If the equation [tex]ax^2+2hxy+by^2+2gx+2fy+c=0[/tex] describes a pair of straight lines, then the equations m1+m2=-2h/b and m1m2=a/b, where m1 and m2 are the slopes of the straight lines, apply.
Simple line equation: what is it?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
How can I determine a line's slope?Determine the coordinates of two points along the line that you choose.
Find the difference between these two points' y-coordinates (rise).
Find the difference between these two points' x-coordinates (run).
Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
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please help I'm struggling.
Answer: 6
Step-by-step explanation: Very simple, just do 17 - 11 and you'll get 6. I hope that's the correct answer
Function or not a function?
6(4y+8)-2 rewrite in the simplest form
Answer: 24y+46
Step-by-step explanation:
6(4y+8)-2
=24y+48-2
=24y+46
= 2(12y+23)
Answer: 24y+46
Step-by-step explanation:
multiply 6 by 4y = 24y
multiply 6 by 8 = 48
you have left 24y + 48 - 2
subtract 2 from 48 and get 46
Is an example of quadratic inequality?
The following is an example of a quadratic inequality: x^2 + 2x - 8 > 0.
This is an example of a quadratic inequality because it is an inequality involving a quadratic function (x^2 + 2x - 8) which is of the form ax^2 + bx + c where a, b, and c are constants.
Quadratic inequalities can be solved by factoring the quadratic expression, using the Quadratic Formula, or graphing the inequality. In order to solve a quadratic inequality, it is important to understand the types of solutions that can be expected.
Solutions may include one solution, two solutions, or no solutions. Additionally, when graphing a quadratic inequality, the graph may be a line or a region. To determine which type of graph to use, the type of inequality must be identified (greater than or less than). If the inequality is a greater than or less than inequality, then the graph will be a region. If the inequality is an equal to inequality, then the graph will be a line.
Solving and graphing quadratic inequalities is an important skill in algebra as it allows us to visualize and solve complex problems.
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If a1=6 and an= -5an-1 + 4 then find the value of a5.
Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.
What does the word arithmetic mean?The group's arithmetic average, often known as the mean, is calculated by multiplying the sum of all the entries in a list by the number of products in that list, then dividing that sum by both. This follows the same mathematical development. The number 3 is the median of the numbers 9, 11, and 7. For instance, the number 7 is obtained by dividing 21 (there are actually three numbers) by the equation 5 + 7 + 9.
Here,
It speaks about sequences where every other term is provided as a rule but needs on a number of the preceding terms, as opposed to implicit series where an expression.
The order is as follows:
The order is as follows:
=> a1 = 6
=> an= -5a(n-1) + 4
To calculate the value of a5, follow these steps:
=> a2= -5(6) + 4 = -26
=> a3= -5(26) + 4 = 134
=> a4= -5(134) + 4 = -666
=> a5= -5(-666) + 4 = 3334.
Therefore , the solution of the given problem of arithmetic mean comes out to be a5 = 3334.
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2(x + 3) = x - 4 Linear equations
Answer: x=−10
Step-by-step explanation:
2(x+3)=x−4
Use the distributive property to multiply 2 by x+3.
2x+6=x−4
Subtract x from both sides.
2x+6−x=−4
Combine 2x and −x to get x.
x+6=−4
Subtract 6 from both sides.
x=−4−6
Subtract 6 from −4 to get −10.
x=−10
Step-by-step explanation:
2(x+3)=x−4
Step 1: Simplify both sides of the equation.
2(x+3)=x−4
(2)(x)+(2)(3)=x+−4 (Distribute)
2x+6=x+−4
2x+6=x−4
Step 2: Subtract x from both sides.
2x+6−x=x−4−x
x+6=−4
Step 3: Subtract 6 from both sides.
x+6−6=−4−6
x=−10
Evaluate the expressions for x =5. 2x^2-x
The solution to the expression 2x²-x will be 45.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 2x²-x. The solution of the expression at x= 5 will be calculated as,
E = 2x²-x
E = 2 x ( 5 )² - 5
E = 2 x 25 - 5
E = 50 - 5
E = 45
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Gordon and Erik got in trouble at football practice and have to run laps as a consequence. Gordon, who runs at a rate of 1 lap per minute, had completed 5 laps already when he was joined on the track by Erik. Erik's pace is 2 laps per minute. At some point, the two will have run the same distance. How long will that take? How many laps will each boy have run?
After____minutes, Gordon and Erik will each have run_____laps.
Answer:
After 5 minutes, Gordon and Erik will each have run 10 laps
Step-by-step explanation:
Let L =lap, M=minute, G=gordon, E=Eric
G=(1L*M)+5
E=(2L*M)+5
Answer:
After 5 minutes, Gordon and Erik will each have run 10 laps
Step-by-step explanation:
Gordon already completed 5 laps and each lap is completed in 1 minute
5 + 5 = 10
Eric completes a lap in 2 minutes
2 x 5 = 10
So after 5 minutes, Gordon and Erik will each have run 10 laps
Hope you get this right :)
Use the cylinder shown to mark each statement as true or false. Rewrite and correct any faise
statements.
9. The height of the cylinder is 4 feet.
10. The area of the base is equal to п(4²).
11. The volume of the cylinder is 31.4 ft³.
d = 4 ft B
2.5 1
The truth values of the statements are:
9. The height of the cylinder is 4 feet (False), the height is 2.5 feet10. The area of the base is equal to п(4²) (False), the area is п(2²)11. The volume of the cylinder is 31.4 ft³How to determine the true statementsThe complete question is added as an attachment, where we have the following parameters:
Height, h = 2.5 feet
Diameter, d = 4
The base area is then calculated as
Area = п(r²)
So, we have
Area = п(2²)
The volume is then calculated as
Volume = Base area * Height
So, we have
Volume = п(2²) * 2.5
Evaluate
Volume = 31.4
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Can a triangle have three sides whose lengths are 4.5 cm 3.8 cm 7.2 cm?
Answer:
Yes because it is a scalene triangle
Step-by-step explanation:
what kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?
A periodic up-and-down motion should be imparted to the nozzle of a garden hose such that the resultant stream of water approximates a sine curve.
A sine curve is a mathematical function that oscillates between a maximum and minimum value in a repeating pattern. To approximate this with a stream of water from a garden hose, the nozzle of the hose should be moved in a periodic up-and-down motion. This motion will cause the water stream to oscillate between a higher and lower height, creating the repeating pattern characteristic of a sine curve. The speed at which the nozzle is moved, as well as the amplitude of the motion, can be adjusted to create a more accurate representation of a sine curve.
Also, the nozzle can be turned to make the water flow in a spiral, which looks even more like a sine curve.
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Verify that f^-1(x) is the inverse of f(x) by showing f(f^-1(x)) = x and f^-1(f(x)) = x
f(x) = x-5 / 3 -x
f^-1(x) = 3x+5 / x+1
f^-1(x) is the inverse of f(x) as the composite functions f(f^-1(x)) and f^-1(f(x)) are both equal to x.
What is composite functionA function is composite when the co- domain of the first mapping is the domain of the second mapping.
We shall evaluate the functions f(f^-1(x)) and f^-1(f(x)) as follows:
f(f^-1(x)) = [(3x+5 / x+1) - 5] ÷ [3 - (3x+5 / x+1)]
changing division to multiplication;
f(f^-1(x)) = [3x + 5 - 5(x + 1)]/(x + 1) × (x + 1)/[3(x + 1) - (3x + 5)]
(x + 1) is common and will cancel out
f(f^-1(x)) = (3x + 5 - 5x - 5)/(3x + 3 - 3x - 5)
f(f^-1(x)) = -2x/-2
f(f^-1(x)) = x
f^-1(f(x)) = [3(x-5 / 3 -x) + 5] ÷ [(x-5 / 3 -x) + 1]
changing division to multiplication;
f^-1(f(x)) = [3(x - 5) + 5(3 - x)]/(3 - x) × (3 - x)/[x - 5 + (3 - x)]
(3 - x) is common and will cancel out
f^-1(f(x)) = (3x - 15 + 15 - 5x)/(x - 5 + 3 - x)
f^-1(f(x)) = -2x/-2
f^-1(f(x)) = x
Therefore, since composite functions; f(f^-1(x)) = x and f^-1(f(x)) = x, then f^-1(x) is the inverse of f(x).
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Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. K = 1/2
The coordinates of the vertices of the polygon, given the scale factor and the coordinates of the original image, would be:
J ' = ( - 2.5, 1 . 5)K ' = ( 1, 1 . 5)L ' = ( 1, - 1. 5 )M ' = ( - 2.5, - 1. 5 )How to find the coordinates ?To find the coordinates of the new image, when a dilation happens at the origin, use the coordinates of the image and multiply it by the scale factor.
The coordinates of the image, shown on the graph are:
J = (- 5, 3 )
K = ( 2, 3 )
M = ( -5, -3 )
L = ( 2, - 3 )
The coordinates of the new image is therefore:
J ' = ( -5 , 3 ) x 1 / 2
= ( - 2.5, 1 . 5)
K ' = ( 2, 3 ) x 1 / 2
= ( 1, 1 . 5)
M' = ( -5, -3 ) x 1 / 2
= ( - 2.5, - 1. 5 )
L ' = ( 2, - 3 ) x 1 / 2
= ( 1, - 1. 5 )
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What is the difference between real function and complex function?
A real function, usually referred to as a real-valued function, is one whose domain is the real numbers. A function from complex numbers to complex numbers is referred to as a complex function.
What is complex function?A true function is a prescription that gives values to its input parameters. According to the notation y = f (x), the function f assigns the value y to the argument's value x. Additionally, we occasionally write the function f as f: x y, which means that it sends x to y. A real function, usually referred to as a real-valued function, is one whose domain is the real numbers. The relation is a function if a vertical line only ever crosses the relation on the graph once in all locations. However, the relation is not a function if a vertical line passes across it more than once. All lines are functions based on the vertical line test, with the exception of vertical lines.A function from complex numbers to complex numbers is referred to as a complex function.
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11x-5y=2
x-5y=-18
solve the system using elimination
The solution to the system of equation is as follows:
x = 2 and y = 4
How to solve system of equation using elimination method?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation using elimination method as follows:
11x - 5y = 2
x - 5y = -18
subtract equation(ii) from equation(i) to eliminate the variable y.
Therefore,
10x = 20
divide both sides by 10
x = 20 / 10
x = 2
Let's find y by substituting the value of x in equation(ii)
x - 5y = -18
2 - 5y = -18
-5y = -18 - 2
-5y = -20
divide both sides by -5
y = -20 / -5
y = 4
Therefore, x = 2 and y = 4.
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Hey! Please hurry! I need help! It'll be useful until 4:00 P.m !
No false answers Please !
Answer:
c = 50
Step-by-step explanation:
The given angles are alternate angles and their measures are equal.
We can write the following equation based on this information:
2c - 3 = 97
Add 3 to both sides.2c = 100
Divide both sides by 2.c = 50
The price of Stock A at 9 A. M. Wa $16. 12. Since then, the price ha been increaing at the rate of $0. 12 each hour. At noon the price of Stock B wa $16. 87. It begin to decreae at the rate of $0. 07 each hour. If the two rate continue, in how many hour will the price of the two tock be the ame
According to the unitary method, after 2.05 hours value of stock will be equal.
Here we have given that the following value are given in the question they are listed as follows:
Stock 1 has price of stock at 9 A.M is $16.12 and the Rate of increase is $0.12 per hour
Similarly, Stock 2 has price of stock at 12 P.M is $16.87 with the Rate of decrease is $0.07 per hour.
Here first we have to calculate price of stock at 12 P.M, then we get the value as,
=> 16.12 + (0.12 x 3) = 16.48
Now, let us consider that x hours after 12 P.M their price will be same
Then the First consider case of stock 1 as,
=> Price of Stock 1 after x hours from 12 P.M
=> 16.48 + 0.12x
For stock 2, the value is calculated as,
=> Price of Stock 2 x hours after 12 P.M
=> 16.87 - 0.07x
Then we have to equate the price of stock x hours after 12 P.M:
=> 16.48 + 0.12x = 16.87 - 0.07x
When we simplify this one then we get,
=> 0.19x = 0.39
=> x = 2.05
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Please!! Can someone help me? I'm not sure of this.
Simplify: (2x⁵)³
THERE ARE TWO ANSWERS. MAKE SURE YOU CHOOSE BOTH.
[tex](2x^5)^3\implies \left(2^3x^{5\cdot 3} \right)\implies 8x^{15}[/tex]
the average of the first 4 weights was 5 pounds. the average of the next 11 weights was 20 pounds. what was the overal average of the weights?
The overall average of the weights is 16.
What is average?The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.
Given that the average of the first 4 weights is 5.
Avg = Total Sum / Total number of weights
Substituting the value of Avg = 5 and Total number of weights= 4 we have:
5 = Sum(4) / 4
Sum(4) = 20
The average of the next 11 weights was 20 pounds.
Substituting the values, we have:
20 = Sum(11) / 11
Sum(11) = 220
The total sum of the 4 weights and the 11 weights is:
Sum = Sum(4) + Sum(11)
= 20 + 220
= 240
The total number of weights are: 4 + 11 = 15
The overall average weight is:
Avg = Sum/ total number of weights
Avg = 240/ 15
Avg = 16
Hence, the overall average of the weights is 16.
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What is the formula for enlargement?
The formula for enlargement = New length = original length × scale factor.
What is enlargement?
A shape's size can be changed by enlarging it. A shape can be made larger by multiplying all of its lengths by the scaling factor. We can calculate how much larger the shape will be by using the scaling factor. For instance, if a shape is scaled up by a factor of 2, all of the sides will lengthen by the same factor.
Here,
We have to determine the formula for enlargement.
We concluded that New length = original length × scale factor.
When we enlarge a shape by a scale factor, the area of the shape is multiplied by the square of the scale factor. When we enlarge a shape by a scale factor, the volume of the shape is multiplied by the cube of the scale factor.
Hence, the formula for enlargement = New length = original length × scale factor.
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Which graph best represents the line y
A.
A
B
C
D
Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph can be used to display a certain kind of data.
What is the slope of the line y =- 1 2x 5?Condense the right side. X X and 12 1 2 combined. Reverse the terms. The slope, calculated using the slope-intercept form, is 12. Since x=5 is a vertical line, the slope is ambiguous and there is no y-intercept. The slope is 15 when expressed in slope-intercept form.x=-5 is a vertical line that is parallel to the y-axis and crosses the x-axis at a distance of 5 units from the origin. A vertical line represents the graph of x=5. The point where x equals 5 is represented by the equation x=5.Consider attempting to plot a few points with an x-value of 5. Several examples include (5, 0), (5, 2), (5,5). By determining the rise and the run using two of the line's points, you may get the slope of the line.Therefore the correct answer is option B .
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pls help me 20 points if you answer correctly
Is the triangle with sides 25cm 5cm and 24cm a right triangle True False?
Answer:
yes
Step-by-step explanation:
how to know if a riemann sum is an overestimate or underestimate
In general, if the rectangles are all the same width and if they are placed to the right of the curve, the Riemann sum will be an overestimate of the true area. On the other hand, if the rectangles are placed to the left of the curve, the Riemann sum will be an underestimate of the true.
Another method to determine if a Riemann sum is an overestimate or underestimate, we can compare it to the exact value of the definite integral. If the Riemann sum is larger than the definite integral, it is an overestimate. If the Riemann sum is smaller than the definite integral, it is an underestimate. Additionally, we can also check the sign of the function being integrated and the width of the rectangles. If the function is positive and the width of the rectangles is decreasing, then the Riemann sum will be "an overestimate". If the function is negative and the width of the rectangles is decreasing, then the Riemann sum will be "an underestimate".
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Write (2x)^3 without exponents
8x
Step-by-step explanation:
2x x 2x x 2x
2 The length of a soda can is 6 Inches. A company would like to create a larger, scale model of the
sool of rome ng 3
OPOT 99 feet. What will the length of the model be?
=1
A. 180 ft
B.
60 ft
C.
30 ft
D.
20 ft
The correct answer is option B: 60 ft.
To find the length of the model, you can use the formula:
Length of model = (Length of original object) x (Scale factor)
The scale factor in this case is 99 feet / 6 inches = 16.5 feet/inch
So the length of the model = (6 inches) x (16.5 feet/inch) = 60 ft
(1/3) to the power of 2×(−10÷14) ASAP PLS
Answer:
The expression (1/3) to the power of 2x(−10÷14) is equal to (1/3)^(-5/7).
Step-by-step explanation:
Calculating this expression in general will give you a decimal value as an outcome, However, since i do not have the ability to perform calculations, i can give you this hint. It will be a small number close to zero but not zero.
It's important to note that the order of operations (PEMDAS) should be followed when evaluating this expression: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Here i a cm cube
thi cuboid i made from centimetre cube
write down the volume of the cuboid
In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.
The volume of a cube is given by the formula:
V = s^3
Where V is the volume and s is the length of one side of the cube.
Since this cuboid is made up of centimeter cubes, it means that the length, width, and height are in centimeters.
It is not mentioned the dimension of the cuboid, so it is not possible to determine the volume of the cuboid.
In order to determine the volume of the cuboid, we would need to know its length, width, and height in centimeters.
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Oliver was trying to beat his old score of 990 points in a video game. If he scores exactly 54 points each round, how many rounds would he need to play to beat his old score?
Answer:
19 rounds
Step-by-step explanation:
To find this, we take
990 / 54 = 18.33
It will not be 18 rounds because Olive needs 18.33 rounds to beat his old score, so we have to round up to 19 rounds.
Answer:
19 rounds
Step-by-step explanation:
990/54=18.33 round to 19
Is r =- 0.85 A strong correlation?
A correlation value of -0.8 or lower denotes a significant negative link, whereas one of -0.3 or lower denotes a negligibly weak relationship.
How to interpret a correlation coefficient?
The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls in step with positively associated variables.
Why is correlation coefficient significant? What does it mean?
As a whole, correlation coefficients are used to evaluate the direction and strength of the linear correlations between two sets of variables. When both variables have a normal distribution, use Pearson's correlation coefficient; otherwise, use Spearman's correlation coefficient.
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