "yes" responses + Number of "no" responses
Total number of responses = 110 + 163 = 273
Probability of "no" = 163 / 273
Simplifying the fraction, we get:
Probability of "no" = 0.5967 or approximately 0.60
So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.
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What value represents the number of ways in which the expected classes are free to vary in the chi‑square goodness‑of‑fit test?
The value that represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test is called the degrees of freedom (df).
It is equal to the number of categories minus one. The degrees of freedom provide a measure of the amount of information available in the sample to estimate the parameters of the distribution.
In a goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus one, which represents the number of ways in which the expected classes are free to vary.
For example, if you are conducting a chi-square goodness-of-fit test to compare the distribution of a categorical variable with expected frequencies, you would have one degree of freedom for each category or class, with the exception of the last category.
The last category's frequency is determined by subtracting the sum of the observed frequencies for all other categories from the total sample size. This means that the last category is not free to vary independently, so it is not counted in the degrees of freedom calculation.
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Question 13
Peng Peng has $4 in quarters and dimes. She has 34 coins. How many quarters and dimes does Peng Peng have?
Part A
Write a system of equations that represents the situation.
0.25x+
+ y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
Step-by-step explanation:
x = number of quarters
y = number of dimes
x + y = 34
therefore, we can say right away
y = 34 - x
0.25x + 0.1y = 4
because a quarter is worth $0.25, and a dime is worth $0.10.
now we are using the first equation in the second :
0.25x + 0.1(34 - x) = 4
0.25x + 3.4 - 0.1x = 4
0.15x + 3.4 = 4
0.15x = 0.6
x = 0.6/0.15 = 4
y = 34 - x = 34 - 4 = 30
the solution is therefore (4, 30).
she has 4 quarters and 30 dimes.
Peng has 4 quarters and 30 dimes.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Peng has $4 in quarters and dimes. She has 34 coins.
we need to find the number of quarters and dimes, does Peng have,
Let x = number of quarters and y = number of dimes
Therefore, establishing the equations :-
x + y = 34
y = 34 - x...(i)
Since, a quarter is worth $0.25, and a dime is worth $0.10.
Therefore,
0.25x + 0.1y = 4.....(ii)
Therefore,
0.25x + 0.1(34 - x) = 4
0.25x + 3.4 - 0.1x = 4
0.15x + 3.4 = 4
0.15x = 0.6
x = 0.6/0.15
x = 4
Put x = 4 in the eq(i)
y = 34 - x = 34 - 4 = 30
y = 30
Hence, she has 4 quarters and 30 dimes.
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What is PPM and How do I calculate it?
PPM stands for "parts per million" and is a way of expressing small concentrations of substances in a larger mixture. To calculate PPM, divide the mass or volume of the substance by the total mass or volume of the mixture and multiply by one million.
To calculate PPM, you need to know the mass of the substance in question and the total mass of the mixture. Here are the steps to calculate PPM:
1. Determine the mass of the substance in question. For example, let's say you have a mixture that contains 0.5 grams of salt.
2. Determine the total mass of the mixture. For example, let's say the total mass of the mixture is 1000 grams.
3. Divide the mass of the substance by the total mass of the mixture. In this example, 0.5 grams / 1000 grams = 0.0005.
4. Multiply the result by 1,000,000 to get the PPM. In this example, 0.0005 x 1,000,000 = 500 PPM.
So, the concentration of salt in the mixture is 500 PPM. Remember to always use the same units of measurement for both the substance and the mixture when calculating PPM.
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Write 10 000 seconds in hours, minutes, and second
The 10,000 seconds can be stated as 166.6777 minutes and 2.7778 hour.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
We have 10,000 sec
As, 1 minute= 60 seconds
So, In minutes
= 10000/60
= 1000/6
= 166.6667 minutes
Now, 1 hour= 60 minutes
So, In hour
= 10000/ 60 x 60
= 10000/3600
= 2.7778 hour
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Question
Which polygon appears to be regular?
Responses
Figure A
Figure B
Figure C
Figure D
The answer would be figure B. (pentagon)
how to calculate hyperboloid of one sheet?
The equation of hyperboloid of one sheet: [tex]\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1[/tex] which is used to calculate hyperboloid.
The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.
Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.
The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.
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Two rectangles each with dimensions
c cm ⇥ b cm are used to form a cross as shown. The arms of the cross are all of equal length.
a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b
b) The area of the cross is:[tex]A= 2cb - 2b^2 \ cm^2[/tex]
c) b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
What is area and perimeter?
The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.
a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.
The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:
a = c - b
Therefore, the perimeter of the cross is:
P = 4a = 4(c - b) = 4c - 4b
b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.
The area of each rectangle is:
[tex]Area_{rect} = c * b[/tex]
The area of each triangle is:
[tex]Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}[/tex]
Since there are four triangles, the total area of the triangles is:
[tex]4A_{tri} = 2cb - 2b^2\ cm^2[/tex]
Therefore, the area of the cross is:
[tex]A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2[/tex]
c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:
[tex]A = 2cb - 2b^2[/tex]
We can rearrange this equation to put it in the form of a quadratic equation:
[tex]2b^2 - 2cb + A = 0[/tex]
This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:
b = (-b ± sqrt(b^2 - 4ac)) / 2a
b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)
[tex]b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
Therefore, b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
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Out of the numbers 1,5,5,6,8 which is the mad
The mean absolute deviation from the given data set is 1.6
What is a Mean Absolute Deviation?The mean absolute deviation measures how far the data points are on average from a center point. Mean, median, mode, or any other random figure can serve as the center point.
The mean is frequently used as the center point, In this situation, The method for computing mean absolute deviation (MAD) is helpful, which represents the average of the absolute departure of the data points from the mean of the data set.
Mean = (1+5+5+6+8)/5
Mean = 25/5
Mean = 5
The distance of each value from the mean is as follows:
Value distance from the mean 5
1 4
5 0
5 0
6 1
8 3
MAD = (4 + 0 + 0 + 1 + 3)/5
MAD = 8/5
MAD = 1.6
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Solve By Substitution
y=-3x
2x-3y=22
Answer:2
Step-by-step explanation:
y = -3x.
Substitute this value in the second equation for y.
=> 2x-3(-3x)=22
=> 2x+9x=22
11x =22
Therefore, x=2.
Hope this helps :)
Two important ingredients for baking
bread are yeast and flour. To make a loaf of bread
of at most 40 servings, maintain a yeast to flour ratio of
1:200. If you're making a loaf of
more than 40 a servings, use a ratio of 1:180.
If you're making 40 servings of bread and using 0.35 oz of yeast, how
many ounces of
flour do you need?
If you're making 90 servings of bread and using 360 oz of flour. how many ounces of
yeast do you need?
NOTE: Enter only numerals for each of your
answers.
Answer:
14 oz of flour. 2 oz yeast.
Step-by-step explanation:
If you're making 40 servings of bread and using 0.35 oz of yeast, you need:
0.35 oz yeast / 1 yeast : 200 flour = 0.35 oz yeast / 1 : 200 flour = 0.00175 oz yeast/flour
So, you need 0.00175 oz yeast/flour * 40 servings * 200 flour/serving = 14 oz of flour.
If you're making 90 servings of bread and using 360 oz of flour, you need:
1 yeast : 180 flour = 360 oz flour / 90 servings / 180 flour/serving = 2 oz yeast.
Which of the following inequalities would have solutions of -4, 0, 2, 3?
Mark all that apply.
Answer:
Step-by-step explanation:
n
What measure is equivalent to 3/4
Answer: 12 tablespoons
Step-by-step explanation: 3/4 of a cup is equal to 6 fluid ounces or 12 tablespoons.
Oliver is going on a 200 mile trip.
He leaves at 10 am and travels for
3 hours at an average speed of 38 mph.
How fast would he need to travel for the
remainder of his journey in order to arrive
at 3 pm?
Answer:
We know it's 1 P.M., and he's traveled 114 miles by now, he needs to go 86 more miles before he reaches his destination. He would need to travel 43 mph to reach his destination by 3.
Step-by-step explanation:
At 1, he has two more hours, and he has 86 more miles to go, so four times two is 8, and 3 times two is 6, so 46. There's probably a proper way to do this but yup 43 mph I hope I'm right and I helped you out :')
Answer:
Oliver would need to travel 43 mph for the remainder of his journey.
Step-by-step explanation:
First, we need to find out how many miles Oliver traveled for those 3 hours.
3 speed × 38 mph = 114 mph in total.
Now we need to know how many remaining miles Oliver needs to travel.
200-mile trip - 114 miles driven = 86 miles left.
Next, We need to know what time Oliver is currently at to know how many hours he needs to travel until it's 3 pm.
10 am + 3 hours = 1 pm
So, we have 2 hours left until it's 3 pm. Oliver needs to go 86 miles in 2 hours to arrive at his destination. So then divide the 86 miles by those 2 hours.
86 miles left ÷ 2 hours = 43 mph
What is the value of 6/3 x 2 3
Answer: 16
Step-by-step explanation:
6 ÷ 3 = 2
[tex]2^{3}[/tex] = 2 x 2 x 2
2 x 2 x 2 = 8
2 x 8 = 16
please help ill give brainliest!!
1.
a) Length = 6 inches
Width = 2 inches
Height = 7 inches
Base Area = 6 x 2 = 12 inches
b) V = l x w x h = 6 x 2 x 7
c) V = B x h = 12 x 7
d) V = 84 inches cubed
Answer: explained below (answers you need to fill in are in bold)
Step-by-step explanation:
1.
a. the dimensions of the box are
l = 6
w = 2
h = 7
B = 12 ... B means base. When finding base, you simply just multiply L x W. In this case, you do 6 x 2 = 12 which will be your base
b.
V = l x w x h = 6 x 2 x 7
c.
V = B x h = 12 x 7
d.
V = 84 ... ( 12 x 7 = 84)
which expression is equal to 8/3 A.3 x 1/8 B. 8 x 1/3 C.8 x 1/8 D.3 x 1/3
Answer:
B. 8*1/3
Step-by-step explanation:
Dayton Photography Studio is taking graduation portraits for students at local schools.
Eighth graders from Dayton Elementary School ordered 50 basic portrait packages and 52
deluxe portrait packages, for a total of $8,544. The seniors at Greenwood High ordered 93
basic portrait packages and 73 deluxe portrait packages, for a total of $13,591. How much
does each type of package cost?
4) A basic package costs $
and a deluxe package costs $
The basic portrait packages costs $70 and deluxe portrait packages costs $97.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the basic portrait packages costs $x.
and, the deluxe portrait packages costs $y.
So, the system of Equation
50x + 52y = 8544..............(1)
93x + 73y = 13591.............(2)
Solving above two equation we get
x=70 and y= 97.
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Aisha and her children went into a grocery store and will buy apples and bananas. Each apple costs $1.25 and each banana costs $0.60. Aisha has a total of $10 to spend on apples and bananas. Write an inequality that would represent the possible values for the number of apples purchased, a, and the number of bananas purchased, b
The required inequality, which represents the possible values for the number of apples and bananas purchased is 2a + 0.6b ≤10.
What is inequality?
Inequality can be defined as the relation of the expression containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let, the number of apples purchased, a, and the number of bananas purchased, b.
According to the question, Each apple costs $1.25 and each banana costs $0.60. London has a total of $10 to spend on apples and bananas.
So,
1.25a + 0.6b ≤10
Thus, the required inequality, that represents the possible values for the number of apples and bananas purchased is 1.25a + 0.6b ≤20.
In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.The distributions of finishing times for both groups are approximately Normal.if the distributions of finishing times are not nearly normal, would the values of the standard score in part a change? explain your reasoning.
Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.
To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:
For Leo:
Z = (4948 - 4313) / 583 = 1.01
For Mary:
Z = (5513 - 5261) / 807 = 0.33
So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.
As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.
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What is the simplified form of x+7/2 subtracted by x+4/2
The simplified form of subtraction is 3/2.
About subtractionThe simplified form of x+7/2 subtracted by x+4/2 is 3/2.
1. Start with the original expression: x+7/2 - (x+4/2)
2. Distribute the negative sign: x+7/2 - x - 4/2
3. Combine like terms: 7/2 - 4/2
4. Simplify by subtracting: 3/2
So the simplified form is 3/2.
Subtraction is an arithmetic operation tat represents the operation of removing an object from a collection. Subtraction is indicated by a minus sign, −. For example, in the image next to it, 5 − 2 peaches—meaning 5 peaches with 2 picked for a total of 3 peaches.
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The graph shows the distance, y, in miles, of a bird from its nest over a certain amount of time, x, in minutes.
Based on the graph, what is the initial value of the graph and what does it repr
0.5 mile per minute; it represents the speed of the bird
0.5 mile; it represents the original distance of the bird from its nest
10 miles; it represents the original distance of the bird from its nest
10 miles per minute; it represents the speed of the bird
need it right now fast!!!
Answer:
10 miles; it represents the original distance of the bird from its nes
Step-by-step explanation:
Casey claims the linear equation for the relationship shown by the graph is c=25j. Use numbers and words to support Casey's claim.
Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given that, Casey claims the linear equation for the relationship shown by the graph is c=25j.
We have points on it,
(1, 25), (3, 75), (5, 125) and (7, 175)
Put each point in the equation,
c = 25j
Put j = 1, 3, 5, and 7
We get the corresponding value, 25, 75, 125, 175
That means, the points are satisfying the equation,
Hence, Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.
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The given graph is :-