The point of intersection for lines (m) and (n) is (3.5, -1.5). Line (m) equation: (y = x - 5). Line (n) equation: (y = -3x + 9).
To find the point of intersection of two lines, you can use the point-slope form of a line and set the equations of the lines equal to each other. Let's first find the equations of the lines ( m ) and ( n ) using the given points.
Line ( m ) passes through the points ( (6,1) ) and ( (2,-3) ). Let's find the slope of line ( m ) first:
[tex]\[ \text{Slope of } m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
[tex]\[ \text{Slope of } m = \frac{{-3 - 1}}{{2 - 6}} = \frac{{-4}}{{-4}} = 1 \][/tex]
Now we can use the point-slope form of a line to find the equation of line ( m ):
y - y_1 = m(x - x_1)
Let's use the point ( (6,1) ) to find the equation of line ( m ):
y - 1 = 1(x - 6)
y - 1 = x - 6
y = x - 6 + 1
y = x - 5
So, the equation of line ( m ) is ( y = x - 5 ).
Now let's find the equation of line (m and n) passing through the points
( (2,3) ) and ( (5,-6) ):
[tex]\[ \text{Slope of } n = \frac{{-6 - 3}}{{5 - 2}} = \frac{{-9}}{{3}} = -3 \][/tex]
Using the point ( (2,3) ) to find the equation of line ( n ):
y - 3 = -3(x - 2)
y - 3 = -3x + 6
y = -3x + 6 + 3
y = -3x + 9
So, the equation of line ( n ) is ( y = -3x + 9 ).
Now, we'll set the equations of ( m ) and ( n ) equal to each other to find the point of intersection:
x - 5 = -3x + 9
Now, solve for ( x ):
x + 3x = 9 + 5
4x = 14
[tex]\[ x = \frac{{14}}{4} \][/tex]
x = 3.5
Now, substitute ( x = 3.5 ) into either equation to find ( y ). Let's use the equation of line ( m ):
y = 3.5 - 5
y = -1.5
So, the point of intersection of lines ( m ) and ( n ) is ( (3.5, -1.5) ).
what is the answer to 6 – 4r = -3r
Donna put $450 into a 6-month certificate of deposit that earns 4.6% simple annual interest. How much interest did the certificate earn?
Answer:
10.35
Step-by-step explanation:
If f(x)=5/2x+17, then find the value of f(12), f(-4), and f(0)
The function f(x) = 5/2x + 17 evaluated at the points 12, -4, and 0 yields values of 47, 7, and 17, respectively.
The student appears to be asking for the evaluation of a function f(x) at specific points, which is a common task in mathematics, specifically in algebra and pre-calculus courses. Assuming the correct function is indeed f(x) = 5/2x + 17, let's evaluate it at the requested points:
f(12) = (5/2) × (12) + 17f(-4) = (5/2) × (-4) + 17f(0) = (5/2) × (0) + 17By performing these calculations:
f(12) = 30 + 17 = 47f(-4) = -10 + 17 = 7f(0) = 0 + 17 = 17So the values of f(12), f(-4), and f(0) are 47, 7, and 17, respectively.
Corey walked three blocks east and then six blocks north. All the blocks were the same length. What is the value of the slope of the line from where Corey began walking to where he finished?
The answer is 2........................................
Answer:
C. 2
Step-by-step explanation:
Jack and Tyler ate a total of 35 cupcakes Tyler ate 5 more than jack how many did each person eat
WHAT IS 9 percent of 3600
9 percent of 3600 is 324.
In order to find 9 percent of 3600, you need to use the formula for finding a percentage of a number. Here is the step-by-step process:
Convert the percentage to a decimal by dividing by 100. For 9%, this is: 9/100 = 0.09.Multiply the decimal by the number in question. For 3600, this is: 0.09 × 3600.Perform the multiplication: 0.09 × 3600 = 324.Therefore, 9 percent of 3600 is 324.
Melanie is making desserts for a holiday party. For one recipe, she needs 1/3 cup of flour, for another, she needs 1 3/4 of flour, and for another recipe, she needs 4 1/2 cups of flour. If she has 10 cups of flour in a bag, how much flour will be left in the bag?
stans steakhouse has a server to cook ratio of 5 to 2 the total number of servers and cooks is 42 how many servers does Stans steakhouse employ
Selina is planning to paint a large picture on a wall. She draws a smaller version first. The drawing is 8 inches by 6 inches. If the scale of the drawing is 2 in : 1 ft, what is the area of the actual picture on the wall?
If it's possible, can you list step-by-step the procedures? Thanks!
Final answer:
To find the actual picture's area, multiply the drawing's dimensions by the scale factor of 6, convert it to feet, and calculate the product to get 12 square feet.
Explanation:
The student asks for the area of an actual picture on a wall based on its scale drawing. The scale of the drawing is stated as 2 inches to 1 foot, which means each 2 inches on the drawing corresponds to 12 inches (1 foot) in reality. The steps to calculate the area are as follows:
Calculate the scale factor: Since 2 inches on the drawing corresponds to 12 inches, in reality, the scale factor is 12 inches \/ 2 inches = 6.Determine the actual dimensions: Multiply the dimensions of the drawing by the scale factor. The actual width is 8 inches * 6 = 48 inches, and the actual height is 6 inches * 6 = 36 inches.Convert dimensions to feet: Since 1 foot is 12 inches, the actual dimensions in feet are 48 inches \/ 12 inches per foot = 4 feet (width) and 36 inches \/ 12 inches per foot = 3 feet (height).Calculate the actual area: Multiply the actual dimensions. Area = width * height = 4 feet * 3 feet = 12 square feet.Therefore, the area of the actual picture on the wall is 12 square feet.
A square has a perimiter of 36 millimeters, What is the area of the square?
PLZ
Using Hooke's law, F spring=k delta x, find the distance a spring with an elastic constant of 4 N/cm will stretch if a 2 newton force is applied to it.
A.) 2 cm
B.) 1/2 cm
C.) 4 cm
D.) 8 cm
Hello!
Using Hooke's law, F spring=k delta x, find the distance a spring with an elastic constant of 4 N/cm will stretch if a 2 newton force is applied to it.
Data:
Hooke represented mathematically his theory with the equation:
F = K * Δx
On what:
F (elastic force) = 2 N
K (elastic constant) = 4 N/cm
Δx (deformation or elongation of the elastic medium or distance from a spring) = ?
Solving:
[tex]F = K * \Delta{x}[/tex]
[tex]2\:N = 4\:N/cm*\Delta{x}[/tex]
[tex]4\:N/cm*\Delta{x} = 2\:N[/tex]
[tex]\Delta{x} = \dfrac{2\:\diagup\!\!\!\!\!N}{4\:\diagup\!\!\!\!\!N/cm}[/tex]
simplify by 2
[tex]\Delta{x} = \dfrac{2}{4}\frac{\div2}{\div2}[/tex]
[tex]\boxed{\boxed{\Delta{x} = \dfrac{1}{2}\:cm}}\Longleftarrow(distance)\end{array}}\qquad\checkmark[/tex]
Answer:
B.) 1/2 cm
_______________________
I Hope this helps, greetings ... Dexteright02! =)
Addison pays $36 for a 12-month magazine subscription. How much does Addison pay per month?
Answer:
3$
Step-by-step explanation:
just divide 36 by 12 to get 3.
Chris has a loan for $4200 at a rate of 8% annually. If the interest is not compounded, how much interest will he pay in 6 years?
Answer:
The Answer is $2016.00
Step-by-step explanation:
i = prt = (4200)(0.08)(6) = 2016
Use the formula i = prt, where
p = principal or starting amount
r = interest rate expressed as a decimal
t = time in years
Rita is hiking a trail that is 13.2 miles long so far she hiked along one -tenth of the trail how far did Rita hike
there are 9 positions on the softball team. Three people are trying out for each position.How many people are trying out ?
where does 1/8 and .25 go in the number line
if a sea otter swam 5.6 miles per hour for 1.5 hours, how many miles did the sea otter swim?
Multiplying the sea otter's swimming speed of 5.6 miles per hour by the time spent swimming of 1.5 hours, we find that the sea otter swam a total of 8.4 miles.
If a sea otter swam 5.6 miles per hour for 1.5 hours, we can calculate the total distance covered by multiplying the speed of the sea otter by the total time swum. This is because distance is the product of speed and time according to the formula:
Distance = Speed ×Time
So, for the sea otter:
Distance = 5.6 miles/hour × 1.5 hours = 8.4 miles
Therefore, the sea otter swam a total of 8.4 miles.
Tom is afraid of heights above 9 feet. He is asked to repair a side of a high deck. The bottom of a ladder must be placed 6 feet from a deck. The ladder is 10 feet long. How far above the ground does the ladder touch the deck? Is tom afraid of the height
How do you compare integers
Comparing integers involves assessing their relative positions on the number line. A positive integer is always greater than a negative one. Among negative integers, the one closer to zero is greater.
Explanation:To compare integers, you should first understand that integers are whole numbers that can be either positive or negative. If two integers are positive, the integer with the higher value is greater. If two integers are negative, the integer with the lower value is greater. If one is positive and the other is negative, the positive integer is always greater.
For example, when you compare the integers 3 and -5, you can say that 3 is greater than -5 because it is a positive number while -5 is negative. When comparing -2 and -7, -2 is greater because its value is closer to zero. It's also important to consider the concept of absolute value; the absolute value of an integer is its distance from zero on the number line, regardless of direction.
In situations that involve ratio problems or interval scale data, the comparison of integers becomes significantly important. For instance, if the scores on an exam are 80, 68, 20, and 92, you can rank the scores from lowest to highest (20, 68, 80, 92), and infer that a score of 92 is 24 points higher than a score of 68.
Learn more about Comparing Integers here:
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Johan's house and his grandparents house are 8.046.72 meters apart.what is this distance in miles
what is the value of x in
150-35x=45
Antoine and 3 friends divide some pennies evenly among themselves. Each friend separates his pennies into 3 equal stacks with 5 pennies in each stack.
Write a multiplication sentence that shows the total number of pennies.
Last month Jordan received a promotion and became a manager he now earns the same amount as Serena how much more money does he earn per hour now that he is manager than he did before his promotions explain your thinking.
To find out how much more money Jordan earns per hour now, you would subtract his old wage from his new wage. For example, if his old wage was $8/hr and his new wage is $12/hr, he is making $4 more per hour now.
Explanation:The question does not provide the exact amount that Jordan was earning before the promotion or the current rate that both Jordan and Serena are earning now. However, you can find out how much more Jordan is earning now by subtracting his old hourly wage from his current wage (which is now equal to Serena's). For example, if Jordan was making $8 an hour before his promotion and is now making $12 an hour as a manager (the same as Serena), then he is earning $4 more per hour since his promotion.
Here's a step-by-step explanation:
Determine Jordan's wage before the promotion (Let's say it was $8 per hour)Find out Jordan and Serena's current wage (Let's say it's $12 per hour, since they are earning the same amount)Subtract Jordan's old wage from his new wage ($12 - $8 = $4) to find out how much more he earns per hour now.This is a mathematical problem dealing with subtraction to figure out the increase in wages.
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A ramp slopes from a warehouse door down to the street. The height of the ramp is 5 feet, and the ramp ends 10 feet from the base of the warehouse. What is the slope of the ramp?
Answer:
the answer is 1/2
Step-by-step explanation:
find the product 7x6,000=
One half u subtracted from 3 times u
The expression 'one half u subtracted from 3 times u' translates into the algebraic expression 3u - (½u), which simplifies to 2½u or 2.5u.
Explanation:The expression 'one half u subtracted from 3 times u' can be translated into an algebraic expression. To do this, we need to understand basic operations with variables. One half of u is ½u or 0.5u, and three times u is 3u. Therefore, the expression would be written as 3u - (½u).
Subtracting one half of u from 3 times u involves the operation of subtraction, and when you subtract ½u from 3u, the resulting expression simplifies to 2½u or 2.5u. This shows how a grasp of fractions and variables allows us to manipulate and simplify algebraic expressions.
Describe how you labeled the bar model and wrote a number sentence to solve exercise 2
Nina can type 45 words per minute. Write the ordered pairs (number of minutes,number of words) Nina can type for 0,1,2, and 3 minutes. Explain your answer
I need help on 12, I don't know how to make that an expression! Thanks! Please explain!
which is cheaper for a 65$ item that costs $7 .25 to ship?
A 10% coupon off the cost of the item or free shipping?