Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A. (3 points)
Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised. (2 points)
Euler's formula, V − E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F, of a polyhedron. Solve Euler's formula for E.
To solve Euler's formula for the number of edges E, you rearrange the formula to E = V + F - 2. This solution requires the basic operations of adding and subtracting from both sides of the equation.
Euler's formula states that V (vertices) minus E (edges) plus F (faces) equals 2 for any polyhedron without holes. Therefore, to solve for E, we need to rearrange the equation as follows:
Starting with the original formula: V - E + F = 2.
Add E to both sides: V + F = E + 2.
Subtract 2 from both sides to solve for E: E = V + F - 2.
This rearranged formula gives us the number of edges E in terms of the number of vertices V and the number of faces F.
The formula for the number of edges (E) in terms of the number of vertices (V) and faces (F) is E = 2 + V - F.
To solve Euler's formula V − E + F = 2 for E, we need to isolate E on one side of the equation. Here's how we can do that:
Add E to both sides of the equation to move the term containing E to one side:
V − E + F + E = 2 + E
V + F = 2 + E
Subtract V and F from both sides:
V + F - V - F = 2 + E - V - F
0 = 2 + E - V - F
Rearrange the terms:
2 = E - V + F
Finally, isolate E by adding V and subtracting F from both sides:
E = 2 + V - F
Therefore, the formula for the number of edges (E) in terms of the number of vertices (V) and faces (F) is E = 2 + V - F.
Write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times. Then, write the product as one power.
The expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times is: [tex]X^{15} \times X^{10} = X^{25}[/tex]
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We need to write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times.
Then, also write the product as one power.
This is exponents so, a number used as a factor fifteen times is X^15.
Then we have to multiplied by a number used as a factor ten times is X^10.
Therefore, the final expression form as;
[tex]X^{15} \times X^{10} = X^{25}[/tex]
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Use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1. The vertex is the . The function is increasing . The function is decreasing . The domain of the function is . The range of the function is
The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf)
The key aspects of the function [tex]f(x) = - x^2 - 2x - 1[/tex] are as follows:
Vertex: The vertex of a quadratic function is the point where the function changes from increasing to decreasing, or vice versa. To find the vertex, we can complete the square or use the vertex formula. In this case, the vertex is (-1,0).
Range: The range of a function is the set of all possible output values. Since the leading coefficient in f(x) is negative, the parabola opens downwards, so the range is all numbers less than or equal to 0, or (-inf,0].
Increasing/Decreasing: A quadratic function is increasing to the left of its vertex and decreasing to the right of its vertex. Therefore, f(x) is increasing on (-inf,-1) and decreasing on (-1,inf).
Domain: The domain of a function is the set of all possible input values. For quadratic functions, the domain is all real numbers, so the domain of f(x) is all real numbers.
Therefore, The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf).
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math question down below
There are 240 students on Misty’s school. This is 5% of the total students in the school district. How many students are there in the school district?
To find the total number of students in the school district, set up a proportion using the given information. Cross multiply to solve for x.
Explanation:To find the total number of students in the school district, we can set up a proportion using the given information. If 240 students represent 5% of the total students, we can write the proportion as:
x/240 = 100/5
Cross multiplying, we get:
x = (240 * 100) / 5
Simplifying, we find:
x = 4800
Therefore, there are 4800 students in the school district.
To find the total number of students in the school district, divide the number of students at Misty's school (240) by the percentage they represent (5%), resulting in a total of 4800 students in the school district.
Explanation:If Misty's school has 240 students, which represents 5% of the total students in the school district, we can calculate the total number of students in the school district using percentages and equivalent fractions. We can set up an equation where 240 students is 5% of the total number of students (let's call this total x).
The equation is 240 = 0.05 * x. To find x, divide 240 by 0.05, which gives us x = 240 / 0.05. This calculation yields x = 4800. Therefore, there are 4800 students in the school district.
what are the three consecutive even integers that add up to 156
The ratio of girls to boys in Liza’s classroom is 5 to 4. How many girls are in her classroom if there is a total of 27 students?
I need help on 4, 5, and 6
Alice serote the prime factorization of 40 as 2x2x4x5. is she correct? if not what is the prime factorization of 40? explain
Answer:
2.2.2.5
Step-by-step explanation:
Manoj rappelled 30 ft down from the top of a canyon. He then rappelled an additional 10 ft down the canyon.
What must he do to return to the top of the canyon?
Answer:
To return to the top of the canyon he rappelled 40 ft above .
Step-by-step explanation:
Given : Manoj rappelled 30 ft down from the top of a canyon. He then rappelled an additional 10 ft down the canyon.
To find : What must he do to return to the top of the canyon.
Solution : We have given
Manoj rappelled down from the top of a canyon = 30 ft.
Again he rappelled an additional down the canyon = 10ft.
So, total distance he covered = 30 ft + 10 ft = 40 ft .
Now , He is 40 ft down from the top of the canyon .
To return to the top of the canyon he rappelled 40 ft above .
Therefore, To return to the top of the canyon he rappelled 40 ft above .
Find the coordinates of quadrilateral V' W' X' Y' after a dilation with the scale factor of 2. Original coordinates: V(6, 2), W(–2, 4), X(–3, –2), Y(3, –5), scale factor of 2
The new coordinates after a dilation with scale factor 2 are: V'(12, 4), W'(-4, 8), X'(-6, -4), Y' (6, -10). The new coordinates are calculated by multiplying both the x and y coordinates of the original points by the scale factor.
Explanation:Dilation is a transformation that alters the size of the figure without changing its shape. It's accomplished by multiplying the original coordinates of the vertices by a specified scale factor.
The original coordinates of quadrilateral VWXY are V(6, 2), W(–2, 4), X(–3, –2), and Y(3, –5). The scale factor given is 2. Let's find the coordinates of each point after dilation.
1. First, we'll start with point V. Its coordinates are (6,2). After dilation with a scale factor of 2, we multiply each coordinate by the scale factor. The new coordinates are (6 × 2, 2 × 2) which gives us (12, 4).
2. The coordinates of point W are (–2, 4). After dilation, we obtain the new coordinates as (–2 × 2, 4 × 2), which gives us (–4, 8).
3. Now we move onto point X. Its coordinates are (–3, –2). After dilation, the new coordinates become (–3 × 2, –2 × 2), which is (–6, –4).
4. Lastly, we have point Y. Its coordinates are (3, –5). After dilation, the new coordinates become (3 × 2, –5 × 2), which gives us (6, –10).
Therefore, the coordinates of the quadrilateral V'W'X'Y' after dilation with the scale factor of 2 are V'(12, 4), W'(–4, 8), X'(–6, –4), and Y'(6, –10).
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Find the product and explain the process and reasoning of $0.79*3.7
What is the equation in point slope form of the line that passes through the point (2,6) and has slope of 5?
A: y+2=5(x+6)
B: y-6=5(x-2)
The equation of the line that passes through the point (2,6) and has slope of 5 is Option B:
y - 6 = 5 ( x - 2 )
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
Given data ,
Let the point be P( x₁ , y₁ ) = P( 2 , 6 )
Slope m = 5
Now , the equation of line is given by the equation
y - y₁ = m ( x - x₁ )
Substituting the values of x₁ , y₁ and m in the equation , we get
y - 6 = 5 ( x - 2 )
Therefore , the equation of the line is y - 6 = 5 ( x -2 )
Hence , equation of the line that passes through the point (2,6) and has slope of 5 is y - 6 = 5 ( x - 2 )
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Jason uses the polynomial identity (x−y)^2=x^2−2xy+y^2 to show that 6² = 36.
what statement describes the relationship between ∆ XYZ and ∆ X'Y'Z'?
There is a special at the store: $34 for 7 roses. Harry is trying to figure out if it's a good deal. Help Harry figure out the unit price (round to 2 decimal places)
Which term correctly labels the blank in the graphic organizer above? A. square B. quadrilateral C. pentagon D. triangle
The term that correctly labels the blank in the graphic organizer depends on the specifics of the organizer itself. It could either be a square, quadrilateral, pentagon, or triangle.
Explanation:
Without seeing the graphic organizer, it is difficult to provide a specific answer. However, each option represents a different type of bidimensional figure in mathematics. A square is a specific type of quadrilateral with all sides equal and all angles being 90 degrees. A quadrilateral is a polygon with 4 sides, which can be of different lengths and angles. A pentagon is a polygon with 5 sides. A triangle is a polygon with 3 sides. Depending on what the graphic organizer is showing, any one of these could be the correct answer.
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Answer:B Quadrilateral
Step-by-step explanation:
Answer:B Quadrilateral
Step-by-step explanation:
Solve. 6(x+20)=168
A) x=4 2/3 B) x=8
C) x=24 2/3 D) x=28
team won 4/5 of games Lily scored points in 2/3 of the games won what fraction of her team's winning games did LILY score point?
PQ and RS are two lines that intersect at point T, as shown below:
Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent.
Which statement is used to prove that angle PTR is always equal to angle STQ?
a. Lines PQ and RS do not have a fixed length.
b. Angle PTR and angle PTS are supplementary angles.
c. Lines PQ and RS intersect at an angle less than a right angle.
d. Angle PTR and angle PTS are complementary angles.
The following question has two parts. First, answer part A. Then, answer part B.
Part A
A high school athlete ran the 100 meter sprint in 13.245 seconds. Round the time to the nearest tenth. Enter the answer in the box.
Part B
Explain how you arrived at the answer. Include any rules that you followed.
There are values of t so that sin t = 5/4. True or false.
Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether the following statement is TRUE of FALSE :
"There are values of t so that [tex]\sin t=\dfrac{5}{4}.[/tex]"
We know that the range of sine function is the close interval [-1, 1].
That is,
the value of sine of any angle cannot be less than -1 and greater than 1.
According to the given information, we have
[tex]\sin t=\dfrac{5}{4}=1.25>1.[/tex]
So, no such values of t exists for which [tex]\sin t=\dfrac{5}{4}.[/tex]
Hence, the given statement is FALSE.
The greatest common factor of 60w^5 y^3 and 78wy^2 is _____.
2wy^2
6wy^2
6w^5y^3
13w^5y^3
will mark best answer!
Answer: The required greatest common factor of the given expressions is [tex]6wy^2.[/tex]
Step-by-step explanation: We are given to find the greatest common factor of the following two expressions :
[tex]E_1=60w^5y^3,\\\\E_2=78wy^2.[/tex]
The factorization of the given expressions can be written as :
[tex]E_1=2^2\times3\times5\times w^5\times y^3,\\\\E_2=2\times3\times13\times w\times y^2.[/tex]
Therefore, the greatest common factor of the given expressions is
[tex]GCD(E_1,E_2)=2\times3\times w\times y^2=6wy^2.[/tex]
Thus, the required greatest common factor of the given expressions is [tex]6wy^2.[/tex]
PLS HALP MEH!!!! A soccer ball is kicked from the ground in an arc defined by the function,h(x) = -2x^2 + 8x. What is the height of the ball after 3 seconds?
Answer:
6 feet
Step-by-step explanation:
A soccer ball is kicked from the ground in an arc defined by the function,
[tex]h(x) = -2x^2 + 8x[/tex]
h(x) is the height of the ball and time is t.
we need to find out the height when t= 3 seconds
Plug in 3 for t
[tex]h(x) = -2x^2 + 8x[/tex]
[tex]h(3) = -2(3)^2 + 8(3)[/tex]
[tex]h(3) =-18+24=6[/tex]
The height of the ball after 3 seconds is 6 feet.
Use a bar model to find the unknown value: 3/6 = ?/7
The solution to the problem 3/6 = ?/7 when using a bar model to visualize it, is 3.5. This can be calculated by understanding equivalency between fractions.
Explanation:To solve this problem using a bar model, imagine dividing a bar into 6 equal parts (representing the denominator of the fraction on the left). If 3 of those parts (representing the fraction’s numerator) equals 3/6 or 0.5. Now, we want to know how many sevenths would be equivalent to that same amount. Since 1/2 is equivalent to 3.5/7, the answer to the question 3/6 = ?/7 would be 3.5.
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Write a rule for dividing a positive and negative decimal
Sixteen is seven plus three times a number. Find the number
Initially a pool contains 250 gallons of water. A hose is placed in the pool, and the water is turned on. The hose adds 5.4 gallons of water per minute. Write a linear model that represents the amount of water, V, in the pool as a function of time, t, in minutes.
Answer:
The amount of water in pool after t minutes V = 250 + 5.4 t
Step-by-step explanation:
Amount of water in pool = 250 gallons.
The hose adds 5.4 gallons of water per minute.
Rate at which hose is adding water = 5.4 gallons per minute
We need to write a linear model that represents the amount of water, V, in the pool as a function of time, t, in minutes
We have
V = 250 + 5.4 t
The amount of water in pool after t minutes V = 250 + 5.4 t
Convert 9 over 16 to a decimal.
A. 0.4225
B. 0.5225
C. 0.5625
D. 0.7455