As slope is undefined, then the slope of the line is parallel to the x axis.
How to determine the slope of a line
In this problem we have a line that passes through two points, the slope is determined by definition of secant line:
m = [- 9 - (- 6)]/(8 - 8)
m = - 3/0
As slope is undefined, then the slope of the line is parallel to the x axis.
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v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
what does a irrational number look like
A irrational number is a number that can't be expressed as a ratio of two whole numbers. That's it.
For examples (in increasing order of difficulty)
1 is a rational number because it is 1/1
0.75 is a rational number because it is equal to 3/4
2.333... (infinite number of digits, all equal to three) is rational because it is equal to 7/3.
sqrt(2) is not a rational number. This is not completely trivial to show but there are some relatively simple proofs of this fact. It's been known since the greek.
pi is irrational. This is much more complicated and is a result from 19th century.
As you see, there is absolutely no mention of the digits in the definition or in the proofs I presented.
Now the result that you probably hear about and wanted to remember (slightly incorrectly) is that a number is rational if and only if its decimal expansion is eventually periodic. What does it mean ?
Take, 5/700 and write it in decimal expansion. It is 0.0057142857142857.. As you can see the pattern "571428" is repeating in the the digits. That's what it means to have an eventually periodic decimal expansion. The length of the pattern can be anything, but as long as there is a repeating pattern, the number is rational and vice versa.
As a consequence, sqrt(2) does not have a periodic decimal expansion. So it has an infinite number of digits but moreover, the digits do not form any easy repeating pattern.
Balu had a collection of coins. 1/2 of the coins are from asian countries, 1/3 of them from european countries, 36 are from america, how many asian coins are there
The total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
We assume the total coins with Balu to be x.
The fraction of coins from Asian countries = 1/2.
Thus, the number of coins from the Asian countries = 1/2 of x = x/2.
The fraction of coins from European countries = 1/3.
Thus, the number of coins from the European countries = 1/3 of x = x/3.
The number of coins from America = 36.
Thus, the total number of coins = x/2 + x/3 + 36.
But, we assumed that the total number of coins is x.
Thus, we get a linear equation in one variable as follows:
x = x/2 + x/3 + 36.
We solve this equation as follows:
x = x/2 + x/3 + 36,
or, x - x/2 - x/3 = 36,
or, (6x - 3x - 2x)/6 = 36,
or, x/6 = 36,
or, x = 36*6 = 216.
Thus, the total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
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Which expression belongs
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
How to Simplify Algebraic Expressions?
We are given the algebraic expression;
(5x² + 25x + 20)/(7x)
Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;
5(x² + 5x + 4) = 5((x + 1)(x + 4))
Now, we see that the expression that simplifies the algebra is given as;
[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]
Now, the numerator and denominator can be factorized to get;
[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]
Thus, x + 1 will cancel out to get;
[(x + 1) * ( )]/[( ) * 7x]
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
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. In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
The width of the rectangular backyard is 9 yards.
How to find the width of the rectangle?The width of the yard is three less than four times the length.
Therefore,
w = 4l - 3
Perimeter of a rectangle = 2l + 2w
where
l = length
w = width
Hence,
24 = 2l + 2(4l - 3)
24 = 2l + 8l - 6
24 = 10l - 6
24 + 6 = 10l
30 = 10l
l = 30 / 10
l = 3 yards
Hence,
w = 4(3) - 3
w = 12 - 3
w = 9 yards
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Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?
Answer:
Meena age = 5 yrs Meenas father = 30
Step-by-step explanation:
let,
meena's age = x
meena's father's age = 6x
Five years from now
meena's age will be 1/3(6x)
meena's father's age will be 6x+5
A/Q
x+5+6x+5=2x+6x+5
=x+6x-2x-6x=5-5-5
= -x =-5
= x =5
meena's age = 5
meena's father's age = 6x
= 6×5
= 30
Use the drawing tools to form the correct answer on the provided graph.
Graph the line that represents the equation y= -2/3x + 1
The graph of the line is shown in the attached image.
Given that the equation of the line y=-2/3x+1.
The line equation is an algebraic representation of the set of points, which together form a line in an exceedingly frame of reference.
First, we'll take the intercepts of equation y=-2/3x+1 . find
Find the y-intercept
The y-intercept is that the value of y when the worth of x is adequate zero
For x=0
y=-2/3(0)+1
y=1
The y-intercept is that the point (0.1)
Find the x-intercept
The x-intercept is that the value of x when the worth of y is adequate to zero
For y=0
y=-(2/3)x+1
0=(-2/3)x+1
-1=(-2/3)x
x=3/2 or 1.5
The y-intercept is that the point (1.5,0).
To plot the line on a graph, draw the intercepts and connect the dots as shown within the figure.
Therefore, the graph for the line y=-(2/3)x+1 is attached below.
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What is the partial fraction decomposition of startfraction 7 x squared minus 6 x + 9 over 3 x (4 x squared + 9) endfraction?
Answer:
A:(1/3x)+(x-2/4x^2+9)
Step-by-step explanation:
Edg2022
Determine the equation of the parabola graphed below. A parabola is plotted, concave down, with vertex located at coordinates negative three and four.
The equation of parabola from graph is y = a(x + 1)² - 4.
According to the statement
we have to determine the parabola equation from the graphical representation.
So,
For this purpose we know that
Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
The general equation of parabola is y = a(x-h)2 + k
And The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the vertex given, we have that h = -1, k = -4, hence the equation is:
y = a(x + 1)² - 4
So, The equation of parabola from graph is y = a(x + 1)² - 4.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.
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The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
69 = 7x - 8
x = 6x - 8
69 = 6x - 8
Answer:
[tex]69 = 6x - 8[/tex]
Step-by-step explanation:
All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]
Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.
This leaves you with the one final answer [tex]69 = 6x - 8[/tex]
Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are?
Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.
This is an exercise related to Game Theory.
What are repeated game?The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.
The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.
As contrast to one-shot games, recurring games provide a new set of incentives.
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The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 3 units. Which conclusion can be made from the given information? (1 point) The volume of the prism is half the volume of the cylinder. The volume of the prism is twice the volume of the cylinder. The volume of the prism is equal to the volume of the cylinder. The volume of the prism is not equal to the volume of the cylinder.
Answer:
Step-by-step explanation:
The volume of the prism is not equal to the volume of the cylinder.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cross sectional areas of a triangular prism and a right cylinder.
Volume of cylinder = cross sectional area * height = 3 * x = 3x
Volume of triangular prism = cross sectional area * height = 5 * x = 5x
The volume of the prism is not equal to the volume of the cylinder.
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On May 1 Geraldo Saldana opened a savings account that paid 3.5 percent
interest at Fulton Savings Bank with a deposit of $3,600. Ten days later he
deposited $3,000. Fourteen days later he deposited $5,000. No other deposits
or withdrawals were made. Six days later the bank calculated the daily interest.
Based on the amounts that Geraldo Saldana deposited in the month of May, the total simple interest comes to $18.98.
what amount of simple interest does Geraldo Saldana get?the simple interest earned can be found as:
= (3,600 x 3.5%/360 days x 30 days) + (3,000 x 3.5%/360 days x 20 days) x (5,000 x 3.5%/360 days x 6 days)
= 10.5 + 5.83 + 2.65
= $18.98
rest of the question is:
How much simple interest did his money earn?
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can someone please help mee
Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
Yasmin designed a square table using a scale drawing. The actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet. Choose the figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet.
The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.
How to calculate the length?From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.
The new length will be:
= 2 × 3 2/3
= 7 1/3
Therefore, the new length is 7 1/3 feet.
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Three more than twice a number is five less than the square of the number.What is the number?
2. The Kenya Seed Company sold 6 460 t 760 kg of maize seeds to 95 farmers. The farmers bought equal masses of seeds. What mass of seeds did each farmer buy? fond his cous in equal
Using proportions, it is found that each farmer bought 68,008 kg.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:
6460 x 1000 + 760 = 6,460,760 kg
The amount per farmer is:
6,460,760/95 = 68,008 kg.
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If a circle has a radius of 4 meters, what is its circumference?
Answer: 12.56
Step-by-step explanation:
4 x 3.14
pi = 3.14
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 meters per second². If the acceleration of the object becomes 4 meters per second², what is the force?
Answer:
8
Step-by-step explanation:
F=ma
10=5m
4m=10*4/5
4m=8
So the answer is 8
The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers
Answer:
56
Step-by-step explanation:
small brain :(
Charlie owns a computer repair service. For each computer, they charge $50 plus $45 per hour of work. A linear equation that expresses the total amount of money Charlie earns per computer is y
The linear equation is 45x+50
Linear equation is the equation having the degree 1
Given that the charge per computer repair service is $50
The charge per hour of work is $ 45
We need to show the linear equation that expresses the total amount of money Charlie earns per computer is y
So , Let the number of hours be x
Therefore, the Charlie working hours charge will be 45x
The total amount of money Charlie earns per computer is y
Therefore the linear equation will be
y = 50+45x
Where y = Total amount of money
x = number of hours
Hence the linear equation is y = 45x+50
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A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable
Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.
What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.That is, the input of the function is the independent variable and the output is the dependent variable.In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:
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In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
Answer: 9 yards
Step-by-step explanation:
Let's make equations to represent each situation.
The first equation says that the width is 3 less than 4 times the length, so let's put that into an equation:
[tex]w=4l-3[/tex]
Next, we can use the perimeter equation that [tex]P=2l+2w[/tex]. Since we know the perimeter is 24 yards, we can replace it for P.
[tex]24=2l+2w[/tex]
Now that we have two equations with two variables, we can use either elimination or substitution to solve them. Since w is already solved for in the first equation, let's plug it in the second equation.
[tex]24=2l+2(4l-3)\\ 12=l+4l-3\\ 12=5l-3\\ 15=5l\\ l=3[/tex]
Now, let's put l back into the first equation to solve for w.
[tex]w=4(3)-3\\ w=12-3\\ w=9[/tex]
The width is 9 yards
first sequence: 3 8 13 18 23 second sequence: -2 4 10 16 . find the TWO numbers that are in both number sequences.
[tex]a(n) = 3 + 5n[/tex]
[tex]b(n) = - 2 + 6n[/tex]
[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]
[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]
triangle properties help
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the
resulting statements true.
(a) B __ A (b)C __ A (c) B __ C (d) ∅ __ B (e) C __C
Answer:
Answer
Step-by-step explanation:
(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)
(e) C ⊂ C (reflexitivity).
successor of -501 is
Answer:
-500
Step-by-step explanation:
since 501 has a negative sign,add 1 to to the number,the next number will be -500
-501 +1 = -500
successor in this case means a number that succeeds another
What is the common ratio of the geometric sequence below?
10, 15, 22.5, 33.75, ...
A. 2/3
B. 1.5
C. 5
D. 7
The common ratio of the geometric sequence is 1.5
Common ratio can be described as difference between two numbers in a sequence.
The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term
= 15/10
= 1.5
Hence the common ratio of the sequence is 1.5
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Answer:
B
Step-by-step explanation:
The common ratio of the geometric sequence is 1.5
Common ratio can be described as difference between two numbers in a sequence.
The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term
= 15/10
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1.5
A 1500 pound car is stopped in traffic on a hill that is at an incline of 10°. determine the force that is required to keep the car from rolling down the hill.
Answer: about 260 Lb
Step-by-step explanation:
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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