The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.
Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.
Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:
y - 5 = -6(x - 3)
Simplifying the equation, we get:
y - 5 = -6x + 18
y = -6x + 23
Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.
Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
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If both a and b are positive numbers and ( b)/(a) is greater than 1, then is a-b positive or negative?
If both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.
This is because when (b)/(a) is greater than 1, it means that b is greater than a. So when you subtract a from b, you will get a negative number.
For example, let's say a = 2 and b = 5.
(b)/(a) = (5)/(2) = 2.5, which is greater than 1.
So when we subtract a from b, we get:
b - a = 5 - 2 = 3, which is a positive number.
But when we subtract b from a, we get:
a - b = 2 - 5 = -3, which is a negative number.
Therefore, if both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.
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the mean of five numbers is 15. Four of the numbers are 3, 19, 8, and 32. What is the fitch number.
Answer:
,15
Step-by-step explanation:
ez
How do the average rates of change for the pair of functions compare over the given interval?
f(x)x
g(x)x
x
Question content area bottom
Part 1
The average rate of change of f(x) over x is
enter your response here. The average rate of change of g(x) over x is
enter your response here. The average rate of change of g(x) is
enter your response here times that of f(x). (Simplify your answers. Type integers or decimals. )
The average rate of change of g(x) over the interval [2, 5] is -2.1.
The formula to calculate the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
slope = (y₂ - y₁) / (x₂ - x₁)
Using this formula, we can calculate the slopes of the two secant lines for f(x) and g(x) over the interval [2, 5]. Let's start with f(x):
slope_f = (f(5) - f(2)) / (5 - 2)
= (-0.1(5)² - (-0.1(2)²)) / (5 - 2)
= (-0.1(25) + 0.1(4)) / 3
= (-2.5 + 0.4) / 3
= -2.1 / 3
= -0.7
Therefore, the average rate of change of f(x) over the interval [2, 5] is -0.7.
Now, let's calculate the average rate of change of g(x):
slope_g = (g(5) - g(2)) / (5 - 2)
= (-0.3(5)² - (-0.3(2)²)) / (5 - 2)
= (-0.3(25) + 0.3(4)) / 3
= (-7.5 + 1.2) / 3
= -6.3 / 3
= -2.1
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Complete Question:
how do the average rates of change for the pair of functions compare over the given interval
f(x)= -0.1x²
g(x)= -0.3x²
2≤x≤5
Javier took out a loan for $2700 at 12% interest, compounded annually. If he
makes yearly payments of $320, will he ever pay off the loan?
OA. No, because $320 is greater than the amount of interest he is
charged per year
OB. No, because $320 is less than the amount of interest he is
charged per year
OC. Yes, because $320 is less than the amount of interest he is
charged per year
OD. Yes, because $320 is greater than the amount of interest he is
charged per year
The correct statement regarding the monthly payments is given as follows:
D. Yes, because $320 is greater than the amount of interest he is
charged per year.
What is the monthly payment formula?The monthly payment formula is defined by the equation as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed as follows:
P is the initial amount, which will be paid/divided over a period of time.r is the interest rate, as a decimal.n is the number of payments, in the period through which the monthly payments will be paid.The parameter values for this problem are given as follows:
P = 2700, r = 0.12, n = 12.
Hence:
r/12 = 0.12/12 = 0.01.
Hence the monthly payment is calculated as follows:
A = 2700 x 0.01 x (1.01)^12/(1.01^12 - 1)
A = $240.
The interest is less than $320, hence he will manage to pay off the loan.
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What Is 1 + 1 ?
A. Window
B. Two
C. Eleven
Correct Answer Gets Brainliest!
Answer: B -_-
Step-by-step explanation:
0 0=2
A (-1,6)
Work out the length of AB.
Give your answer to 3 significant figure
O
B (5, 3)
thagoras' Theorem - Line on a Graph
8
X
Answer:
AB = 6.71
Step-by-step explanation:
The vertical leg of the right triangle
= absolute value of difference in y-coordinates between A(-1, 6) and B(5, 3)
= |6 - 3| = |3|
= 3
The horizontal leg of the right triangle
= absolute value of difference in x-coordinates between A(-1, 6) and B(5, 3)
= |- 1 - 5|
=|- 6|
= 6
By the Pythagorean theorem, the hypotenuse AB is related to each of these two legs by the formula
AB² = 3² + 6²
AB² = 9 + 36
AB² = 45
AB = √45
or
AB = 6.7082039324
= 6.71 significant to 3 significant figures
Significant figures means number of digits excluding leading and trailing zeros
pls asnwer
due in 10 mins
give simple working
Step-by-step explanation:
a = 55° because angles on a straight line (around a single point on one side of the line) add up to 180°.
b = 75° because alternate angles (with parallel lines) are equal.
c = 50°, because alternate angles (with parallel lines) are equal.
d = 50°, because corresponding angles (with parallel lines) are equal.
A jet flying at 200 m/s north accelerates at a rate of 18.2 m/s² for 15 seconds. What is the jet's final velocity?
The final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.
What is meant by velocity?When observed from a specific point of view and as measured by a specific unit of time, velocity is the direction at which an item is moving and serves as a measure of the pace at which its position is changing. How quickly or slowly an object is travelling can be determined by its velocity and speed. Being a vector quantity, we need to define velocity in terms of both magnitude (speed) and direction. A body is considered to be accelerating if the magnitude or direction of its velocity changes.
Given,
The initial velocity u = 200 m/s
Acceleration of jet a = 18.2 m/s²
Time taken t = 15s
We are asked to find the final velocity v of the jet.
W can use the following formula to find the final velocity.
v = u+ at
= 200 + (18.2) × 15
= 473 m/s (north)
Therefore the final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.
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What is the difference in area betwee circle with its of 10 centimeters a square inscribed in it, to the neares whole?
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is 114 cm².
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.
First, calculate the area of the circle using the formula
A = πr²,
where A is the area and r is the radius.
A = π(10)² = 100π ≈ 314.16 square centimeters
Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.
Using the Pythagorean theorem, we can find the side length of the square:
s² + s² = (20)²
2s² = 400
s² = 200
s ≈ 14.14 centimeters
The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.
Finally, subtract the area of the square from the area of the circle to find the difference:
314.16 - 199.97 ≈ 114.19 square centimeters
To the nearest whole, the difference in area is 114 square centimeters.
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(5)/(x+6)=(7)/(5x+30)-2 If there is more than one solution, separate If there is no solution, click on "No solution" x
The solutions are x ≈ -2.744 and x ≈ -17.106.
To solve this equation, we need to get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators. The LCM of x+6 and 5x+30 is (x+6)(5x+30).
Multiplying each term by the LCM gives us:
(5)(x+6)(5x+30)/(x+6) = (7)(x+6)(5x+30)/(5x+30) - 2(x+6)(5x+30)
Simplifying the fractions and distributing the terms gives us:
5(5x+30) = 7(x+6) - 2(x+6)(5x+30)
Expanding and simplifying the terms gives us:
25x + 150 = 7x + 42 - 10x^2 - 180x - 360
Combining like terms and rearranging gives us:
10x^2 + 198x + 468 = 0
Using the quadratic formula, we can find the values of x:
x = (-198 ± √(198^2 - 4(10)(468)))/(2(10))
Simplifying gives us:
x = (-198 ± √(39204 - 18720))/(20)
x = (-198 ± √20484)/(20)
x = (-198 ± 143.126)/(20)
The two solutions for x are:
x = (-198 + 143.126)/(20) ≈ -2.744
x = (-198 - 143.126)/(20) ≈ -17.106
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1) Louis is dilating triangle ABC at right. He
multiplied each x-coordinate and y-coordinate of
triangle ABC by -2.
a. What are the new coordinates of the points?
To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:
New x-coordinate = -2 * old x-coordinate
New y-coordinate = -2 * old y-coordinate
Let's apply these formulas to each point in triangle ABC:
Point A: (-3, 4)
New x-coordinate of A = -2 * (-3) = 6
New y-coordinate of A = -2 * 4 = -8
New coordinates of A: (6, -8)
Point B: (1, 1)
New x-coordinate of B = -2 * 1 = -2
New y-coordinate of B = -2 * 1 = -2
New coordinates of B: (-2, -2)
Point C: (5, -2)
New x-coordinate of C = -2 * 5 = -10
New y-coordinate of C = -2 * (-2) = 4
New coordinates of C: (-10, 4)
Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:
A: (6, -8)
B: (-2, -2)
C: (-10, 4)
5 3/10 = 5 ?/50
If anyone can please help me with the rest
Answer:
See explanation
Step-by-step explanation:
50 is 5*10, so multiply 3 by 5 also to get 5 and 15/50. First answer is 15
5 and 15/50 is also equal to 4 and 65/50. second answer is 65
carry the numerator on the second line to get 30 for the third answer.
finally, subtract 3 from 4 to get 1, and subtract 30 from 65 to get 35/50.
last two answers are 1, and 35.
Multiplicative property of equality with whole numbers Solve for u. 78=6u Simplify your answer as much as possible. u
The multiplicative property of equality states that the same number can be added to or multiplied by both sides of an equation to obtain an equivalent equation. In this case, dividing both sides by 6 gives us u = 78/6 = 13.
The multiplicative property of equality states that if two numbers are equal, then multiplying both sides of the equation by the same number will also result in an equation that is still equal. In other words, if a=b, then ac=bc. We can use this property to solve for the variable u in the equation 78=6u.
To isolate the variable on one side of the equation, we can divide both sides by 6. This will give us:
78/6 = 6u/6
Simplifying the equation gives us:
13 = u
So the solution for u is 13.
In conclusion, the multiplicative property of equality with whole numbers was used to solve for the variable u in the equation 78=6u. The solution is u=13.
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15. \( x=-5, \quad x=4, \quad x=-\frac{1}{2} \) factored form standard form 16. \( x=3, \quad x=-7, \quad x=0 \) (multiplicity of 2) factored form standard form
\[ \text { 17. } x=\frac{2}{3} \text {
The standard form to this equation is x=2/3.
This equation is in the form of a linear equation in one variable, where the variable is x.
The equation is written as x=2/3, meaning that the value of x is equal to 2/3.
The equation can be interpreted as the ratio of two numbers, 2 and 3. The numerator, 2, represents the number of parts, and the denominator, 3, represents the total number of parts.
This equation can be used to solve for the fraction of the total number of parts represented by the numerator. In this case, the fraction is 2/3, or 2 parts out of a total of 3 parts.
The equation can also be interpreted as a proportion. If we make the numerator the unknown value, x, then the equation becomes x/3 = 2/3. This equation can be solved using the cross-multiplication method.
By multiplying the denominators together and setting them equal to each other, then solving for x, we get x = 2/3. This equation shows that the value of x is equal to 2/3 of the total number of parts.
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select the 2 linear functions A) (y=6x+14), B) (y= x/4 + 1), C) (y=x^3), D) (y=3/x +2)
The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Let's check all the options, then we have
A) y = 6x + 14, the equation is a linear equation because the degree is one.
B) y = x/4 + 1, the equation is a linear equation because the degree is one.
C) y = x³, the equation is a cubic equation because the degree is three.
D) y = 3/x +2, the equation is a non-linear equation because the degree is negative one.
The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.
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kierna is starting a lawn-mowing buisness in her neighborhood. she creats a graph to help her determine what to charge customers per lawn to maximize her profits. she uses c to represent the number of lawns she mows and y to represent her profit in dollars.
The profit is maximum when 40 lawns are mowed.
What is function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given is that Kieran is starting a lawn-mowing buisness in her neighborhood. She creates a graph to help her determine what to charge customers per lawn to maximize her profits. She uses {c} to represent the number of lawns she mows and {y} to represent her profit in dollars.
The profit is maximum when 40 lawns are mowed as at this point the the peak of the parabola occurs.
Therefore, the profit is maximum when 40 lawns are mowed.
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Miguel has started training for a race. The first time he trains, he runs 0. 5 mile. Each subsequent time he trains, he runs 0. 2 mile farther than he did the previous time.
a) What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?
b) A marathon is 26. 2 miles. What is the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon?
Answer:
hope this helps.
Step-by-step explanation:
PLEASE HELP
A cylinder-shaped container is used to store water. The container has a height of 6 feet and
diameter of 3 feet.
About how much water is in the container when it is 3/4 full?
o 127 cubic feet
o 42 cubic feet
o 32 cubic feet
o 14 cubic feet
Answer:
32 cubic feet
Step-by-step explanation:
The formula for a cylinder is [tex]\pi r^{2} h[/tex].
The radius of the cylinder is equal to 1.5 feet, since it is [tex]\frac{diameter}{2}[/tex].
Plugging in, the cylinder's full volume is [tex]6\pi 1.5^2[/tex] which is approximately 42.4 cubic feet.
To find the amount of water when it is 3/4 full, multiply 42.4 x .75, to get around 31.8, and 32 when rounded
write three rations that are equivalent to 6/9
Answer:
12/18, 2/3, and 18/27.
Step-by-step explanation:
In order to find ratios that are equivalent to a certain fraction they must have common divisibles.
In this case...
[tex]\frac{6}{9}[/tex]
If the common divisible is two....
[tex]6\times2=12[/tex]
[tex]9\times2=18[/tex]
[tex]=\frac{12}{18}[/tex]
You could also simplify the ratio:
[tex]\frac{6}{9} \div3=\frac{2}{3}[/tex]
[tex]=\frac{2}{3}[/tex]
If the common divisible is three:
[tex]6\times3=18[/tex]
[tex]9\times3=27[/tex]
[tex]=\frac{18}{27}[/tex]
Ava was playing a game online. She had a great first round and the second round she increased her point total by 25%. On the third round she decreased her point total by 3/5. She had a great fourth round increasing her total points by 75%. On the fifth and final round she lost 2/7 of her total ending the game with 50 points. How many points did Ava have at the end of round one?
To find out how many points Ava had at the end of round one, we need to work backwards from the end of the game using probability. Here are the steps to do so:
Step 1: At the end of the game, Ava had 50 points. This was after she lost 2/7 of her total points in the fifth round. Let's call the number of points she had before the fifth round X. So:
50 = X - (2/7)X
Step 2: Solve for X by combining like terms:
50 = (5/7)X
Step 3: Multiply both sides of the equation by 7/5 to isolate X:
X = 70
Step 4: Now we know that Ava had 70 points before the fifth round. This was after she increased her total points by 75% in the fourth round. Let's call the number of points she had before the fourth round Y using probability. So:
70 = Y + (75/100)Y
Step 5: Solve for Y by combining like terms:
70 = (175/100)Y
Step 6: Multiply both sides of the equation by 100/175 to isolate Y:
Y = 40
Step 7: Now we know that Ava had 40 points before the fourth round. This was after she decreased her point total by 3/5 in the third round. Let's call the number of points she had before the third round Z. So:
40 = Z - (3/5)Z
Step 8: Solve for Z by combining like terms:
40 = (2/5)Z
Step 9: Multiply both sides of the equation by 5/2 to isolate Z:
Z = 100
Step 10: Now we know that Ava had 100 points before the third round. This was after she increased her point total by 25% in the second round. Let's call the number of points she had before the second round A using probability. So:
100 = A + (25/100)A
Step 11: Solve for A by combining like terms:
100 = (125/100)A
Step 12: Multiply both sides of the equation by 100/125 to isolate A:
A = 80
Step 13: Now we know that Ava had 80 points before the second round, which means she had 80 points at the end of the first round.
Therefore, the answer is 80 points using probability.
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Ver en español
Felix and his friends attended the opening of the new community center at Forest Ridge Park. The mayor unveiled a parallelogram-shaped decorative plaque at the entrance to the park with the date of the special event. Its bottom edge is 9 inches long, and its area is 126 square inches.
Which equation can you use to find how tall the plaque is, h?
How tall is the plaque?
Write your answer as a whole number or decimal. Do not round.
inches
The answer to this question is as follows The plaque measures 14 inches equation tall as a result.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Because we are aware that the plaque has a parallelogram shape, we may determine its height using the formula for a parallelogram's area. The formula for a parallelogram's area is:
Base area x height
In this instance, we are aware that the area is 126 square inches, and the base (the bottom border) is 9 inches. Thus, we can enter those values into the formula to find the height:
126 = 9h
h = 126/9
h = 14
The plaque measures 14 inches tall as a result.
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In order for following to be consistent,
-3x +4y +7z =-4
-11x +24y +kz = -45
2x -5y -8z =9
solve for k≠ ?
please show full steps
In order for the system of equations to be consistent, k must not be equal to 31.6087.
In order for the system of equations to be consistent, the determinant of the coefficient matrix must not be equal to zero. The coefficient matrix is:
| -3 4 7 |
| -11 24 k |
| 2 -5 -8 |
The determinant of this matrix is:
(-3)(24)(-8) + (4)(k)(2) + (7)(-11)(-5) - (7)(24)(2) - (4)(-11)(-8) - (-3)(k)(-5)
Simplifying this expression gives:
576 + 8k + 385 - 336 - 352 + 15k = 0
Solving for k gives:
23k = 727
k = 727/23
k ≈ 31.6087
Therefore, in order for the system of equations to be consistent, k must not be equal to 31.6087.
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5.22. Exercise. Make a ruler-and-compass construction of a line thru a given point that is perpendicular to a given line.
This construction is also known as the "perpendicular bisector" construction.
To construct a line through a given point that is perpendicular to a given line using a ruler and compass, you will need to follow these steps:
Place the point of the compass on the given point.Open the compass to a width that is wider than the distance between the given point and the given line.Draw an arc that intersects the given line at two points.Without changing the width of the compass, move the point of the compass to one of the intersection points and draw another arc.Move the point of the compass to the other intersection point and draw another arc that intersects the first arc.Use the ruler to draw a line through the given point and the intersection of the two arcs. This line will be perpendicular to the given line.By following these steps, you have used the ruler and compass to construct a line through a given point that is perpendicular to a given line. This construction is also known as the "perpendicular bisector" construction.
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Convert the angle to degrees, minutes, and seconds notation.
124.32 ∘
124.32 ∘
=
Convert the angle measure
48 ∘
36 ′
36 ′′
to decimal degrees.
48 ∘
36 ′
36 ′′
=
(Type an integer or decimal rounded to the nearest thousandth as needed.) Find the angle of least positive measure (in degrees, not The measure is equal to the given measure) that is coterminal with
A
.
A=725 ∘
Give an expression that generates all angles coterminal The correct expression is
240 ∘
+
with the given angle.
240 ∘
This expression will generate all angles coterminal with 240 degrees.
To convert an angle from degrees to degrees, minutes, and seconds, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds
First, we need to convert the decimal part of the angle to minutes:
0.32 degrees * 60 minutes/degree = 19.2 minutes
Next, we need to convert the decimal part of the minutes to seconds:
0.2 minutes * 60 seconds/minute = 12 seconds
So, the angle 124.32 degrees is equal to 124 degrees, 19 minutes, and 12 seconds:
124.32 ∘ = 124 ∘ 19 ′ 12 ′′
To convert an angle from degrees, minutes, and seconds to decimal degrees, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds
First, we need to convert the minutes to degrees:
36 minutes / 60 minutes/degree = 0.6 degrees
Next, we need to convert the seconds to degrees:
36 seconds / 3600 seconds/degree = 0.01 degrees
So, the angle 48 degrees, 36 minutes, and 36 seconds is equal to 48.61 degrees:
48 ∘ 36 ′ 36 ′′ = 48.61 ∘
To find the angle of least positive measure that is coterminal with a given angle, we need to use the formula:
A = A + 360n
Where A is the given angle, and n is an integer. We need to find the smallest positive value of n that makes the expression equal to a positive angle less than 360 degrees.
For the given angle A = 725 degrees, we can use n = -2:
A = 725 + 360(-2) = 725 - 720 = 5 degrees
So, the angle of least positive measure that is coterminal with 725 degrees is 5 degrees.
To find an expression that generates all angles coterminal with a given angle, we can use the formula:
A = A + 360n
Where A is the given angle, and n is an integer. For the given angle A = 240 degrees, the expression is:
240 ∘ + 360n
This expression will generate all angles coterminal with 240 degrees.
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Distance (Yards)
Races
60
20-
(1, 12)
(2,24)
Mario & Peach 4
Time (Seconds)
6
Can you create the two equations for Mario and Peach
in y = mx + b form?
Mario
Submit
Peach
12
The linear functions of the scenario are y = 12x and y = 24/2x
How to determine the linear functionsFrom the question, we have the following parameters that can be used in our computation:
(1, 12) and (2,24)
From the question, we understand that the function is a linear function
A linear function is represented as
y = mx + c
Using the above as a guide, we have the following equations
m + c = 12
2m + c = 24
Subtract the equations
m = 12
Substitute 12 for m in m + c = 12
12 + c = 12
Evaluate
c =0
So, the equation is y = 12x
An equivalent equation is y = 24x/2
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"twice the difference of some number and 8 amounts to the quotient of 112 and 14 " written as an equation is
The solution to the equation is x = 12.
The equation for "twice the difference of some number and 8 amounts to the quotient of 112 and 14" can be written as:
2(x - 8) = 112/14
Where x is the unknown number.
First, simplify the right side of the equation by dividing 112 by 14 to get:
2(x - 8) = 8
Next, distribute the 2 on the left side of the equation:
2x - 16 = 8
Finally, solve for x by isolating the variable on one side of the equation:
2x = 8 + 16
2x = 24
x = 24/2
x = 12
Therefore, the solution to the equation is x = 12.
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equation x^(4)+6x^(3)-3x^(2)-24x-4=0, complete the following Il possible rational roots. synthetic division to test several possible rational roots in order to identify on
The equation x^(4)+6x^(3)-3x^(2)-24x-4=0 has possible rational roots ± 1, 2, 4, ± 1/2, 1/4.
Given the equation: $x^4+6x^3-3x^2-24x-4=0$
To identify possible rational roots we use Rational Root Theorem which states that:
If a polynomial function with integer coefficients has any rational roots then the numerator must divide the constant term and the denominator must divide the leading coefficient. Let's identify possible rational roots. The constant term is -4 and the leading coefficient is 1. Therefore, the possible rational roots are as follows:± 1, 2, 4± 1/2, 1/4
We use synthetic division to test several possible rational roots in order to identify the roots of the equation.
x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4±1 is the root of the equation since the remainder is zero. Therefore, divide the polynomial by x − 1.x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)
The roots of the equation are x = 1, -2 ± i, where i = √(-1).
Hence, we have completed the following:
Possible rational roots: ± 1, 2, 4, ± 1/2, 1/4
Synthetic division to test possible rational roots: x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4
Possible rational root: ±1
Divide polynomial by (x-1): x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)
Roots of the equation: x = 1, -2 ± i, where i = √(-1).
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Math 1149 Worksheet Chapter 8 Lesson 4 1. 1-cos²x / sinx 2. Cos X – Cos x. 3. (sin^2 + tan^2 u + cos^2 u) / (sec u) 4. (sec^2 x – tan^2 c) / (cos^2 x + sin^2 x)
5. (sec^2 + csc^2 x) - (tan^2 x + cot^2 x) 6. tan x cot x 7. cot u sin u 8. sec (-x) cos (-x)
9 cot (-θ) tan (-θ)
10. sec^2 (-x) – tan^2 (-x)
11. sec u sin u
1. 1-cos²x / sinx = sin²x / sinx = sinx
2. Cos X – Cos x = 0
3. (sin^2 + tan^2 u + cos^2 u) / (sec u) = (1 + tan^2 u) / (sec u) = sec^2 u / sec u = sec u
4. (sec^2 x – tan^2 c) / (cos^2 x + sin^2 x) = (1/cos^2 x - sin^2 x / cos^2 x) / 1 = (1 - sin^2 x) / cos^2 x = cos^2 x / cos^2 x = 1
5. (sec^2 + csc^2 x) - (tan^2 x + cot^2 x) = (1/cos^2 x + 1/sin^2 x) - (sin^2 x / cos^2 x + cos^2 x / sin^2 x) = (sin^4 x + cos^4 x) / (sin^2 x cos^2 x) = 1 / (sin x cos x)
6. tan x cot x = (sin x / cos x) * (cos x / sin x) = 1
7. cot u sin u = (cos u / sin u) * sin u = cos u
8. sec (-x) cos (-x) = (1 / cos (-x)) * cos (-x) = 1
9. cot (-θ) tan (-θ) = (cos (-θ) / sin (-θ)) * (sin (-θ) / cos (-θ)) = 1
10. sec^2 (-x) – tan^2 (-x) = (1/cos^2 (-x)) - (sin^2 (-x) / cos^2 (-x)) = (1 - sin^2 (-x)) / cos^2 (-x) = cos^2 (-x) / cos^2 (-x) = 1
11. sec u sin u = (1 / cos u) * sin u = sin u / cos u = tan u
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what smaller 5.75 or 9/7
Answer:
9/7 is smallerrrr
i need help 16 divided by 6032 full solution
Answer:
0.00265251989
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