Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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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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x+y=12 and2x+5y=36 what are the values of x and y
The values of x and y that satisfy the system of equations are x = 8 and y = 4.
What are the values of x and yTo solve for the values of x and y in the system of equations:
x + y = 12
2x + 5y = 36
We can use the method of substitution. Solving the first equation for x, we get:
x = 12 - y
We can substitute this expression for x into the second equation and solve for y:
2(12 - y) + 5y = 36
24 - 2y + 5y = 36
3y = 12
y = 4
Now that we know y is 4, we can substitute this value back into the first equation and solve for x:
x + 4 = 12
x = 8
Therefore, the values of x and y that satisfy the system of equations are x = 8 and y = 4.
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Factor the following polynomial. 98x^3 - 18x
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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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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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)
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!
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer:
A
Step-by-step explanation:
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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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
Find the length of ST.
The length of ST is 24.
Describe Tangents?In geometry, a tangent is a line that touches a curve at a single point, without crossing over the curve at that point. This point of contact is called the point of tangency.
For example, in a circle, a tangent is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at the point of tangency.
Tangents are important in geometry because they allow us to find the slope of a curve at a specific point. The slope of the tangent line at a point on a curve is equal to the derivative of the function representing the curve at that point.
To find the length of ST, we need to find the length of SR and add it to the length of RT.
Using the tangent-tangent theorem, we know that RP is perpendicular to RT at point R. Therefore, angle RPT is a right angle.
We can use the Pythagorean theorem to find the length of RT. Let's call the length of RP "a" and the length of PT "b". Then, we have:
a² = (x+6)² + b² (from right triangle PQR)
a² = (2x-9)² + (b+3)² (from right triangle PSR)
Setting these two equations equal to each other, we have:
(x+6)² + b² = (2x-9)² + (b+3)²
Expanding and simplifying, we get:
x² - 24x + 90 = 0
Solving for x using the quadratic formula, we get:
x = (24 ± √(24² - 4190)) / (2*1) = 15 or 6
Since x cannot be negative, we take x = 15.
Now we can use the Pythagorean theorem to find the length of SR:
a² = (2x-9)² + (b+3)²
a² = (2*15-9)² + (b+3)²
a² = 276 + (b+3)²
We also know that SR = 3, so:
3² = (b+3)²
9 = b² + 6b + 9
b² + 6b - 0 = 0
Solving for b using the quadratic formula, we get:
b = (-6 ± √(6² - 410)) / (2*1) = -3 or 0
Since b cannot be negative, we take b = 0.
Therefore, we have:
a² = (x+6)² + b²
a² = (15+6)² + 0²
a² = 441
So, RT = a = √(441) = 21.
Finally, we have:
ST = SR + RT = 3 + 21 = 24.
Therefore, the length of ST is 24.
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find the values of variables, then find the lengths of the sides of each quadrilateral
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x² /2x +6 divided by 3x -5/ x+3
Answer:
(7x² / 6x - 10)
Step-by-step explanation:
To divide rational expressions, we flip the second fraction (the divisor) and multiply it with the first fraction (the dividend). Then we simplify the resulting expression, if possible.
So,
(7x² /2x +6) ÷ (3x -5/ x+3)
= (7x² /2x +6) * (x+3/3x -5)
= 7x²(x+3) / 2(x+3)(3x -5)
= 7x² / 6x - 10
Therefore, the quotient of the given rational expressions is (7x² / 6x - 10), which cannot be further reduced.
Answer:
2
7x
3
+18x+3−
x
5
Short Solution Steps
7x
2
/2x+63x−5/x+3
Express
2
7x
2
x as a single fraction.
2
7x
2
x
+6×3x−
x
5
+3
Multiply 6 and 3 to get 18.
2
7x
2
x
+18x−
x
5
+3
To add or subtract expressions, expand them to make their denominators the same. Multiply 18x+3 times
2
2
.
2
7x
2
x
+
2
2(18x+3)
−
x
5
Since
2
7x
2
x
and
2
2(18x+3)
have the same denominator, add them by adding their numerators.
2
7x
2
x+2(18x+3)
−
x
5
Do the multiplications in 7x
2
x+2(18x+3).
2
7x
3
+36x+6
−
x
5
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply
2
7x
3
+36x+6
times
x
x
. Multiply
x
5
times
2
2
.
2x
(7x
3
+36x+6)x
−
2x
5×2
Since
2x
(7x
3
+36x+6)x
and
2x
5×2
have the same denominator, subtract them by subtracting their numerators.
2x
(7x
3
+36x+6)x−5×2
Do the multiplications in (7x
3
+36x+6)x−5×2.
2x
7x
4
+36x
2
+6x−10
Step-by-step explanation:
PLEASE GIVE ME BRAINLIEST I AM LOOKING FOR A FRIEND
____ are characteristics of samples, whereas ______ are characteristic of populations.
AConcepts; statistics
BParameters; statistics
CStatistics; parameters
DParameters; estimations
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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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
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!
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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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:
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]
find the surface area of the figure
The surface area of the square pyramid is 416.23 ft²
How to find the surface area of a square pyramid?
The surface area of a square pyramid is given by the formula:
A = a² + 2a√(a²/4 + h²)
Where a is the base length of the square pyramid and h is the height of the square pyramid.
From the figure, we have: a = 10 ft and h = 15 ft
A = a² + 2a√(a²/4 + h²)
A = 10² + 2*10√(10²/4 + 15²)
A = 100 + 20√(100/4 + 225)
A= 100 + 20√250
A = 416.23 ft²
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shayla is buying a birthday present for her mother. she decides to buy a bracelel for 20$. the sales tax is 6%. what is the total cost of the bracelet.
The total cost of the bracelet after tax cost addition would be = $21.2
How to calculate the total cost of bracelet?The initial cost of the bracelet = 20$
The percentage of tax = 6%
The cost of tax = 6/100 ×20/1 = $1.2
The total cost of the bracelet after the addition of tax would be = 20+1.2 = $21.2
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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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When making bread from scratch, the recipe calls for 3/4 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/9th of the recipe?
Answer:0.67
Step-by-step explanation:
Given vectors u = ⟨3, 4⟩ and v = ⟨4, 3⟩, what is the measure of the angle between the vectors?
The measure of the angle between the vectors is approximately 41.41 degrees.
Define Angle and its properties ?When we join two line segments at a single point, an angle is formed, or we can say, an Angle is a combination of two line segments at a common endpoint. This common point is called Vertex of the angle and the two line segments are sides or arms of the angle formed.The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
To find the angle between two vectors, we can use the dot product formula:
cos(theta) = (u · v) / (|u| |v|)
where u · v is the dot product of u and v, and |u| and |v| are the magnitudes of u and v, respectively.
First, let's calculate the dot product of u and v:
u · v = 3 × 4 + 4 × 3 = 24
Next, we need to calculate the magnitudes of u and v:
|u| = √(3² + 4²) = 5
|v| = √(4² + 3²) = 5
Now we can plug these values into the formula for cosine:
cos(theta) = (u · v) / (|u| |v|)
cos(theta) = 24 / (5 * 5)
cos(theta) = 24 / 25
To find the measure of the angle, we need to take the inverse cosine (or arccos) of this value:
theta = arccos(24/25)
theta ≈ 0.7227 radians or 41.41 degrees
So the measure of the angle between the vectors is approximately 41.41 degrees.
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you want to hire a band for a school dance. The live band charges $75 to play for three hours and each student will pay a $2.00 admission prices, p. a, how much money will you make if 100 students attend the dance
b, how much money will you make if 100 students attend the dance
c, how many students would need to attend the dance for you to “break even” after you aging the band?
Answer:
38 stduentstudents
Step-by-step explanation:
2(100)=$200, if 100 students attend.
38(2)=$76
Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.
What is the image of ( − 8 , 2 ) after a reflection over the line y=x?
Answer: The reflection of (-8,2) after a reflection over the line y=x is (2,-8)
Step-by-step explanation: The reflection on a graph refers to the preimage that has been reversed.
So, if we take an example of (x,y), over a reflection on the y-axis, then the answer would be (y,x)
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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.
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
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