To rotate a point 90° counterclockwise about the origin, multiply the y -coordinate by -1 and then interchange, the x - and y -coordinates are (x,y) -> (-y,x)
What does the term "coordinates" mean?
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). There are various coordinate systems that mathematicians, physicists, and engineers frequently utilize.Rotation of 90° counter-clockwise about origin-
Think about the location (X, Y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 in order to rotate this point by 90 degrees around the origin in the opposite manner.
This would be expressed mathematically as follows
(x ,y) → ( -y ,x)
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Find the geometric mean between pair of numbers.
3√5/4 and 5√5/4
The geometric mean of 3√5/4 and 5√5/4 is 5√3/4.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 3√5/4 and 5√5/4 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 3√5/4, and x2 = 5√5/4
GM = √(3√5/4)(5√5/4)
GM = √(75/16)
GM = 5√3/4
Hence, the geometric mean of 3√5/4 and 5√5/4 is 5√3/4.
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Simplify each sum or difference. State any restrictions on the variables.
5y + 2 / x y² + 2 x-4 / 4xy
Simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .
As given in the question,
Given equation is [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex]
Simplify the given equation by taking the least common multiple,
[tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}\\\\\\= \frac{20y +8+2xy-4y}{4xy^{2}}\\ \\\\= \frac{2xy+16y+8}{4xy^{2}}\\ \\\\= \frac{xy+8y+4}{2xy^{2}}[/tex]
Restriction on the variables are x≠0 , y≠0.
Therefore, simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .
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Find the sum of each finite arithmetic series. 5+6+7+ . . . . . . +11
The sum of the given arithmetic series 5+6+7+ . . . . . . +11 is 56.
Suppose we are given an arithmetic series:
a(1) + a(2) + a(3) + a(4) + .... + a(n)
Then, each term of the series follow the general formula:
a(n) = a(1) + (n-1) . d
Where:
a(n) = nth term
a(1) = first term
d = common difference = a(n) - a(n-1)
We are given:
5+6+7+ . . . . . . +11
Parameters we get from this series:
a(1) = 5
d = 6 - 5 = 1
a(n) = 11
We need to find n that results in a(n) = 11
Substitute a(n) = 11, a(1) = 5, and d = 1:
a(n) = a(1) + (n-1) . d
11 = 5 + (n-1) . 1
11 = n + 4
n = 7
The sum of the first n terms of an arithmetic series is:
S(n) = n/2 [ a(1) + a(n) ]
S(7) = 7/2 (5 + 11)
= 7 . 8 = 56
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Two shops are selling the same DVD. In Tesco the DVD cost £11.49. In Asda the DVD
costs £13.99. Asda have an offer- "20% off all DVDs". Which shop should you buy the DVD
from?
Is -71 - 43 positive or negative?
Answer:
Negative
Step-by-step explanation:
1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x-2y = -16
Ographing
substitution
O elimination
distributive
(1 point)
Anyone know how to solve ?
Evaluate this exponential expression.
5•(3+6)²-62
Answer:
343Step-by-step explanation:
5×(3+6)²-62=
5×9²-62=
5×81-62=
405-62=
343
Need as soon as possible please
Answer:
Just graph, first one Y int: 2 and X is rise over run 1 and 2
Step-by-step explanation:
It is given that M is the midpoint of segment . Therefore by the definition of a midpoint. It is also given that Angles and are right angles. Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem, . Then, it follows that by the criteria. In congruent triangles, corresponding sides are congruent, thus . In conclusion by definition of congruent angles.
The congruency can also be tested by three postulates shown in the lesson: ASA (angle-side-angle), SAS (side-angle-side), and SSS (side-side-side). The first one claims that triangles are congruent if two angles and one side (between the angles) of one triangle are equal to two angles and one side of another triangle.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
A ∠ ≅ ∠ .
Vertical Angles Theorem: ...
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. ...If two angles are congruent and supplementary, then each is a right angle.Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).
Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem.
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Consider the set t = {1, 2, 3, 4, 5, 6}. let r = {(a, b) | a divides b} be a relation on the set t. the tabular representation for the ordered pairs of the given relation r on the set t is:_________
The ordered pairs of the given relation r on the set t is ungrouped data.
What is ungrouped data?The data you initially collect from an experiment or study is known as ungrouped data. The data is unsorted, unclassified, or otherwise grouped; it is therefore considered to be raw. A list of numbers is an ungrouped piece of data.
Ungrouped data is a distribution type where each piece of information is presented in its rawest form. For instance, a batsman's five most recent scores are 45, 34, 2, 77, and 80.
Raw data is another name for ungrouped data.
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What is line parallel to -x?
Answer:
I think its -y
Step-by-step explanation:
Answer:
x is my answer
Step-by-step explanation:
i don't know sorry
Samuel Sandoval sells furniture. He earns 4% commission on the first $2000 of sales. He earns 6%commission on all sales over $2000. Last week his furniture sales totaled $8230. How much did he earn make sure to show your work.
Answer:
Step-by-step explanation:
hi
Help wanted! Im I’m desperate need of assistance!
Answer:
-2/5
Step-by-step explanation:
Hi there!
We find slope by using rise over run.
For this problem, identify two points on the line. I'll use (0, 3) and (5, 1).
[tex] m = \frac{{y} - {y} }{ {x} - {x}}[/tex]
You can plug the coordinates into this formula, making sure they stay in the right order. Subtract the first y coordinate from the second y coordinate, and the first x coordinate from the second x coordinate. (Just make sure one point is on the left, and the other on the right).
[tex] \frac{3 - 1}{0 - 5} = \frac{2}{ - 5} [/tex]
2/-5 is the same as -2/5, so that is your answer
The temperature yesterday was 14 degrees Celsius. Today the
temperature dropped 14 degrees Celsius.
What is the current temperature?
Answer:
0
Step-by-step explanation:14 subtracted by 14 is 0
Complete the congruence statements for each pair of congruent figures below
Triangles are congruent if their matching interior angles and sides are all congruent.
What is congruence in math?
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.
Congruent figures: what are they?
Congruent figures have sides that are the same length and angles that are the same measurement. In other terms, two figures are said to be congruent when they are superimposed upon one another. Even when they are flipped or rotated, they perfectly fit on top of one another.What is congruent shapes?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.Learn more about congruent
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Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.
a. 11,60,61
The following set of numbers, 11, 60, and 61, can be the measures of the sides of a right triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 11, b = 60, and c = 61
a + b > c 11 + 60 > 61 71 > 61 True
a + c > b 11 + 61 > 60 72 > 60 True
b + c > a 60 + 61 > 11 121 > 11 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
11^2 + 60^2 = 3721
2. Compare it to the square of the largest side.
61^2 = 3721
3721 = 3721
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle.
if they are smaller, then it is an obtuse triangle.
Hence, 11, 60, and 61 can be the measure of the sides of a right triangle.
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A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.
The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
The largest angle is twice the smaller angle minus 30 degrees.
The sum of the triangle's interior angles is x + y + z = 180.
Which two equations represent the remaining angle relationships?
Select each correct answer.
1) x=y−z+40
2) x=2z−30
3) x=y+z−40
4) x=30−2z
5) x = y + z + 40
The correct answer would be option 2 and 3:
2) x=2z−303) x=y+z−40How to solve for the anglesWe have to sove the problem by carefully trying to understand the statements
x = largest angle
y = next largest angle
z = smallest.
1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.
largest angle < y + z
This would be represented as
x = y + z - 40
2. The largest angle is twice the smaller angle minus 30 degrees.
This is represented as
2 times of smallest = 2 * z = 2z
minus 30 degrees = 2z - 30
Hence the solutions to the question from the option that we have would be the options
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Answer:
2) x=2z−30
3) x=y+z−40
Step-by-step explanation:
The telephone company offers two billing plans for local calls. Plan 1 charges $23 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)
a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23
b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1
c. the number of monthly calls x is x > 100
What is inequality ?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Plan 1: $23 per month for unlimited calls
Plan 2: $19 per month + $0.04 per call
Let the number of calls be x
a. 19 +0.04x >23
0.04x >4
x > 100
b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.
On solving the above inequality, we get over 100 calls should be made so that Plan 1 is more economical than Plan 2.
c. x > 100
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what is a non-repeating decimal, give examples of nom repeating decimals.
Answer:
Recurring Decimal
Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).
Examples are
0.6666666666,
1.456456456
Step-by-step explanation:
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PLEASE ANSWER THIS!! ASAP! GIVE EXPLANATION OF HOW YOU GOT THE ANSWER (show your work!!) ASAP MATHE QUESTION
For this, we need to make ratios(unit per unit, in this case, red paint per white paint).
Sydney's Mix - [tex]\frac{7 red}{4 white}[/tex]
Maria's Mix - [tex]\frac{5 red}{3 white}[/tex]
Both of these fractions are improper, so you can make mixed fractions and then find their common denominators:
Sydney's Mix - 1[tex]\frac{3}{4}[/tex] = 1[tex]\frac{9}{12}[/tex]
Maria's Mix - 1[tex]\frac{2}{3}[/tex] = 1[tex]\frac{8}{12}[/tex]
Therefore, they do not have the same shade of pink because 1[tex]\frac{9}{12}[/tex] [tex]\neq[/tex] 1[tex]\frac{8}{12}[/tex] :)
please help with math homework
Using the Pythagorean Theorem, it is found that:
a) The hypotenuse is of 9.49 cm.
b) The new area of the triangle is of 30 cm².
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, the sides are given as follows:
3 cm and 9 cm.
Hence the hypotenuse is given by:
h² = 3² + 9²
h = sqrt(3² + 9²)
h = 9.49 cm.
The hypotenuse is of 9.49 cm.
What is the area of a right triangle?The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:
A = 0.5ab.
For this problem, we have that:
The side of 3 cm is increased by 2 cm, hence a = 5 cm.The side of 9 cm is increased by 3 cm, hence b = 12 cm.Then:
A = 0.5 x 5 x 12 = 30 cm².
The new area of the triangle is of 30 cm².
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PLEASE PLEASE PLEASE HELP!! ASAP!! BRAINLIEST FOR WORK THAT SHOWS ALL STEPS AND CORRECT ANSWERS!! :)
1. Factor the expression: x^6–729. Show your work for full credit.
2. Solve the equation 2x^2+16x–11= -7 by completing the square. Show your work for full credit.
3. Factor over the complex numbers. Show your work for full credit. x^4–5x^2–36
1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18
3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)
How to factorize expressions?
1) We are given the expression; x⁶ - 729
It can also be written as;
(x²)³ - 9³
Now, from factorization of algebra, we know that;
a³ - b³ = (a - b)(a² + ab + b²)
Thus;
(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)
= (x² - 9)(x⁴ + 9x² + 81)
= (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.
Add 7 to both sides to get;
2x² + 16x – 11 + 7 = -7 + 7
2x² + 16x – 4 = 0
Divide through by 2 to get;
x² + 8x – 2 = 0
Add 2 to both sides to get;
x² + 8x = 2
Take half of the x term and square it and then add the result to both sides to get;
x² + 8x + 16 = 2 + 16
Rewrite the perfect square on the left to get;
(x + 4)² = 18
Take square root of both sides to get;
x + 4 = ±√18
Subtract 4 from both sides to get;
x = -4 ± √18
x = -4 + √18 or -4 - √18
3) We want to factorize x⁴ – 5x² – 36
Using the difference of squares identity, we know that;
a² - b² = (a + b)(a - b)
Thus;
x⁴ – 5x² – 36 = (x² + 9)(x² - 4)
Now, (x² + 9) factored over the complex numbers gives;
(x² + 9) = (x + 3i)(x - 3i)
Thus;
x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)
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find the average of -1/12 + 4/17 - 3/28
Answer:
16/1071
Step-by-step explanation:
The average is the given by summing all the numbers and deciding by how many numbers you have
So, the answer is given by:
(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071
write each subtraction equation as an addition equation
a - 9 = 6
p - 20 = -30
z - (-12) = 15
x - (-7) = -10
Answer:
try it's your self i am sure you can do it.
Step-by-step explanation:
Let's go together
Find the sum of pair of vectors. <6,-31> + (-22,3)
According to the given statement The sum of pair of vectors are = (-16 , -28).
What precisely is vector addition?The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.
According to the given data:Given two vectors are:
a =(6,-31)
b = (-22,3)
The vector sum is,
M = (a1 + b1, a2 + b2)
= (Mx, My).
Substitution of the value we get:
M = (6 + (-22), (-31) + (3))
= (-16 , -28)
The sum of pair of vectors are = (-16 , -28).
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Suppose a total of 15 ounces of medicine is added to the original mixture (so that the total volume is now 25 ounces with 18 ounces of medicine and 7 ounces of water). How much water must now be added so that the mixture has the same proportion of medicine and water as the original mixture?
We have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
Given,
The quantity of medicine added to the original mixture = 15 ounces
New quantity of medicine in the mixture = 18 ounces
Quantity of water in the mixture = 7 ounces
Total new quantity of mixture = 18 + 7 = 25 ounces
Original quantity of medicine in the mixture = 18 - 15 = 3 ounces
Original quantity of water in the mixture = 7 ounces
Total original quantity of mixture = 3 + 7 = 10 ounces
We have to find the amount of water to add into the new mixture to make the proportion of medicine and water same as the original mixture.
Here,
Proportion of medicine and water in original mixture = 3:7
Quantity of medicine and water in new mixture = 18:7
Now,
18 ÷ 3 = 6
Then, 7 × 6 = 42
So, 42 - 7 = 35
Therefore, we have to add 35 ounces of water to the mixture to make the proportion of medicine and water same as the original mixture.
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An electronic store has television sets marked down 30 percent. What is the total price of five television sets that regularly sell for $115.75, $218.95, $320.75, $125.65, and $221.75?
Answer:
why did the teacher give an exam
A group of friends were working on a student film that had a budget of $1400. They
used 67% of their budget on props. How much money did they spend on props?
Answer:
That is wrong it is not $938 its $322
Step-by-step explanation:
STRUCTURE The students in Mrs. Mangione’s class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles. Select all that apply.
The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.
How to illustrate the information?When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:
= 2 × m
= 2m
The expression that represents the difference between the student's guess and the actual number of marbles will be:
= 1206 - 2m
= 2(603 - m)
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