write the equation of a line that is perpendicular to the line 5x-3y=12 and passes through point (3,1)
I know that the answer is y=-3/5x+14/5
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).
find the value of x and y
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Margo spends 0.25 of her paycheck on a new dress, 1/8 of her paycheck on shoes, and $24 on a birthday present. If she spent $60 altogether, how much was Margo’s paycheck?
Answer:
$96
Step-by-step explanation:
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Answer: The answer is A
You have a circle that depicts the Equator of the earth saw from top (From the Artic Polar Circle). Knowing that the Equator is in 0º of latitude, the Tropic of Cancer in 23º of latitude, and the diameter of the circle that depicts the equator is 4 cm, how can i mesure in the same scale WHERE is the tropic of cancer?
Answer:
what's the answer pls help me.
Step-by-step explanation:
To one decimal point, how many millimeters are there in 57 inches?
There are 1447.8 millimeters in 57 inches. which is determined by multiplying 57 by 25.4.
How to convert Inches to millimeters?The methodology to convert inches to mm is relatively simple. To convert inches to millimeters, you must multiply the unit by 25.4.
For example, if you have to convert 5 inches to millimeters, you need to multiply 5 by 25.4.
Therefore, 5 inches = 5 × 25.4 = 127 millimeters
We determine the number of millimeters there in 57 inches.
We have to convert 57 inches to millimeters,
We need to multiply 57 by 25.4.
So, 5 inches = 57 × 25.4 = 1447.8 millimeters
Therefore, there are 1447.8 millimeters in 57 inches.
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Amy is in a craft store looking at packages of Pom-poms. Amy sees packages of four red pom-poms. Amy says she can buy seven packages of four pom-poms or four packages of seven pom-poms because she will get the same total of pom-poms. Is Amy correct? Show all mathematical thinking.
Amy is incorrect because both options will give her the same total number of pom-poms.
Explanation:Amy is incorrect in her statement. Let's calculate the total number of pom-poms in each scenario. If she buys 7 packages of 4 pom-poms, she would have 7 * 4 = 28 pom-poms. On the other hand, if she buys 4 packages of 7 pom-poms, she would have 4 * 7 = 28 pom-poms as well. So, both options result in the same total number of pom-poms.
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PLEASE HELP ME ASAP!
Which unit rate is the lowest price per ounce?
Choice A: 5 ounces of raisins for $1.49
Choice B: 12 ounces of raisins for $3.59
Choice A
Choice B
The unit rates are equal.
The unit rates cannot be determined.
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2x - y = 4
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Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems. They find that 14 of the 134 cars stopped have at least one safety violation. They want to estimate the percentage of all cars that may be unsafe.
To estimate the percentage of all cars that may be unsafe, divide the number of cars with safety violations by the total number of cars stopped, and then multiply by 100. Based on the data from the auto checkpoint, approximately 10.45% of all cars may be unsafe.
Explanation:To estimate the percentage of all cars that may be unsafe, we can use the proportion of cars with safety violations found at the auto checkpoint. We can calculate the percentage by dividing the number of cars with safety violations by the total number of cars stopped, and then multiplying by 100.
In this case, 14 of the 134 cars stopped had safety violations. So, the percentage of cars that may be unsafe is (14/134) x 100 = 10.45% (rounded to two decimal places).
Therefore, we can estimate that approximately 10.45% of all cars may be unsafe based on the data from the auto checkpoint.
Some conveyor belts have two pulleys. If one pulley has a diameter of 45 cm and another has a diameter of 20 cm, what is the ratio of the smaller diameter to the largest diameter?
The heaviest bowling ball made by a bowling ball company weighs 21 pounds and costs $45. During the past year, the company sold 10 5 105 of these balls. How much money did the company earn?
A. $4,500
B. $45,000
C. $4,500,000
D. $45,000,000 Previous Next
The required money earned by the company after selling 10⁵ balls is $4500000. Option C is correct.
A bowling ball manufacturer's heaviest bowling ball weighs 21 pounds and costs $45. The corporation sold 10 5 105 of these balls throughout the course of the previous year. To determine how much money did the company earn.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Number of balls sold = 10⁵
Cost for 1 ball = $45
Total selling price = 45 * 10⁵ = $4500000
Thus, the required money earned by the company after selling 10⁵ balls is $4500000. Option C is correct.
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