Hence, we proved that if n is an integer, then either n= 2mod3 or n^2=n mod6.
In the given question we have to prove that prove if n is an integer, then either n= 2mod3 or n^2=n mod6.
If n=2mod3 then tere is nothing to prove.
If n≠ 2mod3 then either n=0mod3 or n=1mod3
Case (1)
n=0mod3 ⇒ 3 | n⇒n=3m for mϵZ
n^2-n=(3m)^2-3m
n^2-n=9m^2-3m
n^2-n=3m(3m-1)
So, 3|3m, in this case 3m is even or 3m-1 is even.
i.e. 2|3m(3m-1) and also 3|3m(3m-1)
⇒6|3m(3m-1)
⇒6|n(n-1)
⇒6|(n^2-n)
⇒n=n mod6 (Proved)
Case (2)
n=1mod3 ⇒ 3 | (n-1)⇒n=3m+1 for mϵZ
n^2-n=(3m+1)^2-(3m+1)
n^2-n=9m^2+6m+1-3m-1
n^2-n=9m^2+3m
n^2-n=3m(m+1)
So, 3|3m, in this case 3m is even or 3m+1 is even.
i.e. 2|3m(3m+1) and also 3|3m(3m+1)
⇒6|3m(3m+1)
⇒6|n(n-1)
⇒6|(n^2-n)
⇒n=n mod6 (Proved)
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The write question is
Prove that if n is an integer, then n = 2 mod 3 or n^2 = n mod 6.
The product of three conecutive whole number i 46620. What i the um of thee number?
The required three consecutive numbers are 35, 36, 37
Let the three consecutive numbers as per the questions are x , x+1 , x+2
Since, According to the question, the product of these three consecutive numbers are 46620
Therefore, we can write
x ( x+1 )( x+2 ) = 46620
x([tex]x^{2}[/tex] + 2x + x + 2 ) = 46620
[tex]x^{3}[/tex]+ [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x = 46620
Now, [tex]x^{3}[/tex] + [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x - 46620 = 0
[tex]x^{3}[/tex] + [tex]3x^{2}[/tex] + 2x - 46620 = 0
After factorization, we get
( x- 35 )( [tex]x^{2}[/tex] + 38x + 1332 ) = 0
x - 35 = 0 Since ( [tex]x^{2}[/tex] + 38x + 1332 ) will always be a positive number
Therefore, x = 35
So, x + 1 = 35 + 1 = 36
x + 2 = 35 + 2 = 37
Therefore, the numbers are 35 , 36 , 37
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Calculate the solubility at 25 °C of CuBr in pure water and in a 0.0060 M CoBr2 solution. You'll find Ksp data in the ALEKS Data tab. Round both of your answers to 2 significant digits. ? ? solubility in pure water: ×10 solubility in 0.0060 M CoBr2 solution: L.
CuBr is soluble in pure water at a solubility of 0.2583 g/L, while CoBr₂ is soluble at a solubility of 7.50 × 10⁻⁶ g/L
Given,
The equation of reaction as; CuBr₂ → Cu²⁺ + 2Br⁻
In pure water, the Ksp of the solution is 6.27 * 10^-9
Ksp = [Cu²⁺] [Br⁻]²
Ksp = x³
Let's substitute and solve
x³ = 6.27 × 10⁻⁹
x = [tex]\sqrt[3]{6.27 * 10^{-9} }[/tex]
x = 0.0018
The molecular weight of CuBr₂ is 143.5 g/mol
The solubility of CuBr₂ is
0.0018 × 143.5 = 0.2583 g/L
The solubility in 0.0060M of CoBr₂
The equation of dissociation is given as
CoBr₂ → Co²⁺ + 2Br⁻
0.012 0 0
0 0.120 2 * 0.0060 = 0.012M
The dissociation of copper bromide is
CuBr₂ → Cu²⁺ + Br⁻
c 0 0.012
c - s s s + 0.012
The Ksp of this reaction is
[Ksp] = [Co²⁺] [Br⁻]
The Ksp of CuBr₂ = 6.27 × 10⁻⁹
6.27 × 10⁻⁹ = s(s + 0.012)
s + 0.012 = 0.012
0.012 > > > s
6.27 × 10⁻⁹ = s × 0.012
s = 6.27 × 10⁻⁹ / 0.012 = 5.225 × 10⁻⁷ mol / l
Let's convert this into g/L
s = 5.225 × 10⁻⁷ × 143.5 = 7.50 × 10⁻⁶ g/L
Therefore,
The solubility of CuBr in pure water is 0.2583 g/L and the solubility in CoBr₂ is 7.50 × 10⁻⁶ g/L
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Where is infinity and negative infinity on a graph?.
The positive infinity and negative infinity on a graph is explain below.
What is infinity?the idea of something limitless, interminable, without bound. The normal sign of infinity, ∞, was concocted by the English mathematician John Wallis in 1655. Three principal sorts of vastness might be recognized: the numerical, the physical, and the supernatural
According to question:Positive infinity is shown by rightmost point on the graph.Its symbol is +∞.
Negative infinity is shown by leftmost point on the graph.Its symbol is -∞.
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What is 2-digit number example?.
Answer:
10
Step-by-step explanation:
2-digit numbers are numbers that have two digit which they start from 10-99 so in this question i chose 10 as an example.
Clear-cut harvesting of wood from forest creates long periods of time when certain animals cannot use the forest as habitats. Partial cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, and squirrels per plot, 2 to 4 years after partial cut harvesting, and the percent of trees that were harvested in each of 11 Forests. Which of the following is the best description of the relationship displayed in the scatterplot?
From the given graph we can see that the line is downwards and linear. So the correct answer is Negative, linear and strong.
In the given question,
Clear-cut harvesting of wood from forest creates long periods of time when certain animals cannot use the forest as habitats.
Partial cut harvesting is increasingly used to lessen the effects of logging on the animals.
The following scatterplot shows the relationship between the density of red squirrels, and squirrels per plot, 2 to 4 years after partial cut harvesting, and the percent of trees that were harvested in each of 11 Forests.
We have to find which of the following is the best description of the relationship displayed in the scatterplot.
From the given graph we can see that the line is downwards and linear. So the correct answer is Negative, linear and strong.
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we can extend our defintion of the average value over a continous function to an infinite interval by defining the average value f on the interval [0, infinity) to be
We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be [tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex] .
The definition of the average value of a continuous function f(x) can be expanded to include the infinitely long interval [a,∞] as follows:
[tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex]
Let's assume that f(x) is any continuous function. Assume that the integral [tex]\int\limits^i_0 {f(x)} \, dx[/tex] is divergent and that f(x)≥0 in the range [a,∞].
Show that, if this limit exists, [tex]f_{ave} = \lim_{x \to \infty} f(x)[/tex] .
Hence, We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be [tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex] .
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What is another way to express 11 + 77
Another way to express 11 + 77 is to using absolute values making it equal to
|-11 + -77|How to find another way to express equationThe use of equality sign introduces a number or equation which is equal and hence can be used to replace another item
solving this expression gives 11 + 77 = 88
The equation can also be replace in equation terms using absolute values
where it can be written as
|-11 + -77|
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please someone help me
In order to keep the Bermuda Triangle on the Flat Earth from toppling over, it was balanced on the hole which leads to the interior of the hollow Earth. If the vertices of the Bermuda Triangle are given by (1,3) , (2,7) , and (6,2). In order to find the hole we will need to find the intersection of at least 2 lines. Name 2 points through which one of those lines will pass (in the form (x,y),(x,y))
The two lines are given as follows:
y = 4x - 1.y = -1.25x + 10.5.Their intersection is:
(2.19, 7.76).
The two points in which the line y = 4x - 1 passes are:
(2.19, 7.76) and (3,11).
How to define the linear functions?The format of the linear function is given by:
y = mx + b.
The linear function is defined taking a pair of points, and then:
The slope is the change in y divided by the change in x.The intercept is found replacing one point into the equation y = mx + b after the slope is found.For the first line, the two points are:
(1,3) and (2,7).
The slope is:
m = (7 - 3)/(2 - 1) = 4.
Hence:
y = 4x + b.
When x = 1, y = 3, hence the intercept b is obtained as follows:
3 = 4 + b
b = -1.
Then the first line is:
y = 4x - 1.
For the second line, the points are:
(2,7) and (6,2).
Hence the slope is of:
m = (2 - 7)/(6 - 2) = -5/4 = -1.25.
Then:
y = -1.25x + b.
When x = 2, y = 7, hence the intercept b is obtained as follows:
7 = -1.25(2) + b
b = 10.5.
Hence the second line is:
y = -1.25x + 10.5.
The x-coordinate of the intersection is given as follows:
4x - 1 = -1.25x + 10.5
5.25x = 11.5
x = 11.5/5.25
x = 2.19.
The y-coordinate of the intersection is:
y = -1.25(2.19) + 10.5 = 7.76.
Another point in which the line y = 4x - 1 passes is:
y = 4(3) - 1 = 11.
Hence point (3,11).
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Let the random variable X be the number of days that Spongebob needs to be in STAT107's office hour to do his project 1. Suppose X has the distribution as follows; P(X) 0.16 0.2 You can find it 0.36 Find the standard deviation of days Spongebob needs to be in the office hour SD(X). You can express your answer as a fraction, or a decimal. If you asnwer in decimal, include at least 2 NON-ZERO digits after the decimal point.
The standard deviation of days Spongebob needs to be in the office hour is 3.29.
How to calculate standard deviation?First, we must find all probability distribution. Keep in mind, total probability is always equal to 1. So,
∑P(X) = 1
∑P(X) = P(X=3) + P(X=6) + P(X=7) + P(X=12)
1 = 0.16 + 0.2 + P(X=7) + 0.36
1 = 0.72 + P(X=7)
P(X=7) = 1 - 0.72
P(X=7) = 0.28
Next, to find standard deviation (σ) we can use this formula,
σ = [tex]\sqrt{\sum X^2\times P(X) - (\sum X\times P(X))^2[/tex]
= [tex]\sqrt{(3^2\times 0.16+6^2\times 0.2+7^2\times 0.28 + 12^2\times 0.36)-(3\times 0.16+6\times 0.2+7\times 0.28+12\times 0.36)}[/tex]
= [tex]\sqrt{74.2-(7.96)^2}[/tex]
= [tex]\sqrt{10.8384}[/tex]
= 3.29
So, standard deviation X or SD(X) is 3.29
Thus, standard deviation is 3.29 days for Spongebob needs to be in the office hour.
Your question is incomplete, but most probably your full question was (image attached)
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our basketball team has 12 members, each of whom can play any position. in how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard?
By permutation, in 95040 ways we can choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard
What does permutation mean?A permutation is a set up of things in a certain sequence. Here, the members of sets or their constituent parts are sorted in a linear or sequential manner.
How is a permutation determined?Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to find the number of permutations. For instance, four-character PINs have a total of 10 possible combinations because each digit can vary from 0 to 9.
[tex]12^P_{5} = \frac{12!}{(12-5)!} =\frac{12!}{5!} = 12 X 11 X 10 X 9 X 8 = 95040[/tex]
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at a certain fast food restaurant, 77.5% of the customers order items from the value menu. if 14 customers are randomly selected, what is the probability that at least 9 customers ordered an item from the value menu? use excel to find the probability.
The probability that at least 9 customers ordered an item from the value menu is 0.927.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and and 1.
Subtract the preceding probability from 1 to get the likelihood of 9 to 14 people ordering out from value menu.
The likelihood is 1 x 0.073 = 0.927.
Therefore, the probability that at least 9 customers ordered an item from the value menu is 0.927.
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between the ages of 18 and 25, the average adult in the united states:group of answer choicesbuys a first house.has held seven jobs.has had two or three children.has a 20 percent chance of divorce.
Between the ages of 18 and 25, the average adult in the United States B. has held seven jobs.
How to illustrate the information?Emerging adulthood has been proposed as a new life stage between adolescence and young adulthood, lasting approximately 18 to 25 years. The majority of people in America are educated.
People in America between the ages of 18 and 25 want to work for themselves. As a result, they will use their educational credentials to obtain employment. So they can earn money and live their lives as they please. They do not limit themselves to one job. They always want to do so many things. So they can make more money.
As a result, the average adult in the United States worked seven jobs between the ages of 18 and 25. Therefore, based on the information given, the correct option is B.
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What is 4. 5 as a fraction?.
Answer:
[tex]4\frac{1}{2}[/tex] or [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
1. 0.5 means a half of 1 so it would be equivalent to [tex]\frac{1}{2}[/tex]
2. 4 in this case equals to [tex]\frac{8}{2}[/tex]
3. if you add them together you would get [tex]\frac{9}{2}[/tex]
4. after simplifying you would get [tex]4\frac{1}{2}[/tex]
5. so in this case both [tex]\frac{9}{2}[/tex] and [tex]4\frac{1}{2}[/tex] would be the answer
My friend ha $672 to pend on a fence for her rectangular garden. She want to ue cedar
fencing which cot $17/yard on one ide, and cheaper metal fencing which cot $7/yard for the
other three ide. What are the dimenion of the garden with the larget area he can encloe?
The dimensions of the garden with the largest area she can enclose is 24×14 square yards.
We know very well that the area (A) of the rectangle is given by =Length ×Breadth
The maximum of y=ax²+bx occurs at x = -b/2a
Let assume the length and width of the garden be L and W respectively.
We have given some information like my friend is using same type of fencing for three sides and different type of fencing on the remaining side.
Rate of cedar fencing is $17/yard
So, we can say that she has to pay for cedar fencing = 17W
Rate of cheaper metal fencing is $7/yard
Then she has to pay for metal fencing = 7W+7*2L = 7W+14L
Then according to given condition, total cost paid by my friend is $672.
It means sum of cost of cedar fencing and cost of cheaper metal fencing is $672.
=>17W+7W+14L = 672
=>24W+14L = 672
=>12W+7L = 336
=>7L = 336-12W
=>L = (336-12W)/7
Then the area of the rectangular garden is given by,
A = L×W
So, here after comparison we got that a = -12/7 and b = 48
Then maximum of W occurs at,
W = -48/(2×(-12/7)) = (48×7)/(2×12) = 336/24 = 14
Then maximum width = 14 yards
then length (L) = (336-12×14)/7 = 168/7 = 24 yards
Hence, the dimensions are 24×17 square yards.
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What is the congruent of SAS?.
The triengle ABC and XZY are proved to be congruent by SAS.
Explain the concept of congruence.Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.
By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)
According to given figures:Here in he given triangle,
BC=YZ
AC=XZ
∠ACB=∠XZY
By SAS ΔABC≅ΔXYZ
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line of best fit algebra: the number of steps per second that a runner takes is called the stride rate
The number of steps per second that a runner takes is not typically called the stride rate.
What is Stride Rate?Stride rate is a measurement of how frequently a person makes steps when walking or jogging. It is typically expressed in steps per minute and is calculated by dividing the total number of steps taken by the time it takes for each step to be completed. A person is often traveling faster if they have a greater stride rate. Numerous variables, such as a person's height, leg length, and muscular strength, can influence stride pace. The kind of exercise being done and the surface on which a person is walking or jogging might also have an impact. People may assess their development and modify their training plan to increase their speed and efficiency by keeping an eye on their stride rate.
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What is the 10th Amendment say?.
According to 10th Amendment it defines the Federal Government only has those powers delegated in the Constitution .
No law establishing a particular religion, forbidding its practice, restricting press or speech freedom, or restricting the right of the people to peacefully assemble and petition the government for redress of grievances may be passed by Congress.
An amendment is a change or improvement that essentially maintains the integrity of the original document. The Bill of Rights is the collective name for the first ten Amendments of the Constitution. It describes Americans' constitutional rights in relation to their government. People are granted civil liberties and rights, such as the freedom of speech, the press, and religion.
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The length of the arc of a semicircle is 10pi feet. What is the area of the semicircle
The area of the semicircle is [tex]157.1 \ \text{ft}^2[/tex].
What is the are of a cirlcle?
The area of a circle is given by the following expression:
[tex]A=\pi r^2[/tex]
Here, A is the area and r is the radius of the circle.
Lenght of the perimeter of a circle is given by the following formula:
[tex]C=2\pi r[/tex]
Here, C is the perimeter and r is the radius of the circle.
Now, length of the arc of a semicircle is given by the following formula:
[tex]\frac{C}{2}=\pi r[/tex]
Now, substitute values.
[tex]10\pi=\pi r\\r=10 feet[/tex]
Now, area of a circle is given by the following expression:
[tex]A=\pi r^2[/tex]
Here A is the area of the circle.
Now, area of the semicirle is given by the following expression:
[tex]\frac{A}{2}=\frac{1}{2} \pi r^2\\[/tex]
Now, substitute value in the above expression.
[tex]\frac{A}{2}=\frac{1}{2} \pi (10\ \text{ft})^2\\=157.1 \ \text{ft}^2[/tex]
Hence, the area of the semicircle is [tex]157.1 \ \text{ft}^2[/tex].
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three cards are drawn at random from a standard deck of cards, without replacement. find the probability that the suits of the cards are spades, hearts, spades, in that order.
There is this
13/52 for spades
13/51 for hearts
12/50 for spades
Since one is removed we have 51 cards for the next, 50 for the 3rd
Multiply them.
The probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.
According to the give question.
Three cards are drawn from a standard deck of cards without replacement.
Since,
The total number of cards in a standard deck = 52
Total number of spade cards = 13
Total number of heart cards = 13
Now,
The probability of getting first card as a spade card = 13/52 = 1/4
The probability of getting second card as heart card = 13/(52 -1) (cards are drawn without replacement)
= 13/51
The probability of getting third card as a spade card = (13 - 1)/52 -2
= 12/50
= 6/25
Therefore, the probability that suits of the cards are spades, hearts, spades
= 1/4 × 13/51 × 6/25
= 39/850
= 0.046
Hence, the probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.
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In bobby's school, math grades for the year are calculated from assignments, tests and a final exam. Assignments count 30%, tests 20%, and the final exam 50%. If bobby has an assignment grade of 85, a test grade of 72, and an exam of 61, what is bobby's overall grade?.
the overall grade of bobby is 70.4%
What is the percentage?%, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
Why is it called percent?The word percentage comes from the Latin adverb per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period. Later, the period was eliminated, and the two parts were combined to create the current one-word form of percent.
We must figure out what proportion of the overall grade each grade corresponds to in order to answer this challenge. Therefore:
85 times 30%, or 85 times 30 per 100, equals 25.5%.
tests = 72*20% = 72*20/100 = 14.4%
exam = 61*50% = 61*50/100 = 30.5%
sum of all tests, assignments, and exams
total = 25.5 + 14.4 + 30.5 = 70.4
The total grade for Bobby is 70.4%.
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One of the legs of a right triangle measures 17 cm and its hypotenuse measures 19 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
The length of the other leg is 8.48 cm
What is Pyhtagorean Theorem?
The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse (the side opposite the right angle)
Solution:
Given that:
Length of One Leg = 17 cm
Length of Hypotenuse = 19 cm
To Find:
Length of the other leg
= We know that by pythagorean theorem
[tex]base^{2} + length^{2} = hypotenuse^{2}[/tex]
17*17 + x^2 = 19*19
289 + x^2 = 361
x^2 = 72
x = 8.48 cm
The length of the other leg is 8.48 cm
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equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)
The equation of the circle centered at the origin and passing through the point (-4,0) is [tex]x^2+y^2=16[/tex].
Equation of a circle
A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.
We know that,
Equation of the circle passing through the origin is given by:-
[tex]x^2+y^2=r^2[/tex]
Where,
r is the radius of the circle, and
(x,y) are the coordinates of each point of the circle.
Hence, we can write,
The radius of the circle will be :-
[tex]\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units[/tex]
Hence, r = 4 units.
Hence, the equation of the circle is given by:-
[tex]x^2+y^2=16[/tex]
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Given triangles abc and def. what is the simplest transformation that could produce triangle def from triangle abc?
We have a series of 3 transformation.
i) rotation about A 90 degree.
ii) Shifting to right by 7 units
iii) shifting up by 6 units
Given that,
In the given picture we can see 2 triangles.
Triangles abc and def are offered.
We have to find how can triangle abc be transformed into triangle def in the simplest possible way.
We know that,
ABC is transformed into DEF.
We find from the pictures given that
There are three processes in the transformation of ABC into DEF, the first of which is the Triangle transformation. ABC is 90 degrees rotated around Vertex A.
Then we would get a right triangle with AC horizontal on top and AB vertically down with vertex A same as (-5,-4)
Next is a straightforward transformation that shifts A to D, or a vertex (-5,-4) to (2,2)
To accomplish this, an initial movement of 7 units to the right is made A as (2,-4)
Now next is vertically up by 6 units so that A becomes (2,2)
Therefore, We have a series of 3 transformation.
i) rotation about A 90 degree.
ii) Shifting to right by 7 units
iii) shifting up by 6 units
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If in a school the bell rings every ¼ hour - how many times does the bell ring in 1 2/7 hours? the answer is =
Answer:6 times
Step-by-step explanation:12/7 divide 1/4
Answer: 6 times
Step-by-step explanation:
Which of these systems of linear equations has an infinite number of solutions?.
The systems of linear equations has an infinite number of solutions are 3x + 6y = 22 & 6x +12y = 44.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Main body:
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
When both the lines(represented by both the equations) are coincident(lying over each other), then there will have an infinite solution since in that case, they will have infinite points in common.
In the given equation
3x + 6y = 22 & 6x +12y = 44.
we can see that the cofficient are proportional to each other
[tex]\frac{x_{1}}{x_{2} } =\frac{y_{1}}{y_{2} } = \frac{z_{1}}{z_{2} }[/tex]
= 1/2
Thus, the equation must be 3x + 6y = 22 & 6x +12y = 44.
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*** 50 POINTS****
Use any method to determine the zeros of each function.
a. f(x)= −x²−8x−18
b. g(x)= 2x²-2x+3
c. h(x)= -3x²-4x-4
The zeros of each function are;
a. f(x)= −x²−8x−18 :-4 ± 2√(2)/2i
b. g(x)= 2x²-2x+3 : 0.5 ± √(5)/2i
c. h(x)= -3x²-4x-4 : -0.6 ± 4√(2)/6i
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that the quadratic equation are;
a. f(x)= −x²−8x−18
It has Complex Roots.
Roots: -4 + 1.414213i, -4 - 1.41421i
Root Pair: -4 ± 2√(2)/2i
Factored: f(x) = -1(x + 4 + 1.4i)(x + 4 - 1.4i)
b. g(x)= 2x²-2x+3
It has Complex Roots.
Roots: 0.5 + 1.118i, 0.5 - 1.118i
Root Pair: 0.5 ± √(5)/2i
Factored: f(x) = 2(x - 0.5 + 1.118i)(x - 0.5 - 1.118i)
c. h(x)= -3x²-4x-4
It has Complex Roots.
Roots: -0.66+ 0.94i, -0.66 - 0.94i
Root Pair: -0.6 ± 4√(2)/6i
Factored: f(x) = -3(x + 0.6+ 0.9i)(x + 0.6 - 0.9i)
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The table how the quantity and unit price for the item Camillo bought. Total cot for bread:
$48. 75
Total cot for peanut butter:
$384
Total cot for jelly:
If he would have pent $986. 50 without better-buy unit price, how much money did he ave?
Using the addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.
It is given to us that -
The total cost for bread = $48.75
The total cost for peanut butter = $384
and, the total cost for jelly = $192
It is also given to us that Camillo has spent $986. 50.
We have to find out the money he has left.
Firstly, we have to find out the total costs spent by Camillo by adding the costs spent on bread, peanut butter, and jelly.
Total costs = $48.75 + $384 + $192 = $624.75
The total amount that Camillo had with him initially is given by $986. 50.
So, in order to find out the money that Camillo is left with, we have to subtract the total costs spent by Camillo from the initial total amount that Camillo had.
Thus, money left = $986. 50 - $624.75 = $361.75
Therefore using addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.
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Answer: Camillo had $361.75.
Step-by-step explanation:
What are the steps in solving problems involving systems of linear equations in two variables by graphing?.
A system of linear equations is created when two or more linear equations are put together.
What are linear equations?Systems involving two linear equations in two unknowns will be the main topic of discussion in this section. In a subsequent chapter of this book, we will solve larger systems of equations.
Below is an illustration of a system of two linear equations. A brace is used to demonstrate how the two equations are combined to form a system of equations.
x-2y=6
2x+y=7
A two-variable linear equation like 2x+y=7 has an endless number of solutions. It has a linear graph.
Always keep in mind that every point on the line represents a solution to the problem, and vice versa.
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If two variables are correlated to each other, which of the following are characteristics of the dependent variable?
a. In a cause and effect relationship, it is the cause.
b. It is usually shown on the horizontal axis of a scatter diagram.
c. It is usually shown on the vertical axis of a scatter diagram.
d. In a cause and effect relationship, it is the effect.Answer: c. It is usually shown on the vertical axis of a scatter diagram.
d. In a cause and effect relationship, it is the effect.
Option C is correct, If two variables are correlated to each other It is usually shown on the vertical axis of a scatter diagram.
In statistics, correlation or dependence is any statistical dating, whether or not causal or no longer, among random variables or bivariate records. Even though in the broadest sense, “correlation” may additionally imply any sort of association, in statistics it normally refers back to the diploma to which a couple of variables are linearly related.
Acquainted examples of based phenomena consist of the correlation between the peak of mother and father and their offspring, and the correlation between the rate of an excellent and the amount the clients are inclined to buy, as it’s far depicted within the so-referred to as call for the curve.
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each marble bag sold by nicole's marble company contains orange marbles for every red marbles. if a bag has orange marbles, how many red marbles does it contain?
If a bag has 25 orange marbles, then it contains 40 red marbles.
In this question, we have been given each marble bag contains 5 orange marbles for every 8 red marbles.
We need to find the number of red marbles if a bag has 25 orange marbles.
Let there are n red marbles in a bag.
Using proportionality we get,
5/8 = 25/n
If we simplify this we get an equation,
n = 25 * (8/5)
n = 5 * 8
n = 40
Therefore, a bag contains 40 red marbles.
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