The height of the helium tank is 49 inches.
What is Volume?Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.
The volume V of a cylinder is given by the formula:
V = πr²h
where r is the radius of the base and h is the height of the cylinder.
Since the diameter of the helium tank is given as 14 inches, the radius r is half of the diameter, which is 7 inches.
We also know that the volume inside the tank is 2,401π cubic inches. Therefore, we can write:
2,401π = π(7)²h
Simplifying the right-hand side, we get:
2,401π = 49πh
Dividing both sides by 49π, we get:
h = 2,401π / 49π
Simplifying, we get:
h = 49
Therefore, the height of the helium tank is 49 inches.
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Answer:
49
Step-by-step explanation:
I took the test and got it right :)
Please answer number 15 and 16 show work
Algebra 2
The exponential function that models the percentage as a function of P is given as follows:
P(t) = 100(0.705)^t.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.The parameters for this problem are given as follows:
a = 100, as when x = 0, y = 100, from the second row of the table.b = 70.5/100 = 0.705, as when x increased by one, y was multiplied by 0.705.Hence the function that models the data in the table is defined as follows:
P(t) = 100(0.705)^t.
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Aquations (Level 2) , 10:02:21 PM atch help video for all values of x. x-(x+5)/(x+8)=(3)/(x+8)
The values of x that satisfy the equation are x = -8 and x = 1.
To find all values of x that satisfy the equation x-(x+5)/(x+8)=(3)/(x+8), we can follow the steps below:
1. Multiply both sides of the equation by (x+8) to eliminate the fractions:
(x+8)(x) - (x+5) = 3
2. Distribute the (x+8) on the left side of the equation:
x^2 + 8x - x - 5 = 3
3. Combine like terms on the left side of the equation:
x^2 + 7x - 5 = 3
4. Subtract 3 from both sides of the equation to get the equation equal to zero:
x^2 + 7x - 8 = 0
5. Factor the left side of the equation:
(x+8)(x-1) = 0
6. Set each factor equal to zero and solve for x:
x+8 = 0 or x-1 = 0
x = -8 or x = 1
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This is a little more of a bigger problem, but this honestly confuses me and I need a lot of assistance.. thanks
Answer:
Step-by-step explanation:
4. 16 players enter the tournament. f(0) = 16(1/2)° = 16
This is the value of y when x=0
5. After 4 rounds, 1 player is left. f(4) = 16(1/2)⁴ = 1
6. Rate of change = Δy/Δx = (4-8) / (2-1) = -4
f(1) = 16(1/2)¹ = 8
f(2) = 16(1/2)² = 4
The average rate of change between rounds 1 and 2 is 4, meaning 4 players are eliminated.
Write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. Display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places. All numbers are to be right justified. The columns of the table should have appropriate headings.
To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:
#include <iostream>This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.
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8. An escalator in a mall must lift customers to a height of 22 ft. If
angle between the escalator stairs and the ground floor will be 30°, what will be the
length of the escalator?
The length of the escalator, considering the trigonometric ratios, is of
38.1 ft.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 30º, we have that:
The adjacent side is the length.The opposite side is of 22 ft.Hence the length of the escalator is obtained with the tangent as follows:
tan(30º) = 22/l
l = 22/tangent of 30 degrees
l = 38.1 ft.
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Find the inverse function of f(x) = - Vx+1+6. Specify the domain for f^-1(x) f^-1(x)__________ Domain of f-1(x) using interval notation:________
The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).
The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:
1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1
The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:
x+1 ≥ 0
x ≥ -1
So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).
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Given the following information, find sin 2x, cos 2x, and tan
2x. (10pts) sinx=1/7, x in QII
sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.
Answer:
Given the information sin x = 1/7, x in QII. The second quadrant (QII) lies between 90° and 180°.Therefore, we know the following about the values of the trigonometric functions:cos x is negative because it is in the second quadrant.tan x is negative because it is in the second quadrant.Therefore, cos x = -sqrt(48)/7 and tan x = -1/4.To find sin 2x, cos 2x, and tan 2x, we will use the following trigonometric identities: sin 2x = 2sin x cos x cos 2x = cos² x - sin² x tan 2x = 2tan x / (1 - tan² x)Substituting in the values for sin x and cos x, we get:sin 2x = 2(1/7)(-sqrt(48)/7) = -4sqrt(3)/49cos 2x = (-sqrt(48)/7)² - (1/7)² = 47/49tan 2x = 2(-1/4) / (1 - (-1/4)²) = -8/15Therefore, sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.
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59. Standard Normal areas Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.
(1) z > -1.66
(2) -1.66 < z <2.85
The proportion of observations in a standard Normal distribution that satisfies each of the given statements are:
1) P(z > -1.66) = 0.95154
2) P(-1.66 < z <2.85) = 0.94936
How to find the probability of the z-score?Z table or z-score table is defined as a mathematical table that provides the values of cumulative density function for standard normal variates. It is used to determine the probability of a standard normal variate lying in a given interval.
We have to find the proportion of observations from a standard normal distribution that has a z-score between -1.66 and 2.85.
1) z > -1.66
From normal probability distribution table, we have that:
P(z > -1.66) = 0.95154
2) -1.66 < z <2.85
From normal probability distribution table, we have that:
P(-1.66 < z <2.85) = 0.94936
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To indirectly measure the distance across a river, Arun stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Arun draws the diagram below to show the lengths and angles that he measured. Find
�
�
PR, the distance across the river. Round your answer to the nearest foot.
P
R
O
C
E
The distance across the river is approximately 597 feet.
When is the Law of Cosines employed in trigonometry, and what does it mean?The Law of Cosines is a formula that connects a non-right triangle's sides and angles. When the lengths of two sides and the angle between them, or the lengths of all three sides, are known, it is used to determine the length of a side or measure of an angle.
For the given figure:
Using trigonometry, we can find the length of PR as follows:
tan(43) = QR/PS
PS = QR/tan(43)
tan(68) = QR/RU
RU = QR/tan(68)
Since PS + RU = PR,
PR = QR/tan(43) + QR/tan(68)
Since triangle PQR is a right triangle, we can use the Pythagorean theorem:
QR² = PS² + RU²
Substituting the expressions for PS and RU gives:
QR² = (QR/tan(43))² + (QR/tan(68))²
QR ≈ 325.4 feet
Now we can substitute this value into the expression for PR to get:
PR ≈ 596.7 feet (rounded to the nearest foot)
Therefore, the distance across the river is approximately 597 feet.
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The complete question is:
Help!! please answer asap
Express as a trigonometric function of one angle.
cos 9 sin(−6) − cos 6 sin 9
The expression can be explained as the trigonometric function of an angle as follows sin(15).
The given expression can be simplified using the trigonometric identity for the sine of the difference of two angles:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Substituting the given values for a and b, we get:
sin(9 - (-6)) = sin(9)cos(-6) - cos(9)sin(-6)
Simplifying further, we get:
sin(15) = sin(9)cos(6) - cos(9)sin(-6)
Therefore, the given expression can be expressed as a trigonometric function of one angle as follows:
sin(15) = sin(9)cos(6) - cos(9)sin(-6)
-sin(15) = cos(9)sin(-6) - sin(9)cos(6)
So the final answer is -sin(15).
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Computations In Exercises 1 through 6, list the elements of the subgroup generated by the given subset. 1. The subset{2,3}ofZ122. The subset{4,6}ofZ123. The subset{8,10}ofZ18(4.) The subset{12,30}ofZ365. The subset{12,42}ofZ6. The subset{18,24,39}ofZ
{18, 36, 24, 48, 39, 72}
In Exercises 1-6, the subgroup generated by the given subset is a set of elements that are all powers of the same element.
1. The subset {2,3} of Z12 generates the subgroup {2, 4, 8, 3, 9, 6, 12}.
2. The subset {4,6} of Z12 generates the subgroup {4, 8, 6, 12}.
3. The subset {8,10} of Z18 generates the subgroup {8, 16, 10, 18}.
4. The subset {12,30} of Z36 generates the subgroup {12, 24, 30, 36}.
5. The subset {12,42} of Z6 generates the subgroup {12, 6}.
6. The subset {18,24,39} of Z generates the subgroup {18, 36, 24, 48, 39, 72}.
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Consider the following vectors v1 = 1 , v2 = 2 , and v3 = -1 . For what values (s) -1 1 3
2 1 h
of h is the set. {v1, v2, v3] linearly dependent? Work must be shown for this question. h = -4
h = 4
all real number h ≠ 4 all real number h ≠ -4
The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:
a*1 + b*2 + c*(-1) = 0
We can rearrange this equation to solve for h:
h = -a - 2*b + c
Now we can plug in the values for v1, v2, and v3:
h = -1 - 2*2 + (-1)*(-1)
h = -4
Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.
Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:
| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |
Simplifying this equation gives:
h - 6 - 2 + 1 + 2 - 6 = 0
h - 11 = 0
h = 11
Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.
So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.
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pls help me
Let f(t) = 10 and g(t) = 65t. The distance, in miles, that a car is from a city can be modeled by f(t) + g(t), where t represents time, in hours. Riordan claims that the car is 150 miles from the city after 2 hours of driving, since (10 + 65) = 75(2) = 150. Decide if Riordan is correct. If he is correct, enter 150 below. If he is incorrect, enter the correct distance. miles
Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:
d(t) = f(t) + g(t) = 10 + 65t
So, after 2 hours of driving, the distance that the car has traveled from the city is:
d(2) = 10 + 65(2) = 10 + 130 = 140 miles
Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.
Step-by-step explanation:
wing system of equations. If there is a solution, write your ans 4x+8y=40 6x+3y=6
The solution of the given system of equations is x = -1 and y = 4.
The given system of equations is 4x + 8y = 40 and 6x + 3y = 6.
To solve this system of equations, we need to use elimination method. We can subtract 6x from both sides of the second equation and subtract 4x from both sides of the first equation. We get:
8y = 40 - 4x and 3y = 6 - 6x
We can now divide both sides of the second equation by 3 to obtain y = 2 - 2x.
We can substitute the value of y from the second equation into the first equation to get 4x + 8(2 - 2x) = 40, which simplifies to -8x = 8. We can solve this equation for x by dividing both sides by -8, resulting in x = -1.
Substituting the value of x into either equation, we can obtain y = 4. So, the solution of the given system of equations is x = -1 and y = 4.
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irst, rewrite (11)/(20) and (13)/(25) so that they have a common denominator
Answer:
55/100 and 48/100, in decimal form it will be 0.55 and 0.48
Step-by-step explanation:
11/20 and 12/25
The common denominator in this question will be 100
55/100 and 48/100
An angle measures 60°. What is the measure of its complement?
What is the expression written using each base only once? 48 x 43 O A 411 O B. 1211 O C. 424 O D. 6411
The expression written using each base only once is 4¹¹ , the correct option is (a).
The expression 4⁸×4³ can be simplified using the rule of exponents,
The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.
which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;
In this case the expression is: 4⁸×4³ , it has common base as "4",
So, by the rule of exponents, the power(exponents) gets added up ;
The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,
Therefore, Option(a)4¹¹, is the expression written using each base only once.
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The given question is incomplete, the complete question is
What is the expression written using each base only once? 4⁸×4³
(a) 4¹¹
(b) 12¹¹
(c) 4²⁴
(d) 64¹¹.
Select all expressions equivalent to (2-³.24) 2.
4
04
26.2-8
02-5.22
Accοrding tο the given infοrmatiοn, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.
What is an algebraic expressiοn?An algebraic expressiοn is a mathematical phrase that can cοntain numbers, variables, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Algebraic expressiοns are used tο represent quantities οr values that can vary, depending οn the values assigned tο the variables in the expressiοn. Algebraic expressiοns can be simple οr cοmplex, and they can have οne οr mοre variables.
We can simplify the expressiοn (2-³.24) 2 as fοllοws:
(2-³.24) 2 = (2-0.24) 2 = (1.76) 2 = 3.52
The expressiοn (2-³.24) 2 is equivalent tο 3.52.
Therefοre, nοne οf the expressiοns a), b), c), οr d) are equivalent tο (2-³.24) 2.
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hdlppppppppppp asapppp 50 points
Answer:
5
Step-by-step explanation:
Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -1, 1-i f(x) = 0 = Х 3 ?.
The polynomial f(x) of degree 3 with real coefficients and the given zeros is f(x) = x³ - x² + 4x + 2.
To find a polynomial f(x) of degree 3 with real coefficients and the given zeros, we need to use the fact that if a polynomial has a complex root, then its conjugate is also a root. This means that if 1-i is a root, then 1+i is also a root.
So, our polynomial f(x) has the following roots: -1, 1-i, 1+i.
We can write the polynomial as the product of its factors:
f(x) = (x - (-1))(x - (1-i))(x - (1+i))
Simplifying the factors:
f(x) = (x + 1)(x - 1 + i)(x - 1 - i)
Multiplying the factors:
f(x) = (x + 1)(x² - 2x + 2)
Expanding the polynomial:
f(x) = x³ - 2x² + 2x + x² - 2x + 2
Simplifying the polynomial:
f(x) = x³ - x² + 4x + 2
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Write an equivalent expression to m-(8-3m) without parentheses
m - (8 - 3m)
m - 8 + 3m
m + 3m - 8
4m - 8
Answer:
Step-by-step explanation:
m-(8-3m)
m-8 + 3m
=m+3m-8
=4m-8
how do you solve 83 = y/5?
Answer: 415
83 = [tex]\frac{y}{5}[/tex]
83(5) = y
415 = y
Answer:
y = 415
Step-by-step explanation:
83 = y/5
83 x 5 = y
415 = y
Help me please with this
g(x) = -f(x) - 4
===========================================================
Explanation:
The point (0,1) is on the the red f(x) curve. It's the y-intercept.
If we reflected that point over the x axis, then it moves to (0,-1). Shift it down 4 units to get to (0,-5)
The point (0,-5) is on the purple g(x) curve.
This process of...
reflect over the x axisshift down 4 unitsis applied to every point on the red curve to arrive at a corresponding point on the purple curve. The order of the transformations matters. We can't shift down first before reflecting (or else g(x) will be in a different spot).
We stick a negative sign in front of the f(x) to reflect over the x axis. This is to change the sign of the y coordinate from positive to negative. Our answer choices are narrowed to either B or C.
The answer is choice B since that -4 at the end means "shift each point 4 units down". We're subtracting 4 from each y coordinate.
GeoGebra and Desmos are two useful tools to help verify the answer.
Identify the terms, the degree of each term and the degree of the polynomial. Then identify the leading term, the leading coefficient, and the constant term. -5s^(7)-8s^(4)+6s^(3)+4s-6
Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6
Degree of each term: 7, 4, 3, 1, and 0
Degree of the polynomial: 7
Leading term: -5s^(7)
Leading coefficient: -5
Constant term: -6
The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.
The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.
So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.
Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6
Degree of each term: 7, 4, 3, 1, and 0
Degree of the polynomial: 7
Leading term: -5s^(7)
Leading coefficient: -5
Constant term: -6
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Mary has $250 to spend. She buys gift cards for $130. She will use the rest of the money to buy candy bars that cost $1. 50 each. Which inequality can be used to find the greatest number of candy bars she can buy with the rest of the money?
Answer:
80
Step-by-step explanation:
we will write an inequality of 1.50x + 130 =250
We subtract 130 from each side, so we have
1.50x=120
Now we divide by 1.50 on each side
X=80.
Let p be a prime. Using induction on n prove that n^p−n is always divisible by p.
By the principle of mathematical induction, the statement is true for all positive integers n.
To prove that n^p−n is always divisible by p, we can use the principle of mathematical induction.
When n = 1, we have 1^p - 1 = 0, which is divisible by p.
Assume that the statement is true for n = k, i.e., k^p - k is divisible by p. Now, we need to prove that the statement is also true for n = k+1, i.e., (k+1)^p - (k+1) is divisible by p.
Expanding (k+1)^p using the binomial theorem, we get:
(k+1)^p = k^p + pk^(p-1) + ... + p(k^2) + p(k) + 1
Subtracting (k+1) from both sides gives:
(k+1)^p - (k+1) = k^p - k + pk^(p-1) + ... + p(k^2) + p(k)
Since k^p - k is divisible by p by the induction hypothesis, and all the other terms on the right-hand side are multiples of p, we can conclude that (k+1)^p - (k+1) is also divisible by p.
Therefore, by the principle of mathematical induction, the statement is true for all positive integers n.
We have proved that n^p−n is always divisible by p for any prime p using induction on n.
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The table below shows how much Eloise spent on ribbon at two different shops. What is the difference in the price of 300cm of ribbon between shop A and shop B? Give your answer in pounds (£).
The difference in price of both the shops is £0.25.
What is price?
Price is the amount of money one pays for a good or service. It is determined by a variety of factors, such as supply and demand, the cost of production, and the availability of resources. Prices are also affected by government regulations, taxes, inflation, and other economic and market forces. The price of a product or service is an important factor in determining whether consumers will purchase it or not.
Shop A | Shop B
200 cm | £0.50 | 300 cm | £0.75
The difference in the price of 300cm of ribbon between shop A and shop B is £0.25. Eloise spent £0.50 on 200cm of ribbon at shop A, and £0.75 on 300cm of ribbon at shop B. Therefore, the difference in price is £0.25.
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Find the distance travelled by sibi if she takes three rounds of square garden of side 60m
Answer:
720m
Step-by-step explanation:
60×4 = 240
240×3 = 720
Determine the y-intercept.
Answer:
y=-x-2
Step-by-step explanation:
All of them are solved, but I will help to find the relationship.
I found the pattern in my head as I thought about absolute value and proportionality.
Feel free to ask more questions.
what is the slope intercept for
(5,1) and (2,16)
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
What distinguishes a linear equation?If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (5,1) and (x2, y2) = (2,16)
m = (16 - 1)/(2 - 5) = -5
So the slope of the line is -5.
To find the y-intercept b, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (5,1) and the slope m = -5, we get:
y - 1 = -5(x - 5)
Simplifying this equation, we get:
y = -5x + 26
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
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