Final answer:
To find the equation of a line that is perpendicular to 5x-3y=12 and passes through (3,1), we first identify the slope of the given line, find the negative reciprocal to determine the perpendicular slope, and then use the point-slope form to derive the equation, resulting in y = -3/5x + 14/5.
Explanation:
The question asks us to write the equation of a line that is perpendicular to the given line 5x-3y=12 and passes through the point (3,1). Perpendicular lines have slopes that are negative reciprocals of each other. First, we find the slope of the given line by rearranging it into slope-intercept form:
5x - 3y = 12
-3y = -5x + 12
[tex]y = \(\frac{5}{3}x - 4\)[/tex]
This reveals the slope of the given line is [tex]\(\frac{5}{3}\).[/tex] The slope of the line perpendicular to it would therefore be [tex]\(-\frac{3}{5}\)[/tex]since [tex]\(-\frac{3}{5}\)[/tex]is the negative reciprocal of [tex]\(\frac{5}{3}\).[/tex] Next, we use the point-slope form for the equation of a line with the known point (3,1):
y - y1 = m(x - x1)
[tex]y - 1 = \(-\frac{3}{5}\)(x - 3)[/tex]
Multiplying out, we get:
[tex]y - 1 = \(-\frac{3}{5}\)x + \(\frac{9}{5}\)[/tex]
Finally, adding 1 to both sides to solve for y:
[tex]y = \(-\frac{3}{5}\)x + \(\frac{9}{5}\) + 1[/tex]
[tex]y = \(-\frac{3}{5}\)x + \(\frac{14}{5}\)[/tex]
This is the equation of the line that is perpendicular to 5x-3y=12 and passes through (3,1).
4x27+5x34-94=n what is the value of n
Roxanna earns 1.5 her normal hourly rate for overtime pay. Last week, Roxanna earned 72.00 I'm overtime pay for 4 hours. What is Roxanna's normal hourly pay?
Roxanna's normal hourly pay is $12.00.
Explanation:To find Roxanna's normal hourly pay, we need to first calculate her overtime pay rate. We know that she earns 1.5 her normal hourly rate for overtime pay. Since she earned $72.00 in overtime pay for 4 hours, we can set up an equation to solve for her normal hourly pay:
Overtime Pay = Normal Hourly Pay × Overtime Hours × Overtime Rate
$72.00 = Normal Hourly Pay × 4 × 1.5
Simplifying the equation, we have:
Normal Hourly Pay = $72.00 / (4 × 1.5)
Normal Hourly Pay = $72.00 / 6
Normal Hourly Pay = $12.00
Therefore, Roxanna's normal hourly pay is $12.00.
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Solve the equation, justify each step with an algebraic property:
3(2-x)=24
Simplify the expression. 9 3 × 2 a. 15 b. 21 c. 24 d. 48
The function graphed is f(x). What is the function rule? Write the rule in function notation, using the slope-intercept form of a line. Enter your answer in the box.
Answer: i did it
Step-by-step explanation:
what is a close but easier numbers to estimate the answer to the problem
Why could the mean of the data set below be misleading? ages of teachers: 29, 38, 39, 26, 29, 29, 39, 77, 38, 29
Jin’s pays 3.48 for a bag of 12 tangerines find the unit price in dollars per tangerine if necessary round your answer to the nearest cent
Answer:
0.29
Step-by-step explanation:
Final answer:
To find the unit price of tangerines Jin bought, divide the total cost of $3.48 by 12. This gives a unit price of $0.29 per tangerine.
Explanation:
To find the unit price of the tangerines that Jin purchased, you need to divide the total cost by the number of tangerines.
Jin paid $3.48 for a bag of 12 tangerines. Therefore, to calculate the price per tangerine, use the following equation:
Unit Price = Total Cost / Number of Units
Unit Price = $3.48 / 12 tangerines
Unit Price = $0.29 per tangerine
If necessary to round to the nearest cent, the unit price remains $0.29 since it is already at the cent level.
Your friend has 5 more then twice as many game tokens as your sister. Let T be the number of game tokens your sister has. Write and expression for the number of game tokens your friend has
The number of game tokens that the friend has can be represented as the algebraic expression '2T + 5', where 'T' represents the number of game tokens the sister has.
Explanation:The question asks to express the number of game tokens your friend has in terms of 'T', the number of game tokens your sister has. As the information provided states, your friend has '5 more than twice' the amount which your sister has.
The mathematical expression for this will be '2T + 5', where 2T is twice the number of tokens your sister has and 5 is the extra tokens your friend has over twice your sister's total.
So, if your sister has 'T' number of game tokens, your friend will have '2T + 5' number of game tokens.
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Whole number between 9 4/9 and square root of 144
Answer:
Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex] are 10 and 11.
Step-by-step explanation:
To find : Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex]?
Solution :
Writing numbers into simpler forms,
[tex]9\frac{4}{9}=\frac{85}{9}\approx 9.44..[/tex]
[tex]\sqrt{144}=12[/tex]
So, The number between 9.44.. and 12.
i.e. [tex]9.44..<x<12[/tex]
Whole number is defined as a number without fractions or decimal.
Between 9 and 12 the whole numbers are 10 and 11.
Therefore, Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex] are 10 and 11.
Which expression is equivalent to (^4√5^3)^(1/2)
5^6
5^3/8
5^16/3
5^2/3
8 story building each story was 15 4/5 in height how tall was the building
Final answer:
To calculate the height of an 8-story building, where each story is 15 4/5 feet tall, multiply the height of one story by the number of stories, resulting in a total height of 126.4 feet.
Explanation:
The question asks how tall a building would be if it has 8 stories, with each story being 15 4/5 feet in height. To find the total height of the building, you need to multiply the height of one story by the number of stories. The height of one story is 15 4/5 feet, which can also be written as 15.8 feet when converted to a decimal. Therefore, the calculation would go as follows:
15.8 feet/story × 8 stories = 126.4 feet
This calculation shows that the total height of the building is 126.4 feet. This example demonstrates how to apply multiplication in real-life scenarios, specifically in calculating the height of structures based on the height of individual stories.
Answer:
[tex]\displaystyle \frac{632}{5} \;units\;\text{or}\; 126\;\frac{2}{5}\;units \;\text{or}\; 126.4\;units[/tex]
Step-by-step explanation:
We can multiply the number of stories (8) by the height of each story (15 4/5 units) to find how tall the building is.
[tex]\displaystyle 8*15\frac{4}{5}=8*\frac{79}{5} =\frac{8*79}{5} = \frac{632}{5} \;units\;\text{or}\; 126\;\frac{2}{5}\;units \;\text{or}\; 126.4\;units[/tex]
8. The population of Grand City in 1990 was 5,250. Assume the population is increasing at 2.5% per year. What was the population in Grand City in 2010 (round answer to the nearest person)?
A flat-screen television has a length that is 1 more inch than its width. The area of the television's screen is 1500 in cubed. To the nearest whole inch, what are the dimensions of the television
Final answer:
The dimensions of the flat-screen television with an area of 1500 square inches are approximately 38 inches in width and 39 inches in length.
Explanation:
To find the dimensions of a flat-screen television with an area of 1500 square inches and a length that is 1 inch more than its width, we can set up a quadratic equation. Let the width be w inches, then the length would be w + 1 inches. The area of the television's screen is given by the formula:
Area = width × length
Substituting the given values, we get:
1500 = w × (w + 1)
This simplifies to:
w² + w - 1500 = 0
Solving this quadratic equation, we find two potential solutions for w, but only the positive value makes sense in this context. Once we find the value of w, the width, we can then add 1 to get the length.
After calculating, we find that the width w is approximately 38 inches, and the length is approximately 39 inches. Therefore, the dimensions of the television are 38 inches by 39 inches to the nearest whole inch.
On a grid Joe’s house is marked at ( -5, -3 ) and Andy’s house is marked at ( 3, -1 ). What is the distance, on the grid, between Joe’s house and Andy’s house?
Answer:
The distance is [tex]\sqrt{68} =2\sqrt{17}[/tex]
Step-by-step explanation:
Locating the points on the plane we can form a right triangle between them and solve the problem using the Pythagorean theorem.
*see attached image*
The sides of the triangle formed measure 8 and 2, so by pythagoras, the unknow side [tex]x[/tex] wich is the distance between the houses is:
[tex]x^2=8^2+2^2\\x^2=64+4\\x^2=68\\x=\sqrt{68}=\sqrt{4*17}=2\sqrt{17}[/tex]
So the distance, on the grid, between Joe’s house and Andy’s house is [tex]2\sqrt{17}[/tex]
A friend asks you to think of a number, double it, then add 5. Write an algebraic expression to describe your friend's directions, and make a table of possible values.
Elio Makes candles that are 14 cm tall. Each candle burns eight hours before going out. He is wondering how many hours a 21 cm tall candle can burn for.
Final answer:
A 21 cm tall candle should burn for 12 hours, as it is 1.5 times taller than a 14 cm candle which burns for 8 hours.
Explanation:
The problem is one of direct proportion where the height of the candles is directly proportional to the burning time. If a 14 cm tall candle burns for 8 hours, then a 21 cm tall candle, which is 1.5 times taller, should burn for 1.5 times longer. Hence, to calculate the burning time for the 21 cm candle, we multiply 8 hours by 1.5.
Calculation:
21 cm / 14 cm = 1.5
8 hours × 1.5 = 12 hours
Therefore, a 21 cm tall candle should burn for 12 hours.
The number of people who purchased a new car from Force Motor Company is 170% of the number of people who purchased a new car from Ampere Motors. If 60 people purchased a car from Ampere Motors, how many people purchased a car from Force Motor Company? A. 60 B. 70 C. 102 D. 170
Answer:
c
Step-by-step explanation:
102 people purchased a car from Force Motor Company
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The number of people who purchased a new car from Force Motor Company is 170% of the number of people who purchased a new car from Ampere Motors.
If 60 people purchased a car from Ampere Motors, then we need to find number of people who purchased a car from Force Motor Company.
We will find it by
170%×60
170/100×60
1.7×60
102
Hence 102 people purchased a car from Force Motor Company
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evaluate the expression
Which statements include two quantities in the real world that are additive inverses? Select each correct answer.
A. A diver descends 18 feet and then ascends 5 feet.
B. A person pours 6 ounces of water out of a glass and then pours 6 ounces of water back in to the glass.
C. The outside temperature increases 15 degrees from the morning to the afternoon, and then decreases 6 degrees from the afternoon in to the evening.
D. A person loses 12 points playing a game and then earns 12 points.
Did the test B and D are correct
Simon tosses a coin 20 times. The coin lands heads up 7 times. Based on these results, how many times can Simon expect the coin land heads up in the next 100 tosses?
Answer choices:
28
21
14
35
Janita practices on the track field 1.5 hours each day before a track meet. If there are 6 days until the track meet, how many hours will Janita practice?
divide use partial quotients. 2950÷67
Cole had 3/4 of an hour of free time before dinner he spent 2/3 of that time playing the guitar how long did he play the guitar
Is this question impossible? If not help with a solution
Tell wether the relationship is a proportional relationship or not.
The length of a particular rectangle is 4 greater than the width of the rectangle. If the perimeter of the rectangle is 16, what is the area of the rectangle?
A class of 12 girls and 14 boys is going to choose 3 students to represent them in student government. Allie suggested that the first 3 students to arrive in class the next day should be the representatives. Bobby suggested that each student roll 2 numbers cubes and the 3 students with the highest sum should be the representatives. Whose method would result in a fair sample that represents the class population, and why?
find the coordinates of the midpoint of HK if H(-1,2) and K(-7,-4)
Answer:
The midpoint of HK is (-4, 1)
Step-by-step explanation:
We are given two coordinates H(-1, 2) and K(-7, -4)
We need to find the midpoint of HK.
We have formula to find the midpoint.
[tex](\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} }[/tex]
Here [tex]x_1 = -1, y_1 = 2, x_2 = -7 and y_2 = -4[/tex]
Now plug in these values in the above formula, we get
[tex](\frac{-1 + (-7)}{2} , \frac{2 +(-4)}{2} )[/tex]
[tex](\frac{-8}{2}, \frac{-2}{2} ) = (-4, -1)[/tex]
So, the midpoint of HK is (-4, 1)
Starting at 1:00 pm the temperature changes -4 degrees per hour. How long will it take to reach -1 degrees?
please explain your anwser