To classify shapes, one can use the distance formula to calculate the lengths of a shape's sides and the slope formula to determine angles between sides. Analyzing these measurements helps identify if a shape is a rectangle, square, etc., based on side length equality and perpendicular angles.
Classifying Shapes Using Distance and Slope Formulas
To classify shapes using the distance and slope formulas, you'll need to analyze the lengths of sides and the angles between them. The distance formula helps determine the length of sides by calculating the distance between two points. On the other hand, the slope formula is used to find the inclination of sides, which can indicate whether lines are parallel or perpendicular.
Here's an example. Suppose we have a quadrilateral with vertices at (1,1), (1,4), (5,4), and (5,1). We'd calculate the distance between consecutive vertices to determine if the sides are equal. If the distances are the same, our shape might be a square or a rectangle. Next, we calculate the slopes of adjacent sides using the formula (y2-y1)/(x2-x1) (rise over run). If the slopes of adjacent sides are negative reciprocals of each other, the lines are perpendicular, which is a characteristic of rectangles and squares.
Applying the slope formula to our example, the slope from (1,1) to (1,4) would be (4-1)/(1-1), which is undefined, suggesting a vertical line. Between (1,4) and (5,4), the slope is (4-4)/(5-1), which is 0, indicating a horizontal line. Therefore, the expected behavior for a square's or rectangle's sides is observed. By further calculating all side lengths and slopes, we could definitively classify our shape.
Factor. x(3y−5)+3(3y−5)
Answer: The required factored form is [tex](x+3)(3y-5).[/tex]
Step-by-step explanation: We are given to factor the following polynomial :
[tex]P=x(3y-5)+3(3y-5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following factorization formula :
[tex]a(b+c)+d(b+c)=(a+d)(b+c).[/tex]
So, from expression (i), we get
[tex]P\\\=x(3y-5)+3(3y-5)\\\\=(x+3)(3y-5).[/tex]
Thus, the required factored form is [tex](x+3)(3y-5).[/tex]
Michelle jumps from a plane at an altitude of 1000 m. After 10 seconds her parachute opens. The graph shows the relationship between her altitude and time. How long does it take for her to be half way between the plane and the ground?
Answer: 1 minute
Step-by-step explanation: Michelle jumped from the plane at the altitude of 1000 m. To find the half way point, from the plane she jumped from and the ground; all you have to do is cut the altitude in half:
1000/2 = 500m which Is labeled at 1 minute
Meaning that it took 1 minute for her to be halfway from the ground
I have done this problem and taken the test, it is 100% correct
Good luck hope it helps! :D
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
f(x) = –3x – 6
f(x) = –3x – 4
f(x) = –3x + 16
f(x) = –3x + 14
answer asap
The linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.
What is point-slope equation?"In a Point-slope form it is likely to be y - y1 = m(x - x1). This form of a linear equation is derived from a equation for finding the slope of a line."
Given
The point-slope equation y + 1 = –3(x – 5)
By solving the above equation
y + 1 = -3x + 15
⇒ y = -3x + 15 - 1
⇒ y = -3x + 14
Replace y with f(x)
⇒ f(x) = -3x + 14
Hence, the linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.
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On scrap paper, determine if the triangle with the following vertices is a right triangle.
A(-3, 5), B(1, 4), and C(-1, 0).
in the box below, tell whether or not the triangle is a right triangle. Explain how you arrived at your answer.
Answer:
not a right triangle
Step-by-step explanation:
The slope of AB is -1/4; the slope of BC is 2. These are not negative reciprocals of one another.
15b - 10c - 10b + 5=
MATH HELP > WILL AWARD BRAINLIEST
The graph below shows the graphs of the linear function y=7x and the exponential function y=7^x
True or False: The growth rate of the exponential function exceeds the growth rate of the linear function for 1
Answer: True.
Step-by-step explanation:
Given: The graph below shows the graphs of the linear function y=7x and the exponential function [tex]y=7^x[/tex]
Both of the function have same value of rate =7
But in linear function y=7x , 7 is the constant of proportionality.
In exponential function [tex]y=7^x[/tex], 7 is the multiplicative rate of change.
For [tex]1\leq x\leq 3[/tex]
For y=7x ,
x y
1 7
2 14
3 21
For [tex]y=7^x[/tex]
x y
1 7
2 49
3 343
Thus, we can see the growth rate of the exponential function exceeds the growth rate of the linear function for [tex]1\leq x\leq 3[/tex].
Answer:
D
Step-by-step explanation:
Just took test on it
which functons have graphs that are less steep than the graph of f(x)=2x^2
(select each correct answer)
h(x)= -2x^2
g(x)= -3x^2
m(x)= 3x^2
j(x)= -x^2
k(x)= x^2
Answer:
[tex]k(x) = x^{2} \\j(x) = -x^{2}[/tex]
Step-by-step explanation:
The slope has to be steep and the ones given above are all greater than 2 except for k(x) and j(x).
Solve for x. x + 5 = 2x
The solution to the equation x + 5 = 2x is x = 5.
We have,
To solve the equation x + 5 = 2x, we want to find the value of x that makes the equation true.
We start by isolating the variable x on one side of the equation.
In this case, we can do that by subtracting x from both sides of the equation.
By subtracting x from both sides, we have:
x + 5 - x = 2x - x
The x term on the left side cancels out, leaving us with:
5 = x
This means that x is equal to 5, and substituting x = 5 back into the original equation gives us:
5 + 5 = 2(5)
10 = 10
The equation is true, confirming that x = 5 is the correct solution.
Therefore,
The solution to the equation x + 5 = 2x is x = 5.
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M and N are the acute angles of an isosceles right triangle.
Select the true statements.
cosM = sinM
cosM = cosN
cosM = tanN
sinN = cosM
tanM = tanN
EASYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Which equation is a point slope form equation for line AB?
A.y+1=3/2(x-1)
B.y+1=-3/2(x-1)
7x-y-17 = 0 Hope this helps!
Explain why the t-distribution has less spread as the number of degrees of freedom increases
it will be 12 degrees tonight. the weatherman predicts it will be 25 degrees warmer by noon tomorrow. what will the temperature be by noon tomorrow?
is 8.23 a rational number?
Shen’s mother gave him $10 to go buy groceries. He picked up a gallon of milk for $3.49, three pounds of oranges that cost $1.14 per pound, and a box of cereal for $3.46. Shen used front-end estimation to determine whether he had enough money for the groceries. How much did he estimate the total cost would be?
Answer:
$9.
Step-by-step explanation:
We have been given that Shen’s mother gave him $10 to go buy groceries. He picked up a gallon of milk for $3.49, three pounds of oranges that cost $1.14 per pound, and a box of cereal for $3.46.
In front-end estimation, we round whatever number is in front instead of rounding each number to a given place value.
We can see that in $3.49, front number is and second number is less than 5, so we will round it down to $3.
Similarly, in $3.46, 1st number is 3 and second number is less than 5, so we will round it down to $3.
In $1.14, front or 1st number is 1 and second number is less than 5, so we will round down to $1. Cost of three orange boxes would be [tex]\$1*3=\$3[/tex].
[tex]\text{Total estimated cost}=\$3+\$3+\$3[/tex]
[tex]\text{Total estimated cost}=\$9[/tex]
Therefore, the total estimated cost of groceries is $9.
Which property justifies the procedure used to eliminate fractions and decimals from equations?
Division Property of Equality
Identity Property of Multiplication
Multiplication Property of Equality
Addition Property of Equality
By multiplication property of equality, we can eliminate fractions and decimals from equations. Option C is correct.
Given that,
To determine which property justifies the procedure used to eliminate fractions and decimals from equations.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Suppose the equation
1 / 4 = 0.25
Now multiply both sides by 4
4 * 1/ 4 = 0.25 * 4
1 = 1
So, by multiplication property of equality, we can eliminate fractions and decimals from equations.
Thus, by multiplication property of equality, we can eliminate fractions and decimals from equations.
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A circle has a diameter with endpoints at –3 + 18i and 7 – 6i. Which point is also on the circle?
Answer:
D. 14+11i
Step-by-step explanation:
Edge
Factor 16x 4 – 81 completely. First factor each term. 16x 4 = (_____)2 81 = ___ 2 Then use a2 – b2 = (a – b)(a + b) twice. Show your work. 16x 4 – 81 =
The completely factored form of expression 16x⁴ - 81 is (4x² - 9)(4x² + 9).
To factor the expression 16x⁴ - 81 completely, let's first factor each term:
16x⁴ can be written as (4x²)² since (4x²)²= 16x⁴.
81 can be written as 9² since 9² = 81.
Now, we can rewrite the expression:
16x⁴ - 81 = (4x²)² - 9²
Using the formula a² - b² = (a - b)(a + b).
we can apply it twice to factor the expression further:
(4x² - 9)(4x² + 9)
Therefore, the completely factored form of 16x⁴ - 81 is (4x² - 9)(4x² + 9).
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Katy buys 3 dvds every two weeks. how many dvd's will she buy in 14 weeks?
Answer:
21 dvds
Step-by-step explanation:
Set up a proportion in terms of DVDs to weeks and solve.
3/2 = x/14
(2)(x) = (3)(14)
2x = 42
x = 21
Therefore, Katy will buy 21 DVDs in 14 weeks.
Population has a mean of 180 and a standard deviation of 24. a sample of 64 observations will be taken. the probability that the mean from that sample will be between 183 and 186 is
The probability that the sample mean is between 183 and 186 would be 0.1359.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of a population
N = number of observations of population
X = mean
μ = population mean
It is given that the Population has a mean of 180 and a standard deviation of 24. a sample of 64 observations will be taken.
So, µ = 180, σ = 24 and n = 64.
By the Central Limit Theorem, the sample mean is normally distributed with a mean of 180 and a standard deviation of 24
Therefore, 24/√64
= 24/8 = 3.
Now let's convert the 183 and 186 into z -scores.
So, the z-score for 183 is (183–180)/3 = 1
The z-score for 186 is (186 –180)/3 = 2.
We can see that the area to the left of z = 1 is 0.8413
The area to the left of z = 2 is 0.9772.
The probability that the z is between 1 and 2 can be calculated as the difference between the area of z.
= 0.9772 – 0.8413
= 0.1359.
Thus, the probability that the sample mean is between 183 and 186 would be 0.1359.
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Henry drove 195 miles in 3 hours. How many miles per hour was he driving?
666-601=65
boom
it wont let me put it in without these words\
What is 1/4+1/2+x=−3/4?
1/4+2/4+x=−3/4
1/4+2/4+x-1/4=-3/4-1/4
2/4+x-2/4=-1-2/4
x=-1 1/2
The front of a tent is an equilateral triangle with the ratio of its base, b, to its height, h, given by b over h equal fraction numerator 2 over denominator square root of 3 end fraction. What equation can be used to find the tent's height?
I don't understand this :((
Find the critical value z subscript alpha divided by 2zα/2 that corresponds to the given confidence level
The critical value zα/2 that corresponds to a given confidence level can be found by subtracting the confidence level from 1, dividing by 2, and looking up this value in the Z-table. For a 90% confidence level, the corresponding zα/2 is approximately 1.645.
Explanation:To find the associated critical value zα/2 for a given confidence level, you would first subtract the confidence level from 1, then divide by 2. This will give you α/2. You would then look up this value in the Z-table to find the corresponding critical value of z. Now, let's consider an example.
Assume a confidence level of 90%. We subtract this from 1, which gives us 0.10, and then dividing by 2 gives us 0.05. Now we look up 0.05 in the Z-table, and find that the corresponding value of z is approximately 1.645. Therefore, the critical value zα/2 that corresponds to a 90% confidence level is approximately 1.645.
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Write an inequality to model the situation. a number exceeds 9.
Answer:
n ≥ 9
Step-by-step explanation:
The _____ of a cone is the curved surface that connects the base of a cone to the apex of the cone.
The lateral surface of a cone is the curved surface that connects the base of a cone to the apex of the cone.
The lateral surface of a cone refers to the curved surface area that connects the base of the cone to its apex (the pointed top).
It forms the sloping sides of the cone.
In a cone shape, the base is a circle, and the lateral surface is the part that wraps around the sides to meet at the apex.
This surface does not include the base or the tip of the cone. It is only the curved part that connects the two.
The lateral surface area of a cone can be calculated using the formula A = πrl, where A represents the lateral surface area, r is the radius of the base of the cone, and l is the slant height, which is the distance from the apex to any point on the edge of the base.
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Kyle bought a 5 pound pumpkin for $2.60. How much did he pay per pound?
Suppose that 18% of people have a dogdog, 34% of people have a cat, and 88% of people own both. What is the probability that someone owns a dog
or a cat
Molly earns $8 per hour at her job. Last month, Molly worked for 45 hours. On her paycheck, Molly noticed that she paid $38.50 for federal income tax, $22.32 for Social Security, and $5.22 for Medicare. Molly's net income was
Molly's gross income is $360, and after subtracting her total deductions ($66.04), her net income is $293.96. This demonstrates the difference between gross and net income.
Explanation:To find Molly's net income, we will first need to calculate her gross earnings, and then subtract her deductions. Molly's gross earnings are her hourly wage multiplied by the number of hours she worked, so: $8/hr * 45 hours = $360.
Next, we add up Molly's deductions: $38.50 (federal tax) + $22.32 (Social Security) + $5.22 (Medicare) = $66.04.
Finally, to determine Molly's net income, we subtract her total deductions from her gross earnings: $360 - $66.04 = $293.96.
This example illustrates the concept of gross income versus net income. Gross income is the total amount earned before deductions, and net income is the amount left after deductions have been subtracted, which is the exact amount the employee receives in their paycheck.
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