Sole for y intercept and slope -2x -4y=12
Answers
Answer:
y-intercept: -3
slope: -1/2
Explanation:
The given expression is
- 2x - 4y = 12
To know the y-intercept and slope we need to solve for y, so we get:
\(\begin{gathered} -2x-4y=12 \\ -2x-4y+2x=12+2x \\ -4y=12+2x \\ \\ \frac{-4y}{-4}=\frac{12}{-4}+\frac{2x}{-4} \\ \\ y=-3-\frac{1}{2}x \end{gathered}\)Then, the y-intercept is the constant and the slope is the number besides x, so the answer is
y-intercept: -3
slope: -1/2
Related Questions
HELP ASAP GIVING BRAILIEST!!!!!!!
15 POINTS
photo of problem below>>
Answers
Answer:
B) y = 4/5x - 2
Answer:
B
Step-by-step explanation:
First, we can find the slope of the graph.
The distance of x between the two points is 5, and the distance of y between the two points is 4.
The slope formula is (Increase in y)/(increase in x)
So the slope will be 4/5.
The y-intercept is (0,-2), so the number at the very end of the equation will be -2.
With all this in mind, we can be sure that our answer is B: y=4/5x-2
URGENT, please!!
Use the given information to write an equation of each parabola:
The parabola has focus (0,6) and vertex at the origin.
Answers
The equation of the parabola is:
\(y = 24x^2\)
---------------------------
The equation of a parabola of vertex (h,k) and focus (0,f) is given by:
\(y = 4p(x - h)^2 + k^2\)
Vertex at the origin means that \(h = 0, k = 0\).Focus (0,6) means that \(p = 6\)Thus, the equation of the parabola is:
\(y = 4p(x - h)^2 + k^2\)
\(y = 4(6)(x - 0)^2 + 0^2\)
\(y = 24x^2\)
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Which of these shapes will tessellate without leaving gaps? A. Hexagon B. Octagon C. Pentagon D. Circle
Answers
The shape that can tessellate without leaving gaps is the hexagon (option A).
The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).
A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.
On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.
A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.
In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).
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Francis bought 5 holiday gifts that were between $42 and $87. What is a reasonable amount that he paid for the items?
Answers
Answer:
322.5$Step-by-step explanation:
Francis bought 5 holiday gifts that were between $42 and $87. What is a reasonable amount that he paid for the items?
we find the average between 42 and 87 and multiply by 5
[(42 + 87) : 2] * 5 =
(129 : 2 ) * 5 =
64.5 * 5 = 322.5$
An advertiser claims that 80% of people stream their TV, 10% have cable, and the rest do not watch TV. To evaluate this claim, they take a sample and calculate a test statistic of
. If their rejection region is, what would their conclusion be?
Answers
The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.
What is the rejection region?This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.
This happens when the rejection region is found to be around the area that is in the critical value.
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Which number is the largest? 7.2 • 10-^6, 3.09 • 10^3, 2.04 • 10^4, 5 • 10^3
[question and answer choices are also in the pic above^^]
Answers
Answer:
(c) 2.04×10^4
Step-by-step explanation:
When numbers are expressed in scientific notation, the one with the largest exponent of 10 is the largest. Its most-significant digit is in the number place farthest to the left, giving it the highest value.
The largest of these numbers is 2.04 · 10⁴.
Amazing Computers sells a gaming laptop for R24 516. If the profit margin (on cost price) of the laptop is 8%, what is the cost price of the laptop?
Answers
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answers
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
he function a = –2x2 + 8x + 5 models the altitude a in feet of a ball thrown in the air and the horizontal distance in feet that the ball travels. Which is the vertex form of the function? (i just need part b answer)
Answers
Answer:
for part b the vertex is (2, 13)
Step-by-step explanation:
no (ice)
Answer:
It could be (2, 13)..
Step-by-step explanation:
Absolute vale of x+2 if x is less than 2
Answers
Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).
Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).
the following regression output is for predicting annual murders per million from percentage living in poverty in a random sample of 20 metropolitan areas. (intercept) poverty% estimate -29.901 2.559 std. error 7.789 0.390 t value -3.839 6.562 pr(>|t|) 0.001 0.000 40 30 20 10 s
Answers
a) The value if y is -29.901 + 2.559 * poverty%. b) option c is the correct choice, c) option a is the correct choice. d) option a is the correct choice.
a) The regression equation will be:
y = Intercept + slope * poverty%
y = -29.901 + 2.559 * poverty%
b)
Expected poverty with no murders is b0, which is -269.901 billion, which is not practically possible.
Option C is the right answer.
c)
When the independent variable is increased by a unit, then the increase in the dependent variable will be b1.
Option A says the same.
d)
R^2 says that the change in the dependent variable, which is murders here, can be R^2 percent explained by the variation in the independent variable, which is poverty here.
Option A is the right answer.
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Complete question
the following regression output is for predicting annual murders per million from percentage living in poverty in a random sample of 20 metropolitan areas. (intercept) poverty% estimate
Using the central limit theorem, what is the (shape of) distribution of sample means when the population distribution is:
rectangular
uniform
normal
positively skewed
nonmodal
multimodal
negatively skewed
(Privitera, 2019, p. 186, #19)
Answers
The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
what is normal distribution?
A normal distribution is a bell-shaped probability distribution that is symmetrical and characterized by its mean (μ) and standard deviation (σ). It is also known as a Gaussian distribution, after the mathematician Carl Friedrich Gauss.
However, for smaller sample sizes, the distribution of sample means may still resemble the shape of the population distribution.
Here are some more specific descriptions of the distribution of sample means for different population distributions:
1. Rectangular distribution: The distribution of sample means will approach a normal distribution as the sample size increases, with the mean and median at the center of the distribution.
2. Uniform distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, with the mean at the center of the distribution.
3. Normal distribution: The distribution of sample means will be a normal distribution regardless of sample size, with the mean and median at the center of the distribution.
4. Positively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be higher than the median.
5. Nonmodal distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the nonmodal distribution.
6. Multimodal distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the multimodal distribution.
7. Negatively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be lower than the median.
Therefore, central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
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Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
Answers
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (2, 0). Everything to the right of the line is shaded. The solutions to the inequality y ≤ 2x − 4 are shaded on the graph. Which point is a solution? (−1, 1) (1, −1) (3, 2) (2, 3) Mark this and return
Answers
The solution to the inequality y ≤ 2x − 4 is (3, 2).
The correct option is C.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
On a coordinate plane, a solid straight line has a positive slope and goes through (0, -4) and (2, 0).
Everything to the right of the line is shaded.
The solutions to the inequality y ≤ 2x − 4 are shaded on the graph.
From the given choices:
Substituting x = 3,
we get,
2 ≤ 2(3) − 4
2 ≤ 6 − 4
2 =2.
Therefore, (3, 2) is a solution to inequality.
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A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props.
Answers
The required amount of the space available is 0.045 cubic meter.
We need to determine Space inside the steps.
What is volume?The Volume is defined as the mass of object per unit density.
The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2
= 0.06 - 0.015
= 0.045 cubic meter
Hence, the required amount of the space available will be 0.045 cubic meter.
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Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
Answers
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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Show step by step
6.1 x 7.4
Answers
Answer:
ya the answer is 45.14 we just have to multiply them as normal multiplication and then once the ans comes start pointing the answer from the right
Step-by-step explanation:
mark as brainliest plzzzz
If there are three boys for every four girls in the chorus what the ratio to represents the relationship between the number of girls in the chorus and the number of students in the chorus.
Answers
Answer:
4/7
Step-by-step explanation:
I think this is the awnser
Cindy tried to find the sum of the exterior angles of the hexagon. What was her error?
will mark brainiliest!
Answers
Step-by-step explanation:
Simple, she found the sum of the interior angles not exterior angles.
The exterior angles of any polygon add up to 360 degrees.
What Cindy did was found the total interior angle measure of a hexagon which is 720
the population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Answers
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
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12
Select the correct answer.
The scatter plot represents the purchase prices and selling prices of X-ray machines made by five different manufacturers. Which of the following
points show errors of prediction or residuals?
OA.
OB.
O C.
O D.
Points (14, 25) and (15, 25)
Points (15, 25) and (18, 26)
Points (14, 25) and (16, 25)
Points (12, 24) and (18, 26)
Estimated Selling Price (in $1,000)
26.5
26-
25.5
25
24.5
24
23.5
10
11
12 13 14 15 16 17 18 19 20
Purchase Price (in $1,000)
Answers
The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.
Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.
The graph that represent this data using the points is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The x and y values
Where
x = stars
y = price
To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph
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(x - 3)3 = 27(2x - 1)3
Answers
Answer:
24
x= ____
53
Step-by-step explanation:
the right answer
Answer:
x=24/53
Step-by-step explanation:
(x-3)3=27(2x-1)
3x-9=(54x-27)3
3x_9=162x-81
3x-162x=-81+9
-159x=-72
x=-72/-159
x=24/53
10-
Next O
Post Test: Linear Equations
10
Select all the correct answers
Which lines in the graph have a slope greater than 1 but less than 27
line 1
line 2
line 3
line 4
line 5
3 4
5
Answers
The slope of the straight line in the graph that expresses proportional relationship indicates that the lines in the graph that have a slope greater than 1 but less than 2 are;
Line 3Line 4What is the slope of a graph of a straight line?The slope of the graph of a straight line is the ratio of the rise to the run on the line.
The slope of a graph with a slope of 1 has an increase in the y-value of 1 for each increase in the x-value of 1
Slope = 1 = Δy/Δx
When the slope is greater than 1, we get;
Δy/Δx > 1, therefore Δy is larger than 1 when Δx is 1.
Similarly, the slope of a graph with a slope of 2 has an increase in the y-value of 2 for each increase in the x-value of 1
Slope = 2 = Δy/Δx
When the slope is less than 1, we get;
Δy/Δx < 2, therefore Δy is less than 2 when Δx is
The lines in the graph that have a slope greater than 1 but less than 2 are therefore the graphs with the coordinates;
Line 3; (0, 0), (4, 6); Slope = 6/4 = 3/2, therefore; 1 < slope = 3/2 < 2
Line 4; (0, 0), (5, 6); Slope = 6/5, therefore; 1 < Slope < 2
The line 5 has a slope of 1, and the line 1, has a slope of 3, line 2 has a slope of 2
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Find the equations for a helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane).
Answers
By the equations according to the cylindrical system of coordinates, the equation for a helix are x = 8 · cos (2π · t /T), y = 8 · sin (2π · t /T) and z = 6 · (t/T).
How to derive the equations of a helix in cylindrical form
According to the cylindrical system of coordinates, helix can be described by the following equations:
Radius
x = r · cos (2π · t /T) (1)
y = r · sin (2π · t /T) (2)
Height
z = H · (t/T) (3)
Where T is the period of one complete revolution.
If we know that r = 8 and H = 6, then the equations for the helix is:
x = 8 · cos (2π · t /T)
y = 8 · sin (2π · t /T)
z = 6 · (t/T)
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What is the greatest common factor of 48x3, 12x4, and 36x5?
Answers
You need to give 250 mcg of adrenaline, and you have a 1 mL ampoule of 1:1000 adrenaline. How many mL do you want?
Answers
The volume of adrenaline you want is 0.25mL
How to determine the volume you wantFrom the question, we have the following parameters that can be used in our computation:
Amount to give = 250 mcg of adrenaline
Available = 1 mL of 1 : 1000 of adrenaline
The expression 1 mL of 1 : 1000 of adrenaline means that
1:1000 contains 1 mg in 1 mL (i.e. 1000 microgram/mL)
So, we have
Available = 1 mL * 1000 microgram/mL
Evaluate
Available = 1000 micrograms
This can be expressed as
Available = 1000 mcg
So, we have
Amount to give = 250 mcg of adrenaline
Available = 1000 mcg of adrenaline
When converted to mL, we have
Available = 1 mL of 1 : 1000 of adrenaline
Divide by 4
Amount = 1 mL of 1/4 : 1000/4 of adrenaline
Evaluate
Amount = 1 mL of 1/4 : 250 of adrenaline
This implies that
Amount = 1 mL of 1/4
Evaluate
Amount = 0.25 mL
So, the amount is 0.25 mL
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95% of what number is 114?
Answers
114 is 95% of 120
100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.
114 is 95 Percent of What Number?
Formula = Number x 100
Percent = 114 x 100
95 = 120
The following shows the steps to derive this formula and find out 95% of the number is 114.
Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.
114
95% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
95Y = 114 x 100
95Y = 11400
Y = 11400
100 = 120
To make a fruit punch recipe, combine 2 cups of pineapple juice with 4 cups of grape juice and 6 cups of apple juice.
Create a diagram or double number line to represent the quantities of each ingredient in this recipe.
Use your diagram to choose the correct sentence.
Group of answer choices
The ratio of pineapple juice to grape juice to apple juice is 2 : 6 : 4.
The ratio of grape juice to pineapple juice to apple juice is 2 : 4 : 6.
The ratio of grape juice to apple juice to pineapple juice is 6 : 2 : 4.
The ratio of apple juice to pineapple juice to grape juice is 6 : 2 : 4.
Answers
Answer:
The ratio of apple juice to pineapple juice to grape juice is 6 : 2 : 4.
Step-by-step explanation:
You can factor out all of the other answers due to the order of the Pineapple, Grape, and Apple juice in the answers. You need to ensure the #'s in the ratios align with that of the numbers for each of the juices.
Answer: it’s the last one (c)
For 9$ a shoekeeper buys 13 dozen pencils.However 3 dozen broke in transit. At what price per dozen must the shoekeeper sell the remaining pencils to make back 1/3 of the whole cost
Answers
Answer: $0.30 per dozen.
Step-by-step explanation:
Given: The whole cost of 13 dozen pencils = $9
If 3 dozen broke in transit, remaining dozens of pencils = 13-3 = 10 dozens
Also, Selling price of theses 10 dozens = \(\dfrac{1}{3}\times\text{whole cost}\) [given]
\(=\dfrac{1}{3}\times9=\$3\)
Then, the selling price of each dozen = \(\dfrac{\$3}{10}=\$0.30\)
Hence, the shopkeeper sells the remaining pencils at $0.30 per dozen.
What is the distance between the points (7,5) (4,9)
Answers
The Distance will be 5.
The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.
Let point (7,5) be A and point (4,9) be B
Distance formula =
Ab = √(x1- x2) ² + (y1 -y2) ²
Then Distance AB will be
Ab = √(7-4) ² + (5 -9) ²
= √ 3² + 4²
= √ 9 + 16
= 5
Hence the distance will be 5.
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The points \((7,5)\) \((4,9)\) are separated by a distance of \(5\) units.
The distance between the two points is given by the length of the segment between them.
The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).
The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.
Use the distance formula to get the distance between two places.
\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)
In the posted query,
\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)
Distance formula,
\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)
\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)
\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)
\(d = \sqrt{ 9+16 }\)
\(d = \sqrt{ 25 }\)
\(d = 5\)
Therefore, the points \((7,5)\) \((4,9)\) are at a distance of \(5\) units.
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