A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2) are the coordinates of the image after dilation.
Given,
Triangle ABC is dilated with a scale factor 2 at the origin.
We have to find the coordinates of the image;
Dilation;
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Here,
The vertices of the triangle; A(1, 1), B(1.5, 3), C(2, 1).
After the dilation of a scale factor 2, the new point;
A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).
That is,
The coordinates of the image after dilation is, A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).
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Triangle a is reflected in the x-axis to give b which is the reflected in the line y=x.
Triangle a is reflected in the x-axis to give b which is reflected in the line y=x. The coordinates of triangle C are (-5,4) , (-2,2) and (-2,4)
Coordinates for Triangle A are (4,5), (2,2), and (4,2)
Triangle B is created by reflecting triangle A along the x-axis.
The x-axis coordinates stay the same after reflection in the x-axis, while the y-axis coordinates go negative with the same magnitude.
Consequently, triangle B's coordinates are (4, -5), (2, -2), and (4,-2)
The x and y coordinates of triangle B are now reversed as it is reflected by the line y = x to create triangle C.
Triangle C's coordinates are (-5,4), (-2,2), and (-2,4)
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Jacqui has 162 trading cards. She buys 25 more trading cards. Then, she puts her trading cards into a binder. Each page of the binder holds 9 cards. After filling as many pages as she can, Jacqui gives the rest of the trading cards to her brother.
Answer: She can fill up 21 packs or sets of 9
Step-by-step explanation: She has 162 then she adds 25 so that's 197 cards then we do 9 times 21 which is 189. So she has 8 left over to give to her brother.
Help! I am struggling
Answer:
34
Step-by-step explanation:
First you arrange the data in an ascending order and the median is the middle value. if the number of values is an even number, then the median will be the average of the two middle numbers. In this case, the median is 34.
A baker is making cookies. The recipe calls for 1/2 cups of flour and 2 1/4 cups of sugar. How much flour does the baker need if he used 1 cup of sugar?
2/9 cups of flour is required for baker if he use 1 cup of sugar.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that the baker is making cookies.
The recipe calls for 1/2 cups of flour and [tex]2\frac{1}{4}[/tex] cups of sugar.
We need to find the flour required to baker for 1 cup of sugar.
Let us form a proportional equation.
x be the flour required for 1 cup of sugar.
[tex]2\frac{1}{4}[/tex] /1/2=1/x
Apply cross multiplication
9/4x=1/2
Divide both sides by 9/4
x=1/2×4/9
x=2/9
Hence, 2/9 cups of flour is required for baker if he use 1 cup of sugar.
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there is a line that includes the point ( 0, 10 ) and has a slope of 10. what is its equation in slope-intercept form?
Answer:
y=10x+10
Step-by-step explanation:
Remember, y=mx+b, where m is the slope and b is the y-intercept.
In this case, the slope, or m, is 10 and the y-intercept, or b, is 10. We then substitute m=10 and b=10 in and get the equation y=10x+10.
If 3x + 7 = 20, what is 3x + 10?
Answer:
22.9
Step-by-step explanation:
22.9
3x+7=20
-7 -7
3x=13
/3 /3
x= 4.3
3(4.3)+10
12.9+10
22.9
(i think you put something in wrong. the answer usually shouldnt have a decimal)
help pleaseeeeeeeeeeeee
By using the slope intercept form of equation of line, it can be calculated that-
a) Equation of the graph
[tex]y = -\frac{5}{3}x +10[/tex]
b) Slope = [tex]-\frac{5}{3}[/tex]
It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream
c) y - intercept is 10.
It means Katie started eating with 10 ounces of ice cream
d) When y = 0, x = 6
It means Katie finished eating the ice cream in 6 minutes.
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
a) From the figure, it is clear that the graph passes through (6, 0) and (0, 10)
Slope = [tex]-\frac{10}{6}[/tex]
Slope = [tex]-\frac{5}{3}[/tex]
Equation of the graph
[tex]y - 0 = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}x +10[/tex]
b) Slope = [tex]-\frac{5}{3}[/tex]
It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream
c) y - intercept is 10.
It means Katie started eating with 10 ounces of ice cream
d) When y = 0, x = 6
It means Katie finished eating the ice cream in 6 minutes.
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What happens to a figure when you dilate by a scale factor less than 1 but greater than 0?
When you dilate the figure by a scale factor less than 1 but greater than 0, then the size of the figure decreases
The dilation is the one form of the transformation of the figure, the change the size of the figure
The scale factor is the ratio between the original size of the figure and the new size of the figure.
When the dilate the figure by a scale factor greater than one then the size of the figure increases, but when the scale factor is between 0 and 1 then the size of the figure decreases
Therefore, the size of the figure decreases after dilation
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Use the rise and the run from point C to point D to find the slope of the line.
What is the slope equal to?
Enter your answer as a fraction in the lowest terms, formatted like this: 42/53
Answer:
slope = -5/8
Step-by-step explanation:
Use the rise and the run from point C to point D to find the slope of the line.
C is at (7 , -2)
D is at (15 , -7)
slope = change in y / change in x
slope = (-2 - (-7)) / (7 - 15)
slope = (-2 + 7) / -8
slope = 5/-8
slope = -5/8
What is perimeter of a figure class 6?
The length of the boundary of any closed figure is called its perimeter.
Perimeter is calculated only of 2-dimensional shape, or a 1-dimensional length. This means that shapes like cubes, cones, and cylinders don't have a perimeter.
The perimeter of any shape is calculated by adding up the length of all its sides. A side is referred to as any continuous uninterrupted length of the shape between two points.
A point to be noted is that the perimeter of a circle is calculated by its radius and a mathematical number called pi. This is denoted by π. All other curved sides are calculated in a similar manner as well.
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Please help pleasee 40 points
which inequality do I pick for the word problem
The height to ride the roller coaster mist be at least 3 feet but no more than 6 feet
tall
A)x< 3 or x > 6
B) 3 < x < 6
C) 3 <= x <= 6
D) x <= 3 or x => 6
the <= means greater than or equal too
please help, answers only!!
The linear function in slope intercept form is y = -3x + 6
What is a linear function?A linear function is a function represented by a straight line.
What is slope intercept form?Slope intercept form of a linear function is y = mx + c where
m= slope and c = y-interceptHow to write the linear function in slope-intercept form?To write the linear function in slope intercept form, we need to know its slope, which is given by
m = (y₂ - y₁)/x₂ - x₁) where
y₁ = f(2) = 0, y₂ = f(4) = -6, x₁ = 2 and x₂ = 4Substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/x₂ - x₁)
m = (-6 - 0)/4 - 2)
m = -6/2
m = -3
Next we find the equation of the linear function in slope-point form which is
m = (y - y₁)/x - x₁) where
m = -3y₁ = f(2) = 0 and x₁ = 2Substituting the the values of the variables into the equation, we have
m = (y - y₁)/x - x₁)
-3 = (y - 0)/x - 2)
-3 = y/(x - 2)
-3(x - 2) = y
-3x + 6 = y
y = -3x + 6 which is the slope-intercept form
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What is the 1st square number answer?
The 1st square number answer is one.
A square number is an integer that is the square of another integer. It is also referred to as a perfect square. It is the result of multiplying the number by itself. The square number is an integer with the form n×n or n², where n is any positive integer.
The square number can only end with 0, 1, 4, 6, 9, or 25. The first ten square numbers are
1×1 = 1,
2×2 = 4,
3×3 = 9,
4×4 = 16,
5×5 = 25,
6×6 = 36,
7×7 = 49,
8×8 = 64,
9×9 = 81,
10×10 = 100.
The first square number from the above sequence is 1. Then, the answer is 1.
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help please, which graph is it
Answer:
it is the linear graph
hope it helps
For positive acute angles A and B, it is known that sin A = 21/29 and tan B = 24/7
Find the value of cos(A - B) in simplest form.
The value of cos(A - B) in simplest form is 651/203.
What is acute angles?An acute angle is an angle that is less than 90 degrees, or less than a right angle. Acute angles are typically found in everyday life, such as the shape of a slice of pizza or the corner of a triangle. Acute angles are also found in shapes such as pentagons, hexagons, and octagons. Acute angles are important for engineering, architecture, and construction, as angles that are too wide or too small can affect the structural integrity of a building or other structure. Acute angles are also important in geometry, as they can be used to solve for the area, perimeter, and interior angles of a given shape.
We can use the formula for cos(A - B):
cos(A - B) = cos A cos B + sin A sin B
cos(A - B) = (21/29) * (24/7) + (21/29) * (7/24)
cos(A - B) = (504 + 147)/29 * 7
cos(A - B) = (651/203)
Therefore, the value of cos(A - B) in simplest form is 651/203.
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c. The discount price of a l
a hat is $38. What is the regular price? Today, everything at the store is on sale. The store offers a 20% discount.
Answer:
the hat is $47.50.
Step-by-step explanation:
To determine the regular price of the hat, you can use the formula for calculating the sale price of an item, which is:
regular price * (1 - discount percentage) = sale price
In this case, we can set up the equation as follows:
regular price * (1 - 0.20) = $38
Solving for the regular price, we get:
regular price = $38 / (1 - 0.20)
regular price = $38 / 0.80
regular price = $47.50
Therefore, the regular price of the hat is $47.50.
1. An amusement park charges a $10 entry fee and $2.50 a ride.
determine the slope and y-intercept of line that represents the linear relationship
Answer:
Slope: 2.5, Y-Intercept: 10
Step-by-step explanation:
We can set up an equation, with
y = 2.5x + 10
The slope is 2.5, and the y-intercept is 10.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67. 8 with a standard deviation of 11. 5. The standard error of the mean for a sample of 70 students is , and the margin of error of the mean is. (round off your answers to the nearest hundredth. ).
Standard error of the mean is 1.375 and margin of error of the mean is 2.694.
Based on the provided information, mean µ = 67.8 and standard deviation σ = 11.5. The sample size n = 70
The standard error (SE) of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation.
Standard error (SE) is given by:
SE = σ/√n = 11.5/√70 = 1.375
The margin of error (MOE) refers to a statistic demonstrating the amount of random sampling error in the results of a survey.
Margin of error (MOE) is the standard error multiplied by a Z value that correspondence to a confidence percentage. Assuming a 95% confidence the Z value is 1.96. Hence,
MOE = z * σ/√n = 1.96 x 1.374 = 2.694
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(2x² + 15x+20) ÷ (x+5)
Answer:
To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.
Here's how the long division would look:
2x² + 15x + 20
===
x + 5
2x
_______
15x - 10x
15x + 20 - 10x - 20
___________
5x - 20
After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:
(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)
Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.
You please help me with the second part i need it to pass this by friday
The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week
What is inequality ?A relationship between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.
According to the given information
Let x be the more items that Julie will sell after First week
Number of items soled in First week = 6
So
The inequality formed will be
x + 6 > 20
Solving the inequality is
x > 20 - 6
x > 14
So
The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week
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What is the result when the number 20 is increased by 20%?
Answer:
When the number 20 is increased by 20%, the result is 24. To find this, first multiply 20 by 20%, which is 0.20. Then, add this result to the original number 20 to find the final result, which is 20 + 0.20 = 24.
Step-by-step explanation:
A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $4000 when sold. A ranch style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.6 million of capital on hand, how many houses of each type should she build for maximum profit? Will any of the lots be vacant?
Morvinia raised $15 each Kilometer she walked while participating in walkathon. Her goal is to raise a maximum of $800 on Saturday and Sunday. On Sunday, she raised $375. What is the least number of kilometers Morvinia has to walk on Sunday to reach her goal?
Answer:B
Step-by-step explanation:hope this will solve your problem
Answer:B
Step-by-step explanation:
→Will give 80 points and brainliest!!←
Please don't give a link, and give the full answer, not just half.
Thank you!
A; The distance between the starting point to Obstacle 2 is 13 meters
B; There are 10 meters around one lap of course.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
Part A;
Starting point: (-12, 5); Obstacle 2: (0, 0)
(x₁, y₁) and (x₂, y₂)
Therefore,
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(0 - (-12))² + (0 - 5)²
d = √(12)² + (- 5)²
d = √144 + 25
d = √169
d = 13 meters
B. Starting point: (-12, 5); Obstacle 2: (0, 0);
Obstacle 1: (-12, 0)
(Starting Point + Obstacle 2)
Now,
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(0 - (-12))² + (0 - 5)²
d = √(12)² + (- 5)²
d = √144 + 25
d = √169
d = 13 meters
Therefore, (Starting Point + Obstacle 1)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-12 - (-12))² + (0 - 5)²
d = √(0)² + (-5)²
d = √25
d = 5 meters
(Obstacle 2 + Obstacle 1)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-12 - 0)² + (0 - 0)²
d = √(-12)² + (0)²
d = √144
d = 12 meters
Total = 12m + 5m + 13m = 30
30 ÷ 3 = 10 meters
we can conclude that 10 meters around one lap of course.
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Answer now with steps and I will give Brainliest! Use picture below.
Answer:
Step-by-step explanation: Here is your answer 97
in a scientific research, a statistical test resulted in a -value of 0.026. match each value with the correct decision. (a) do not reject h0 (b) reject h0 group of answer choices significance level equals 0.01 (a) significance level equals 0.05
Any p-value less than 0.05 is a cause to reject the null hypothesis.
What is Null Hypothesis?
The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.
Explanation:
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).
Any p-value less than 0.05 is a cause to reject the null hypothesis.
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In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn. What type of variable is fff?.
fff is a random variable in a game of luck
A random variable is a formula that gives each result in a sample space a numerical value.
There are two types of random variables: discrete and continuous. If a random variable only takes specified values inside an interval, it is said to be discrete. It is continuous if not.
We typically use capital letters, such X and Y, to designate the random variables
A random variable must be measured in order to be able to assign probabilities to a set of potential values. It is evident that the outcomes depend on a number of unpredictable physical elements.
According to the question,
In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn.
Here, fff is a Random variable.
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During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Amos's free-throw shooting percentage is lower and is only 52.5%. After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points Amos makes when he shoots two free-throw shots.
I’m not entirely sure but i believe it’s 1.05
7. Brad is planning a garage sale. To direct customers to his house, he is painting six
arrow signs.
a) Calculate the area of one sign.
b) Each can of paint can cover 1 m².
How many cans of paint
should Brad buy for all six signs. Explain your answer.
The solution is
a) The area of the sign is 3950 cm²
b) The total number of cans of paint is 3 cans of paint
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the total area of the sign be = S
Now , the area of the triangle be = T
Let the area of the rectangle be = R
The height of the triangle = 50 cm
The base of the triangle = 50 cm
So , the area of the triangle = ( 1 / 2 ) Height x Base
Area of Triangle T = ( 1/2 ) x 50 x 50
Area of Triangle T = 1250 cm²
Length of the rectangle = 90 cm
Width of the rectangle = 30 cm
Now , the area of rectangle R = Length x Width
Area of the rectangle R = 90 x 30
Area of the rectangle R = 2700 cm²
And , the area of the sign = Area of the rectangle R + Area of Triangle T
Substituting the values in the equation , we get
Area of the sign = 2700 cm² + 1250 cm²
Area of the sign = 3950 cm²
b)
Each can of paint covers = 1m²
So , Each can of paint covers = 10000 cm²
The number of signs = 6 signs
So , the total area of 6 signs = 6 x Area of the sign
The total area of 6 signs = 6 x 3950
The total area of 6 signs = 23700 cm²
And , the number of cans of paint for 6 signs = The total area of 6 signs / Area covered by each can
Substituting the values in the equation , we get
The number of cans of paint for 6 signs = 23700 / 10000
The number of cans of paint for 6 signs = 2.37 cans
The number of cans of paint for 6 signs ≈ 3 cans
Hence ,
a) The area of the sign is 3950 cm²
b) The total number of cans of paint is 3 cans of paint
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Find the equation of the least squares regression line. State the value of the slope of the regression line rounded to the nearest hundredth
y=10x+235 is the equation of the least squares regression line.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find the equation of the least squares regression line.
The value of the slope of the regression line can be find by using any two points from the table.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
(58, 335) and (70, 450)
Slope of line = 450-335/70-58
=115/12
=10
The equation of line is y=10x+b
335=10(10)+b
335=100+b
335-100=b
235=b
Hence, the equation of the least squares regression line is y=10x+235.
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