Answers
So we're trying to find the equation of a line using the provided x and y values in the chart. We should start by finding the slope of the line, since that's easiest!
We know that the equation for slope is [tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]
All we need to do is pick two points (two x and y coordinates) and respectively plug them into the equation! I want to note that it does not matter which two points you choose! You will always get the same slope!
Alright, so using the two points (-2, -17) and (0, 23) I'll calculate the slope!
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{23-(-17)}{0-(-2)}\\m=\frac{23+17}{0+2}\\m=\frac{40}{2}\\m=20[/tex]
(Just to prove that you can use any two points I'm going to do another example. The only thing you need to keep in mind is that y values are always on top and x values are always on the bottom! In this example I'm using (-6, -97) and (2,63)!)
[tex]m=\frac{63-(-97)}{2-(-6)}\\m=\frac{160}{8}\\m=20[/tex]
As we can see, no matter which points you use, it will always simplify to the same slope!
Now that we have the slope, we need to find the x and y intercepts! An x intercept is the point where y = 0 on the x-axis. A y intercept is the pint where x = 0 on the y-axis!
We already have a y intercept given to us, as you can see in the table there is a point (0, 23). This point is where x = 0! This will be our value next to the y in the equation. So so far, our equation looks like this:
[tex]y-23=20(x-x_1)[/tex]
And how do we know what the x intercept (x1) is? Well, we have a table full of values, so we can use those to plug in for y and x! I want to note again, you do not need to worry about which values you use! Just make sure you have your x and y straight and plug in whichever pair of coordinates you want! I will use the point (-2, -17).
[tex](-17)-23=20((-2)-x_1)\\-40=20(-2-x_1)\\-2=-2-x_1\\x_1=0[/tex]
So it looks like this line goes straight through the origin! If you want to confirm your findings, you can just use another point. This time I'll just use (2, 63)!
[tex](63)-23=20(2-x_1)\\40=20(2-x_1)\\2=2-x_1\\x_1=0[/tex]
This also makes sense to be our x-intercept value since if it was any other number, our y intercept would not be (0, 23) and the given values wouldn't be true anymore! (This is just another way to confirm that it's right!)
Therefore, our final equation is:
y - 23 = 20 (x - 0)
y = 20x + 23 (same answer, just in a different form)
Related Questions
Akira is setting tables at the restaurant where she works. She starts with a pile of 85 napkins, and she places 6 napkins on every table she sets
Write an equation that shows how the number of napkins remaining, y, depends on the number of tables akira sets, x
Answers
Answer: y = 85 - 6x
Step-by-step explanation:
Number of napkins remaining: y
Number of tables set: x
Akira starts out with 85 napkins. So, every time she sets a table, she is losing 6 napkins. The steady rate of napkins lost can be written with the following expression, as she is losing 6 napkins per table.
[tex]-6x[/tex]
These napkins are being removed from the total of 85 napkins:
[tex]85 - 6x[/tex]
The above equation also expresses the number of napkins remaining. Writing it as a proper equation:
[tex]y = 85 - 6x[/tex]
The final answer is: y = 85 - 6x
Subtract the sum of 9 3/4 and 3 1/8 from 18 7/16
help pls
Answers
Answer:
-26/25
Step-by-step explanation:
I took the quiz and I got an A+
Answer:
5 7/16
Step-by-step explanation:
First off, make all the numbers have the same denominator.
In this case, the best one would be 16.
For 9 3/4, the four goes into 16 four times. So you multiply the 3 by four, and get 12 in the numerator. So it is now 9 12/16.
Next we have 3 1/8. 8 goes into 18 2 times. So you multiply 1 by 2 and get 2 in the numerator. So it is now 3 2/16.
Now, lets add the two together:
3 2/16+9 12/16 =
12 14/16
Now we know the sum of the two numbers.
Lets subtract this from 18 7/16:
18 7/16-12 14/16
=
5 7/16
This is your answer!
Hope this helps! :)
PIEVIOUS
Select the correct answer from each drop-down menu.
B
De
B
CH
Quadrilateral A'B'C'D'is obtained by a reflection across the y-axis of quadrilateral ABCD, followed by a translation 3 units to the left and 3
units down. Create a function modeling the reflection and the translations.
Rx y = 1
Reset
Next
First drop down selection :
X+3
-x+3
X-3
-x-3
Second drop down selection:
Y+3
-y+3
Y-3
-y-3
Answers
9514 1404 393
Answer:
f(x, y) = (-x-3, y-3)
Step-by-step explanation:
Reflection across the y-axis is ...
r(x, y) = (-x, y)
Translation left and down 3 units each is ...
t(x, y) = (x -3, y -3)
Then the composition of reflection then translation is ...
f(x, y) = t(r(x,y)) = t(-x, y)
f(x, y) = (-x-3, y-3)
If p= (5,4) find the image of p under 90 degree counterclockwise about the origin
Answers
Bennet stated that the opposite of the opposite is always negative Kylie disagreed with bennet and stated that the opposite of the opposite of any number is always positive which erson is correct or are neither correct and explain how u know
Answers
Both Kylie and Bennet are correct.
Opposite of the opposite of a number is negative if the number is a positive number.
Opposite of the opposite of a number is positive if the number is a negative number.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = x
The Opposite of x is -x.
Opposite of -x.
= -(-)
= x
Number = -x
The opposite of -x.
= -(-x)
= x
The opposite of x.
= -x
Thus,
Both the person is correct.
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if the lines x+y=5 and 2x +2y+6=0 are parallel, find the distance between them
Answers
$576.188 rounded to the nearest hundredth I see
Answers
Answer:
$576.19
Step-by-step explanation:
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X is the age of the crab in months and Yˆ is the predicted value of Y, the size of the male crab in cm. Yˆ=9.1411+0.4775X What is the value of Yˆ when a male crab is 23.2417 months old?
Answers
Answer:
[tex]Y = 20.239[/tex]
Step-by-step explanation:
Given
[tex]Y = 9.1411 + 0.4775X[/tex]
Required
The predicted value of [tex]Y[/tex] when [tex]X = 23.2417[/tex]
To do this, we substitute [tex]X = 23.2417[/tex] in the given equation
So, we have:
[tex]Y = 9.1411 + 0.4775X[/tex]
[tex]Y = 9.1411 + 0.4775 * 23.2417[/tex]
[tex]Y = 9.1411 + 11.0979[/tex]
[tex]Y = 20.239[/tex]
Kurt is flying his airplane over a
campground. He spots a small fire below at
an angle of depression of 32°. If the
horizontal distance from Kurt's plane to the
fire is 3600 feet, find the approximate
altitude of his plane.
A. 2,250
B. 2,575
C. 2,825
D. 3,150
Answers
Answer:
5761
Step-by-step explanation:
Using trigonometry to solve the question which has been represented by the attached triangle :
To obtain the value of h, altitude of airplane ;
Tan x = opposite /Adjacent
Tan 32 = 3600 / h
h = 3600 / tan 32
h = 3600 / 0.6248693
h = 5761.2043
1
The function g that associates each
U.S. city with the state it resides in.
What is g(Los Angeles)?
Answers
Answer:
g(Los Angeles) = California
Step-by-step explanation:
The function g that associates each U.S. city with the state it resides in.
This means that the input of the function is an U.S. city, and the output is the state of the city.
For example:
g(Buffalo) = New York
What is g(Los Angeles)?
Los Angeles is in California. So
g(Los Angeles) = California
Find the volume of the composite solid. Round your answer to the nearest hundredth.
Answers
Answer:
9,114.81 ft³
Step-by-step explanation:
The solid is composed of a cylinder and a hemisphere
Volume of the solid = volume of the cylinder + volume of the hemisphere
= πr²h + ⅔πr³
Where,
r = 8 ft
h = 40 ft
Plug in the values into the equation
Thus:
Volume of the solid = π*8²*40 + ⅔*π*8³
= 8,042.4772 + 1,072.33029
= 9,114.80729
= 9,114.81 ft³ (nearest hundredth)
alice fox and basil cat are searching for a treasure they start at the old oak tree in the field of dreams and walk 240 m, each counting her own number of steps. Basil cat takes 100 fewer steps than alice fox. find the length of alice's step and the length of basil's step if basil's step is 20 cm longer than alice's step
Answers
alice fox's step is 3/5 m and basil cat's step is 4/5m.
note: i will be using 1/5m instead of 20 cm to keep the units consistent
1. Set up table
| Step Length | # of steps | Distance
A | x | 240/x | 240
B | x+1/5 | 240/x+1/5 | 240
2. set up equation
240/x - 100 = 240/x+0.2
3. Multiply the bases to make it:
240x+48 - 100x^2 -20x = 240x
= 100x^2-20x+48=0
4. Use vieta's theorem or quadratic equation to solve for x
x= 3/5, -4/5 but -4/5 doesnt work bc distance can't be negative
5. plug back in
A | 3/5
B | 3/5+1/5
so: alice fox's step is 3/5 m and basil cat's step is 4/5m.
hope this was helpful!!
Answer:
Alice Fox’s step is 3/5, and Basil cat’s step is 4/5.
Step-by-step explanation:
The curved surface area of a cylinder is
250 cm2. If the cylinder is 12 cm high, find
its volume.
Answers
9514 1404 393
Answer:
414.5 cm³
Step-by-step explanation:
The lateral area of a cylinder is given by the formula ...
LA = 2πrh
Then the radius is ...
r = LA/(2πh)
The volume of the cylinder is given by ...
V = πr²h
Using the above expression for r, this becomes ...
V = π(LA/(2πh))²h = LA²/(4πh)
V = (250 cm²)²/(4π·12 cm) ≈ 414.47 cm³
The volume of the cylinder is about 414.5 cm³.
PLIS HELP
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation y = 5x + 62, where x represents the number of t-shirts sold. If they sell 74 shirts, what will the total cost be?
Answers
The total cost of the 74 shirts will be;
⇒ $432
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Now,
Since, The equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Hence, For 74 shirts, the cost is fund by substitute x = 74 in above equation,
⇒ y = 5x + 62
⇒ y = 5 × 74 + 62
⇒ y = $432
Thus, The total cost of the 74 shirts = $432
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Can someone help? I answered it, but I want second opinions.
Answers
Tim worked for a total of 7 and half hours on Monday and earned $56.25 gross pay.
What is gross pay and net pay?Prior to payroll deductions, earned wages are referred to as gross pay. Employers utilize this amount—$60,000 per year or $25 per hour—when talking to employees about pay. Additionally, the federal and state income tax brackets sometimes refer to gross salary.
The amount of pay that employees get after payroll deductions varies; some may be optional, while others may be required.
Given, On Monday of his time card Tim clocked in at 8:15 am and clocked out at 4:15 pm.
So, The total number of hours she worked is 8 hours, 8:15 to 12:15 is 4 hours, and another four hours.
Also given the time he took for lunch is half an hour.
Therefore, The total hour he worked is 7:30 hours.
He earns $7.5 per hour so his gross pay for Monday is $(7.5×7.5).
= $56.25.
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Can anyone tell me how to do this? Step by step
Answers
Step-by-step explanation:
f(x)=x^2-4x-9
g(x)=-3x-5
so when f(g(x)) that x is a number
-3x-5 equals the number in f(x) so that x is -3x-5
f(-3x-5) and if f(x)=x^2-4x-9
then inserting in -3x-5 for x in f(x) and distrubute
(-3x-5)^2-4(-3x-5)-9
9x^2+42x+36
I hope that helps :)
Answer:
9x^2 + 42x + 16
Step-by-step explanation:
f(g(x))
Plug in the expression for g(x)
f(g(x)) = f(-3x - 5)
f(x) = x^2 - 4x - 9
For every x in f(x) replace it with -3x - 5
f(-3x - 5) = (-3x - 5)^2 - 4(-3x -5) -9
Expand
f(-3x - 5) = (9x^2 + 30x + 25) + (12x + 20) - 9
Combine like terms
f(-3x - 5) = 9x^2 + 42x + 16
f(g(x)) = 9x^2 + 42x + 16
98 +23=
Miss Diaz wants her students to practice making the next ten.
a. Circle the problems Miss Diaz should give her students.
12 + 23
38 + 22
64 +99
36 + 40
79 +48
b. Explain why Miss Diaz should give the problems you circled.
Answers
here, on solving company reduced the size of their percentage container of dishwashing soap to 4.5 ounces from its original 5 ounce capacity.
what is percentage ?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
The initial size was x.
Since 100% - 10% = 90%, 0.9x is 10% smaller than the original size.
90% of the original size is equal to 4.5 ounces,
hence the calculation we use to determine the original size x is:
0.9 x = 4.5 x
= 4.5 / 0. 9 x = 5
The bottle's initial capacity was 5 ounces.
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If 1 US Dollar is worth 0.80 Euros, how many US Dollars is 1 Euro worth?
Answers
search in to find answer
Ian shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the number of aces he observes.
Have the conditions for a binomial setting been met for this scenario?
Yes, a success is “ace.”
Yes, all four conditions in BINS have been met.
No, we do not know how many aces will occur in those first four cards.
No, the cards are not being replaced, so the independence condition is not met.
Answers
Answer:
D No, because the cards are not being replaced in the deck after they are turned over, the independence condition has not been met.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
lucky guess
Beth poured 1/2 of the juice from a 5-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
Answers
Answer:
2.5 litres
Step-by-step explanation:
Hey can someone pls help me? I’m confused. It says “find the value of x using complementary angels.”
Answers
Answer:
x = 9 if there is any confusion, please ask questions
Step-by-step explanation:
so in math, a complementary angle is when two angles add up to 90 degrees.
to find this, you have to do 90-81
90 - 81 = 9
5j + 5j + j - 3j
Submit
Answers
Answer:
8j
Step-by-step explanation:
hope this helps!
Jared bakes 2 apple pies. He cuts the two pies into pies. Each piece is 1/8 of a pie. How much pie did Jared. cut?
Answers
He cut 16 pieces
I really hope this helps :D
Please help with this question pls
Answers
Answer:
4+m
Step-by-step explanation:
You can't put them together 'cause they aren't like terms, so you just keep the sign that put them together in the first place.
hello i need help with my math question please thank.
Answers
The three ways to purchase a vehicle include: (1) On lease (2) On hire purchased and (3) On cash basis
How to purchase a vehicle?A vehicle can be purchased on the following ways:
Lease: This involves granting the user access on the property over a period of time before he could make payment
Hire purchase: In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis
Cash: In this method the buyer pays cash at prompt or on the point of purchase
Advantages include:
It places the buyer on good life without cash
He enjoys the luxurious life
Disadvantages:
He can run away with the vehicle
The seller looses in cash of accident taking the life of the buye
Additional expenses include
Cost of maintenance
Repairs
Fueling
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slove system equations
x+y=8
x-y=4
x=? y=?
Answers
Answer:
Step-by-step explanation:
To solve this system of equations, you can use the substitution method.
In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.
To solve this system using substitution, we can solve the second equation for y:
y = x - 4
Then, we substitute this expression for y in the first equation:
x + (x - 4) = 8
Combining like terms, we get:
2x - 4 = 8
Adding 4 to both sides, we get:
2x = 12
Dividing both sides by 2, we find that:
x = 6
Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:
x - y = 4
Substituting 6 for x, we get:
6 - y = 4
Subtracting 6 from both sides, we find that:
y = 2
So the solution to the system of equations is x = 6 and y = 2.
Answer:
x=6, y = 2
Step-by-step explanation:
If you add 2 expressions, 2x = 12, so x = 6.
So the other one y = 2.
Ratio is equivalent to the ratio of 120 to 36
Answers
Explanation
120/36 = 6 x 20/6x6
=20/6
=2x10/2x3
=10/3
120:36 is equivalent to 10:3
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"The trick with ratios is to always multiply or divide the numbers by the same value.
Given here the ratio is 120:36≡10:3
Hence, 120:36 is equivalent to 10:3
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Find the median of the following set of numbers. 98, 67, 98, 102, 74, 95, 99
Answers
Answer:
98
Step-by-step explanation:
to find median you put the numbers in order from least to greatest then you see what number is in the middle
Answer:
98Step-by-step explanation:
The median of an information set is found by putting the information set in ascending numerical order and identifying the center number. If there are an odd number of data values within the data set, the median could be a single number. If there are an excellent number of data values within the data set, the median is that the average of the 2 middle numbers. Sorting the information set for the values entered above we have:
98, 67, 98, 102, 74, 95, 99
Since there's an odd number of data values during this data set, there's just one middle number. With 7 data values, the center number is that the data value at position 4. Therefore, the median is 98.
Use the figure shown to answer the question that follows.
What is the order of rotation of this figure?
2
4
6
8
Answers
On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
What is the order of rotation?The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.
If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
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Amya is making a swayed flower bed with a circular fountain in the middle she wants to figure out mthe area if the part where she will plant flowers
Answers
Answer:
A
Step-by-step explanation: if u read closely and think about it hard enough youll see