Find the area of the parallelogram determined by the points (1,4),(−1,5),(3,9), and (5,8). How can you tell that the quadrilateral determined by the points is actually a parallelogram?
Answers
The area of the parallelogram determined by points (1,4), (−1,5), (3,9), and (5,8) is 6 square units. We can tell that the quadrilateral determined by the points is actually a parallelogram because the vectors formed by the opposite sides are equal or proportional.
To find the area of the parallelogram determined by the points (1,4), (−1,5), (3,9), and (5,8), we can follow these steps:
1. Calculate the vectors formed by the given points: AB, BC, and AD.
AB = (−1 - 1, 5 - 4) = (-2, 1)
BC = (3 - (-1), 9 - 5) = (4, 4)
AD = (5 - 1, 8 - 4) = (4, 4)
2. Verify if the quadrilateral is a parallelogram. A quadrilateral is a parallelogram if the opposite sides are parallel, which means the vectors formed by the opposite sides should be equal or proportional.
AB and BC are not opposite sides, but AB and AD are, as well as BC and CD (CD = AD).
Since AB = -2 × AD and BC = CD, the quadrilateral is a parallelogram.
3. Calculate the area of the parallelogram using the Shoelace formula or by calculating the cross product of the vectors:
Area = (1/2) × |AB x BC|
First, find the cross-product of AB and BC:
AB x BC = (1 × 4) - (-2 × 4) = 12
Now, calculate the area:
Area = (1/2) × |12| = 6
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Question-The center of circle A with equation (x – 7)2 + (y – 1)2 = 16 is mapped to the center of circle B with equation (x + 8)2 + (y – 2)2 = 16. Determine the translation needed for this mapping.
Answers-
A. (x, y) ⟶ (x - 15, y + 1)
B. (x, y) ⟶ (x - 12, y + 9)
C. (x, y) ⟶ (x - 8, y + 2)
D. (x, y) ⟶ (x + 15, y - 1)
Answers
The solution is Option A.
The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the equation for the circle A be represented as
( x - 7 )² + ( y - 1 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )
Let the equation for the circle A be represented as
( x + 8 )² + ( y - 2 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )
So , the translation of circle A to B is given by
( 7 , 1 ) to ( -8 , 2 )
So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up
Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
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Eric owns shares of a certain stock. If he sells off 8 shares each month for a year, find the change in the number of shares of stock he owns.
Answers
After solving the word problem, the change in the number of shares of stock he owns, is x-96.
In the given question we have to find the change in the number of shares of stock he owns.
As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.
Let Eric owns x shares of a certain stock.
If he sells off 8 shares each months for a year.
So as we know that in a year have 12 months.
In 1 month = 8 shares sells
12 months = 12×8 shares sells
12 months = 96 shares sells
So in a year Eric sells 96 shares and he have total x shares.
So the remaining shares are x-96.
Hence, the change in the number of shares of stock he owns, is x-96.
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Yvonne made 12 more cupcakes than she did yesterday. She made a total of 68 cupcakes over the two days. How many cupcakes did she make the second day?
Answers
Answer:
56
Step-by-step explanation:
68-12=56
Answer:
56
Step-by-step explanation:
56
using only the digits 0 and 1 how many different numbers consisting of 8 digits can be formed
Answers
The first digit must be 1. The remaining seven ones must be either 0 or 1.
Therefore, there can be formed \(2^7=128\) different numbers.
Identify the sampling technique used to obtain the following sample. the first 35 students leaving the library are asked how much money they spent on textbooks for the semester. Choose the correct sampling technique below. A. Systematic sampling B. Convenience sampling C. Cluster sampling D. Stratified sampling E. Random sampling
Answers
The sampling technique used to obtain the described sample is A. Systematic sampling.
In systematic sampling, the elements of the population are ordered in some way, and then a starting point is randomly selected. From that point, every nth element is selected to be part of the sample.
In the given scenario, the first 35 students leaving the library were selected. This suggests that the students were ordered in some manner, and a systematic approach was used to select every nth student. Therefore, the sampling technique used is systematic sampling.
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Solve 3(3x - 5) =21
Answers
Answer:
x=4
Step-by-step explanation:
What function is a vertical shift of f(x) = x?
A) g(x) = 3f(x)
B) g(x) = f(x - 3)
C) g(x) = f(x) + 4
D) g(x) = 1/2 f(x)
Answers
Answer:
C) g(x) = f(x) + 4
Step-by-step explanation:
A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A
-anumber would slide the function DOWN instead.
As for the other answers:
A) the 3multiplied in front is a vertical STRETCH.
D) the 1/2 multiplied in front is a vertical shrink (smash)
B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.
If sintheta = cos theta then the value of acute angle is
Answers
Answer:
45 degrees
Step-by-step explanation:
Here, we want to get the value of the acute angle
From the question, we have it that the sin of the acute angle equals its cosine
Recall;
cos A = sin (90-A)
Hence, if A is 45, then Cos A and Sine A will be the same
This means the value of theta which is the acute angle is 45 degrees
PLZ HELP IM HAVING TROUBLE ON MY RSM!
Answers
Answer:
=
64 / 7x -2
Step-by-step explanation:
You multiply 16 and 4/7 than you take away 2 I think im bad at this-
LOGIC, Use the model universe method to show the following invalid.
(x) (AxBx) (3x)Ax :: (x) (Ax v Bx)
Answers
The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).
To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.
Let's consider the following interpretation:
Domain of discourse: {1, 2}
A(x): x is even
B(x): x is odd
Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).
However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).
In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.
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Can somebody help me, please
Answers
Answer:
uh I don't even know what this is
Answer: x = 500
Step-by-step explanation:
Use the Pythagorean Theorem
a²+b²=c²
300² + 400² = x²
90000 + 160000 = x²
250000 = x²
√250000 = √x²
500 = x
hope i explained it :)
A pizza parlor offers 10 toppings. How many 3-topping pizzas could they put on their menu? Assume double toppings are not allowed.
Answers
Using combination and permutation we found out that there are 30240 ways to make varieties of pizza with 3 toppings.
Given 10 toppings
10C3 =10!/3! 7! =120
10P5 =10!/5! =30240 ways
A permutation is a process of placing objects or numbers in order. Combining is the ability to select an object or number from a group of objects or collections such that the order of the objects does not matter.
In mathematics, a combination is the selection of elements from a set with different members, so the order of selection does not matter.
The process or state of binding. Some combination: A combination of ideas. Combined: A chord is a combination of notes. Alliance of Individuals or Parties: Combinations to restrict transactions.
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9.9. Let S T be sets. Prove that S CT, if and only if, 25 C 2T. 9.10. Let S, T be sets. Prove that 23 n 21 = 2SNT.
Answers
For 9.9: To prove the first statement, it is assumed that S CT, and then it is shown that 25 C 2T. To prove the second statement, it is assumed that 25 C 2T, and then it is shown that S CT.
For 9.10: The statement "23 n 21 = 2SNT" is proved by constructing a bijection between the set of ordered pairs (A, B) where A is a 2-element subset of {1, 2, 3} and B is a 1-element subset of {1, 2}. The bijection is defined by the function f(A, B) = (x, y, z), where x is the largest element of A, y is the unique element of B, and z is the remaining element of {1, 2, 3} - A - {y}
For 9.9: To prove that S CT if and only if 25 C 2T, we need to show two things: 1. If S CT, then 25 C 2T. 2. If 25 C 2T, then S CT.
To prove the first statement, assume S CT. This means that every element of S is also an element of T (i.e., S is a subset of T). We want to show that 25 C 2T, which means that every 2-element subset of 25 is also a subset of T.
Let A be an arbitrary 2-element subset of 25. Since A has exactly two elements, we can write it as A = {a, b}, where a and b are distinct elements of 25. Since 25 C T, we know that a and b are both elements of T. Therefore, A is a subset of T, and we have shown that 25 C 2T.
To prove the second statement, assume 25 C 2T. This means that every 2-element subset of 25 is also a subset of T. We want to show that S CT, which means that every element of S is also an element of T.
Let x be an arbitrary element of S. We want to show that x is also an element of T. Since 25 C 2T, we know that {x, y} is a subset of T for every y in S (i.e., every pair of elements from S is also a pair of elements from T). In particular, this means that {x, x} (i.e., the set containing only x) is a subset of T. But this means that x is an element of T, since every subset of {x} is also a subset of {x, x}.
Therefore, we have shown both directions of the "if and only if" statement, and we can conclude that S CT if and only if 25 C 2T.
For 9.10: To prove that 23 n 21 = 2SNT, we need to show that there is a bijection between the set of ordered pairs (A, B) where A is a 2-element subset of {1, 2, 3} and B is a 1-element subset of {1, 2}, and the set SNT (i.e., the set of all ordered triples (x, y, z) where x is an element of {1, 2, 3}, y is an element of {1, 2}, and z is an element of {1, 2, 3} - {x} - {y}).
To construct the bijection, we will define a function f from the set of ordered pairs (A, B) to SNT, and show that f is both injective (i.e., no two different ordered pairs map to the same element of SNT) and surjective (i.e., every element of SNT is the image of some ordered pair under f).
Let (A, B) be an arbitrary ordered pair in the domain of f. We will define f(A, B) to be the ordered triple (x, y, z), where x is the largest element of A, y is the unique element of B, and z is the remaining element of {1, 2, 3} - A - {y}.
To see that f is injective, suppose that (A, B) and (A', B') are two different ordered pairs in the domain of f such that f(A, B) = f(A', B'). This means that x = x', y = y', and z = z', where x and x' are the largest elements of A and A', respectively, y and y' are the unique elements of B and B', respectively, and z and z' are the remaining elements of {1, 2, 3} - A - {y} and {1, 2, 3} - A' - {y'}, respectively.
Since x and x' are both elements of A and A', respectively, and A and A' are both 2-element subsets of {1, 2, 3}, we must have x = x'. But then y = y' and z = z', since these are uniquely determined by x and the choice of A or A'. Therefore, we have (A, B) = (A', B'), and f is injective.
Since x is an element of {1, 2, 3}, we can write {1, 2, 3} - {x} = {a, b} for some distinct elements a and b of {1, 2, 3}. Let A = {x, a}, which is a 2-element subset of {1, 2, 3}. Since y is an element of {1, 2}, we can write {1, 2} - {y} = {c} for some element c of {1, 2}. Let B = {y}, which is a 1-element subset of {1, 2}.
Therefore, since f is both injective and surjective, it is a bijection between the set of ordered pairs (A, B) and the set SNT, and we have shown that 23 n 21 = 2SNT.
1. S ⊆ T, if and only if, some condition related to 25 and 2T.
2. A relationship involving intersection (denoted by ∩) and union (denoted by ∪) between sets S and T, possibly involving their complements (denoted by S' and T').
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how do the factor theorem and remainder theorem work together to help find zeros of a function
Answers
Answer: factor...
Step-by-step explanation: If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x - c) must be a factor.
What is an equation of the line that passes through the points (5, 8) and (5, 3)?
Answers
Answer:
x = 5
Step-by-step explanation:
Use the slope formula and slope-intercept form y = m x + b to find the equation.
Hope this helps:)
What factor is represented by the blue shading in the model? [Hint: Include the overlapping area.]
1 4/5
4/5
4/15
1 2/3
![What factor is represented by the blue shading in the model? [Hint: Include the overlapping area.]1 4/54/54/151](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/GDqmofZ0kHSTm75CDvP8POrPcEIjPcyb.gif)
Answers
Answer:
i would say the last one or A.
Step-by-step explanation:
So sorry if i am wrong!
Answer:
4/5
Step-by-step explanation:
Remember yellow and blue make green. Remember to count the entire shaded area both green and blue for the numerator. The denominator will be all the colors yellow, blue and green squares.
Total Green and blue 24 (numerator)
Total Green, blue Yellow 30 (denominator)
=24/30 next you simplify to (divide numerator and denominator by 6 )
equals 4/5
Use the distributive property to expand Negative 4 (Negative two-fifths 3 x). Which is an equivalent expression? Negative StartFraction 8 over 5 EndFraction 12 x Negative StartFraction 8 over 5 EndFraction minus 12 x StartFraction 8 over 5 EndFraction 12 x StartFraction 8 over 5 EndFraction minus 12 x.
Answers
The A option is correct.
SimplificationSimplification is to make something easier to do or understand and to make something less complicated.
Linear systemIt is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
\(4(-\dfrac{2}{5} + 3x)\) is a linear function.
To findThe equivalent.
How to find it?\(4(-\dfrac{2}{5} + 3x)\) ic a linear function.
In simplifying, we get
\(-\dfrac{8}{5} + 12x\)
Thus, the A option is correct.
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Answer:8/5-12x
Step-by-step explanation:
the unknown side of a trapezium.
Answers
Answer:
11 mm
Step-by-step explanation:
121=area of a rectangle and area of triangle
121=x*8+(0.5)*x*(14-8), 11x=121, x=11
Answer:
\(11mm\)
Step-by-step explanation:
Let the unknown side be x
\(Area \: \: \: of \: \: the \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: \: the \: \: parallel \: sides) \times height \\ 121= \frac{1}{2} \times (8 + 14) \times x \\ 121 \times 2 = 22x \\ 242 = 22x \\ \frac{242}{22} = \frac{22x}{22} \\ 11 = x\)
9y/x + z²-w=
W=5 and x=3 and y=4 and z=8
(THE / IS DIVISION)
Answers
Substitute the given values in the expression:
9y/x + z²-w = 9(4)/3 + 8² - 5
Simplify by performing multiplication and addition inside the parentheses first, then the exponentiation, and finally the division:
= 12 + 64 - 5
= 71
Therefore, 9y/x + z²-w = 71 when w=5, x=3, y=4, and z=8.
71
Step by step solved:
Substituting the given values of x, y, z, and w into the expression, we have:
9y/x + z² - w = 9(4)/3 + 8² - 5
= 12 + 64 - 5
= 71
Therefore, the value of the expression with the given values of x, y, z, and w is 71.
The perimeter of a train ticket is 60 centimeters. It is 17 centimeters long. How tall is it?
Answers
If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter
What is perimeter of a rectangle?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;
P = l+l+w+w
P= 2(l+w)
60 = 2( 17+w)
60 = 2( 17+w)
17+w= 60/2
17+ w = 30
w = 30-17
w = 13cm
Therefore the height of the train ticket is 13cm
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a-2b+c=-6 and a+5c=-12 and -a+6b+4c=3
what is a, b and c
Answers
An elephant can eat up to 440 pounds of vegetation every day. How many grams per
minute is this? (Can I get a step by step please)
Answers
Answer: 138.598 grams per minute
Step-by-step explanation:
You have 440 pounds. Convert this to grams so that it is easier.
There are roughly 199581 grams in 440 pounds (453.592 grams in 1 pound).
Now that you have the number of grams it eats in a day. You now have to convert days to minutes.
There are 24 hours in a day so divide 199581 grams by 24 hours to get the number of grams eaten in 1 hour.
199581/24 = 8315.875
Now you have the number of grams eaten in 1 hour.
There is 60 minutes in 1 hour so divide 8315.875 by 60 to get the number of grams every minute.
8315.875 / 60 = 138.598
So the number of grams every minute the elephant eats is roughly 138.598 grams.
At Weichert Realty, each agent earns 7% commission on their sales. If they sell a house for $300,000, they would earn $21,000. How much would
they have to sell in order to earn $35,000?
$50,000
B) $25,000
$2,450
$500,000
Answers
Sell $500,000 worth of real estate in order to earn a commission of $35,000 at a rate of 7%. So the correct answer is D) $500,000.
Use the given information to set up a proportion and solve for the unknown sales amount:
Commission earned / Sales amount = Commission rate
$21,000 / $300,000 = 0.07
Now we can use this proportion to find the sales amount needed to earn $35,000:
$35,000 / 0.07 = $500,000
Therefore, they would need to sell $500,000 worth of real estate in order to earn a commission of $35,000 at a rate of 7%. So the correct answer is D) $500,000.
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7x + 8 + 3x2 - 5x + 9
Can someone show me how I would solve this equation? (Step by step please)
Answers
Answer:
2x+23
Step-by-step explanation:
1
Simplify 3\times 23×2 to 66.
7x+8+6-5x+97x+8+6−5x+9
2
Collect like terms.
(7x-5x)+(8+6+9)(7x−5x)+(8+6+9)
3
Simplify.
2x+23
Done
Solve the system algebraically.
2x + y - 10 = 0
x-y-5=0
What is the value of y?
-5/3
5
Answers
Answer:
5 is the value of y
PLZ FRIEND ME!!
Select whether the pair of lines is parallel, perpendicular, or neither.
y = 5, y = −3
Answers
The given pair of lines are parallel lines.
What are parallel lines?Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel. A line with the same slope is said to be parallel. To put it another way, these lines won't ever cross. At the interception, perpendicular lines always intersect and form right angles.So, graph the lines on the given equation:
y = 5y = -3(Refer to the graph attached below)
We can easily look at the graph and tell that the given lines of the equations are parallel to each other.
Therefore, the given pair of lines are parallel lines.
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle.
y = ex, y = x2 − 1, x = −1, x = 1
Find the area of the region.
Answers
The area of the region is rectangles
The given curves are y = x2 and y = 2 − x2. They intersect at x = 1, y = 1. See the graph below. The shaded region enclosed by the curves is the region whose area we wish to find.To find the area of the shaded region,
The left part of the region is the part bounded by the x-axis, the curve y = x2, and the line x = 1. This region is shown below. To find the area of this region, we integrate with respect to y from y = 0 to y = 1. Along the curve y = x2, the values of x are ± y1/2. So we have to integrate from x = −y1/2 to x = 1.
Thus the area of the right part of the region isThus the total area of the shaded region is Approximating rectangle The area of each approximating rectangle is given by height times width. Since we are dividing the region into two parts we
A typical rectangle is shown below. The value of x corresponding to the lower end of the rectangle is x = −y1/2 and the value of x corresponding to the upper end of the rectangle is x = 1. So the height of the rectangle is x2 and the width is Δy = 1/n. Therefore, the area of the rectangle isSince the rectangle is located below the curve, this approximation underestimates the true area of the region.
Therefore, the area of the rectangle is Since the rectangle is located above the curve, this approximation overestimates the true area of the region. By computing the sum of the areas of all the approximating rectangles and taking the limit as n approaches infinity, we can find the exact area of the region.
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Find the slope of the line passing through (2, 10) and (8, 7)
Answers
Slope= -1/2
Solution:The slope formula will help us find the slope.This is the formula:\(\displaystyle\frac{y2-y1}{x2-x1}\)\(\displaystyle\frac{7-10}{8-2} =\frac{-3}{6} =-\frac{1}{2}\)Hope it helps.
Do comment if you have any query.
Slope:-
m=7-10/8-2m=-3/6m=-1/2Can someone help ???????? Thanks
Answers
I think this is correct, but sorry if not.
Hope this helps x
A simple random sample of 49 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. Find the 99% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answers
Answer:
0.142
Step-by-step explanation:
From the question, we identify the following parameters;
n = 49
p = 82% = 82/100 = 0.82
alpha, α = 1-0.99 = 0.01
Zα/2 = Z_0.005 = 2.575
margin of error = Zα/2 * √( p(1-p)/n)
Margin of error = 2.575 * √(0.82)(1-0.82)/49
Margin of error =0.1416005 which is approximately 0.142