What is the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin?
The image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).
What is the image of the point?To rotate a point counterclockwise about the origin, we can use the following formulas:
(x', y') = (y,-x)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point
In this case, we want to rotate the point (-1, 2) by 270° counterclockwise about the origin.
So, we have
(x', y') = (2,1)
Therefore, the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).
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Which phrase can be represented by the expression 25.75x + 10?
The phrase represents that the expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.
Which phrase represents the expressionThe expression 25.75x + 10 represents a phrase that involves a numerical value that is dependent on a variable x.
We can think of this expression as a linear function, where x is the independent variable and 25.75x is the dependent variable that is multiplied by a coefficient of 25.75.
The constant term of 10 represents a fixed value that is added to the result of the multiplication.
One possible phrase that can be represented by this expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.
The variable x in this case would represent the number of units of the product being purchased.
Multiplying the price per unit by the number of units purchased (25.75x) gives us the variable component of the cost, and adding the fixed cost of $10 to this gives us the total cost of the purchase.
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Express the ratio below in its simplest form.
4.5: 3 1/2
Answer:
9 : 7
Step-by-step explanation:
4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7
Utilizando los siguientes datos: 9, 9, 14, 7, 12, 8, 11, 19, 15, 11, se pueden calcular las siguientes medidas estadísticas:
Media: 11
Mediana: 11
Rango: 12
Moda: 11 (aparece dos veces, junto con el número 9)
Rango intercuartil (IQR): 6
Mínimo y máximo: 7 y 19, respectivamente.
using the same data as above, make the following data displays.
Box plot:
Line plot:
Answer: Box plot: | o
19 |
18 |
17 |
16 |
15 | o
14 | o
13 |
12 | o o
11 | o o o
10 |
9 | o o
8 | o
7 | o
|___________
Line plot: 19|
18|
17|
16|
15| o
14| o
13|
12| o o
11|o o o
10|
9|o o
8| o
7|o
|___________
1 2 3 4 5 6 7 8 9 10 (data index)
Step-by-step explanation:
5) A rectangle has an area of 30x2y. The length of one of its sides is 6xy. What is its width?
The width of the rectangle is 5.
What is area of rectangle?The area of a rectangle is given by the formula:
Area = Length x Width
where Length and Width are the measurements of the two adjacent sides of the rectangle.
For example, if a rectangle has a length of 6 units and a width of 4 units, then its area would be:
Area = Length x Width
Let's start by using the formula for the area of a rectangle:
Area = Length x Width
We are given that the area of the rectangle is 30xF²y and that one of its sides (length) is 6xy. Substituting these values into the formula, we get:
30x²y = (6xy) x Width
Simplifying the right-hand side by multiplying 6xy by Width, we get:
30x²y = 6x²y x Width
Dividing both sides by 6x²y, we get:
Width = 30x²y / 6x²y
Simplifying the right-hand side by canceling out the common factors of 6, x², and y, we get:
Width = 5
Therefore, the width of the rectangle is 5.
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HELP!!!!!!!!!!!!!!!!!
What did I do wrong on 6,7, and 8??
Once there is an answer… Please no one else answer!
The transformation in words for picture 6 is a rotation of 90° counterclockwise or 90° counterclockwise rotation.
The algebraic rule for the above transformation is (x, y) → (-y, x).
The transformation in words for picture 7 is a reflection across the line x = -3.
The algebraic rule for the above transformation is [tex]Ref_{x=-3} \triangle ABC[/tex].
The transformation in words for picture 8 is a reflection across the x-axis.
The algebraic rule for the above transformation is (x, y) → (x, -y).
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of quadrilateral RSTUVW, the coordinates of W of the image is as follows:
(x, y) → (-y, x)
Ordered pair W = (-1, 3) → Ordered pair R' = (-(3), -1) = (-3, -1).
What is a reflection?In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). Therefore, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
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Enter the correct answer in the box.
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of What is the equation of function g?
Substitute a numerical value for k into the function equation.
Answer:
The equation of function g after horizontal compression by a factor of 3 is:
g(x) = 7(3x) + 1 = 21x + 1
To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.
Step-by-step explanation:
When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.
The equation for the horizontally compressed function is:
g(x) = f(x/k)
Substituting f(x) = 7x + 1, we get:
g(x) = 7(x/k) + 1
Simplifying, we get:
g(x) = (7/k)x + 1
Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.
For example, if the compression factor is 3, then:
g(x) = (7/3)x + 1
And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:
g(x) = (7/2)x + 1
In a microscope, the image of a 0.25-millimeter paramecium appears to be 12 millimeters long. What is the scale factor of the dilation?
The scale factor of the dilation is 48.
The scale factor is a mathematical concept that describes the ratio of the lengths, areas, or volumes of two similar geometric figures. Similar figures have the same shape but may have different sizes.
When one figure is a dilation (a type of transformation that changes the size of a figure without changing its shape) of another figure, the scale factor is the ratio of the corresponding side lengths or dimensions of the two figures.
The scale factor of the dilation is the ratio of the length of the image to the length of the original object. In this case, the length of the image is 12 millimeters and the length of the original object is 0.25 millimeters. Therefore, the scale factor is:
scale factor = length of image/length of the original object
scale factor = 12 mm / 0.25 mm
scale factor = 48
So the scale factor of the dilation is 48.
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I need help with this question!!!
Answer:
A. m∠X = 50°, AC = 3 cm
Step-by-step explanation:
If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:
∠A = ∠X
∠B = ∠Y
∠C = ∠Z
and
AB = XY
BC = YZ
AC = XZ
Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°
And because we know XZ is equal to 3 cm and XZ and AC are congruent then AC is also 3 cm
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer:
A
Step-by-step explanation:
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
show work please
Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
What is the percentage?A% is a mathematical figure or ratio that denotes a percentage of 100.
Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.
The symbol "%" is generally written after the integer to denote percentages.
A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.
So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:
= 460/100 * 20
= 4.60 * 20
= 92 grams
Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.
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____ are characteristics of samples, whereas ______ are characteristic of populations.
AConcepts; statistics
BParameters; statistics
CStatistics; parameters
DParameters; estimations
Find the sum or difference.
1. -80+77 =
2. 77 + 160 =
3. -64+ (-33) =
4. 104-(-92) =
5. -105-(-122) =
6. 185-(-154) =
7. -53-(-59) =
8. -6+ (-35) =
9. 15-(-26)-(-39) =
10. -93 +191+ (-179)
Find the product or quotient.
11. 60+ 12 =
12. -194+ (-2)=
13. 88 (-2) =
14. -12 10 =
15. -10 (-11) =
16. 90+ (-6)=
17. 3 (-59) =
18. -7 (-2) =
19. 100 (0) =
20.100/0=
After answering the presented question, we may conclude that the solution of the expressions are as follows.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
the solution of the expressions are as follows -
-3237-97196173396-4152-8172-196-176-12011084-177140undefined (division by zero is undefined)To know more about expressions visit :-
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I need help with this question
(4x+3)5=2x/6
please i need your help for today please i would really appreciate it help
The area of circle is represented by quadratic expression A = π · x², for a radius x = 5 units, the area of circle equals 25π square units.
How much is the area of a circle?
In this question we need to derive the area formula for a circle as a function of radius and compute the value of the figure for a given radius. According to geometry, the area of a circle (A), in square units, is described by following quadratic equation:
A = π · x²
Where x is the radius of the circle, in units.
If we know that x = 5, then the area of the circle is now computed:
A = π · 5²
A = 25π
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Is anyone good at “describe linear and nonlinear function” please help ASAP!
Answer:
A
If u plug it into desmos u get a straight line
Question 10
Find a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36.
a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
How to find the 5 degree polynomial?Let us begin by writing the polynomial factors using the supplied zeros:
Because -2 is a zero, the polynomial has a component of (x + 2).
Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).
Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).
Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.
When we add these components together, we get:
[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]
Extending on this, we get:
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
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The diameter of a circle is 22 m. Find its area to the nearest whole number.
Answer:
380
Step-by-step explanation:
The formula for the area of a circle is A = pi r^2
radius is half the diameter so you would do 11 (half of diameter) to the second power, which is 121. Now you would do 121 times pi, which would be 380.132711084. When rounded to the nearest whole, it is 380.
SORRY IF THIS DIDN'T MAKE SENSE!
Factor Special Polynomials:
Factor each of the following expressions, please
Answer:
2) [tex](3x+2)^{2}[/tex]
3) [tex](2x+5)(2x-5)[/tex]
4) [tex](x^{2} +8)(x^{2} -8)[/tex]
Step-by-step explanation:
A method I was taught was the snowflake method whenever there were numbers in front of [tex]x^{2}[/tex] (ex [tex]4x^{2} and 9x^{2}[/tex]) picture shown below (you can search up some videos if you would like)
The snowflake method is really efficient and helps factor polynomials faster
For 3 and 4, you basically have to find the square root of the number without the [tex]x^{2}[/tex] and make sure (for example 25) one parenthesis had -5 and the other had +5. Number 4 had [tex]x^{4}[/tex], [tex]x^{2}*x^{2}[/tex] is [tex]x^{4}[/tex] so you would include that in the equation. To double check, use foil.
i need help please also need the answer.
The correct answer as a trinomial in descending degree order is -2x^2 + 6x + 4
How to solve
Here's the step-by-step solution with the figures:
(5x^2 + 10x - 5) - (7x^2 + 4x - 9)
= 5x^2 + 10x - 5 - 7x^2 - 4x + 9 (distribute the negative sign)
= (5x^2 - 7x^2) + (10x - 4x) + ( -5 + 9) (collect like terms)
= -2x^2 + 6x + 4 (simplify and arrange in descending degree order)
Therefore, the simplified expression in descending degree order is -2x^2 + 6x + 4.
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What is the area of the regular pentagon?
Answer:300
Step-by-step explanation:
We can find the answer the simple way.
There are 10 triangles in a regular pentagon
We used pythagorean theorm to find side b, 12
12*5*0.5 is 30
30*10 is 300
find the values of variables, then find the lengths of the sides of each quadrilateral
Help me on number 4. 14 points
Answer:[tex]18\frac{3}{8}[/tex] yards
Step-by-step explanation:
Formula:
Base x Height ---> [tex]3\frac{1}{2}[/tex] x [tex]5\frac{1}{4}[/tex] = [tex]18\frac{3}{8}[/tex]
-2
-3
1
Attempt: 1 of
Initial
height
5
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=6+44t-16r²
Find all values of t for which the ball's height is 26 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
ground
IH
seconds
DD
X
S
The values of t for which the height of the ball is of 26 feet are given as follows:
t = 0.57 s and t = 2.18 s.
How to model the situation?The quadratic function that models the height of the ball after t seconds is given as follows:
h(t) = -16t² + 44t + 6.
The height of the ball is of 26 feet when:
h(t) = 26
Hence:
-16t² + 44t + 6 = 26
16t² - 44t + 20 = 0.
The coefficients are given as follows:
a = 16, b = -44, c = 20.
Using a quadratic function calculator, the solutions to the quadratic equation are given as follows:
t = 0.57 s and t = 2.18 s.
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Mark to split a 50 pound bag of dog food between a seven dogs how many pounds of food should each dog get
Answer: 7 [tex]\frac{1}{7}[/tex] lbs
Step-by-step explanation:
We will divide the 50 lbs bag by 7, to represent te 7 dogs.
50 lbs food / 7 dogs = 7 [tex]\frac{1}{7}[/tex] lbs
Consider the following equation. 5x+3y=8 Step 1 of 2 : Determine the missing coordinate in the ordered pair (3,?) so that it will satisfy the given equation.
Answer: (3, -2.333) or (3, -7/3)
Step-by-step explanation:
We're given an x value (x=3) when looking at the coordinate, so we're trying to find what y is equal to given the equation. We can plug in x=3 into 5x+3y=8 and isolate for y.
[tex]5(3)+3y=8\\15 + 3y=8\\3y=-7\\y=-\frac{7}{3}[/tex]
Answer:
y= -2 1/3
Step-by-step explanation:
Since you have x, you put x into the equation and work through the problem.
5(3)+3y=8
15+3y=8, then subtract 15 from both sides
3y=(-7), then divide both sides by 3
y=(-7)/3 or (-2 1/3)
10 workers can create 20 products in 40days. all workers are equally productive. A company has only 5 workers.
how many days will it take to create all 20 products?
The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days
What is the work rate of 1 worker?Work rate is the rate at which a specified work is completed.
The number of days it will take 10 workers to create 20 products = 40 days
Therefore;
The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days
Where 1 worker can create 20 products in 400 days, then;
The work rate for one worker indicates;
The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5
5 workers will take = 400 days ÷ 5 = 80 days
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Anumeha knows the following information about a set of
20
2020 numbers:
9
99 numbers are a multiple of
3
33 but not a multiple of
4
44.
10
1010 numbers in total are a multiple of
3
33.
10
1010 numbers in total are a multiple of
4
44.
Can you help Anumeha organize the results into a two-way frequency table?
A
Step-by-step explanation:
There is 1 number that is a multiple of both 3 and 4.
9 numbers are a multiple of 4 and not 3.
9 numbers are a multiple of 3 and not 4.
1 number is not a multiple of 3 or 4.
Hope this helps!
Adriel just got hired for a new job and will make $65,000 in his first year. Adriel was told that he can expect to get raises of $5,000 every year going forward. How much money in salary would Adriel make in his 29th year working at this job?
Using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.
What are mathematical operations?The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.
The steps that we can memorize using PEMDAS include parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right), and so on.
So, we know that:
Adriel will earn $65,000 this year.
She will get a raise of $5,000 each year.
Then, her salary after 29 years would be:
= (5000 * 29) + 65,000
= 1,45,000 + 65,000
= $2,10,000
Therefore, using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.
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A cafe sells small, medium and large mugs of coffee. A small mug has a capacity of 100 ml. A medium mug has double the capacity of a small mug. A large mug has double the capacity of a medium mug. Work out the capacity, in litres, of a large mug.
Answer:
Answer:
12 ounces
Step-by-step explanation:
Let x = Small Mug
& y = Large Mug
Then we write the given statement in an equation form as below:
2x + 1y = 20 ounces of coffee ---------------> EQUATION 1
3y - 1x = 32 ounces of coffee ----------------> EQUATION 2
Let us solve the above equation for y;
Multiply Equation 2 by '2', we get;
-2x + 6y = 64 ----------------------> Equation 3
Add Equation 1 and Equation 3, we get;
(2x + y) + (-2x + 6y) = 64 + 20
7y = 84
Divide the above equation by 7, we get;
y = 84 / 7
or, y = 12
Hence, One Large mug can hold 12 ounces of coffee.
Step-by-step explanation: