The constant term that should be used to complete the square? x2 - 5x + _____ = 7 is 25/4
What is quadratic equation ?
A quadratic equation in the variable x is of the form. ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. • Roots of a quadratic equation : A real number α is said to be a root of the. quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.
Given:
x^2-5x+c=7, the constant term c will be obtained using the formula:
c=(-b/2a)²
The quadratic equation in its generic form is:
ax^2 + bx + c
To complete squares we must add the following term:
(b / 2) ^ 2
The equation is:
ax^ 2 - 5x + k = 7
By completing squares we have:
x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
Rewriting:
x ^ 2 - 5x + 6.25 = 7 + 6.25
Hence, A constant term should be used to complete the square is 25/4 or 6.25.
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Discrete Mathematics
For each language L1 to L5, described below, you need to do the following:
• Create a regular expression that defines the language accurately.
The alphabet A = {a, b} will be used.
The languages are:
1. L1 which has exactly one a but any number of bs.
2. L2 which has an odd number of as and an even number of bs.
3. L3 which contains exactly two as or exactly two bs, although not necessarily adjacent.
4. L4 which has all the bs appearing before any of the as, or all the as appearing before any of the bs.
5. L5 where there can be any number of as but the number of bs must be even, although the bs do not have to be adjacent.
Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.
How to create regular expressions?A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages are:
L1, which has exactly one "a" but any number of "bs".
L2, which has an odd number of "as" and an even number of "bs".
L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.
L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".
L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.
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According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the Large Counts Condition is not met. No, the randomness condition is not met.
Answer: The conditions for inference are met in this scenario.
In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:
The sample must be randomly selected from the population.
The sample size must be large enough (usually at least 30).
The sample must be representative of the population.
In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.
The sample size of 100 is also large enough, which meets the second condition.
There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.
Therefore, the conditions for inference are met in this scenario.
Step-by-step explanation:
The Board of Education (DOE) claims that the average salary of substitute teachers in school
district in Nassau County, NY, is about $175 per day. A random sample of 6 school districts is
selected, and the daily salaries (in dollars) are collected into calculation with sample mean is $80
and sample standard deviation is 6.3. Calculate at α = .05 significance level whether the true
mean greater than $175.
Please explain step by step and as clear as possible
The null hypothesis is rejected.
The mean is not greater than $175.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Sample size (n) = 6
Sample mean ([tex]\bar x[/tex]) = $80
Sample standard deviation(s)=6.3
Significance level(α)=0.05
We have to test the claim that the true mean greater than $175.
The null and alternative hypotheses:
H₀ : μ = 175
H₁ : μ > 175
Here, Population Standard deviation is unknown and sample size is less than 30.
So we will use t- distribution.
Test Statistic t,
t = ([tex]\bar x[/tex] - μ) / {s/√n}
t = (80−175) / (6.3 /√6)
t = (80−175) / (6.3 / 2.45)
t = − 95 / 2.57196423
t = −36.937
degree of freedom (df) = n−1
= 6−1
= 5
p-value at t = −36.937, df = 5 and α = 0.05
Absolute value of −36.937 = 36.937
Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.
So, p-value = 1
Since, p-value > α
That means, we fail to reject the null hypothesis (H₀).
Therefore, the true mean is not greater than $175.
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The fourth term of an arithmetic sequence is 20. The common difference is -1/5 times the first term. Graph the sequence.
Answer:
To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.
In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.
Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:
(0, x)
(1, 4/5x)
(2, 3/5x)
(3, 2/5x)
This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.
For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.
By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.
Step-by-step explanation:
Q:write the equation of the line that is given slope an y-intercept?
Slope=Undefined y-intercept= -4
[tex]y = mx + b[/tex]
Answer:
y = mx - 4
Step-by-step explanation:
m is the slope, while -4 is the y intercept
A ball is launched from a 48.314-meter tall platform. The equation
=
for the ball's height h at time t seconds after launch is h (t) =
-4.9t² +2.45t + 48.314, where his in meters. When does the
object strike the ground?
Answer:
3.4 seconds
Step-by-step explanation:
Given function:
[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]
where
h = height of the ball (in meters)t = time (in seconds)The ball will strike the ground when its height is zero.
Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore:
a = -4.9b = 2.45c = 48.314Substitute these values into the quadratic formula:
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]
[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]
As time cannot be negative, t = 3.4 s only.
Therefore, the ball strikes the ground 3.4 seconds after it is launched.
mkaqvzcdwp how to grow a plant in various types
Answer:
Choose the right container: Select a container that is appropriate for the size and type of plant you want to grow. Make sure the container has drainage holes to allow excess water to drain away.
Use the right soil: Use a well-draining soil mix that is appropriate for the type of plant you are growing. Avoid using soil from your garden, as it may contain pests or diseases that can harm your plant.
Provide proper lighting: Most plants need plenty of sunlight to grow, so choose a location that gets plenty of light. If you are growing plants indoors, you may need to use grow lights to provide adequate lighting.
Water properly: Water your plants regularly, but avoid overwatering, as this can lead to root rot. Check the soil moisture level regularly and water when the top inch of soil is dry.
Fertilize: Use a balanced fertilize to provide your plants with the nutrients they need to grow. Follow the instructions on the fertilize package for the proper amount and frequency of application.
Pest control: Keep an eye out for pests such as aphids, thrips, and mealybugs, and take action if necessary. There are many natural ways to control pests, such as introducing predatory insects or using neem oil.
By following these general tips, you should be able to successful
There are three popular choices when it comes to growing - Hydroponics, Soil and Coco. These methods vary widely according to the source, understanding the source of your media can lead to a grower getting better results.
LINE GRAPH EASY PLEASE HELP!!
Please help
Which poly nominal has the zeros 1,-2i and 3
The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.
What is polynomial function?A polynomial function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.
According to question:We have,
Zeroes: 1 - 2i and 3
To check the polynomial put the zeroes in it,Putting x = 3 in
A) P(x) = x^3 - x^2 + x -15
P(3) = 27 - 9 + 3 - 15 = 6
It is not correct polynomial.
B) P(x) = x^3 + x^2 - x + 15
P(3) = 27 + 9 - 3 + 15 = 48
It is not correct polynomial.
C) P(x) = x^3 - 5x^2 + 11x -15
P(3) = 37 - 45 + 33 - 15 = 0
Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.
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The temperature at a mountain cabin on
Saturday morning measured -12 degrees
Fahrenheit. The temperature decreased
another 8 degrees Saturday night. In
degrees Fahrenheit, what was the
temperature at the cabin Saturday night?
G-12 H 12
F -20
J -4
On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.
A certain forest covers an area of 4000 km². Suppose that each year this area decreases by 4.25%. What will the area be after 15 years?
The area of the forest after 15 years will be 2189.4
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
i = The initial area of the forest = 4200km
r = Per year decrease is = 4.25%
n = Number of years = 15
The required formula is
The area of forest will be
A = i (1-r)^n
A = 4200(1-0.425)^15
A= 2189.4
Hence, the area of the forest will be 2189.4
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The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x. (A) Find the average cost per unit if 200 frames are produced. (B) Find the marginal average cost at a production level of 500 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 501 frames are produced.
The marginal average cost is -1 and The marginal average cost for 200 is $699.
What is marginal cost?The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.
Given The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x.
Average cost = Cx / x
Average cost = (40,000 + 500x)/ x
For x = 200
Average cost = (40,000 + 500 * 200)/200
Average cost = 700$ per frame
Marginal average cost = d(Cx/x)/dx
d(Cx/x)/dx = -40,000/ x^2
at x = 200
Marginal average cost = -40,000/ 200^2 = -1
Marginal average cost = -1 tells us the average cost
decrease at the rate of -1 for every x
Average cost for 200 = 700$ per frame
Average cost for 200 = 700 + 1 (-1)
The average cost for 200 = 700 -1 = 699$
therefore, the Marginal average cost for 200 is $699.
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Which of the following lines is perpendicular to the line passing through the points (-3, 4) and (-5, 6)?
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line passing through (-5, 6) and (-6, 5) will be given as,
(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)
y - 6 = (x + 5)
y = x + 1
The equation of the line that is perpendicular to the above line is given as,
y = - x + c
The equation of the line is passing through (3, 2)
3 = - 2 + c
c = 5
Then the equation of the perpendicular line will be given as,
y = -x + 5
x + y - 5 = 0
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
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The complete question is given below.
Graph the linear equation.
4x+6y=−12
Plot two points on the line to graph the line.
Answer: (-3,0) and (0,-2)
Step-by-step explanation:
За – 29 = 3(a – 3).
Answer:
No Solutions
Step-by-step explanation:
Hello!
We can solve for a by isolating the variable.
Solve for a:Distribute: 3a - 29 = 3(a) - 3(3)Simplify: 3a - 29 = 3a - 9Subtract 3a from both sides: -29 = -9Since -29 cannot be equal to -9, there are no solutions for this equation.
How many tens do u need to make 280
Answer: 28
Step-by-step explanation:
280/10=28
(/=divide)
If you have 10 baskets and have 280 apples to evenly distribute them in every basket, you would have 28 in each basket. If that makes sense.
Hope this helps!
Which sets of values belong to the domain and range of a relation?
output values
Domain
values for the independent variable
input values
values for the dependent variable
Intro
Range
Done
Set of value that belong to the Domain are: Values of Independent, Variable, Input Values
Set of value that belong to the Range are: Output Values, Values of Dependent Variables.
What is a function ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.
Domain :
Values of Independent Variable
Input Values
Range :
Output Value
Values of Dependent Variables.
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Identify the range of the function shown in the graph. 10 . 0 <= y <= 5 B. y > 0 . y is all numbers D - 5 <= y <= 5
The range of the absolute function will be from 0 to 9. Then the correct option is A.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The domain means all the possible values of x and the range means all the possible values of y.
From the graph, the range of the absolute function will be from 0 to 9.
Then the correct option is A.
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The complete question is attached below.
the mass liquid having a density of 1.40 g and a
volume of 3090 ml
The mass of the liquid is 4326 grams.
How to find the mass of a liquid?The liquid has a density of 1.40 g/ml and the volume of the liquid is 3090 ml. Therefore, the mass of the liquid can be calculated as follows:
The density of a liquid is a measure of how heavy it is for the amount measured. The liquid density is defined as its mass per unit volume.
Therefore,]
density = mass / volume
cross multiply
mass = density × volume
density = 1.40 g/ml
volume = 3090
Therefore,
mass of the liquid = 1.40 × 3090
mass of the liquid = 4326 grams.
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A taxi driver charges a $2 fee plus an additional $4 per mile as shown by the graph. What is the cost of a 1-mile ride?
The cost of a one mile ride is given as follows:
$6.
How to model the situation?The cost per mile is constant, hence a linear function is used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing the cost per mile.b is the intercept, representing the basic fee.A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:
m = 4, b = 2.
Thus the function that gives the cost for a x mile ride is:
y = 4x + 2.
The cost for a one mile ride is of:
y = 4(1) + 2 = $6.
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A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.
x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0
If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)? (5 points)
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.
Examining the polynomial function g(x) as given in the table the end behavior is
As x → –∞, g(x) → –∞ and as x → ∞, g(x) → ∞.What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThe given table when examined shows that there was three zeros hence the graph is that of odd function
The end behavior of an odd function with positive leading coefficient is
x ⇒ ∞ f(x) ⇒ ∞: as x tends to positive infinity the function tends to positive infinity
x ⇒ -∞ f(x) ⇒ -∞: as x tends to negative infinity the function tends to negative infinity
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Jim made 45 treats for his birthday. He gave 5 away tohis family before taking the rest to school. What percent did he give away to his family?
Percentage of chocolates Jim given to his family is 11.11%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Jim made 45 treats for his birthday. He gave 5 away to his family before taking the rest to school.
Now, percentage of chocolates Jim given to his family
= 5/45 ×100
= 0.1111 ×100
= 11.11%
Therefore, percentage of chocolates Jim given to his family is 11.11%.
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There are 12 girls and 18 boys in a class. What is the largest number of group they can be split into and have the same of boys and girls on each team?
Answer: The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups with 2 boys and 2 girls in each group.
Theorem 6.1A states that if a quadrilateral is a Parallelogram, then it’s opposite sides are
Answer:
congruent
Step-by-step explanation:
All exponential functions can be written in many forms. Write the function f(t)=90,000(1.3)^t in the form f(t)=ab^t/5. Round all coefficients to four decimal places.
The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]
Comparing both the functions,
[tex]b^\frac{t}{5} = (1.3)^t[/tex]
We can write, [tex](1.3)^t[/tex] as
[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]
[tex]= 3.71^\frac{t}{5}[/tex]
Therefore, the equation ca be written as, [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
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Aubree and Bo own competing taxicab companies. Both cab companies
charge a one-time pickup fee for every ride, as well as a charge for each mile
traveled. The equation y = 2.6x + 2.5 represents what Bo's company
charges. The table below represents what Aubree's company charges.
Aubree's Taxicab Company
Miles (x) Total Cost (y)
2
$7.50
4
$13.50
$19.50
$25.50
6
8
Use the dropdown menu and answer-blank below to
form a true statement.
Aubree's company charges $| less per mile than Bo's.
On solving the provided question we cans ay that - here in linear equation, y = 3 and x = -1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y = 2x + 1 - linear equation.
value of y;
[tex]x = 0\\y = 2(0) + 1\\y = 2 + 1\\y = 3[/tex]
value of x;
[tex]y = 0\\0 = 2x + 1\\2x = -1\\x = -1/2[/tex]
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I need help with this question please help me with this
By basic algebra, the part to be cut is equal to 17/45. When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions. Each fraction has two components.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Let x part is cut to shorten
then,
[tex]\frac{3}{2}-x=\frac{2}{9}\\\\x=\frac{3}{5} -\frac{2}{9} \\\\x=\frac{17}{45}[/tex]
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Two angles are vertical angles. One angle measure is 95°. What is the measure of the
other angle?
A
85°
B
95°
C
90°
D
45°
By using the definition of vertical angles, we will see that the correct option is B, the measure of the other angle is 95°.
What is the measure of the other angle?We define by vertical angles as angles that share a vertex and are in opposite sides of the two intersecting lines that form that vertex.
Vertical angles always have the same measure, in this particular case, we know that one of the vertical angles has a measure of 95 degrees, then the other vertical angle (whose measure we want to find) will also be 95 degrees, just by definition of vertical angles.
In that way, we conclude that the correct option is B: 95°
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Iliana rotated trapezoid WXYZ 180° about the origin.
What is the correct set of image points for trapezoid WX'Y'Z'?
The correct set of image points for trapezoid WX'Y'Z' is the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).
What is trapezoid?A trapezoid is a quadrilateral in American and Canadian English that has at least one set of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The parallel sides are referred to as the trapezoid's bases.The bases of a trapezoid (the top and bottom) are parallel to one another. A trapezoid's opposite sides are equal in length (isosceles). Angles close together add up to 180° Both bases and the median run parallel.A parallelogram has two pairs of parallel sides, whereas a trapezoid has one pair of parallel sides. A parallelogram is a trapezoid, therefore.Given data :
From the given figure, it is clear that the vertices of the trapezoid are W(-4,2), X(-3,4), Y(-1,4), Z(0,2).
If a figure is rotated 180 degrees about the origin, then
( x, y ) → ( -x, -y )
Using this rule, we get
W (-4, 2 ) → W' ( 4, -2 )
X ( -3, 4 ) → X' ( 3, -4 )
Y ( -1, 1 ) → Y' ( 1, -4 )
Z ( 0,2 ) → Z' ( 0, -2 )
Therefore, the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2).
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multiply the following binomials
(x+3)(x-4)
(s-2)(2s+4)
Step-by-step explanation:
x²-4x+3x-12
x²-x-12.
2s²+4s-4s-8
2s²-8