Answer: Given a line represented by the equation 3x + y = 9, the slope of the line is -3/1. Since we know that the slope of the line perpendicular to this line is the negative reciprocal of the original line's slope, we can find the slope of the perpendicular line by taking -1/-3 = 1/3.
To find the equation of the perpendicular line that passes through the point (1,-2), we can use the point-slope form of the line equation, which is: y - y1 = m(x - x1) where m is the slope of the line and (x1,y1) is a point on the line.
Therefore, the equation of the perpendicular line that passes through the point (1,-2) is:
y - (-2) = (1/3)(x - 1)
y + 2 = (1/3)x + (1/3)
y = (1/3)x - (2/3)
So the final equation of the perpendicular line is y = (1/3)x - (2/3)
Step-by-step explanation:
What is the equation of the line that passes through the point (−6,−7) and has a slope of 1/3?
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-6)}) \implies y +7= \cfrac{1}{3} (x +6) \\\\\\ y+7=\cfrac{1}{3}x+2\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-5 \end{array}}[/tex]
Answer:
I think it is y=1/3x -7
Step-by-step explanation:
Anita is an airline attendant. Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers. The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers. How many seats were on each type of flight?
Answer:
Small jet seat capacity: 73
Large jet seat capacity = 90
Step-by-step explanation:
Let x be the number of seats on the small jet
Let y be the number of seats on the large jet
From the word description for last week:
Last week, she worked on flights on 1 small jet and 2 large jets, which could seat a total of 253 passengers
we can formulate the equation
1x + 2y = 253 .............(1)
For the week before:
The week before, she was assigned to flights on 5 small jets and 4 large jets, which could seat a total of 725 passengers
5x + 4y = 725 ...............(2)
Equation (1) x 2 ==>
2x + 4y = 2(253)
2x + 4y = 506 ..............(3)
So our two equations are:
5x + 4y = 725 . .............(2)
2x + 4y = 506 ..............(3)
Equation (2) - Equation (3) will eliminate the y terms making it possible to solve for x
(5x + 4y) - (2x + 4y) = 725 - 506
5x + 4y - 2x - 4y = 219
5x -2x +4y - 4y = 219
3x = 219
x = 219/3
x = 73
Plugging this value back into equation (1): 1x + 2y = 253 we get
1(73) + 2y = 253
73 + 2y = 253
2y = 253 - 73
2y = 180
y = 180/2
y = 90
Answer
Small jet seat capacity: 73
Large jet seat capacity = 90
Which of the following tables shows a rate greater than 1 kilometer per hour? The answer to that is B and the question after that says Hailey chose C as the correct answer. How might she have gotten that answer.
It should be noted that the rate will be gotten by dividing the distance by the time taken.
How to explain rate?A rate in mathematics is a ratio that contrasts two distinct quantities with dissimilar units. Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator
By reducing them to their simplest form, we can express the rate. By way of illustration, if a person walks 30 steps in 20 seconds, their walking speed is 30 steps/20 seconds, or 3 steps/2 seconds.
The information above was given as your information is incomplete. The table wasn't shown.
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The table shows the results of a survey of 100 people selected at random Airport
at an airport. Find the experimental probability that a person selected at Destinations
random is going to City B.
Number of
Destination Responses
City
A
28
City B
40
City C
16
City D
14
City E
2
The experimental probability that a person selected at random is going to City Bis 1
(Simplify your answer. )
The experimental probability that a person selected at random is going to City C is 4/25.
Number of responses from destination A = 22
Number of responses from destination B = 40
Number of responses from destination C = 16
Number of responses from destination D = 14
Number of responses from destination E = 8
As we know, the formula of experimental probability is
Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.
Number of responses from destination C = 16
Total number of responses from all destinations = 100
∴ Probability of an Event P(C) = 16/100 = 4/25
--The given question is incorrect; the correct question is
"The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City C."--
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Algebra 2 volume 2 question 60
The value of function fg(x) is -x^4-4x^3.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
given functions are f(x)=-x^3 and g(x)=x+4
so, fg(x)=f(x)*g(x)=-x^3(x+4)
Therefore, the value of
fg(x) = -x^4-4x^3
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The value of function fg(x) is -x^4-4x^3.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
given functions are f(x)=-x^3 and g(x)=x+4
so, fg(x)=f(x)*g(x)=-x^3(x+4)
Therefore, the value of
fg(x) = -x^4-4x^3
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Stanley feeds each of his dogs 1/6 of a can of food each day. He uses a total of 1/2 of a can of food each day. How many dogs does Stanley have?
Answer: 3 dogs
Step-by-step explanation:
Each dog eats 1/6 cans of food
Stanley uses a total of 1/2 cans of food
[tex]\frac{1}{2}[/tex] / [tex]\frac{1}{6}[/tex] = 1/2 * 6
= 3 dogs
Select 2 expressions that can be used to find the value of x.
14sin(55)
14cos(35)
14sin(35)
14cos(55)
Answer:
14sin(55) and
14cos(35)
Step-by-step explanation:
Greetings!!
just remember trigonometric ratios which are
[tex]sin = \frac{opposite}{hypotenus} \\ cos = \frac{adjecent}{hypotenus} \: and \\ tan = \frac{opposite}{hypotenus} [/tex]
following that substitute given values to solve for x.
[tex]sin55 = \frac{x}{14} [/tex]
solve for x
[tex]x = 14 \sin(55) [/tex]
And
[tex] \cos(35) = \frac{x}{14} [/tex]
solve for x
[tex]x = \cos(35) [/tex]
Hope it helps!!!
if a point is on the perpendicular bisect or if a segment then what is it
Answer: It is equidistant from the segment's endpoints
Step-by-step explanation: This can also be called "a locus of point" and this is now the perpendicular bisector theorem.
solve the equations 2x+y=9 and 2x+5y=37 by combining the equations
Answer:
4x+6y = 46
Step-by-step explanation:
you just add by column
2x+2x
y+5y
9+37
Find the function rule
X. Y
-2, -3
1, 3
3, 7
5, 11
Answer:
The function rule for this set of ordered pairs is y = 2x + 1.
This can be determined by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
The slope (m) can be calculated by using the formula:
m = (change in y) / (change in x)
For the ordered pair (1, 3) and (3, 7), we can see that change in x = 3 - 1 = 2 and change in y = 7 - 3 = 4, so m = 4/2 = 2.
Then, using any of the point we can find the b which is y-intercept. let's take the point (-2, -3) and substitute the values in the function y = 2x + b
-3 = 2(-2) + b
-3 = -4 + b
b = 1
So, the function rule is y = 2x + 1
if i run 5280 feet in 5.00 minutes, what is my speed in miles per hour (to the appropriate number of significant figures)?
When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 5280 feett = 5 minutesv (miles/hour) = ?Applying the velocity formula, we get:
v = x /t
v = 5280 feet / 5 minutes
v = 1056 feet/ minutes
By converting the unit from feet to miles and from hours to minutes, we have:
1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour
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I need help on this question it’s on similar figures
Answer:
a) the triangles are similar triangles because they are the same shape. The angles in both triangles have the same value.
b) The similarity ratio between the two triangles is 0.5, because the lengths of the sides of the triangle on the right are double the value of the lengths of the sides of the triangle on the left.
c) angle U = angle G. angle V = angle H. angle T = angle F.
UV/GH = VT/HF = TU/FG = 0.5
Directions: Set up a proportion and then solve. Remember to label your answer. 1) Goodyear can make 100 Tires in 45 minutes at their factory in Akron, Ohio! b. How long will a. How many tires can they make in 135 minutes?
Answer:300 tires
Step-by-step explanation: I set it up like this 100:45
X : 135
Then I am trying to find x. I cross multiplied. (100 times 135) and (45 times x) which is 45x= 13500 then if you know simple algebra then you get x by itself so you divide 13500 and 45 which equals 300.
Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test.
How long did Jordan spend studying for each test?
134 hours
35 hour
15 hour
123 hours
As per the concept of fraction, the amount time spend for each test is 1.67 hours
In math the term called fraction is known as the number is expressed as a quotient in which the numerator is divided by the denominator.
Here we have know that Jordan spent 5 hours over the weekend studying for 3 tests.
In order to find the amount of time spend for each test, we have to divide the total number of subject by the time spend by him.
Here the value of total subjects = 5 and the amount of time spend by him is 3.
Then the amount of time time spend for each test is calculated as,
=> 5/3
=> 1.67 hours
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the isosceles triangle has two sides of equal length that are longer then the length of the base the perimeter of the triangle is 15.7 centimeters the equation 2a+b=15.7 models this information if one of the longer sides is 6.3 centimeters which equation can be used to find the length of the base
The length of the base is 3.1 cm when you subtract 12.6 from btohs ides b is15.7.
The definition of an isosceles triangle?There are two equal sides and two equal angles in an isosceles triangle. The word is a combination of the Greek words iso (same) and skelos (leg). Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
Equilateral triangles are those in which all of the sides are equal, while scalene triangles are those in which none of the sides are equal.
The equal sides of an isosimple triangle are longer than the base's length.
We know that identical sides are greater, thus 6.3 is one of the identical sides in the perimiter=15.7 equation, which is 2a+b=15,7.
2a denotes the two identical sides: 2(6.3) + b = 15.7
The answer is base=3.1 cm when you subtract 12.6 from btohs ides b=15.7.
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The value of a house increased by 30% to $156,000.
What was the original price of the house?
The original price of the house is 156,000
How to calculate the original price of the house?
From the question,
The house was increased by 30% which leads to an increase to 156000
To get the original price of the house
Let the value of the house be x
We then multiply the original price of the house(x) by 30%
we have 0.30*x
0.30x = 156000
Divide both sides by 0.30
x = 520,000
Hence, 520000 is the original price of the house
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a graph of a linear equation passes through (-2,0) and (0,-6). Is 3x-y=-6 an equation for this graph? (Yes or no question)3. Explain your reason of how you know
well, let's find the equation of the line through those points then, and let's see
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]
a living room needs to be re-carpeted. it measures 18 feet long by 15 feet wide. how many square yards of carpet will need to be purchased?
Answer:
66?
Step-by-step explanation:
18+18= 36
15+15= 30
30+36= 66
90 is 0.6 of what number
Answer:
150
Step-by-step explanation:
90/0.6 = 150
Check:
150*0.6 = 90
Then:
90 is 0.6 of 150
A student is simplifying the expression below. Find the student's error and correct it. -3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2
The error is that the student did not distribute the -3 to the x and 2 inside the parentheses.
The correct answer is 3x - 6
How to find the student's error and correct it?Simplification of an algebraic expression is defined as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The student's error is that the student did not distribute the -3 to the x and 2 inside the parentheses when simplifying the expression.
The correct simplification of the expression is:
-3(x + 2) + 6x = -3x - 6 + 6x = -3x + 6x - 6 = 3x - 6
Therefore, the student's answer is 3x + 2, but the correct answer is 3x - 6.
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The student made error when removing the bracket. The correct simplification of the expression is 3x - 6
How do I determine the error of the student?We can spot the error of the student by carefully observing the student's answer. This is illustrated below:
-3(x + 2) + 6x = -3x + 2 + 6x = 3x + 2
From the student's work, we can see that the student made an error when removing the bracket.
How do I correct the student?We can correct the student's error by carefully removing the bracket as shown below:
-3(x + 2) + 6x
Remove bracket by multiplying through by -3
-3x - 6 + 6x
Rearrange by bring the numbers with x variables together
-3x + 6x - 6
3x - 6
Thus, the correct answer to the simplification is 3x - 6
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i need sm help lol ahhhhhhhh
Answer:
????????????????????
Which of the following is equivalent to
O A 1 + √5
2
OB. 1-√√5
2
O C. √5-1
2
OD √5-2
2
1 + √5
2
The equivalent expression is (a) 1 + √5
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
√5 + 1
The additive property of equality states that
a + b = b + a
using the above as a guide, we have the following:
√5 + 1 = 1 + √5
This means that the equivalent of √5 + 1 is 1 + √5
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Complete question
Which of the following is equivalent to √5 + 1
O A 1 + √5
OB. 1-√√5
O C. √5-1
OD √5-2
Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He ued 3.9 gallon on a recent trip.
The percent of the gas in the tank remaining is equals to the 53.6..
The capacity of Wilon's car's gas tank
= 15 gallons
The amount of gas in Wilon's car's tank
= 8.4 gallon
The amount of gas in tank used on a recent trip = 3.9 gallons
The remaining amount of gas in tank
= amount of gas in Wilon's car's tank before trip - amount of gas in tank used on a recent trip.
= 8.4 gallons - 3.9 gallons
= 4.5 gallons
Percent is calculated as the value diving by total value and then multiply with hundred. Now, the percent of the gas in the tank remaining = (4.5/8.4)× 100
=( 45/84)100
= 4500/84
= 53.57 ~ 53.6 %
Hence, the percent of the gas in the tank remaining is 53.6 .
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Complete question:
Wilon’ car hold 15 gallon of gaoline in it tank. Wilon had 8.4 gallon of gaoline in the tank. He used 3.9 gallon on a recent trip. What is the percent of the gas in the tank remaining?
Write the slope-intercept form of the equation of the line through the given points.
through: (2, -4) and (2,-5)
Answer
undefined
Step-by-step explanation:
Answer:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
To find the equation of a line passing through two given points, we can use the slope-intercept form, and use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Given the points (2, -4) and (2, -5), we can see that the x-coordinates are the same, which means that the line is a vertical line.
Since the line is vertical, the slope is undefined, and we can say the line can be represented by the equation x = 2
This is the equation of the line passing through the given points (2, -4) and (2, -5) in slope-intercept form.
Complete the rule that describes the translation.
Answer:
(2,4)
Step-by-step explanation:
The point that's on the origin (0,0) goes to the right by 2 which is your x-axis and goes up 4 which is your y-axis.
Answer:
Translation: (2,4)
Step-by-step explanation:
The dot/point that's in the middle which is always (0,0) goes to the right by 2 (x-axis) meaning that the first coordinate would be 2. It then goes up 4 (y-axis) meaning that the second coordinate would be 4.
Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school. She needs 0. 65 meter of string for the banner and the same length string for each pennant. What length of string will be used to hang each pennant? Write and solve a two-step equation
The length of string will be used to hang each pennant is 3.9 meters.
The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.
Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.
And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.
the length of the string needed for 5 pennants is calculated as,
=> 0.65 x (5 + 1)
=> 3.9 meter.
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Select ALL factors of 27. (Be sure to select ALL correct factors for full credit).
Question 4 options:
3
1
2
16
54
27
9
81
Answer:1, 3, 9, 27
Step-by-step explanation:
graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,220) and (7,385) to find the number of soda bottles the machine can make each minu
55 is the number of soda bottles the machine can make each minute.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, the graph shows the relationship between time and the number of soda bottles a machine can make. Use points (4,220) and (7,385)
Since this graph is a straight line graph and also it goes through the origin that means time is directly proportional to the number of soda can manufactures
To prove this theory
the ratio between cans to the time taken by machine = 220/4 = 385/7
Since the ratio is the same for two points.
Thus,
Soda machine makes in 4 hours = 220 cans
Soda machine makes in 1 hours = 220/4 = 55 cans
Therefore, the number of soda bottles the machine can make each minute is 55.
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Please Help I Need Help With This Problem.
The equation can be written as 6 + (-6y) = -6y - 1 + (7).
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The given is an equation with missing parts.
The left hand side of the equation does not contain a term with variable, but the right hand side contains it.
Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.
So the right hand side must be equal.
So the expression in the right hand side is -6y - 1 + (7).
Hence the expressions are 6 + (-6y) on the left hand side and -6y - 1 + (7) on the right hand side.
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How do I solve 8-4x>-12
The solution to the given inequality expression is; x < 5
How to solve Inequality expressions?We want to solve the inequality expression;
8 - 4x > -12
Add 4x + 12 to both sides using addition property of equality to get;
8 - 4x + 4x + 12 > -12 + 4x + 12
20 > 4x
Divide both sides by 4 using division property of equality to get;
20/4 > 4x/4
x < 5
That expression is what we will have as our final solution to the inequality expression .
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