In the table below, find the slope, y-intercept, and equation for each racer.
Hint: Time is going to be your independent x / the x-axis. Distance is going to be your dependent y / the y-axis.
Answers
Therefore , the solution of the given problem of slope comes out to be y = 15x + 10.
Explain slope.A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).
Here,
A racer:
Due to the fact that the race begins at the beginning, the y-intercept
is 0.
We can select any two locations from the table and use the following formula to determine the slope:
=> Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:
=> slope = (40 - 10) / (3 - 1) = 30 / 2 = 15
As a result, Racer A's calculation is:
=> y = 15x
Runner B:
As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:
=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15
As a result, Racer B's calculation is:
=> y = 15x + 20
Runner B
The race begins at a distance of 10 feet, so the y-intercept is 10.
We can select any two locations from the table and use the following formula to determine the slope:
Slope Equals (Distance Change) / (change in time)
As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:
=> slope = (65 - 35) / (3 - 1) = 30 / 2 = 15
As a result, Racer C's equation is:
=> y = 15x + 10
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Related Questions
1. Evaluate each expression. Give your answer in radians:
i. Without using a calculator: cos^-1(-√2/2)=
ii. Use a calculator: sin^-1(-0.512)=
Answers
i. π/4
ii. -0.529
1. Evaluate each expression. Give your answer in radians:
i. Without using a calculator: cos⁻¹(−√2/2)Firstly, let us discuss the meaning of the inverse cosine function. The inverse cosine function is the angle (in radians) that corresponds to the cosine value of the input angle. The inverse cosine function returns values in the range [0, pi].cos⁻¹(−√2/2) can be read as "what angle has a cosine of -√2/2?"In a right-angled triangle with angle θ, adjacent is -1, hypotenuse is √2, and opposite is -1. Therefore, we can write the cosine ratio as adjacent over hypotenuse or -1/√2. Let us now solve for θ using the formula for cosine:cosθ = adjacent/hypotenusecosθ = -1/√2θ = cos⁻¹(-1/√2)The exact value of cos⁻¹(-1/√2) is π/4. Therefore, cos⁻¹(-√2/2) = π/4.
ii. Use a calculator: sin^-1(-0.512)As previously mentioned, the inverse sine function is the angle (in radians) that corresponds to the sine value of the input angle. The inverse sine function returns values in the range [-π/2, π/2].sin⁻¹(-0.512) can be read as "what angle has a sine of -0.512?" To find this value, we use a calculator. First, we press the "sin⁻¹" button or "2nd" + "sin" button. Then, we enter the value we want to find, which is -0.512. The final answer is -0.529. Therefore, sin⁻¹(-0.512) = -0.529.
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In8=2.08 in exponential form
Answers
Fell free to ask if u have any question!
Which of the integers are multiples of 40 ? Select all that apply. A. 10,
B. 160 C. 360
D. 20 E. 580
Answers
Answer:
B AND C
Step-by-step explanation:
B AND C ARE THE CORRECT MULTIPLES 40
A shop is having a sale. All items are reduced by 20%. Work out the price of an item that is normally £120
Answers
The price of an item that is normally £120 after a 20% discount is £96.
To find the price of an item that is normally £120 after a 20% discount,
Calculate the discount amount: To find the discount amount, multiply the original price (£120) by the discount rate ( 20% ) in decimal form:
Discount amount = Original price x Discount rate
= £120 x 0.2
= £24
Calculate the sale price: To find the sale price, subtract the discount amount from the original price:
Sale price = Original price - Discount amount
= £120 - £24
= £96
Therefore, the sale price is £96
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Which of the following is a rational number?
Answers
Answer:
-77
Step-by-step explanation:
What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, nth root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.
(Taken from Online)
please help i will give points
Answers
The value of m, n and w are 92, 48 and 88 respectively
What is sum of angle in a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon( 3sided polygon). The sum of angles In a polygon is 180. i.e A+B +C = 180
In the triangle above, The triangle is divided into two.
42+36+w = 180
88+w = 180
w = 180 - 88
w = 92°
From the law of the law of exterior angle of a triangle which states that; The exterior angle of a triangle is equal to the sum of opposite angles.
Therefore;
92 = n + 44
n = 92-44
n = 48°
w = 180-92( angles on a straight line)
w = 88°
Therefore the value of m, n, w are 92, 48 and 88 respectively
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Which set of ordered pairs does NOT represent a function?ResponsesA(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E(-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
Answers
The set of ordered pairs in option C does not represent a function.
What is a function?
A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable.
We know that in a function each input has only one output.
So, on evaluating the options, we get
Option A
This represents a function as each input has only one output.
Option B
This represents a function as each input has only one output.
Option C
This does not represent a function as input 2 has two different outputs which are 2 and 7.
Option D
This represents a function as each input has only one output.
Option E
This represents a function as each input has only one output.
Hence, the set of ordered pairs in option C does not represent a function.
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Question: Which set of ordered pairs does NOT represent a function?
A. (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B. (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C. (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D. (1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E. (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must
also be roots?
Answers
There is no one definite answer.
Given information: If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must also be roots?To find out the other roots of P(x), we have to make use of the Fundamental theorem of algebra which states that every polynomial of degree n has n roots, both real and complex.In order to find out the other roots, we have to divide the polynomial P(x) by its given roots i.e (x-(3-2√5))(x-(6+????)) = 0Let's begin by solving the first root:Since, If 3 −2√5 is the root, thus we can write, x - (3 - 2√5) = 0Or, x - 3 + 2√5 = 0Or, x = 3 - 2√5Similarly, for the second root, 6 + ???? ,
we can write: x - (6 + ???? ) = 0Or, x = 6 + ????Now, Let's combine these two roots and write the polynomial in factored form. Using these two roots, we can write the equation as below: Thus, P(x) = (x - 3 + 2√5)(x - 6 - ???? ) = 0We have found the other roots to be: Other roots = (x - 3 + 2√5)(x - 6 - ???? ) = 0Where ???? can be any value. Therefore, there is no one definite answer.
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A slot machine takes only one-dollar and two-dollars coins and contains a total of thirty six coins altogether. The value of the coins in the machine is ????$55. 4.3.1 Model the statement into two linear equations by letting the number of one-dollar coins to be x and the number of two-dollar coins to be y . (4) 4.3.2 Solve the two equations you formed in 4.3.1 using Cramer’s rule to find the number of coins of each value. (6)
Answers
There are 17 one-dollar coins and 19 two-dollar coins in the machine.
How did we arrive at these values?4.3.1 Model the statement into two linear equations by letting the number of one-dollar coins to be x and the number of two-dollar coins to be y:
Let x be the number of one-dollar coins and y be the number of two-dollar coins in the machine. Then we can form the following two linear equations:
Equation 1: x + y = 36 (total number of coins)
Equation 2: 1x + 2y = 55 (total value of coins)
4.3.2 Solve the two equations you formed in 4.3.1 using Cramer’s rule to find the number of coins of each value:
To solve the two equations using Cramer's rule, we need to write them in matrix form:
| 1 1 | | x | | 36 |
| | x | | |
| 1 2 | | y | | 55 |
Using Cramer's rule, we first calculate the determinant of the coefficient matrix:
D = | 1 1 |
| 1 2 |
D = (1 x 2) - (1 x 1) = 1
Then we replace the first column of the coefficient matrix with the constants from the right-hand side of the equations:
Dx = | 36 1 |
| 55 2 |
And calculate the determinant of this matrix:
Dx = (36 x 2) - (55 x 1) = 17
Similarly, we replace the second column of the coefficient matrix with the constants from the right-hand side of the equations:
Dy = | 1 36 |
| 1 55 |
And calculate the determinant of this matrix:
Dy = (1 x 55) - (1 x 36) = 19
Finally, we can calculate the values of x and y using the formulas:
x = Dx / D = 17 / 1 = 17
y = Dy / D = 19 / 1 = 19
Therefore, there are 17 one-dollar coins and 19 two-dollar coins in the machine.
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PLEASE SOMEBODY HELP
Answers
Step-by-step explanation:
A square has all the sides equal
If AD which is a side is 11, all other sides are 1
BC is 11
AC is a diagonal that divides the square and forms a triangle
AD =11
CD =11
Use Pythagoras theorem to find AC which is hypotenuse
AC² = AD² + CD²
= 121 + 121
=242
If AC² = 242, then AC is square root of 242
AC = 15.56 (approximate if required) 15.6 to 1d.p if required
BD = AC = 15.56
EC is half of BD and AC = 15.56/2
EC = 7.78 (check the decimal place required) 7.8 to 1d.p if required
Angle DAB is 90
Angle AEB is 90
Angle CBD is 45
Angle BAC is 45
(Add the units)
Quadrilateral C with 4 congruent sides is a square, all opposite sides are congruent
Quad L is a parallelogram, consecutive angles are supplementary and opposite angles are congruent
In the diagram below of circle O, PA is tangent to circle O
at A, and PBC is a secant with points B and C on the circle.
A
4
8
B
C
If PA= 8 and PB = 4, what is the length of BC?
Answers
The length of BC is 6 units.
Describe Tangent?In geometry, the tangent is commonly used to describe the relationship between a circle and a straight line. A tangent line to a circle is a line that intersects the circle at exactly one point. This point of intersection is called the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.
By the tangent-secant theorem, we have:
PB^2 = PA(PA + AB)
where AB is the length of the tangent segment from point A to the point of intersection of the secant with the circle.
Substituting the given values, we get:
4^2 = 8(8 + AB)
Simplifying and solving for AB, we get:
16 = 64 + 8AB
8AB = -48
AB = -6
Since AB is a length, it must be positive, so we take the absolute value:
AB = 6
Now we can use the secant-tangent theorem to find the length of BC:
PC(PC + BC) = PB^2
Substituting the given values and using the fact that PC = PA = 8, we get:
8(8 + BC) = 4^2
64 + 8BC = 16
8BC = -48
BC = -6
Again, since BC is a length, it must be positive, so we take the absolute value:
BC = 6
Therefore, the length of BC is 6 units.
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write an equation of the line that passes through (-1,0) and (0,0)
y=
Answers
Answer:
y = 0
Step-by-step explanation:
the 2 points (- 1, 0 ) and (0, 0 ) both have the same y- coordinate.
this indicates the line is horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through )
both points have a y- coordinate of 0 , then
y = 0 ← equation of line
Please help ASAP!
Filipe bought a classic car, originally valued at $60,000, in 2012. He believes that the value of the car depreciates exponentially at a rate of 4% each year.
Round the expected value of Filipe's car after 6 years to the nearest cent.
Click “show your work” and show your steps to solve this problem.
(Hint: You need to use the exponential decay formula)
Answers
In a case whereby Filipe bought a classic car, originally valued at $60,000, in 2012. whee the value of the car depreciates exponentially at a rate of 4% the expected value of Filipe's car after 6 years is $46970
How can the expected value of Filipe's carbe calculated?Based on the given information, the future value when there is a depreciation can be calculated using the formular below:
FV =[ P (1 - r)^n]
where the
R represent the rate of depreciation =4% = 0.04
N represent the number of years = 6 years
FV represent the Future value
P represent the Present value
From the formula we can input the values as :
$60,000 x ( 1 - 0.04)^6 = $42,890
=$46965.5
=$46970 (rounded up)
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Find the exact value using the sum/difference formula.
sin 140 degrees cos 50 degrees-cos 140 degrees sin 50 degrees
Answers
sin (a - b) = sin a cos b - cos a sin b
cos (a - b) = cos a cos b + sin a sin b
Using these formulas, we can write:
sin 140° cos 50° - cos 140° sin 50°
= sin (140° - 50°)
= sin 90°
= 1
Therefore, the exact value of sin 140° cos 50° - cos 140° sin 50° is 1.
The box plot shows a comparison of the heights of gymnasts and basketball players. The mean absolute deviation for each group is approximately 2.
How many mean absolute deviations describe the difference between the two medians?
See image below:
Please give me an answer, work doesn't have to be shown at all, thank you so much.
Answers
Answer:
6.75 in
Analysis:
[tex]\text{The average heights of gymnasts is 60 in, the other is 75 in.}[/tex]
[tex](60+75)\div2=6.75 \ \text{in}[/tex]
The length of a rectangle is twice as long as it’s width. it’s perimeter is 18 in. How long and how wide is the rectangle?
Answers
Answer: Let's start by using algebra to solve the problem.
Let's call the width of the rectangle "w". Then we know that the length of the rectangle is twice the width, or "2w".
The formula for the perimeter of a rectangle is:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width.
We know that the perimeter is 18 inches, so we can substitute the values we have:
18 = 2(2w) + 2w
Simplifying:
18 = 4w + 2w
18 = 6w
Dividing both sides by 6:
w = 3
So the width of the rectangle is 3 inches.
To find the length, we can use the fact that it is twice the width:
l = 2w = 2(3) = 6
So the length of the rectangle is 6 inches.
Therefore, the rectangle is 6 inches long and 3 inches wide.
enjoy!
I NEED HELP ON THIS ASAP!
Answers
Answer
Explanation
A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine
�
p, the number of people who can go to the amusement park.
Answers
Answer:
Hello, your answer is 10
Step-by-step explanation:
Have a good day UwU
Maggie has a bag of different colored marbles the probability of picking an orange marble is 3 out of 10 what is the probability that Maggie will not pick an orange marble is it 3% ,7%, 30%, or 70%
Answers
Answer:
70%
Step-by-step explanation:
3 out of the 10 marbles are not orange, so 7/10 chance you don't, and then you can multiply by 10, and then you have 70 percent
exercise 3.2.5: facts about power sets - true or false. help outline let x be a finite set. for each statement, indicate whether the statement is true or false, or whether more information about x is required to determine if the statement is true.
Answers
The given facts about power sets: Statement 1: False, Statement 2: True, Statement 3: True.
Statement 1: The power set of X is a subset of X. False. The power set of X, denoted by P(X), is a set containing all subsets of X. However, X is not a subset of P(X).
Statement 2: The cardinality of P(X) is greater than the cardinality of X. True. Since the power set of X contains all subsets of X, it has a higher cardinality than X. This can be proven with the equation |P(X)| = 2^|X|.
Statement 3: The cardinality of the power set of the empty set is 1. True. The empty set, denoted by Ø, has no elements, and therefore the power set of the empty set, P(Ø), has one element, which is the empty set itself. Therefore, |P(Ø)| = 1.
In conclusion, each statement is either true or false depending on the given information.
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Solve the equation.
8.88=4.44(x−7)
x = ?
Answers
Answer: x=9
Step-by-step explanation:
Simplify the expression
Add 777 to both sides
Simplify the expression
Divide both sides by the same factor
Simplify the expression
Move the variable to the left-hand side and change its sign
calculate the difference and then divide both sides:)
How can I solve this?
Answers
In conclusion, we need to identify the set of values of x for which either f(x)=-1/4 or f(-x)=-1/4 in order to solve to the equation f(|x|)=-1/4.
How is a function solved?The expression f(|x|)=-1/4 indicates that the absolute value of x's function f is equal to 1/4. Any x values that satisfy this equation are what we are trying to find. We can rewrite the equation as f(x)=-1/4 when x is positive and f(-x)=-1/4 when x is negative because the absolute value of x is always positive.
We must search for values of x such that f(x)=-1/4 or f(-x)=-1/4 in order to identify the answers. Without knowing more about the function, f may be anything, hence we cannot know the precise solutions.
Therefore, we can state that x or -x is a solution to the equation if there is a value of x such that f(x)=-1/4 or f(-x)=-1/4.
As a result, we must identify the range of x values for which either f(x) or f(-x) = 1/4.
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The sum of the areas of the two squares on the legs ( a and b ) equals the area of the square on the hypotenuse ( c )?
Answers
Answer: A^2 + B^2 = C^2
Step-by-step explanation:
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Which pair of angles are corresponding?
A. <1 and <3
B. <3 and <4
C. <1 and <8
D. <2 and <6
Answers
Answer:
2 and 6
Step-by-step explanation:
2 and 6 is the correct option
HELP PLEASE
NUMBER 18
Answer is (1,1)
Answers
i. The points of intesection of the common chords of the curve x² + y² = 4 and y² = 3x are
(1, √3) and (1,-√3)ii. The points of intesection of the common chords of the curve x² + y² = 4 and x² - 4y + 1 = 0 are
(√3, 1) and (-√3, 1)What are common chords of a circle?The common chords of circles are the chords that pass through the points of intersection of the curves.
i. Given the curve x² + y² = 4 and y² = 3x. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and y² = 3x. Substituting the second equation into the first, we have
x² + y² = 4 and y² = 3x.
x² + 3x = 4
Re-arranging, we have
x² + 3x - 4 = 0
Factorizing the quadratic equation, we have
x² - x + 4x - 4 = 0
x(x - 1) + 4(x - 1) = 0
(x + 4)(x - 1) = 0
⇒ x + 4 = 0 and x - 1 = 0
⇒ x = - 4 and x = 1
Now, y² = 3x.
⇒ y = ±√3x
So.substituting x = -4 into the equation, we have
y = ±√3x
y = ±√(3 × -4)
= ±√(-12)
Since the square root is negative, this answer is invalid.
Substituting x = 1 into y, we have
y = ±√3x
y = ±√3(1)
y = ±√3
So, the points of intersection are (1, √3) and (1,-√3)
ii. Given the curve x² + y² = 4 and x² - 4y + 1 = 0. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and x² - 4y + 1 = 0. From the second equation, we have
x² = 4y - 1
Substituting this equation into the first, we have
x² + y² = 4 and x² = 4y - 1
y² + 4y - 1 = 4
Re-arranging, we have
y² + 4y - 1 - 4 = 0
y² + 4y - 5 = 0
Factorizing the quadratic equation, we have
y² - y + 5x - 5 = 0
y(y - 1) + 5(y - 1) = 0
(y + 5)(y - 1) = 0
⇒ y + 5 = 0 and y - 1 = 0
⇒ y = - 5 and y = 1
Now, x² = 4y - 1
⇒ x = ±√(4y - 1)
So, substituting y = -5 into the equation, we have
x = ±√(4y - 1)
x = ±√[(4 × -5) - 1)]
= ±√(- 20 - 1)
= ±√-21
Since the square root is negative, this answer is invalid.
Substituting y = 1 into x, we have
x = ±√(4y - 1)
x = ±√(4(1) - 1)
x = ±√(4 - 1)
x = ±√3
So, the points of intersection are (√3, 1) and (-√3, 1)
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The width of a box is two-third of it's length and height is one-third of it's length. If the volume of the box is 384 cubic meter, find the dimensions of the box.
Answers
Answer:
Length - 12 m, width - 8m, height - 4 m
--------------------------------------
The relation between dimensions of the box:
w = (2/3)l;h = (1/3)l;V = 384 m³.Use volume equation and find the value of l:
V = lwh384 = l*(2/3)l*(1/3)l384 = 2/9l³l³ = 384*9/2l³ = 1728l = ∛1728l = 12 mFind the width and height:
w = (2/3)*12 = 8 mh = (1/3)*12 = 4 mNO EXPLANATION JUST ANSWER!
Answers
Answer:
405mm^3
Hope this helps!
Brainliest and a like is much appreciated!
Answer:
405
Step-by-step explanation:
Answer is above!The radius of a quarter circle is 1 yard. What is the quarter circle's perimeter?
Answers
The perimeter of the quarter circle with radius 1 yard is approximately 2.57 yards.
To find the perimeter of a quarter circle, we need to add up the lengths of its curved edge and its straight edge.
In this case, the curved edge is a quarter of a circle with radius 1 yard. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Since we only need a quarter of the circumference, we can divide the formula by 4:
C = (2πr)/4
Substituting r = 1, we get:
C = (2π(1))/4
C = π/2
Therefore, the curved edge of the quarter circle has a length of π/2 yards. The straight edge of the quarter circle is simply the radius, which is also 1 yard.
So the perimeter of the quarter circle is the sum of the curved edge and the straight edge:
Perimeter = (π/2) + 1
Using 3.14 for π and adding the two terms, we get:
Perimeter ≈ 2.57 yards
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a weather ballon ascends at a constant rate. the height of the ballon 8 minutes after beginning to ascend is 2,320 feet. the height 15 minutes after ascending is 4,350 feet. what is the change in the elevation of the ballon per minute
Answers
Answer:
290 feet/minute
Step-by-step explanation:
2320/9 = 290
4350/15 = 290
simplify 3 c -9 d+7 c+5 d
Answers
10c-9d+5d
10c-4d
Solution:
10c-4d
10c-4d
Answer:10d-4d