The slope of the parallel line is given by the equation m = ( -1/6 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
3x + 18y = -486 be equation (1)
On simplifying the equation , we get
Subtracting 3x on both sides of the equation , we get
18y = -3x - 486
Divide by 18 on both sides of the equation , we get
y = ( -3/18 )x - ( 486/18 )
On further simplification , we get
y = ( -1/6 )x - 27
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = -( 1/6 )
Hence , the slope of the line is m = -1/6
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Two adjacent angles are on a straight line. One angle is (5x−28)° and the other angle is 8x°. What is the degree value of the second angle?(1 point)
Responses
128 degrees
120 degrees
52 degrees
16 degrees
Answer:
128°
Step-by-step explanation:
Adjacent angles on a straight line must add up to 180°
Using the angle measures given,
(5x−28)° + 8x° = 180°
5x - 28 + 8x = 180
13x - 28 = 180
13x = 180 + 28
13x = 208
x = 208/13 = 16
Therefore second angle = 8x° = 8(16)° = 128°
Question The general form of the equation of a circle is x2+y2−25x+5y+5=0. What is the equation of the circle in standard form?
Step-by-step explanation:
please refer to the sketch fir the details
Ted places $1500 in a ten-year certificate of deposit (CD) account at a local bank. The CD account earns interest, compounded annually, at the same rate for 10 years.
Let A(n) represent the amount, in dollars, in Ted's account after n years between n = 0 to n = 10.
Part A:
Write an explicit expression for the function A(n) if Ted's account has $1535.25 after 1 year
Answer:
A(n) = 1500 * (1 + 0.0367)^n
Step-by-step explanation:
Given that Ted's account has $1535.25 after 1 year, we can use that value to write an explicit expression for the function A(n).
The amount in the account after n years is given by the formula:
A(n) = A(0) * (1 + r)^n
where A(0) is the initial amount in the account and r is the interest rate.
Since A(1) = $1535.25 and A(0) = $1500, we can substitute these values into the formula:
1535.25 = 1500 * (1 + r)^1
Solving for r:
r = (1535.25/1500) - 1 = 0.0367
So, the interest rate is 3.67% and the explicit expression for the function A(n) is:
A(n) = 1500 * (1 + 0.0367)^n
What is the height of a triangle of area 67.2 cm² and the corresponding base 16cm?
Answer: hb=8.4cm
Step-by-step explanation:
Using the formula
A=hbb
2
Solving forhb
hb=2A
b=2·67.2
16=8.4cm
This is a test to see how reliable the source is. (AKA if the answer is correct and how long it takes)
7x+9-2x+8^2-41>2
x>-6 there u go
Step-by-step explanation:
an angle is 60 degrees more than its complement. what are the measures of the two angles? list your angles from smallest to largest.
The measures of the two angles is 40° and 50° list your angles from smallest to largest is 40° to 50°.
When two straight lines or rays meet at the same place, an angle is formed. The vertex of an angle is the location at which all points meet. Angle is derived from the Latin word angulus, which means "corner." In the Early Middle Ages, England was home to a particular cultural group known as the Anglo-Saxons. They were the offspring of settlers who came to Britain from continental Europe in the fifth century. However, the ethnogenesis of the Anglo-Saxons occurred in Britain; they did not merely accept a foreign identity.
Let the angle be X
Let the complimentary angle be Y
X + 60 = 2Y … equation 1
Y + X= 90
(complimentary angles always equal to 90°)
Y = 90 - X …. equation 2
Substitute equation 2 into equation 1
[tex]X + 60 = 2 x (90 - X)\\X + 60 = 180 - 2X\\X + 2X = 180 - 60\\3X = 120\\X = 40[/tex] … equation 3
Therefore, the angle (X) equals 40°
To calculate Y, substitute equation 3 into equation 2.
[tex]Y = 90 - 40\\Y = 50°[/tex]
Therefore the complimentary angle is 50°
To check if the answer is correct
The angle (40) plus 60 is 100
The complementary angle (50) divided by two equals 100.
list your angles from smallest to largest is 40° to 50°.
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3. For two cylinders ratio of diameters A and B, the ratio of lengths is 3 : 1 and the is 1:2. Calculate the ratio of their volumes.
Answer:
Alright so the Diameter ratio of cylinder a & b = 1:2 and Length (height) ratio of cylinder a & b = 3:1
We have to find the volume ratio of cylinder a & b.
Let the diameter of cylinder a = 1r and,the diameter of cylinder b = 2r, the length of cylinder a = 3h, and,the length of cylinder b = h
(h & r are assumed as variables)
So,
The radius of cylinder a = 1r/2
The radius of cylinder b = 2r/2 = r
So,
The volume of cylinder a = π × (1r/2)² × 3h = π × 1r²/4 × 3h = 3πr²h/4
The volume of cylinder b = π × (r)² × h = πr²h
Ratio of volume = 3πr²h/4 : πr²h = 3πr²h/4 × 1/πr²h = 3/4 = 3:4
So,the ratio of their volume is 3:4
Hope this helps!^^
Step-by-step explanation:
Can someone PLEASE help me with this?
The factorization of 3x² - 6x - 24 will be (x + 8)(x - 10).
How to express the valueThe equation is a polynomial with leading coefficient 3, the equations os in standard form, where the leading coefficient is positive and the terms are ordered from highest degree to lowest degree.
To solve thw equation goes thus:
3x² - 6x - 24
Divide through by 3
x² - 2x - 80
x² - 10x + 8x - 80
x(x - 10) + 8(x - 10)
(x + 8)(x - 10)
The value will be (x + 8)(x - 10).
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WILL GIVE BRAINLIEST, EASY POINTS, HELP ASAP,
The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 2 heads).
0.8125
0.6875
0.4375
0.0625
Answer:
The probability of getting at least two heads when a coin is tossed four times is 0.8125. This can be calculated using the tree diagram, which shows that there are 15 possible outcomes when a coin is tossed four times and 12 of these outcomes include at least two heads. Therefore, the probability of getting at least two heads is 12/15 or 0.8125.
Step-by-step explanation:
The probability of getting at least two heads when a coin is tossed four times is 0.8125, according to the tree diagram. This information can be found in the article "Probability of at least two heads when a coin is tossed four times" from the website Math is Fun.
COLLEGE Dominick’s grandfather gave him $300 to start his college savings account. Dominick’s grandfather also gives him $75 each month to add to the account. Dominick’s mother gives him $40 each month, but has been doing so for 3 fewer months than Dominick’s grandfather. Write a simplified expression for the amount of money Dominick has received from his grandfather and mother after m months.
The simplified expression for the amount of money that Dominick has received is $180 + $115m.
What is the simplified expression?The expression that represents the total amount of money received from the grandfather is:
amount given to start savings + (amount given per month x number of months)
$300 + ($75 x m)
$300 + $75m
The expression that represents the total amount of money received from the mum is:
amount given per month x (m - 3)
$40 x (m - 3)
= $40m - $120
Total amount of money received = amount received from the grandfather + amount received from the mum
$300 + $75m + $40m - $120
$180 + $115m
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Without graphing, answer the following questions for each of the functions below: F(x) = x^2 + 8x^3 + k F (x) = x^6 + kx^4 - 9x^2 - 27 f (x) = -1/2x^7 - 441x^3 + k What are the end behaviours of this type of function (what quadrant does it begin and end in?) What is the maximum and minimum number of x-What is the maximum and minimum number of turns for this type of function? State if thereintercepts for this type of function? are any restrictions on the domain and range on this type of function
F(x) = x^2 + 8x^3 + k
End behavior: As x approaches positive or negative infinity, F(x) approaches positive infinity.
Maximum/minimum: There is no global maximum or minimum without more information about k.
x-intercepts: There are no x-intercepts for this function.
Restrictions on domain and range: No restrictions specified.
What are the responses for other questions?F(x) = x^6 + kx^4 - 9x^2 - 27
End behavior: As x approaches positive or negative infinity, F(x) approaches positive infinity.
Maximum/minimum: There is no global maximum or minimum without more information about k.
x-intercepts: There are no x-intercepts for this function.
Restrictions on domain and range: No restrictions specified.
f(x) = -1/2x^7 - 441x^3 + k
End behavior: As x approaches positive or negative infinity, f(x) approaches negative infinity.
Maximum/minimum: There is no global maximum or minimum without more information about k.
x-intercepts: There are no x-intercepts for this function.
Restrictions on domain and range: No restrictions specified.
The number of turns and the maximum and minimum number of x-intercepts for this type of function can't be determined without a graph.
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The number of pick up trucks y built on an assembly line at a factory is represented by the equation
Based on how many pickup trucks are built each week and how long the plant operates each day, one truck is built per hour.
How does a linear equation work?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram Math World: linear.
How can I determine the number of assembled trucks?If the automaker facility operates for five days out of the week and 60 trucks are produced each week, then the number of trucks assembled per day is:
= 60 / 5
= daily 12 trucks
The number of trucks assembled every hour at the automaker's plant, which runs for 12 hours in a half-day, is:
= 12 trucks each day/worked hours
= 12 / 12
= One truck every hour
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The complete question is: The number of pick up trucks y built on an assembly line at a factory is represented by the equation y = [tex]\frac{x}{22}[/tex], where x is the time in hours.
1. Which type of vehicle is built at a faster rate?
2. How long does it take to built one of each type of vehicle?
3. Graph the equations that represent pickup trucks. Compare the steepness of the two graphs.
Find the opposite of - |6|.
The opposite of -|6| is -6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
- |6|
= -6
Now,
The opposite of 6 is -6.
So,
- |6|
= -|-6|
= - 6
We see that,
The opposite of -|6| is the same as -|6|.
Thus,
-6 is the opposite of -|6|.
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please help!!
the rubric says to
state what type of function f(x) is and how it’s identified
state what type of function g(x) is and how you identified it
list common key features
f(x) is a linear function because it has a constant slope of -4 and a y-intercept of 5.
g(x) is a polynomial function of degree 3 because the highest power of x is 3.
Both f(x) and g(x) are continuous functions and defined for all real values of x. They also have the same y-intercept of 5.
What is a linear function?The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil.
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Which of the following is a rational number?
√√12
√47
√22
√9
Answer:
√9
Step-by-step explanation:
First, it's important to know that a rational number is a number that can be expressed as a fraction. This means that all whole numbers are rational numbers. Knowing this, let's see if any of the radicals simplify into a fraction or whole number.
√12 = 3.464101615.....
NOT a rational number
√47 = 6.8556546.....
NOT a rational number
√22 = 4.69041576.....
NOT a rational number
√9 = 3
Rational number
So, √9 is a rational number.
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pls help meh with it
The value of the variable x is 11.13
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are made up of variables, terms, coefficients, constants and factors.
These algebraic expressions are also composed of mathematical operations, such as;
SubtractionAdditionMultplicationBracketParenthesesFloor divisionDivisionFrom the information given, we have that;
8.40x - 12.83 = 80. 67
To solve this, collect the like terms
8.40x = 80.67 + 12.83
Add the like terms
8.40x = 93.5
Divide both sides by the coefficient of x, we have
x = 11.13
Hence, the value is 11.13
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Answer:
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Divide both sides of the equation by the coefficient of variable:
Calculate:
Step-by-step explanation:
Answer 11
x^3 – 4y - (6 + 2) written form
The student council has been asked to conduct a survey of the student body to determine the students* lunch preferences. They have determined two ways to do the survey. Which survey option should the student council use?
Sample 1: Write all of the students' names on cards and pull them out in a drawing to determine who will complete the survey.
About surveySurveys can serve many purposes, and researchers can do so in many ways. Survey is a research method used to obtain information and insights on various topics of interest.
Surveys are a method that can provide a source of data and insights. Common types of surveys are written questionnaires, face-to-face or telephone interviews, focus groups, and electronic surveys. Surveys are the basis for gathering information on a large scale.
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Tickets to a family concert cost $10 for adults and $3 for children. The concert organizer collected a total a total of $900 from ticket sales if 42 adults were at the concert how many children attended
The number of children who attended the concert is 160.
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 Tickets to a family concert cost $10 for adults and $3 for children. The concert organizer collected a total of $900 from ticket sales if 42 adults were at the concert.
The expression can be written as;-
10a + 3c = 900
a = 42
10 x 42 + 3c = 900
420 + 3c = 900
3c = 900 - 420
3c = 180
c = 480 / 3 = 160
Hence, there were 160 kids present at the concert.
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a wood, rectangular box, with no top, is constructed with five panels that are each one centimeter thick. the external dimensions of the base are $16$ cm by $24$ cm, and the external height is $10$ cm. when the box is totally submersed in paint, how many square cm of painted surface will there be?
There will be 2216 square cm of the painted surface on the box, which is completely covered with paint.
Explain the term total surface area?The region that includes the base(s) as well as the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of a two areas.For the calculate of the area of rectangles:
Area = length * breadth
So, Outer area.
A1 = 2*16*10 + 2*24*10 + 1*16*24
A1 = 1184 sq.cm
Inner area:
A2 = 2*14*9 + 2*22*9 + 1*14*22
A2 = 956 sq. cm
Top area:
A3 = 16*24 - 14*22
A3 = 76 sq. cm
Complete area A = 1184 + 956 + 76
A = 2216 sq. cm
Thus, there will be 2216 square cm of the painted surface on the box, which is completely covered with paint.
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what is negative 15 divided by negative 1/3?
Answer:45
Step-by-step explanation: Search math w ay on the internet for clarification and any further math questions :)
Answer: 45
Step-by-step explanation:
1. Convert any mixed numbers to fractions then you'll have: [tex]\frac{-15}{1}[/tex] ÷ [tex]\frac{-1}{3}[/tex]
2. Then you multiply the numbers across from each other. (both numerators and denominators)
So, it would then be [tex]\frac{-45}{1-}[/tex]
(remember, when multiplying or dividing negatives and positives, a negative to a positive (vice versa) will always come out to be a negative, and a positive to a positive or negative to a negative, it'll always be a positive)
3. Simplify [tex]\frac{-45}{-1}[/tex], this means you divide -45 into -1, remember from the bolded phrase, this means it'd be a positive 45
So your answer is POSITIVE 45
P.S. I'd recommend checking out the "Mixed Fractions Calculator" on Calculator Soup. I'll provide a link below if you need any other help with further questions in the future.
https://www.calculatorsoup.com/calculators/math/mixednumbers.php
Hope this helps.
Find the number of possible outcomes in the sample space.
A basketball player attempts two free
throws. Each attempt results in a score or
a miss.
A. 7
B. 5
C. 4
D. 8
The number of possible outcome is 4 ( option C)
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Probability = Sample space / total possible outcome
In 2 free throws of either missing or scoring.
Represent missing by M and scoring by S
The outcome of the two throws can be:
MS , SM, SS, MM
Therefore the total possible in outcome is 4
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A 9-ounce bottle of medicine contains 54 doses. How many doses are in a 15-ounce bottle of the same medicine?
Answer:
90
Step-by-step explanation:
54/9= 6 doses per oz
15*6= 90 doses
hope this is correct
333b7jk,,,,,,,7h79p;'/'][
Answer:
Step-by-step explanation: nmbgbhj ,vmxhvgvkhchvc vhkyfdcxvgch cggcfglfflfvhghghjb
find the missing angle measure
The measure of the missing angle in the hexagon is 92°.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments are referred to as its edges or sides.
The figure has six sides so it is a hexagon and we know the sum of all the interior angles in a hexagon is 720°.
Therefore, 142° + 169° + 59° + 131° + 127° + x = 720°.
x + 628° = 720°.
x = 720° - 628°.
x = 92°.
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Picture shown below!
Answer:
B. ⊄
Step-by-step explanation:
There is no Tuesday in the set to the right, so the set to the left is not a subset of the set to the right.
Answer: B. ⊄
help me please 15 points
The simplified value of the expression is 45.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given expression,
8 x 3 ÷ (4² - 13) + 5² + 4 x 3
using PEMDAS to solve the expression,
Parentheses, Exponents, Multiplication, Division (from left to right), and Addition and Subtraction (from left to right).
step 1: Parentheses, (4² - 13)
(16 - 13) = 3
step 2: Exponents 5²
5² = 25,
step 3: Multiplication, 8 x 3 and 4 x 3
24 and 12
substitute the values,
8 x 3 ÷ (4² - 13) + 5² + 4 x 3
24 ÷ 3 + 25 + 12
step 4: Division,
24 ÷ 3 = 8
step 5: addition, 8 + 25 + 12
45
so 8 x 3 ÷ (4² - 13) + 5² + 4 x 3 = 45.
Hence the value of the expression is 45.
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a and b play a series of games. each game is independently won by a with probability p and by b with probability 1-p. they stop when the total number of wins of one of the players is two greater than that of the other player. the player with the greater number of total wins is declared the match winner. a. find the probability that a total of 4 games are played. b. find the probability that b is the match winner. (20 points)
The Probability that 4 games will be played in total and determine the likelihood that b will win the game are 2[(p³(1-p) + p(1-p)³] and p² / [p² + (1-p)²]
Given that,
A and B engage in a number of games. A and B each win a game with a probability of p and 1-p, respectively. They come to an end when one player has two more victories overall than the other player. The contest is decided by whoever player has accrued the most victories overall.
To find : The Probability that 4 games will be played in total and determine the likelihood that b will win the game.
Determine first which exact order of wins causes games.
The first game is won by A: B triumphs in game two ( if A wins again, Awon and the game is over)A or B might win the following two games to give themselves a two-game lead equivalently in the scenario if B triumphs in game one.
The ordering can be ABAA, ABBB, BAAA, or BABB.
P(4 games precisely) = P(ABAA) + P(ABBB) + P(BAAA)+ P(BABB)
P(4 games precisely) = 2[(p³(1-p) + p(1-p)³]
The likelihood that b will win the game is therefore 2[(p3(1-p) + p(1-p)3] and the probability that 4 games will be played overall. as well as p2 / [p2 + (1-p)2]
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About parallels and transversal
The parallels and transversal is discussed above.
What are parallel lines? What is transversal?Parallel lines - Two lines are said to be parallel if they never intersect each other.
Transversal line - In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.
Given are parallel lines and a transversal line.
When a transversal line that passes through the pair of parallel lines, it forms 8 angles. We can write them as -
Two pairs of alternate interior angles.Two pairs of corresponding angles.Two pairs of consecutive interior angles.Therefore, the parallels and transversal is discussed above.
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Select the correct answer.
Why is investing in a mutual fund less risky than investing in a particular company’s stock?
A.
Mutual funds only invest in blue-chip stocks.
B.
Investments in mutual funds are more liquid.
C.
Mutual funds hold a diversified portfolio of stocks.
D.
Investments in mutual funds offer a higher rate of return.
Answer:
I believe it's C. I hope that helps you