Given that initial time for jogging is,
[tex]a_{_1}=14[/tex]After each week the time is increased by
[tex]d=7[/tex]This gives an arithmetic sequence.
To find n such that,
[tex]a_n=70[/tex]Therefore,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]So,
[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]Therefore, 9 weeks before you are up to jogging 70 minutes.
Enter the correct answeach column.5. Bellatrix Lestrange keeps her money in GringottsWizarding Bank. She decided to take $100,000out of her vault and split it among three differentaccounts. She placed part in a savings accountpaying 3% per year, twice as much in Wizard bondspaying 5.5%, and the rest in a mutual fund thatreturned 4%. Her income from these investmentsafter one year was $4,480. How much did Bellatrixplace in each account?11223334.44HOW MUCH DID BELLATRIX PLACE IN THEMUTUAL FUND?556670N (0088
Assum,e that she put x in the account of 3%
So in wizard bonds, she put twice so it is 2x
The rest in the account of 4%
The rest is 100,000 - x - 2x = 100,000 - 3x
The rule of the investment is :
[tex]I=\text{prt}[/tex]I is the interest, P is the money she invested, r is the rate and t is the time
We will make equation for each account
[tex]\begin{gathered} I_1=x(\frac{3}{100})(1)=0.03x_{} \\ I_2=(2x)(\frac{5.5}{100})(1)=0.11x \end{gathered}[/tex][tex]I_3=(100,000-3x)(\frac{4}{100})(1)=4000-0.12x[/tex]The sum of the interest is 4,480, so add them and equate the sum by 4,480 to find the value of x
0.03x + 0.11x + 4000 - 0.12x = 4,480
Add like terms in the left side
0.02x + 4000 = 4,480
Subtract 4000 from both sides
0.02x + 4000 - 4000 = 4,480 - 4000
0.02x = 480
Divide both sides by 0.02
x = 24,000
The value in the mutual fund is 100,000 - 3x, so substitute s by 24,000
The mutual fund = 100,000 - 3(24,000) = 100,000 - 72,000 = 28,000
The mutual fund = $28,000
[tex]f(x) = \sqrt{ {x }^{2} - 121} [/tex]what's the inverse of this equation
EXPLANATION:
The first thing to do in the equation is to interchange the variables in order to do the inverse function and thus solve the equation correctly.
So the equation is as follows:
[tex]\begin{gathered} x=\sqrt[]{x^2-121} \\ Now\text{ we exchange }the\text{ variables x and y;} \\ x=\sqrt[]{y^2-121} \\ y=\sqrt[]{x^2+121};\text{ y}=-\sqrt[]{x^2+121} \\ \sqrt[]{x^2+121\text{ ; }-\sqrt[]{x^2+121}} \\ \text{the answer is : }\sqrt[]{x^2+121\text{ },\text{ }}\text{ }-\sqrt[]{x^2+121^{}} \end{gathered}[/tex]PLEASEEEE HELPPPPAdd. 3+(-7)=
The problem is asking as to perform an addition of signed numbers.
The firs one to add is 3 and the other one is -7.
We can understand the meaning of this type of addition by using the number line forst, and then have a very simple "short cut" every time we fce problems like this.
The number line approach:
locate yourself at the mark "3" on the number line, and then add the number "-7" whichmeans go to the left (as the negative indicates) 7 units. You will see that you move through zero, and then land on the number "-4".
Which graph IS a function?
Answer:
Graph A
Step-by-step explanation:
It is a function of f(x) = 2
Price of PensWhat is the slope ofthe line?Price ($)0-NW A o ovo2Give your answer asa fraction in simplestform.11 2 3 4 5 6 7 8 9Number of Pens
Solution
For this case we can select the following two points:
(0,0) and (4,6)
We can find the slope using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-0}{4-0}=\frac{3}{2}[/tex]then the answer after simplify would be:
3/2
Can you help me find the answer to this equation
Given:
K is the mid-point of FG and L is the mid-point FH.
To find:
The measure of Angle H
Step-by-step solution:
As we are given that K and L are the midpoints of FG and FH respectively.
According to the mid-point theoram,
The segment that connects the mid-point of two sides, is parallel to the third side of that triangle.
Thus,
KL||GH and ∠KLF = ∠GHL
As both of these angles are corresponding angles.
So we can say that m∠H = 85 degrees.
Find the perimeter and area for each figure.
10.
6 in.
P =
A =
3 in.
6 in.
2 in.
5 in.
11.
7 in.
P =
A =
6 in.
(each side is 6 in.)
The perimeter and the area of a rectangle of dimensions 15 cm and 8 cm is given as follows:
Perimeter: 46 cm.Area: 120 cm².What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given, respectively, by these following equations:
Area: A = lw.Perimeter: = 2(l + w).In the context of this problem, the dimensions are given/supposed as follows:
l = 15 cm, w = 8 cm.
Applying the rule, the area, in cm², as the variables are multiplied, is given as follows:
A = 15 x 8 = 120 cm².
The perimeter, in cm, as the measures are added, is given as follows:
P = 2 x (15 + 8) = 2 x 23 = 46 cm.
Missing informationThis problem is incomplete and could not be found on any search engine, hence we suppose that it is a rectangle of dimensions 15 cm and 8 cm.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.y=–4/3x–5x=–3
we have the system
y=–4/3x–5 ------> equation A
x=–3 ------> equation B
Using a graphing tool
see the attached figure
the solution of the system of equations is the intersection point both lines
the solution is the point (-3,-1)Not sure how to approach this question whether to use the factor theorem or to use the synthetic division
EXPLANATION
If x+2 is a factor, we need to equal the factor to zero, isolate x and substitute the value into the function:
[tex]x+2=0\text{ --> x=-2}[/tex]Plugging in x=-2 into the function:
[tex]P(-2)=(-2)^4-2(-2)^2+3m(-2)+64[/tex]Computing the powers:
[tex]P(-2)=16-2*4-6m+64[/tex]Multiplying numbers:
[tex]P(-2)=16-8-6m+64[/tex]Adding numbers:
[tex]P(-2)=72-6m=0[/tex]Adding +6m to both sides:
[tex]72=6m[/tex]Dividing both sides by 6:
[tex]\frac{72}{6}=m[/tex]Simplifying:
[tex]12=m[/tex]In conclusion, the value of m is 12
Help 40 points please (show ur work)
The trail map having a trail length of 7 1/2 in has an actual distance of 3 miles
The amount Kepler paid for the tool not including tax is $120
34% of 850 is 289
How to find the actual length of if 7 1/2 inch in drawingGiven that
5 in ⇒ 2 miles
7 1/2 in ⇒ ?
The question is about scaling a map, the scale is 2miles is represented by 5 inches. This information is used to calculate the actual length when a measure of 7 1/2 inch is taken from the drawing
5 * ? = 7 1/2 * 2
? = 7 1/2 * 2 / 5
? = 3 miles
Hence 7 1/2 inch in the drawing represent an actual distance of 3 miles
How to find the amount Mr Kepler paid for the tool, not including taxGiven that:
with a discount of 40% off the regular price
The regular price was $200
A discount of 40% is given to Mr Kepler. Discount represents amount less the total amount. At a 40% discount Mr Kepler paid 60%
40% = 0.4
40% discount = 1 - 0.4 = 0.6 (equivalent to 60%)
The amount Kepler paid
= 0.6 * 200
= $120
Knowledge of percentage is used here and the amount Mr Kepler paid is $120 not including tax
34% of 850
The statement 34% of 850 means 34 divided by 100 multiplied by 850. The division by hundred takes care of the percent, then "of" means multiplication
34% = 0.34
0.34 * 850 = 289
Hence, we conclude that the concept of percentage and division is used to solve 34% of 850 to get 289
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help meeeeeeeeeeee pleaseee
The solution of the composite function is as follows:
(f + g)(x) = 9x + 1(f - g)(x) = -7x - 17 (f. g)(x) = 8x² - 55x - 72(f / g)(x) = x - 8 / 8x + 9How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
Therefore,
f(x) = x - 8
g(x) = 8x + 9
Hence,
(f + g)(x) = f(x) + g(x) = x - 8 + 8x + 9 = 9x + 1
(f - g)(x) = f(x) - g(x) = x - 8 - ( 8x + 9 ) = x - 8 - 8x - 9 = -7x - 17
(f. g)(x) = f(x) . g(x) = (x - 8)(8x + 9) = 8x² + 9x - 64x - 72 = 8x² - 55x - 72
(f / g)(x) = f(x) / g(x) = x - 8 / 8x + 9
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A sample has a sample proportion of 0.3. Which sample size will produce the widest 95% confidence interval when estimating the population parameter?A. 36B. 56C. 68D. 46
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sample proportion = 0.3
widest 95% confidence interval
sample = ?
Step 02:
p = 0.3
1 - α = 0.95 =>> z α/2 = 1.96
We must check each value to find the solution.
A. sample = 36
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3-0.1499 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3+0.1499 \end{gathered}[/tex]confidence interval (0.1501 , 0.4499)
difference = 0.2998
B. sample = 56
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=0.3\text{ - }0.120 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=\text{ 0.3 + }0.120 \end{gathered}[/tex]confidence interval (0.18 , 0.42)
difference = 0.24
Analyzing these two values, we can conclude that the widest confidence interval will be for the smallest sample.
The answer is:
Sample = 36
A woman transit in her room tour, which got 40 miles per gallon on the highway and purchased a new car which is 28 miles per gallon. What is the percent of decrease in mileage
The percent of decrease in mileage is 30%.
How to calculate the percentage?From the information, the woman transit in her room tour, which got 40 miles per gallon on the highway and purchased a new car which is 28 miles per gallon. The decrease will be:
= 40 - 28 = 12 miles per gallon.
The percentage decrease will be:
= Decrease in mileage / Initial mileage × 100
= 12/40 × 100
= 3/10 × 100
= 30%
This illustrates the concept of percentage.
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an employee at the bank notices an abandoned account with a balance of $360. the bank charges a monthly fee of $8 to maintain an account. the equation for this situation is y = 360 - 8x, where x is the number of months, and y is the balance in dollars. Part A: Find the y-intercept Part B: Find the x-interceptPart C: Interpret the meaning of the x- and y-intercept in terms of the problem.
Given:
There are given the equation:
[tex]y=360-8x[/tex]Explanation:
(A):
To find the y-intercept, we need to put 0 for x and solve the equation for the value of y.
So,
From the function:
[tex]\begin{gathered} y=360-8(0) \\ y=360 \end{gathered}[/tex]Hence, the y-intercept is shown below:
[tex](0,360)[/tex](B):
To find the x-intercept, we need to put 0 for y and find the values for x:
So,
[tex]\begin{gathered} y=360-8x \\ 0=360-8x \\ 8x=360 \\ x=\frac{360}{8} \\ x=45 \end{gathered}[/tex]Hence, the value x-intercept is shown below:
[tex](45,0)[/tex](C):
The interpret the meaning of the x- and the y-intercept is shown below:
In the given context, the y-intercept, and x-intercept, mean x = 0 and y = 0 and also refers to the starting values.
For a time-based exercise, this will be the value when we started talking we read or when we started tracking the time and its related changes.
Write the inequality shown by the shaded region in the graph with the boundary line 2x + 2y = -6
The Solution:
Given the equation of a line below:
[tex]2x+2y=-6[/tex]Step 1:
We shall determine the x-intercept and y-intercept of the given line.
x-intercept: The value of x when y=0
[tex]\begin{gathered} \text{When y=0} \\ 2x+2(0)=-6 \\ 2x=-6 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]\begin{gathered} x=\frac{-6}{2}=-3 \\ \text{ So,} \\ \text{ The x-intercept = (-3,0)} \end{gathered}[/tex]Similarly,
y-intercept: the value of y when x=0
[tex]\begin{gathered} 2(0)+2y=-6 \\ \\ 2y=-6 \end{gathered}[/tex]Dividing both sides by 2, we get
[tex]\begin{gathered} y=\frac{-6}{2}=-3 \\ \text{ hence,} \\ \text{ The y-intercept = (0,-3)} \end{gathered}[/tex]Determine the inequality symbol that will be used to replace the equality sign.
If the straight line is unbroken, it means the points on the line are inclusive. So, the inequality symbol will not be a strict inequality. It will be one of these two inequalities:
[tex]\leq\text{ or }\ge[/tex]Determine the exact inequality symbol that will represent the shaded region.
If the shaded region is below the line, the correct inequality will be:
[tex]\leq[/tex]But where the shaded region is above the line, the correct inequality symbol will be:
[tex]\ge[/tex]From the given graph, it is clear that the shaded region is above the line. So, it follows that the correct inequality is:
[tex]\ge[/tex]Therefore, the correct answer is:
[tex]2x+2y\ge-6[/tex]Solve the quadratic equation using any algebraic method.
X²-11x+30=0
Answer:
5, 6
Step-by-step explanation:
using Vieta's formulas:
x₁ + x₂ = 11
x₁*x₂ = 30
x₁ = 5
x₂ = 6
A total of 350 pounds of cheese is packaged into boxes each containing 1 5 pointsand 3/4 pounds of cheese. Each box is then sold for $1.75. What is the totalselling price of all of the boxes of cheese?150350450550
To solve the exercise, you can first know how many boxes of cheese result with the amount of 350 pounds of cheese.
For this, you can use the rule of three, like this
[tex]\begin{gathered} 1\text{ box}\rightarrow1\frac{3}{4}\text{ pounds of cheese} \\ x\text{ boxes}\rightarrow350\text{ pounds } \end{gathered}[/tex]So, you have
[tex]undefined[/tex]Solve p3 = −512.
p = ±8
p = −8
p = ±23
p = −23
Answer:
B. p = −8
Step-by-step explanation:
Hope this helps you on whatever your doing. :))
if its incorrect, please let me know.
The solution is, the value is, p = −8.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
p^3 = −512.
so, we know, p^3 = p*p*p
and, 512 = 8*8*8
now, we get,
p^3 = - 8*8*8
so, solving we get,
p = -8
Hence, The solution is, the value is, p = −8.
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What interest will be earned if $11,000.00 is invested for 3 years at 11% compounded semi-annual?You would earn $ in interest. (Round to 2 decimal places.)
Answer:
$4,167.27
Explanation:
The amount, A(n) in an account for a Principal invested at compound interest is calculated using the formula:
[tex]\begin{gathered} A(n)=P(1+\frac{r}{k})^{nk}\text{ }where=\begin{cases}P=Prin\text{cipal} \\ r=\text{Annual Interest Rate} \\ k=\text{Compounding Period}\end{cases} \\ n=nu\text{mber of years} \end{gathered}[/tex]In the given problem:
• P = $11,000.00
,• r=11% = 0.11
,• n= 3 years
,• k=2 (semi-annual)
Substitute these into the formula:
[tex]\begin{gathered} A(n)=11,000(1+\frac{0.11}{2})^{2\times3} \\ =11,000(1+0.055)^6 \\ =11,000(1.055)^6 \\ =\$15,167.27 \end{gathered}[/tex]Next, we find the interest earned.
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{Prncipal} \\ =15167.27-11000 \\ =\$4,167.27 \end{gathered}[/tex]You would earn $4,167.27 in interest (rounded to 2 decimal places).
The line plot below shows the number of minutes dog owners in a certain neighborhood spent walking their dogs last month.Which statement describes the data shown?The data has a range of 150 to 40, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 20, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.The data has a range of 150 to 20, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 40, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.
Looking at the graph, the minimum value is 40 and the maximum value is 150, therefore the range is between 150 and 40.
Also, we have a total of 27 points on the graph, which means the median is the 14th value of the data set in crescent order.
Counting the points from the left to the right, the 14th point has a value of 100, therefore the median is equal to 100.
So the correct option is
Which of the following IS a function?
Answer:
The ans C hope it helps u
have a good day
New Orleans is 2 feet below sea level. Salton City has an elevation that is lower than New Orleans. What is a possible elevation, in feet, of Salton City?
Answer:
-4 feet (4 feet below sea level)
Salton City's potential elevation is determined to be 3 feet below sea level by using a number line and the elevation of New Orleans, which is 2 feet below sea level.
What is meant by number line?A number line is a mathematical visual representation of numbers on a straight line. On a number line, the numbers are arranged in order at regular intervals along its length.It often appears horizontally and could extend indefinitely in either direction. A number line is a horizontal line with consistently spaced numerical increments.How the number on the line can be answered depends on the numbers that are present. Given, the elevation indicates that New Orleans is 2 feet below (lower than) sea level.The elevation of Salton City is lower than that of New Orleans. Required; potential rise of Salton CitySalton City's elevation can be calculated using the information below on a number line: We have;& |t; |-3 |-2 |0 > if SL stands for sea level, N for New Orleans, and S for Salton City. On the number line above, a S. N. SLA point to the right of the -2 mark denotes an elevation that is higher than New Orleans, and a point to the left of -2 denotes an elevation that is lower than New Orleans.Therefore,
Salton City should be located to the left of -2, which is a point, at a distance of x -2 feet.
Salton City's elevation, which is determined by the set x -2 feet, is less than 2 feet above sea level.
Since -3 feet is less than -2 feet, Salton City's elevation might be as low as x = 3 feet below sea level, which is less than () 2 feet below sea level.
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2x -1/4y = 1 Solve the equation for y.
Given:
Given the equation
[tex]2x-\frac{1}{4}y=1[/tex]Required: Solve for y.
Explanation:
Subtract 2x on both sides.
[tex]\begin{gathered} 2x-\frac{1}{4}y-2x=1-2x \\ -\frac{1}{4}y=1-2x \end{gathered}[/tex]Multiply both sides by -4.
[tex]\begin{gathered} y=-4(1-2x) \\ =4(2x-1) \end{gathered}[/tex]Final Answer: y = 4(2x - 1)
2 is less than or equal to y
Solution
[tex]2\leq y[/tex]Rachel says when she ran 115 yards she went farther than beth who only ran 327 feet. Is Rachel correct?
Rachel is correct because Rachel ran farther than Beth .
In the question ,
it is given that ,
Rachel ran 115 yards and Beth ran 327 yards ,
For comparing both the distance , we need to convert both the distance in the same unit ,
So , we convert yards to feet ,
we know that,
1 yard = 3 foot ,
So, 115 yard = 3*115 = 345 feet ,
Rachel ran 345 feet and Beth ran 327 feet .
hence , we can conclude that Rachel ran 345 feet which is greater than Beth , who ran only 327 feet .
Therefore , Rachel is correct because Rachel ran farther than Beth .
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an 8-foot ladder leaning against a wall makes an angle of elevation of 70 degrees with the ground how far up the wall is the ladder to the nearest Foot
The length of the ladder is L = 8 foot.
The angle of ladder with ground is 70 degree.
The ladder lean on the wall can be expressed as,
Determine height on the wall to which ladder is up on the wall.
[tex]\begin{gathered} \sin 70=\frac{h}{8} \\ h=0.9397\cdot8 \\ =7.51 \\ \approx8 \end{gathered}[/tex]So up the wall is the ladder is 8 foot.
The scatter plot shows students scores for quiz 1 and quiz 2. a. What is the quiz 1 score for a student who earned a score of 13 on quiz 2? b. Did any student(s) earn the same score on both quiz 1 and quiz 2? Explain. c. The dotted line shows the line of best fit. Write its equation and then interpret the meaning of the slope and y-intercept. Does the y-intercept make sense in the context of the problem? The slope should be represented as a fraction or whole number just to let you know. Here is a picture attached of the graph.
b) Looking at the graph, the scores of quiz 2 are on the y axis while the scores of quiz 1 are on the y axis. Each samll box on both axes is 2 units. This means that half of a samll box is 1 unit. We can locate a score of 15 in quiz 2(halfway between 14 and 16). It also corresponds to a score of 15 in quiz 1. Thus, 1 student earned 15 marks in quiz 1 and 2
c) The equation of the line of best fit is written in the slope intercept form which is expressed as
y = mx + b
where
m = slope
b = y intercept
We would calculate the slope by applying the formula,
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are y coordinates of initial and final points on the line.
x1 and x2 are x coordinates of initial and final points on the line.
Picking points on the graph, we have
when x1 = 10, y1 = 8
when x2 = 16, y2 = 14
By substituting these values into the formula,
m = (14 - 8)/(16 - 10) = 6/6 = 1
We would find the y intercept by substituting m = 1, x = 10 and y = 8 into the slope intercept equation. We have
8 = 1 * 10 + b = 10 + b
b = 8 - 10
b = - 2
Substituting m = 1 and b = - 2 into the slope intercept equation, the equation of the line of best fit is
y = x - 2
The slope is 1 and since it is small, it tells us that for each score of 1 that a student gets in quiz 2, he would likely get a score of 1 in quiz 1.
Since the y intercept is negative, it doesn't make sense in the concept of the problem because a student cannot earn a negative score in any of the quizzes. The y intercept tells us that the student earned - 2 in quiz 2 and 0 in quiz 1
Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa’s age and her sister’s age?
A. x − (x − 4)
B. (x + 4) − x
C. None of these
D. (x − 4) − x
The expression for the sum of Lisa and her sister's age is (x - 4) + x which is the third option that is none of these form the given options.
It is given in the question that Lisa is four years younger than her sister.
Let Lisa's sister's age be x years.
Hence, according to the data given on the question, we can write,
Lisa age = (x - 4) years
Hence, the expression for the sum of the ages of Lisa and her sister will be = (x - 4) + x years.
It is not given in any of the options, hence the answer is none of these.
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Find the distance between the (3,3) and (10,3) coordinates and write the result in the empty box. plsss helppppppppppp
Answer: 7
Step-by-step explanation:
Distance (d) = √(10 - 3)2 + (3 - 3)2
=√(7)2 + (0)2
=√49
=7
Find the equation of the line that is parallel to the line y = -2x +3 and passes through the point (5,4).y = − 1/2x + 6.5y = 2x - 14y = -2x + 14y = 1/2x + 1.5
lets remember how to find the equation of a parallel line
two lines are parallel if they don"t intersect, that means they slopes are the same
y=-2x+3
slope as we see is m=-2
the other line has to pass through point (5,4)
y-y1=m(x-x1)
y-4=-2(x-5)
we solve the equation
y= 4-2x+10
y= -2x+14
i will send you a picture
green line is y=-2x+14