The slope of the linear relationship is 15.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope of a line tangent to a function's graph in differential calculus is determined by the derivative of that function and serves as a representation of the function's instantaneous rate of change with regard to changes in the independent variable. The slope of a tangent line in the graph of a position function, which plots the distance travelled by an object against the passage of time, corresponds to the object's instantaneous velocity.
Given
A linear relationship is given.
y₁ = -9
y₂ = 6
x₁ = 0
x₂ = 1
Slope:
m = y₂ - y₁/x₂ - x₁
m = 6 + 9/1 - 0
m = 15/1
m = 15
The slope of the linear relationship is 15.
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Answer:
Slope = 15
Step-by-step explanation:
Now we have to,
→ find the slope of linear relationship.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Coordinates we use from table,
→ x1 = 0, y1 = -9
→ x2 = 1, y2 = 6
Then the required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (6 -(-9))/(1 - 0)
→ m = (6 + 9)/1
→ m = (15)/1
→ [ m = 15 ]
Hence, the required slope is 15.
14. Between a pair of points on the line y = 5x-2, suppose that the rise is 15.
Then the run is...
(A) 3
(B) 4
(C) 5
(D) 10
Answer:
Below
Step-by-step explanation:
m = slope = rise / run
m = 5 for this equation
rise /run = 5
15 / run = 5
run = 3
rotation 90 degrees counterclockwise about the origin
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
What is the cartesian plane?The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.
What are the quadrants?Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.
Given:
The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)
Angle of rotation = 90° about the origin
According to the question, let's take our start point as A(x, y)
So, A( x, y) will lie in the first quadrant.
After 90° rotation about the origin A' will lies in fourth quadrant.
As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).
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The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
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Question 2
What is the length of the line segment with endpoints P(2, 1,-4) and Q(-1,5,3)?
The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units
How to find the length of a line segment?To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:
length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Substituting the coordinates of P and Q into the formula, we get:
length = √((-1 - 2))² + (5 - 1))² + (3 - (-4)))² )
= √((-3))² + (4))² + (7))² )
= √(9 + 16 + 49)
= √(74)
= 8.60 units
Therefore, the length of the line segment is 8.60 units
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4. 8 friends are lining up to get in to see the Hunger Games: Catching Fire movie,
including Bob and Sam
A) What is the probability that Bob and Sam will be next to each other.
Answer:
1/64
Step-by-step explanation:
1/8 x 1/8 = 1/64
What is sin(60) in degrees?
Answer:
(sqrt3)/2
Step-by-step explanation:
Sin(x)=opposite/hypotenuse
30, 60, 90 right triangle.
ratio of sides are 1, sqrt3, and 2.
Locate the 60 degree angle on the triangle
The opposite side is sqrt3
The hypotenuse is 2
so its (sqrt3)/2
Answer:
√3/2 or 0.866
Step-by-step explanation:
the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have
Write an equation that passes through the point (4,-3) and is perpendicular to the line 4x+y=3
Answer:
y = 1/4x - 4
Step-by-step explanation:
4x + y = 3
y = -4x + 3
Perpendicular slope = 1/4
y = 1/4x + b
-3 = 1/4(4) + b
-3 = 1 + b
b = -4
y = 1/4x - 4
Lindsey's Cafe uses 5 bags of coffee every day. How many days will 1/2 of a bag of coffee last?
When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.
Here,
number of bags needed in a day=5
number of days 1/2 bag last,
=5÷1/2
=10 days
Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.
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Which of the following expressions are equivalent to 16/24? Select all that apply.
After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
So, we have the expression:
16/24
We need to find the equivalent expression from the options as follows:
So, let's take option (E) as it seems the answer and evaluation is:
8/2 * 2/12 (Be LHS)
Now, multiply:
8/2 * 2/12 = 16/24
16/24 = 16/24
Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.
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you are skiing down a mountain with a vertical height of 2900 feet. the distance from the top of the mountain to the base is 5800 feet. to the nearest degree, what is the angle elevation from the base to the top of the mountain?
Answer:
30°
Step-by-step explanation:
You want the angle of elevation to a point 2900 feet up that is 5800 feet distant on a straight line.
SineThe sine of the angle is the ratio of the height to the straight-line distance.
sin(θ) = h/d = 2900/5800 = 1/2
θ = arcsin(1/2) = 30°
The angle of elevation is 30° from the base to the top.
Answer: When doing a problem like this I always draw an example so I can see it. If you do that you see a right triangle with the hypothenuse, 2500 feet, is the distance from the top to the base. The opposite side is 1250 feet. Then remember sine= o/h, (opposite side over hypothenuse). So divide 1250/2500 and you get .5 Now take your calculator and use "inv" or sin-1 button to get the answer of the angle. x = 30
sinθ 1250/2500 = 1/2; θ = sin-1(1/2) = 30°
Step-by-step explanation:
Find the sum of 5.21 × 1019 and 3.149 × 1017.
A. 8.359 × 1019
b. 5.24149 × 1019
c. 5.24149 × 1036
d. 8.359 × 1036
Answer:
B
Step-by-step explanation:
5.21 x 10^19 + 3.149 x 10^17
10^17(5.21 x 10^2 + 3.149)
10^17(521 + 3.149)
10^17(524.149)
5.24149 x 10^17 x 10^2
5.24149 x 10^(17+2)
5.24149 x 10^19
Answer: b. 5.24149 × 1019
Step-by-step explanation: I took the test
49: 1 of 1 question 2 with 1 blank 97: 1 of 1 question 3 with 1 blank 113: 1 of 1 question 4 with 1 blank 632: 1 of 1 question 5 with 1 blank 1.781: 1 of 1 question 6 with 1 blank 3.558: 1 of 1 question 7 with 1 blank 1.006.015: 1 of 1 question 8 with 1 blank 67.224.370: 1 of 1 3
Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.
These numbers in Spanish are:
1. 49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
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Answer:
49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
Step-by-step explanation:
Using composition of functions, determine if the two functions are inverses of each other. , x ≥ 0 , x ≥ 2 A. No, because the functions contain different operations. B. No, because the composition does not result in an answer of x. C. Yes, because F(x) is equal to –G(x). D. Yes, because the composition results in an answer of x for x ≥ 2.
The correct option regarding whether the two functions are inverse functions is given as follows:
B. No, because the composition does not result in an answer of x.
How to verify if the two functions are inverses of each other?Two functions are inverses of each other if the composition of these two function has a result of x.
From the image given at the end of the answer, the two functions in this problem are defined as follows:
[tex]F(x) = \sqrt{x} + 4, x \geq 0[/tex]G(x) = x² - 4, x ≥ 2.Their composition is given as follows:
[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]
[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]
[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]
The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.
The problem is given by the image shown at the end of the answer.
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If EF = 71, FD = 80, ED = 74, IG = 40, and HG = 37, find the perimeter
of AGHI. Round your answer to the nearest tenth if necessary.
The perimeter of the object is the sum of the lengths of all the sides
which is 302 units.
What is the perimeter?Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.
In the case of a circle, we call it perimeter circumference it is the distance around the circle.
Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and
HG = 37.
Now the perimeter of this figure is the sum of the lengths of all the sides which is,
= (EF + FD + ED + IG + HG).
= (71 + 80 + 74 + 40 + 37).
= 302 units.
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Graph the line that has a slope of -4/3 and includes the point ( -6,2)
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Slope intercept form:The slope-intercept form a line is given by
y = mx + c,where m is the slope of a line and c is the y-intercept.
Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line
Here we have
Slope of line = -4/3
The point of the line
As we know y = mx + c is the line Here m is the slope of the line
From the given data, m = -4/3
=> y = (-4/3)x + c
=> 3y = -4x + 3c
Given that the point on the line is (-6, 2)
=> 3(2) = -4(-6) + 3c
=> 6 = 24 + 3c
=> 3c = 18
=> c = 6
Therefore,
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
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If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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need help now i need to finish this delta
Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.
What do you mean by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
What is reflection in mathematics?In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.
Figure H
Mapped onto figure I
The required transformation:
reflection along y=x.
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The probability of winning a certain game is 0. 5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?.
0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.
What is the binomial theorem on probability?The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).
When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."
The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.
Given that,
p = 0.5, So, q = 1 - 0.5 = 0.5.
If 70% of 'n' games are won then 30% of n games must be lost.
Let n = 10.
Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]
or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]
or, P (x = 3) = 120×0.0078×0.125.
or, P (x = 3) = 0.117 Or 11.7% chance.
Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.
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The side of a cube has a length of 4x³y6 cm. The volume of the cube can be found using
the formula V = S³. What is the volume of the cube in cubic centimeters?
PLEASE HELP
Answer:
find my dad
Step-by-step explanation:
Find the table that follows this rule: multiply by 8 and add 5.
A.
Input 5 6 7 8 9 10
Output 40 48 56 64 72 80
B.
Input 5 6 7 8 9 10
Output 45 53 61 69 82 90
C.
Input 5 6 7 8 9 10
Output 45 53 61 59 67 75
D.
Input 5 6 7 8 9 10
Output 45 53 61 69 77 85
Answer:
D
Step-by-step explanation:
multiply by 8 and add 5.
so,
we need to do this for every unit value and see, if the result is the same as the listed output value.
5 -> 5×8 + 5 = 45
6 -> 6×8 + 5 = 53
7 -> 7×8 + 5 = 61
8 - > 8×8 + 5 = 69
9 -> 9×8 + 5 = 77
10 -> 10×8 + 5 = 85
so, D is the correct answer.
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins, what net payout will you be promised in a fair betting game in case your bet works out?
Net payout will you be promised in a fair betting game in case your bet works out is $0 .
Given :
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .
P ( browns ) = 60 / 100 = 0.60
P ( steelers ) = 40 / 100 = 0.40
Net payout = Number of wins * 10 - Number of loses * 10
= 1 * 10 - 1 * 10
= 10 - 10
= $0.
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If using the method of completing the square to solve the quadratic equation x 2 + x + 9 = 0, which number would have to be added to "complete the square"?
Answer:
Below
Step-by-step explanation:
To complete the square, the coefficient of x^2 must be 1 ( it is already)
then take 1/2 of the x coefficient .... 1/2.... square it and add it to both sides of the equation
x^2 + x + 1/4 + 9 = 1/4
then you can reduce this to
( x+ 1/2)^2 + 9 = 1/4 for further 'solving'
PLEASE EXPLAIN WHY YOU GOT YOUR ANSWER PLEASEE!!!!
When Skip was a puppy, he weighed 5.6 lbs. When he visited the vet, he weighed 13.3 lbs. How much weight did Skip gain between the time he was a puppy and his vet visit?
Answer:
7.7
Step-by-step explanation:
I got this by subtracting 13.3 - 5.6
Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
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PLEASE HELP URGENT WITH 4 AND 6
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5+0.75x models the scenario.
Which statement is true?
Responses
The coefficient 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The coefficient 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 5+0.75x.
In the given expression, 5 is constant term and 0.75x is another term.
In the term 0.75x, 0.75 is the coefficient of x
In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.
Therefore, option D is the correct answer.
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If using the method of completing the square to solve the quadratic equation x 2 + 2 x + 16 = 0
Answer:
Step-by-step explanation:
[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]
The solution does not exist because all numbers squared are greater than zero.