Answer:
12[tex]x^{2}[/tex]+4x
Step-by-step explanation:
area = width * height
substitution: area = (3x+1)*4x
distributive property: area = (4x*3x)+(4x*1)
simplify: area = 12[tex]x^{2}[/tex]+4x
Help!!
You flip a coin and roll a dice. The resultant outcome table where H means heads, T means Tails, and the number represents what number was rolled on the dice. The outcome list is as follows: Coin Toss H H H H H H TTTTTT Die Roll 1 2 3 4 5 6 1 2 3 1 2 3 4 5 6 What is the probability that the coin reads heads or tails and the dices number is less than or equal to 6?
The probability that the coin reads heads or tails and the dices number is less than or equal to 6 is 1/3 or approximately 0.333.
How to calculate the probability that the coin reads heads or tails and the dices number is less than or equal to 6?There are 12 possible outcomes in the table where the coin reads heads or tails and the dice roll is less than or equal to 6. These are:
Coin Toss: H, Die Roll: 1
Coin Toss: H, Die Roll: 2
Coin Toss: H, Die Roll: 3
Coin Toss: H, Die Roll: 4
Coin Toss: H, Die Roll: 5
Coin Toss: H, Die Roll: 6
Coin Toss: T, Die Roll: 1
Coin Toss: T, Die Roll: 2
Coin Toss: T, Die Roll: 3
Coin Toss: T, Die Roll: 4
Coin Toss: T, Die Roll: 5
Coin Toss: T, Die Roll: 6
Out of these 12 outcomes, 6 have the coin reading heads and 6 have the coin reading tails. So, the probability that the coin reads heads or tails and the dice number is less than or equal to 6 is:
P(heads or tails and dice number <= 6) = P(heads and dice number <= 6) + P(tails and dice number <= 6)
= 6/36 + 6/36
= 12/36
= 1/3
Therefore, the probability is 1/3 or approximately 0.333.
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Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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MARKING AS BRAINLIST PLS HELP
Answer:
The angle of C is 118.6
Step-by-step explanation:
2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6marks) Shape No. of match-sticks Rule 1 4 2 7 3 10 4 13 6 241 10 40 43 21 82
find the circumference of a circle circumscribed about a right triangle with legs 5 centimeters and 3 centimeters
Answer:
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
Step-by-step explanation:
To find the circumference of a circle circumscribed about a right triangle with legs 5 cm and 3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse, which is also the diameter of the circle.
Using the Pythagorean theorem, we have:
c^2 = 5^2 + 3^2
c^2 = 25 + 9
c^2 = 34
c = sqrt(34)
So the diameter of the circle is sqrt(34) cm, and the radius is half of the diameter, or sqrt(34)/2 cm.
The circumference of a circle is given by the formula:
C = 2 * pi * r
where pi is approximately 3.14 and r is the radius of the circle.
Substituting the value of the radius, we get:
C = 2 * 3.14 * sqrt(34)/2
C = 3.14 * sqrt(34)
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
what is the inverse of f(x)=(4x-9)^1/2
The inverse of f(x) = [tex](4x-9)^{1/2[/tex] when the variables of x and y are switched is [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
What is an Inverse of a Function?Inverse of a function is a function which can be reversed into another function. It is also a function that undoes the action of the another function.
How to determine this
When f(x) = (4x-9)^1/2
To determine the inverse, [tex]f(x)^{-1}[/tex]= y
y = (4x-9)^1/2
y = [tex]\sqrt{4x-9}[/tex]
By squaring both sides
y^2 = 4x - 9
By swapping the variables
x^2 = 4y - 9
Subtracting 9 from both sides
x^2 +9 = 4y
divide through by 4
[tex]\frac{x^{2}+9 }{4}[/tex] = 4y/4
y = [tex]\frac{x^{2}+9 }{4}[/tex]
Therefore [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
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NO LINKS!! URGENT HELP PLEASE!!!
Movies generally lose 23% of its audience for each week it is in the theatre. A movie STARTED with an audience of 196 people per viewing.
a. Equation: ________________
b. Make a chart and fill in the table for the first ten weeks.
c. Graph the function. Label each axis with a title and scale
Answers:
a) The equation is y = 196(0.77)^x
b) The chart is shown below
c) The graph is shown below
================================================
Explanation:
Part (a)
One template of an exponential equation is y = ab^x
a = starting valueb = connected to the growth rate or decay rateIn this case
a = 196b = 1-0.23 = 0.77If 23% of the audience leaves, then 77% remains. This is another way to see where b = 0.77 comes from. Exponential decay will have 0 < b < 1.
Therefore, the equation is y = 196(0.77)^x
Other equations are possible.
-------------------
Part (b)
I'll be using LibreOffice spreadsheet to make the table. Any spreadsheet software will do.
Type x into cell A1
Type 0 and 1 into cells A2 and A3 in that order.
Select cells A2 and A3. Pull down the small marker at the bottom right corner. Pull this marker down to cell A12 to get values 2 through 10 (which will be in cells A4 to A12).
Now move to cell B1. Type in y = 196(0.77)^x in this cell.
In cell B2, type in "=ROUND(196*(0.77)^A2)" without quotes. As you can probably guess, the ROUND function will round to the nearest whole number. The calculation 196*(0.77)^A2 computes the result of y = 196*0.77^x when plugging x = 0 which is in cell A2.
Do not forget about the equal sign up front.
After cell B2 is filled in, hit enter. Then pull down the smaller marker at the bottom right corner to cell B12. A bunch of whole numbers should fill in cells B3 to B12
This is what you should get for your table
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{y} = 196(0.77)^{\text{x}}\\\cline{1-2}0 & 196\\\cline{1-2}1 & 151\\\cline{1-2}2 & 116\\\cline{1-2}3 & 89\\\cline{1-2}4 & 69\\\cline{1-2}5 & 53\\\cline{1-2}6 & 41\\\cline{1-2}7 & 31\\\cline{1-2}8 & 24\\\cline{1-2}9 & 19\\\cline{1-2}10 & 14\\\cline{1-2}\end{array}[/tex]
x = week number
y = viewer count (approximate)
Example calculation:
Plug in x = 5 to get y = 196*0.77^5 = 53.05297 approximately which rounds to y = 53. Therefore, we estimate there would be about 53 people in the audience for week 5.
-------------------
Part (c)
You could use a spreadsheet to make the graph, but I find GeoGebra is more friendly for graphing. But we'll be using the data we just made in the spreadsheet.
Select cells A2 through B12. This is the 11 row by 2 column block of x,y data pairs. Do not select the headers at the top.
Copy that data and paste it into GeoGebra's spreadsheet mode.
Then select that same block of data in GeoGebra. Right-click to go to "create" then to "list of points". It will do as it describes. Eleven points will show up in the graph window. Resize and adjust the window if needed.
I'm using the following window parameters
xMin = -5xMax = 20yMin = -20yMax = 220The graph is shown in the screenshot below.
Answer:
[tex]\textsf{a.} \quad \textsf{Equation:} \;\;\;y=196(0.77)^x[/tex]
b. See below.
c. See attachment.
Step-by-step explanation:
We can model the given situation using an exponential decay equation since the weekly change in audience is a constant percentage change.
Exponential decay formula[tex]\boxed{y=a(1-r)^x}[/tex]
where:
a is the initial value.r is the percentage decrease (in decimal form).x is the time period.Given the movie started with an audience of 196 people viewing, a = 196.
Given the movie loses 23% of its audience each week, r = 0.23.
As the movie loses a constant percentage of its audience each week, let x be the number of weeks.
Substitute the values of a and r into the formula and simplify:
[tex]y=196(1-0.23)^x[/tex]
[tex]y=196(0.77)^x[/tex]
Therefore, the equation that models the given scenario is:
[tex]\boxed{y=196(1-0.23)^x}[/tex]
Create a table for the first ten weeks by substituting the values of x from zero through 10 into the equation. Round each number to the nearest whole number.
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}$Weeks$\;x&$Audience$\;y\\\cline{1-2}\vphantom{\dfrac12}0&196\\\cline{1-2}\vphantom{\dfrac12}1&151\\\cline{1-2}\vphantom{\dfrac12}2&116\\\cline{1-2}\vphantom{\dfrac12}3&89\\\cline{1-2}\vphantom{\dfrac12}4&69\\\cline{1-2}\vphantom{\dfrac12}5&53\\\cline{1-2}\vphantom{\dfrac12}6&41\\\cline{1-2}\vphantom{\dfrac12}7&31\\\cline{1-2}\vphantom{\dfrac12}8&24\\\cline{1-2}\vphantom{\dfrac12}9&19\\\cline{1-2}\vphantom{\dfrac12}10&14\\\cline{1-2}\end{array}[/tex]
The graph of the function is an exponential decay curve, which starts at (0, 196) and approaches zero as x approaches infinity.
The x-axis represents the number of weeks and the y-axis represents the audience size.
Use a scale of x : y = 1 : 10.
Plot the points from the table and draw a smooth curve through them that approaches zero as x approaches infinity.
Please answer this question quickly
FOR 35 POINTS
I WILL GIVE BRAINLIEST
Answer: 0
Step-by-step explanation:
[tex]log_{3} log_{5} log_{2} 32[/tex]
Let's evaluate
[tex]log_{2}32[/tex] this is the same as
[tex]2^{x}=32[/tex] 2*2*2*2*2=32
or
you can think of it as 2 to the what power is 32
so x=5
now substitute that in for [tex]log_{2}32[/tex]
[tex]log_{3} log_{5} 5[/tex]
Now evaluate [tex]log_{5}5[/tex]
5 to the what power is 5
=1
substitute into [tex]log_{3} log_{5} 5[/tex]
[tex]log_{3} 1[/tex]
3 to the what power is 1
=0
Anything to the 0 power is 1 (it's a rule)
2. Why was the Constitutional Convention held?
lengte
A. Each state's government was too weak.
B. Americans wanted to win independence from England.
C. The national government was too weak.
D. The states wanted to form the first American government.
Anyone pls
Linda agreed to lend money to Alex at a rate of 9 percent per year,
contingent he would pay her 300.00 in interest over a four year period. What was the minimum mount Alex could borrow
Answer:
$731.71
Step-by-step explanation:
300 over 4 years = 75$ per yr
9% per year so 4 years interest = (1+9%)^4 = 1.41
so effective int rate for 4 years is 41%.
41% * x = 300
x = $731.71
What questions please help me thanks
1. The monthly payment for Loan A is roughly $516.40.
2. The total interest for Loan A is roughly $1590.4
How do we calculate the monthly payment and total interest?We've been given the formula: PMT = (P(r/n)) / [1 - (1 + r/n)^-nt] to calculate the monthly payment loan.
If we should insert the figures given to the formula, it should be
PMT = (17000(0.059/12)) / [1 - (1 + 0.059/12)^(-12*3)]
PMT = 516.40
To calculate total interest for loan A, we use the formula (PMT x n x t) - P.
If we insert the figure provided, it should be;
(598.87 x 12 x 3) - 17000
= $1590.4
The above answer is in response to the question below as seen in the picture;
Suppose that you decide to borrow $17,000 for a new car. Installment loan A: 3 years at 5.9%. Use PMT = (p(r/n))/ [1 - (1 + r/n)^-nt]
Find the monthly payment and the total interest for loan A. The monthly payment for Loan A is $..............
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part B write a numerical expression of angle C
The index of refraction of the second material is 1.27.
We are given that;
Angle= 59°
Randomized Variables 1 = 1.47θ1 = 59°θ2 = 69°
Now,
To find n2, we can rearrange Snell’s law as:
n2 = n1 sin θ1 / sin θ2
Plugging in the given values, we get:
n2 = 1.47 sin 59° / sin 69°
n2 = 1.47 (0.857) / (0.934)
n2 = 1.27 (rounded to two decimal places)
Therefore, by the expression the answer will be 1.27
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3x+2=8 what is the value of x
Answer:
x = 2
Step-by-step explanation:
3x + 2 = 8
Subtracting both sides by 2 we get,
=> 3x + 2 - 2= 8 - 2
=> 3x = 6
=> x = 6/3
=> x = 2
Indirect measurement, pls help, I am stuck on this question.
The building is 246 feet tall.
What are similar triangles?Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.
To determine the height of the building, we have;
height of pole = 7 ft
total length of the building's shadow = 167 ft
the length of the shadow of the pole = 4.75 ft
Let the height of the building be represented by h. On comparison, we have;
4.75/ 167 = 7/h
4.75h = 167 x 7
= 1169
h = 1169/ 4.75
= 246.11
The building is 246 ft. tall.
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Need some help with this khan academy question, thanks.
The relative frequency of the two frequency table is completed as below
less than 2 years 2 or more years row total
college degree 0.26 0.74 1.00
no coll degree 0.70 0.30 1.00
How to fill the tableThe relative frequency table is filled by comparing the values as below
less than 2 years 2 or more years row total
college degree 5/19 14/19 1.00
no coll degree 16/23 7/23 1.00
The row total
5 + 14 = 19 so we have 5/19 (0.26) and 14/19 (0.74)
16 + 7 = 23 o we have 16/23 (0.70) and 7/23 (0.30)
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Change zero degrees Celsius to Fahrenheit.
Answer: F=32
Step-by-step explanation:formula: F = Celsius*9/5+32
so plug the zero for Celsius, in this case, 0*9/5+32 = 32
The claim is that for a smartphone carrier's data speeds at airports, the mean is 18.00 Mbps. The sample size is n= 14 and the test statistic is t= -2.645 .
whats the P-value?
According to given information the P-value is approximately 0.016.
What is P-value?In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed results, under the assumption that the null hypothesis is true.
According to given information:To find the P-value for this hypothesis test, we need to use a t-distribution with degrees of freedom equal to n-1 = 14-1 = 13. Since the test statistic is t = -2.645, we need to find the area under the t-distribution curve to the left of t.
Using a t-table or calculator, we can find that the area to the left of t = -2.645 with 13 degrees of freedom is approximately 0.008. This is the probability of observing a t-value less extreme than -2.645, assuming the null hypothesis is true.
Since this is a two-tailed test (we are testing whether the true mean is less than or greater than 18.00 Mbps), we need to double the one-tailed P-value to get the two-tailed P-value. Therefore, the P-value is approximately 0.016 (i.e., 2 x 0.008).
So, the P-value is approximately 0.016.
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you need 18 lb of peeled and cored apples to make applesauce.apples have a yield percentage of 78%, how many pounds of whole apples are needed
You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
Explanation:
To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:
Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage
Plugging in the values we have:
Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)
Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
320.041 - 47.96 multiple it for me
Answer:
320.041 - 47.96 = 272.081
Step-by-step explanation:
I need more information on what you want me to do.
Do you want me to:
Multiply 320.041 by 47.96?
Subtract 47.96 from 320.041?
Multiply the difference between 320.041 and 47.96 by 47.96?
Multiplying 320.041 by 47.96 gives 152,399.6896.
Subtracting 47.96 from 320.041 gives 272.08.
Multiplying the difference between 320.041 and 47.96 by 47.96 gives 13049.0048.
Determine the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.
The function is positive and increasing.
Given is an exponential function y = √4x,
So, since all the value of the function will be above x-axis therefore, the function is positive.
Now,
Differentiating the function,
y' = d(√4x)/dx
y' = 1/2 × [tex]4x^{-1/2[/tex]
y' = 1/2√4x
y' = 1/4√x
Since, y' > 0, therefore, the function is increasing.
Now,
For functions with exponential growth, we have the following end behavior.
The end behavior on the left (as x → -∞), it has a horizontal asymptote at y = 0,
The end behavior on the right (as x → ∞), y→ ∞.
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There are only red counters, blue counters and green counters in a bag.
number of red counters: number of blue counters: number of green
counters = 1:3:7
A counter is going to be taken at random from the bag.
Complete the table below to show each of the probabilities that the counter will be red or blue or green.
(2 marks)
Answer:
Color Probability
Red 1/11
Blue 3/11
Green 7/11
Step-by-step explanation:
The total number of counters in the bag is 1+3+7=11. The probability of selecting a red counter is 1/11, because there is only one red counter in the bag. The probability of selecting a blue counter is 3/11, because there are three blue counters in the bag. Similarly, the probability of selecting a green counter is 7/11, because there are seven green counters in the bag.
The Hartford offered an annuity that pays 5.5% compounded monthly.
What equal monthly deposit should be made into this annuity in order
to have $100000 in 10 years?
If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.
In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:
Which is : FV = P × [(1 + r)ⁿ - 1]/r,
where:
FV is "future-value" = $100000,
P = monthly deposit
r = monthly interest rate (5.5%/12 = 0.00458)
n = number of months (10 years × 12 months per year = 120 months)
Substituting the values,
We get,
⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,
⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],
⇒ P ≈ $627,
Therefore, an equal monthly deposit is approximately $627.
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The length of a rectangle is 4 meters less than 3 times the width. The perimeter is 24 meters. Find the width
Answer:
Step-by-step explanation: length of a rectangle is 4 meters less than 3 times the width so we can write L = 3W-4
The formula for the perimeter of a rectangle: P = 2L+2W
Now plug the numbers: P = 2(3W-4)2W
24 = 6W - 8 +2W
24 = 8W - 8
32 = 8W
W = 4
based on an exponential model of the data, what is the predicted value of variable 2 when variable 1=2? round your answer to the nearest whole number.
a. variable 2 ≈ 128
b. variable 2≈ 166
c. variable 2≈ 181
d. variable 2≈ 263
The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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Please help asap!!!!!
Answer:
[tex]f(-1) = -2\\[/tex]
[tex]f(0)=0[/tex]
[tex]f(1)=2[/tex]
Step-by-step explanation:
f(x)=2x
1) f(-1) = 2(-1) = -2
2) f(0) = 2(0) = 0
3) f(1) = 2(1) = 2
How do you write 9.6522 as a percentage
How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
Drag a value or phrase into each box to correctly complete the statements
Answer:
2 root 5
6 root 5
are the same
Step-by-step explanation:
Answer:
[tex]2\sqrt{5} \\6\sqrt{5}[/tex]
are the same
Step-by-step explanation:
(-23u^4 z^2 +32u^7 z^7 -12u^2 z) ÷ -4u^4 z^2
7. El área de un terreno de forma rectangular es 4332 m?. Si de ancho mide la tercera parte de su medida de largo, ¿Cuáles son las dimensiones del rectángulo?
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3, 6) and (1,-2)?
The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
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The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
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