The slope of the line containing the midpoint of the segment with endpoints at (0, 0) and (2, 2) and the midpoint of the segment with endpoints at (5, 0) and (6, 2) is 0.
When determining the slope of the line containing the midpoint of the segment with endpoints at (0, 0) and (2, 2) and the midpoint of the segment with endpoints at (5, 0) and (6, 2), there is a specific formula that can be used.
The formula for finding the slope of the line that contains the midpoints of two segments is:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
where the points (x1, y1) and (x2, y2) are the midpoints of the two segments.
Steps:1. Determine the midpoint of the first segment by using the midpoint formula:
[tex]\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
The midpoint of the segment with endpoints at (0, 0) and (2, 2) is:
[tex](\frac{0+2}{2}, \frac{0+2}{2}) = (1, 1)2.[/tex]
Determine the midpoint of the second segment by using the midpoint formula:
[tex]\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)[/tex]
The midpoint of the segment with endpoints at (5, 0) and (6, 2) is:
[tex](\frac{5+6}{2}, \frac{0+2}{2}) = (\frac{11}{2}, 1)3.[/tex]
Substitute the midpoints into the slope formula and simplify:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{1-1}{\frac{11}{2}-1}=\frac{0}{\frac{9}{2}}=0[/tex]
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if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The above table represents the contents ( colored marble) of a bag. The probability that selected marble had a color other than white or blue is equals to the 0.766234 ( nearest to milinoth).
We have a bag that contains five different types of marbles. See the above table
number of red marbles in a bag = 16
number of green marbles in a bag = 23
number of blue marbles in a bag = 13
number of pink marbles in a bag = 20
number of white marbles in a bag = 5
So, total number of marbles in a bag= 16 + 23 + 5 + 13 + 20 = 77
Now, a single marble is selected and out of the bag. We have to determine probability that it is a color other than white or blue. Let X , Y and Z be three events defined as the following
X = selected marble is white
Y = selected marble is blue
Z = selected marble is other than blue or white
Probability of seclecting white marble, P(X) = 5/77
Probability of seclecting blue marble, P(Y)
= 13/77
Probability of seclecting blue or white marble, P(Y UX) = P(X) + P(Y) = 5/77 + 13/77 = 18/77
So, probability that selected marble has a color other than white or blue, P(Z) = 1 - P( X UY) = 1 - 18/77
= 59/77 = 0.76623376623
Hence, required probability is 0.766234.
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Complete question :
The above table discribes the contents of a bag that contains red,green, blue,pink and white marbles if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO
I don't know but i can help a little
Step-by-step explanation:
But If the slops are the same and the y-intercepts are different, the lines are parallel...
HELP ITS DUE TODAY!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Please give brainliest
1a) 3√49
3 x √49
3x 7 =21
b) 2³√64
2 x √4
2x2 =4
c) (√x+2)²
the square will cancel the square root
= x+2
Answer:
These are correct
Step-by-step explanation:
1. a) 21
1. b) 8
1. c) x+2
2. a) x/10 and subtracting or simplifying it gives you the same answer
2. b) 2(3x-1)/ x+3 the operation is simplifying
2. c) 7x+2/ x(x+1) combine the fractions and find a common denominator
2. d) 6/x simplify
2. e) 2x^2 simplify or divide
3. a) 6x^3 y^4
3. b) 16a^2 b^6
3. c) 4x^2
3. d) 2
for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
PLEASE HELP!!!!!!!!! ASAP!!!!!!
Here are some examples:
Distance to endpoint: |2 - (-2)| = 4
Equation: |x - 2| = 4
When answering questions on Brainly, you should always be factually accurate, professional, and friendly. You should be concise and not provide extraneous amounts of detail. You should also use the following terms in your answer, if they are relevant to the question being asked.
In order to write an absolute value equation in the form |x-c|=d to satisfy a given solution set on a number line, you need to do the following:First, identify the number c, which is the midpoint of the solution set. This is because the absolute value of x-c is equal to the distance between x and c on the number line.
Next, identify the number d, which is equal to the distance between the midpoint c and one of the endpoints of the solution set. This is because the absolute value of x-c can never be greater than the distance between x and c, so the maximum value of x that satisfies the equation is c+d and the minimum value is c-d.Finally, write the equation in the form |x-c|=d using the values of c and d that you identified.
Set of solutions (-3, 1) In the middle: (-3 + 1)/2 = -1
Endpoint distance: |-1 - (-3)| = 2
Formula: |x + 1| = 2
Set of solutions (-4, 4)
Center: (-4 + 4)/2 = 0.
Endpoint distance: |0 - (-4)| = 4
Equation: 4 for |x| Set of solutions (-2, 6)
Center: (-2 + 6)/2 = 2
Endpoint distance: |2 - (-2)| = 4
Equation: 4 for |x - 2|
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PLEASE HELP!! I WILL GIVE SIXTY POINTS I NEED THIS
Honestly I think you need some theray feom reading your tabs
Answer:
6.6
Step-by-step explanation:
The formula for a paralellogram is base x height (not side length). the base in this case is 2.2 and the height is 3, so 2.2 x 3 = 6.6.
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the average on a standardized test of educational achievement is 600, and the standard deviation is 50. what is the percentage of the area between 550 and 725?
37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.
The area between 550 and 725 on a standardized test of educational achievement is equal to the percentage of students whose scores fall within one standard deviation (or 68%) of the mean score of 600. This can be expressed mathematically as:
Percentage = (725 - 550) / (2 * 50) = 37.5 / 100 = 37.5%
To explain in more detail, a standard deviation is a measure of the spread of a dataset around its mean value. The mean value in this case is 600, and the standard deviation is 50. Therefore, one standard deviation from the mean is calculated by subtracting or adding the standard deviation (50) from the mean (600), giving a range of 550 to 650.
Since the area in question spans across two standard deviations (550 to 725), the area is calculated by subtracting the lower range (550) from the upper range (725) and then dividing it by two standard deviations (100). This gives us the area, which is 37.5%.
To summarize, 37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.
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Por la suma de sus medidas, los ángulos se clasifican en _______ cuando suman 90º, y en _______ si suman 180º
Answer:
Complementary angles: a pair of angles are considered complementary when their sum is exactly 90º.
Step-by-step explanation:
To calculate a complementary angle, we will subtract 90 from the angle that the statement tells us and it will give us its complementary. Supplementary angles: A pair of angles are considered supplementary when their sum is exactly 180º.
the skewness coefficient can be used to multiple select question. compare standard deviations. compare two samples with different measurement units. compare means. compare one sample to a known reference distribution.
The skewness coefficient is a measure of asymmetry in a distribution that can be used to compare means and compare one sample to a known reference distribution, but it is not typically used to compare standard deviations or compare two samples with different measurement units.
The skewness coefficient is a measure of the degree of asymmetry in a probability distribution. It indicates the direction and degree of skewness in a distribution, and can be used to compare means and compare one sample to a known reference distribution.
A positive skewness coefficient indicates that the distribution has a longer tail on the right side and that the mean is greater than the median, while a negative skewness coefficient indicates that the distribution has a longer tail on the left side and that the mean is less than the median.
The skewness coefficient can be useful in detecting departures from normality and in identifying outliers that might affect statistical inference.
However, the skewness coefficient is not typically used to compare standard deviations or to compare two samples with different measurement units.
Comparing standard deviations involves analyzing the variability in the data, whereas comparing means and comparing one sample to a known reference distribution involves analyzing the central tendency of the data.
Additionally, comparing two samples with different measurement units requires converting the measurements to a common scale, which is not related to skewness.
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A survey of all being on earth found that 96% preferred orange juice to all other juices if 72 people preferred orange juice, how many beings were surveyed altogether?
As per the given percentage, the total number of beings surveyed is 75.
We are given that 96% of all beings on earth prefer orange juice. This means that if we take a random sample of beings from earth, 96% of them would prefer orange juice. Mathematically, we can express this as:
Percentage of beings who prefer orange juice = 96%
We are also given that 72 people preferred orange juice. We can use this information to find the total number of beings surveyed. Let's assume that the total number of beings surveyed is "x".
Now, we know that 96% of these beings prefer orange juice. We can express this as:
96% of x = 72
To solve for "x", we need to get rid of the percentage sign. We can do this by converting the percentage to a decimal. To convert a percentage to a decimal, we divide it by 100.
So, 96% can be expressed as 0.96 (96/100). Therefore, we can rewrite the above equation as:
0.96x = 72
To solve for "x", we can divide both sides of the equation by 0.96:
x = 72 ÷ 0.96
x = 75
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A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. if each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? approximate using pi equals 22 over 7.
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the cylinder (which is half of the diameter) and h is the height of the cylinder.
For the mini muffins in question, the diameter is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches, or 5/4 inches.
So the surface area of one mini muffin is:
Surface Area = 2π(1)^2 + 2π(1)(5/4)
Surface Area = 2π + 5π/2
Surface Area = 9π/2
To wrap 6 mini muffins, we need to multiply this surface area by 6:
Total Surface Area = 6 x (9π/2)
Total Surface Area = 27π
Approximating π as 22/7, we get:
Total Surface Area ≈ 27 x (22/7)
Total Surface Area ≈ 84.857 inches^2
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Answer:
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
Step-by-step explanation:
Solve the equation
1/4xln(16q^8)-ln3=ln24
We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
given equation:
[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]
[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]
Therefore, the solution to the original equation is:
[tex]q = 9^x\\[/tex]
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Kendrick bought a calculator priced at $71. Shipping and handling cost an additional 25% of the price. What was the total cost of the calculator, including shipping and handling?
Answer:
The answer to our problem is, $17.75
Step-by-step explanation:
First we need to find out what is 25% of 71
25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75
How I got it:
25 percent * 71
= (25:100)* 71
= (25* 71):100
= 1775:100
= 17.75
Percentage solution with steps:
Step 1: Our output value is 71.Step 2: We represent the unknown value with x.Step 3: From step 1 above, 71 = 100%.Step 4: Similarly, x = 25%.Step 5: This results in a pair of simple equations:71 = 100% (1)
X = 25% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have
[tex]\frac{71}{x} = \frac{25}{100}[/tex]
X = 17.75
Thus the answer to your problem is, $17.75
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real objects.
Using the scale factor of 4:1, the side lengths of the real objects are:
B. Side a is 5 inches long and side b is 4.5 inches long.
What is a Scale Factor?A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.
Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.
Therefore, the sides would be:
Side a = 20/4 = 5 in.
Side b = 18/4 = 4.5 in
The answer is B.
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2 people - 0 people = ? people
Solve 5^x=1÷5 solve it as fast as you can
mr. henderson, the principal of blue creek academy, is getting soaked by the splash tank on the last day of school! each time a student hits the target, a 5-quart bucket of water dumps on his head. if 20 students hit the target, how many gallons of water will be dumped on mr. henderson's head?
25 gallons of water will be dumped on Mr. Henderson's head.
To solve the problem, we first need to find the total amount of water dumped on Mr. Henderson's head by all the students. Since each student dumps a 5-quart bucket of water, we can find the total amount by multiplying the number of students by the amount of water per student:
Total amount of water = 20 students x 5 quarts/student = 100 quarts
Next, we convert the total amount of water from quarts to gallons since the problem asks for the answer in gallons. Since 1 gallon equals 4 quarts, we can divide the total amount of water by 4 to get the answer in gallons:
Total amount of water = 100 quarts ÷ 4 quarts/gallon = 25 gallons.
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I need help with this problem. Joe bought a gallon of gasoline for 2. 85 per gallon and c cans of oil for 3. 15 per can
From the given information provided, the expression that need to determine the total amount is Total cost = $2.85/gallon x g gallons + $3.15/can x c cans.
The expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = Cost of gasoline + Cost of oil
We can represent the cost of gasoline as:
Cost of gasoline = price per gallon x number of gallons
Substituting the given values, we get:
Cost of gasoline = $2.85/gallon x g gallons
Similarly, we can represent the cost of oil as:
Cost of oil = price per can x number of cans
Substituting the given values, we get:
Cost of oil = $3.15/can x c cans
Putting it all together, we get:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Expression that can be used to determine the total amount Joe spent on gasoline and oil is:
Total cost = $2.85/gallon x g gallons + $3.15/can x c cans
Question - Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
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DIrections: Find the area of the given quadrilateral or four sided polygon. Please show all of your work in order to receive full credit.
Hint: Decompose and Recompose!
I need help please
The Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².
Given,
Length of the Rectangle is equal to 6 cm.
Breadth of rectangle is 4 cm.
Height of the right angled triangle is 4 cm.
Length of the base of the triangle is 3 cm.
First we need to find the area of single then multiply it with 2 since the lengths of the triangles are same and the area will also be same.
⇒ Area of Triangle = [tex]\frac{1}{2} * b *h[/tex]
Area of Triangle = [tex]\frac{1}{2}[/tex] * 4 * 3
Area of Triangle = 6 cm².
Now, area of two triangles is equal to 2 * 6 cm² = 12 cm².
⇒ Area of Rectangle = length * breadth
Area of Rectangle = 6 * 4
Area of Rectangle = 24 cm²
Now, total area = Area of Triangle + Area of Rectangle
Total area = 12 cm² + 24 cm²
Total area = 36 cm².
Therefore, the Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
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describe the technique used to count the rational numbers (1-1 correspondence with the natural number
Yet because we can compare the set of positive rational numbers exactly to the collection of natural numerals, we may infer that the set of positive rational must have a number of clusters of 0, or n(Q+)=0. Due to the fact that these two numbers must equal one another, 02 = 0.
Since they may be arranged in a one-to-one correspondence with the natural numbers (the integers, such as 1, 2, and 3), Cantor showed in 1873 that the rational numbers, although being infinite, are countable (or denumerable).
How are the rational numbers counted as a group?
To achieve this, we take into account the this double integers grid upon that positive orthogonal. If p and q are positive natural numbers, then p/q may be used to represent any positive valid value.
Simply put, we establish the following values: h(0) = 0, h(2n) = f(n), for all natural numbers n > 0, and h(2n-1) = g(n) = -f(n), for all natural numbers n > 0.
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if the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised?
There is a 2.28% likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised.
Assume that the advertised weight is equivalent to the typical weight of one bag, which is 30 grammes. A pack of nine bags would therefore weigh 9 x 30 = 270 grammes.
Let's now assume that each bag actually weighs 30 grammes on average, with a 2 gramme standard deviation, according to a normal distribution (which represents the variability in the weight of the bags).
We need to apply the central limit theorem to determine the probability that the average weight of the bags in a randomly selected pack is 2 or more grammes less than stated. According to this theorem, the mean of a sufficiently large sample (in this case, nine bags) will have a sampling distribution that is roughly normal, with a mean of 30 grammes and a standard deviation of 2 grammes divided by the square root of the sample size (9 = 0.67 grammes). The mean will also be equal to the population's standard deviation.
We can determine the likelihood that the sample mean of a pack of 9 bags weighs less than 28 grammes using a normal distribution table or calculator (which is 2 grammes less than the advertised weight of 30 grams). This likelihood is roughly 0.0228, or 2.28%.
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alexa started randomly playing a movie and would not stop, despite my repeated orders. what's going on here?
It sounds like you may be experiencing a bug with your Alexa device. This is likely due to a software update or miscommunication between the device and the server.
To resolve this issue, you may need to restart your device by unplugging it from the power source and plugging it back in. You can also try clearing the cache of your device. Additionally, you may need to update the software of your device by visiting the Amazon website and downloading the most recent version of the software. If the issue persists, you may need to contact Amazon customer service for further assistance.
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What is the value of y in the solution to the system of equations?
²x+y=1
-X
2x - 3y = -30
-8
-3
3
O 8
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75. As a result, the answer is y = 31/4.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
the system of equations,
[tex]y = 1 - 2x\\2x - 3(1 - 2x) = -30\\2x - 3 + 6x = -30\\8x = -27\\x = -27/8\\2(-27/8) + y = 1\\-27/4 + y = 1\\y = 1 + 27/4\\y = 31/4[/tex]
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75.
As a result, the answer is y = 31/4.
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alicia had $22 to spend on pencils if each pencil cost $1.50 how many pencils can she buy? What is the Inequality or Equation
If each pencil cost $1.50 and Alicia had $22 to spend on them, she could purchase 14 pencils. This situation's inequality is as follows: 1.5x ≤ 22.
To find out how many pencils Alicia can buy, we can divide her total budget by the cost per pencil:
Number of pencils = Total budget / Cost per pencil
Number of pencils = $22 / $1.50
Number of pencils = 14.67 (rounded to two decimal places)
Alicia cannot buy a fraction of a pencil, so she can buy a maximum of 14 pencils.
The inequality that represents this situation is:
1.5x ≤ 22
Where x represents the number of pencils Alicia can buy. We divide both sides of the inequality by 1.5 to isolate x:
x ≤ 14.67
Since Alicia cannot buy a fraction of a pencil, we round down to the nearest whole number and get:
x ≤ 14
So, Alicia can buy a maximum of 14 pencils.
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for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. 5.1
Bending moment curve equation below point A will be:
M = 15x - 3x² for 0 ≤ x ≤ b
Determination of shear and bending moment curves.
For the beam and loading shown, we can do the following:
Equation of shear curve (above point A):V = RA - w.x
For x = a,V = RA - w.a
For x = b,V = RA - w.b
Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b
Equation of shear curve (below point A):
V = RA - w.x
For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a
The shear curve equation becomes;
V = 15k for 0 ≤ x ≤ a
V = 15 - 6a for a ≤ x ≤ b
Equation of bending moment curve (above point A):
M = RAx - ½w.x²For 0 ≤ x ≤ a,
M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,
M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²
The bending moment curve equation above point A becomes:
M = 15x - 3x² for 0 ≤ x ≤ a
M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b
Equation of bending moment curve (below point A):
M = RAx - ½w.x²For 0 ≤ x ≤ b,
M = 15x - ½(6x²) = 15x - 3x²
The bending moment curve equation below point A becomes;
M = 15x - 3x² for 0 ≤ x ≤ b
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10 1/4 divided by 5 1/2?
Answer:
To divide two mixed numbers, we need to first convert them to improper fractions.
10 1/4 is the same as (10 x 4 + 1)/4 = 41/4
5 1/2 is the same as (5 x 2 + 1)/2 = 11/2
So, we need to divide 41/4 by 11/2:
(41/4) ÷ (11/2)
When dividing by a fraction, we can multiply by its reciprocal (flip the fraction):
(41/4) x (2/11)
Now, we can simplify by canceling out the common factors:
(41 x 2) / (4 x 11) = 82/44 = 41/22
Therefore, 10 1/4 divided by 5 1/2 is equal to 41/22 or approximately 1.86 when rounded to two decimal places.
Por lo tanto, 10 1/4 dividido por 5 1/2 es igual a 41/22 o aproximadamente 1,86 cuando se redondea a dos decimales.
A'B'C' is the image of ABC under a dilation whose center is P and scale factor is 1/3
A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:
Side length AC = 6.7/3 = 2.2
Side length AB = 12.4/3 = 4.1
Side length CB = 12.7/3 = 4.2
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Complete Question:
Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 1/3.
Ethan also wants to buy some shoes that were originally $80. This week they’re on sale for 50% off the original price. Ethan also has a 50% off coupon. Will the shoes be free with coupon? If not, how much will they cost?
Answer:
20$
Step-by-step explanation:
since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer
x(z ÷ 3)^2 where x = 4 and z = 9 calculate
Answer: 36
Step-by-step explanation:
4(9/3)(2) = 36
Answer:
x(z ÷ 3)² = 36
Step-by-step explanation:
Given expression,
→ x(z ÷ 3)²
Now we have to use,
→ x = 4
→ z = 9
Let's simplify the expression,
→ x(z ÷ 3)²
→ 4(9 ÷ 3)²
→ 4 × (3)²
→ 4 × 9
→ 36 => {answer}
Therefore, the answer is 36.
The "Good Ole Times" magazine charges for classified ads by the "column inch". A "column inch" is as wide as one column, and it is one inch high. The cost is $43. 50 per column inch. How much would the magazine charge to print a 1¾ inch ad?
The magazine would cost $33.93 to print a 1¾ inch ad in the "Good Ole Times" magazine.
The cost of a classified ad in the "Good Ole Times" magazine is determined by its size in column inches, with a cost of $43.50 per column inch. To determine how much the magazine would charge to print a 1¾ inch ad, we need to calculate the size of ad in column inches and then multiply that by the cost per column inch.
One way to convert 1¾ inches to column inches is to convert the fractional part (¾) to a decimal by dividing it by 4, which is the number of quarters in an inch. This gives us:
1¾ inches = 1 + ¾ inches = 1 + 0.75 inches = 1.75 inches
To express this measurement in column inches, we divide by the width of a column, which is not given in the problem. Assuming a typical newspaper column width of 2.25 inches, we get:
1.75 inches ÷ 2.25 inches per column = 0.7778 column inches
Rounding this to two decimal places, we get:
0.78 column inches
Now we can calculate the cost of the ad as follows:
Cost = Size in column inches × Cost per column inch
Cost = 0.78 column inches × $43.50 per column inch
Cost = $33.93
Therefore, the magazine would charge $33.93 to print a 1¾ inch ad.
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