You probably already have an idea of what a matrix is; it's a rectangular array of numbers. What they represent is a bit complicated to explain. There's a whole subject about it (see "linear algebra" for more info). Whatever they represent isn't important though, you don't need to know everything about matrices to compute their product (or whether it's even possible).
A quick definition: A matrix of dimension [tex]r[/tex]-by-[tex]c[/tex] is a matrix with [tex]r[/tex] rows and [tex]c[/tex] columns.
Matrix multiplication all comes down to an operation called the "dot product". It's defined by the sum of component-wise products of elements between two lists. What this means is, if [tex]x=\{1,2,0\}[/tex] and [tex]y=\{-1,0,3\}[/tex], then the dot product of [tex]x[/tex] and [tex]y[/tex] is
[tex]x\cdot y=(1)(-1)+(2)(0)+(0)(3)=-1+0+0=-1[/tex]
What we did was take the first elements of each list and multiplied them, and the same for the other two elements, then added them all together. Notice that the product can't be computed if [tex]x[/tex] and [tex]y[/tex] don't thave the same number of elements.
We write this product in matrix form as
[tex]\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}[/tex]
Notice the pattern here: on the left, a matrix with 1 row and 3 columns; on the right, a matrix with 3 rows and 1 column. The number of columns of the first matrix have to match the number of rows of the second.
The orientation makes a big difference. The product above returns a 1-by-1 matrix (or simply a scalar number):
[tex]\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}=\begin{bmatrix}(1)(-1)+(2)(0)+(0)(3)\end{bmatrix}=\begin{bmatrix}-1\end{bmatrix}=-1[/tex]
On the other hand, the alternate orientation would result in a 3-by-3 matrix.
[tex]\begin{bmatrix}1\\2\\0\end{bmatrix}\begin{bmatrix}-1&0&3\end{bmatrix}=\begin{bmatrix}(1)(-1)&(1)(0)&(1)(3)\\(2)(-1)&(2)(0)&(2)(3)\\(0)(-1)&(0)(0)&(0)(3)\end{bmatrix}=\begin{bmatrix}-1&0&3\\\-2&0&3\\0&0&0\end{bmatrix}[/tex]
So the number of rows of the first matrix and number of columns of the second matrix determine the number of rows and columns, respectively, of the matrix product.
I think we have enough information about matrix multiplication to answer this question. If [tex]A[/tex] has dimensions [tex]m\times n[/tex] and [tex]B[/tex] has dimensions [tex]n\times p[/tex], then the matrix product [tex]AB[/tex] exists ([tex]n[/tex] columns in [tex]A[/tex], [tex]n[/tex] rows in [tex]B[/tex]), but the matrix product [tex]BA[/tex] does not ([tex]p[/tex] columns in [tex]B[/tex], [tex]m[/tex] rows in [tex]A[/tex], but [tex]m\neq p[/tex]). So I is not true.
We know [tex]AB[/tex] exists, and with [tex]m[/tex] rows in [tex]A[/tex] and [tex] p[/tex] columns in [tex]B[/tex], we expect [tex]AB[/tex] to have [tex]m[/tex] rows and [tex]p[/tex] columns, so [tex]AB[/tex] has dimensions [tex]m\times p[/tex]. So II is true.
With dimensions [tex]r\times c[/tex], a matrix would contain [tex]rc[/tex] elements. [tex]m,n,p[/tex] are distinct, so [tex]mp\neq n^2[/tex]. So III is not true.
Answer: The correct option is
(d) I and II only.
Step-by-step explanation: Given that matrix A has dimensions m x n and matrix B has dimensions n x p where m, n, and p are distinct positive integers.
We are to select the one that is true from the following :
I. the product of BA doesn't exist
II. the product of AB exists and has dimensions m x p
III. the product of AB exists and has dimensions n x n
We know that two matrices X and Y can be multiplied if the number of columns in X is equal to the number of rows in Y.
Also, if X has dimensions a x b and Y has dimensions b x c, then the product XY is possible and it has dimensions a x c. Also, the product YX doesn't exist.
So, for the given matrices A and B, the following points are true :
(I) the product of BA doesn't exist.
(II) the product of AB exists and has dimensions m x p.
Thus, only I and II are TRUE.
Option (d) is CORRECT.
Which transformations map the strip onto itself?
PLEASE help!!!! Will give BRAINLIEST.
Thank you very much!
Answer: D.
A horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180° rotation.
The transformations that can map a strip onto itself in geometry are reflection, rotation, and translation. Reflection flips the shape over an axis, rotation turns it around a central point, and translation moves it along a vector without changing its orientation.
Explanation:In mathematics, particularly geometry, there are several types of transformations that can map a figure onto itself. Probably you are referring to a strip as in a planar shape, such as a rectangle or square. The main transformations that can map this strip onto itself are: reflection, rotation, and translation.
Reflection is like flipping the strip over an axis. If the strip is symmetrical, it will map onto itself. Rotation means turning the strip around a central point. For instance, rotating a square shape 90, 180, 270, or 360 degrees about its center will map it onto itself. Lastly, translation keeps the strip in the same orientation and moves it along a vector direction. As long as it doesn't interfere with its setting, it would still map onto itself.
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can someone help me with this question?
Answer:
Go to graphing website desmos.com and plug the equation in to see graph
Step-by-step explanation:
1) Starting graph: Linear Graph (x)
Translations:
|x| erase left and copy right, in this case it makes an absolute value graph or a "V graph" informal term
-3(move right)
-2(down 2)
2) Order goes as follows: "||", -3, -2
Graph: see attached
Translations:
The parent graph is y = |x|
a horizontal shift 3 units to the right makes a new graph of: y = |x - 3|
a vertical shift 2 units down makes a newer graph of: y = |x - 3| - 2
Translations are as follows:
horizontal shift 3 units to the rightvertical shift 2 units downIt takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour
Answer:
1 1/4 mph
Step-by-step explanation:
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
I hope this helps :)
Use the distributive property to remove the parentheses.
-5(-6w+3v-5)
Answer:
[tex] 30w - 15v + 25 [/tex]
Step-by-step explanation:
Multiply -5 by each term inside the parentheses.
[tex] -5(-6w+3v-5) = [/tex]
[tex] = -5 \times (-6w) + (-5) \times 3v + (-5) \times (-5) [/tex]
[tex] = 30w - 15v + 25 [/tex]
If the reclusive rule for a geometric sequence is a1 = 6 an = 2an-1.
What would be the explicit rule?
[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=6,\ a_n=2\cdot a_{n-1}.\\\\\text{Therefore}\ r=2.\ \text{Substitute:}\\\\a_n=6\cdot2^{n-1}=6\cdot2^n\cdot2^{-1}=6\cdot2^n\cdot\dfrac{1}{2}=\boxed{3\cdot2^n}[/tex]
How many different ways can the first 12 letters of the alphabet be arranged?
There are 479001600 different ways the first 12 letters of the alphabet can be arranged.
The first 12 letters of the alphabet can be arranged in 479,001,600 different ways.
The question asks how many different ways the first 12 letters of the alphabet can be arranged. This type of problem is addressed by using permutations, which is a concept in combinatorics, a branch of mathematics. When we talk about arranging a set of items, we are often dealing with permutations.
The formula to determine the number of permutations of a set of n distinct objects is given by n!, which is read as 'n factorial'. The factorial of a number n is the product of all positive integers less than or equal to n.
So, for the first 12 letters of the alphabet, which are 'A, B, C, D, E, F, G, H, I, J, K, L', the number of different ways to arrange these letters would be:
12! (12 factorial)
To calculate 12!, you multiply all the whole numbers from 1 to 12 together:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 479,001,600
SUPER EASY MATH QUESTION!!!!!! 25 POINTSSSSS!!!!!!!! PLEASE ANSWER CORRECTLY!!!!!!!!!!!!!!!!
Problem:
Five sisters each bought matching scarves and two pairs of socks. The scarves were priced at $12.00. If the total bill for all 5 sisters was $125.00, what was the price of one pair of socks? (Please answer in equation form. Ex: x = 29).
x - price of one pair socks
The equation:
[tex]5(2x)+5\times12=125[/tex]
[tex]10x+60=125[/tex] subtract 60 from both sides
[tex]10x=65[/tex] divide both sides by 10
[tex]\boxed{x=6.5}[/tex]
Answer: The price of one pair of socks is $6.50.5(2x) - five sisters · two pairs of socks
5 · 12 - five scraves
125 - total cost
Write an equation. Is the given value a solution? A farmer sees 23 of his cows out of the barn. He knows that he has 42 cows altogether. Let c represent the number of cows still in the barn. Could c = 19?
By establishing and solving the equation c + 23 = 42, where c represents the number of cows in the barn, it is demonstrated that c = 19 is indeed a correct solution to the problem.
The student needs to determine if c=19 is a solution for the equation representing the number of cows still in the barn. To represent the total number of cows with those seen outside and those inside, we can write the equation c + 23 = 42. This equation sums the number of cows outside (23) with those still in the barn (c) to get the total number of cows (42).
Calculating the Unknown
Firstly, define the symbol c as the number of cows still in the barn. Then, using our equation c + 23 = 42, we can solve for c by subtracting 23 from both sides of the equation, getting c = 42 - 23, which simplifies to c = 19.
Evaluating the Solution
Substituting c = 19 back into the original equation to check if it makes sense, we get 19 + 23 = 42, which is a true statement, confirming that the value of c is indeed 19 and it is the correct solution.
Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $6plus$3 per mile. The total fare was $24, not including tip. How many miles did Mike travel by taxi on this ride.
Answer:
6 miles
Step-by-step explanation:
AS Mike took the taxi from his home to airport and covered a distance
Initial fee of the ride was $ 6 which is fixed
Now with each mile he has to pay $3
Total he paid = $ 24
Now we have to find the total no of miles traveled by Mike
The tip given is 0
Now from the given we can make an equation
Initial fee + 3 * miles traveled = total Paid
Let total no of miles traveled are x
Putting all the values in the given equation
6 + 3 * x = 24
6 + 3x = 24
3x = 24-6
3x = 18
Dividing both sides by 3
x = 18 /3
x =6 miles
So the total miles traveled by him is 6 miles
The equation is $6 + $3 *m = $24, where m represents the number of miles traveled. Solving this, Mike traveled 6 miles.
The student's question concerns calculating the distance Mike traveled by taxi, given the initial fee and the per mile charge, as well as the total fare. To solve this, we can set up a simple algebraic equation. The initial fee is $6, and the charge per mile is $3. Since the total fare was $24, our equation becomes:
Initial fee + (charge per mile * number of miles) = Total fare
$6 + $3 * m = $24
Where m represents the number of miles Mike traveled. We will solve for m to find the distance Mike traveled
Subtract the initial fee from the total fare: $24 - $6 = $18Divide by the charge per mile to find the number of miles: $18 / $3 = 6 milesThus, Mike traveled 6 miles by taxi on this ride.
A family buys groceries for $154.35, including $10.37 in taxes. The bill includes $27.83 worth of items that are not taxable. Find the sales tax rate.
Your parents have $2745.69 on credit card with a 12.75% apr. They miss their minimum payment and there is a late fee of $29.00. How much is their balance at the beginning of they second month
Answer: Their balance at the beginning of their second month is $2803.86.
Step-by-step explanation:
Since we have given that
Amount on credit card = $2745.69
APR on credit card = 12.75%
Late fee = $29
According to question, they miss their minimum payment .
So, their balance at the beginning of their second month is given by
[tex]2745.69\times \frac{12.75}{12\times 100}\\\\=29.17\\\\\text{After late fees }=29.17+29\\\\=58.17\\\\\text{ Amount in the beginning of their second month }\\\\=\$2745.69+58.17\\\\=2803.86[/tex]
Hence, their balance at the beginning of their second month is $2803.86
Answer:
2,803.86
Step-by-step explanation:
Using the attached link below.
A. Find sin x and csc y
B. Find tan x and cot y
C. Find cos x and sec y
D. And if sin theta = 2/3, find the values of cos theta and tan theta
[tex]\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}[/tex]
[tex]\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}[/tex]
[tex]\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}[/tex]
[tex]A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}[/tex]
[tex]D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}[/tex]
CDs are on sale for $5 each.Jennifer has $45 and wants to buy as many as she can.How many CDs can Jennifer buy?
Answer: (9 CDs)
If she has $45 and the CDs cost $5. The most she can buy is 9 CDs
The number of maximum CDs that Jennifer can buy is 9.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
As per the given,
Cost of one CD = $5
Jennifer budget = $45
Number of CDs can buy = Jennifer's budget/cost of one CD
Number of CDs can buy = 45/5 = 9
Hence "The number of maximum CDs that Jennifer can buy is 9".
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There are 7 students in a class: 2 boys and 5 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?
Answer:
Two sevenths
Step-by-step explanation:
Final answer:
To find the probability that everyone in the group is a girl, we use the combination formula to calculate the number of ways to choose a group of 3 from 7 students and the number of ways to choose 3 girls from the 5 available. The probability is 2/7.
Explanation:
To find the probability that everyone in the group is a girl, we need to consider the total number of ways to choose a group of 3 from the 7 students, and the number of ways to choose 3 girls from the 5 available.
The total number of ways to choose a group of 3 from 7 is given by the combination formula, which is:
C(7, 3) = 7! / (3! * (7-3)!) = 35
The number of ways to choose 3 girls from 5 is:
C(5, 3) = 5! / (3! * (5-3)!) = 10
Therefore, the probability that everyone in the group is a girl is:
P(girls) = C(5, 3) / C(7, 3) = 10 / 35 = 2/7
Three electrical appliances each have power ratings of 1 7/8 watts, and 2 other appliances each have power ratings of 4 3/4 watts.What is the total power used by these appliances?
Answer:
11 3/8 watts
Step-by-step explanation:
1 7/8 converts to 1.875
4 3/4 converts to 4.75
4.75 * 2 = 9.5
9.5 + 1.875 = 11.375
11.375 converts to 91/8 or 11 3/8
M is the midpoint of YZ. If YM = x + 3, and YZ = 3x -1, find MZ
The length of {MZ} will be equivalent to -
MZ = 4 - 2x.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that M is the midpoint of YZ. Also, it is given that YM = x + 3, and YZ = 3x - 1.
Midpoint divides the line into two equal parts.We can write -
YM + MZ = YZ
(x + 3) + MZ = (3x - 1)
MZ = (x + 3) - (3x - 1)
MZ = x + 3 - 3x + 1
MZ = 4 - 2x
Therefore, the length of {MZ} will be equivalent to -
MZ = 4 - 2x.
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Sweets are sold loose, or pre-packed in 120g bags. The 120g bags are ?1.49 each. The loose sweets are ?0.89 for 100g. By calculating the price per gram, determine which is better value.
Answer:
The loose sweets at ?0.89 for 100 g.
Step-by-step explanation:
First, calculate the price per gram. You do this by dividing the price by the grams.
?1.49 / 120 g = 1.49 / 120 = 0.0124 (4 dp)
Because the answer was very long, I have rounded it to 4 decimal places (4 dp).
?0.89 / 100 g = 0.89 / 100 = 0.0089
Next, you must calculate both pre-packed and loose sweets to the same weight. I am calculating them both to 100 g.
0.0124 x 100 = 1.24
0.0089 x 100 = 0.89
Finally, the cheapest product for 100 g will be the better value. In this case, it is the loose sweets.
1 _____ 2
Choose the relationship symbol to make a true statement.
<
=
>
Answer:
The answer =
Step-by-step explanation:
Sarah bought a shirt on sale for $35. The original price of the shirt was three times that amount Sarah also bought a pair of shoes on sale for $28 they original price of the shoes with five times that amount together how much money did the shirt and shoes cross before they went on sale.
Answer:
$245
Step-by-step explanation:
Orignal price for shirt was 105
Original price for shoe sizes was 140
105+140=245
In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE.
To find the measures of the angles in ΔADE, we can apply the angle bisector theorem and the fact that DE is parallel to AB. The measures of ∠ADE, ∠AED, and ∠DAE are denoted as x, y, and z, respectively.
Explanation:In ΔADE, we know that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B. We also know that DE is parallel to AB. Given that m∠ADE is 34° smaller than m∠CAB, we need to find the measures of the angles in ΔADE.
Let's denote the measures of ∠ADE, ∠AED, and ∠DAE as x, y, and z, respectively.
From the angle bisector theorem, we know that ∠CAD = ∠DAB = y+z.
Since DE is parallel to AB, we have ∠ADE = ∠CAB = x+y+z.
Therefore, the measures of the angles in ΔADE are ∠ADE = x, ∠AED = y, and ∠DAE = z.
A bouquet of flowers contains 46 flowers and half of them are roses.How many of the flowers are not roses
Answer:
23
Step-by-step explanation:
46 divided by 2
equals:23
he law of cosines for RST can be set up as 52 = 72 + 32 – 2(7)(3)cos(S). What could be true about RST? Law of cosines: a2 = b2 + c2 – 2bccos(A)
Answer:
The length of RT is 5. The length of RS and ST is either 7 or 3.
Step-by-step explanation:
The Law of Cosine is defined as
[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]
It is given that, the law of cosine for triangle RST can be set up as
[tex]5^2=7^2+3^2-2(7)(3)\cos(S)[/tex]
Therefore the length of opposite side of angle S is 5. The opposite side of angle S is RT, therefore the length of RT is 5.
The length of two other sides are either 7 or 3.
Therefore length of RT is 5. The length of RS and ST is either 7 or 3.
Answer:
answer is d on edge
Step-by-step explanation:
at the beginning of the week, Miguel's odometer reads 87,845. At the end of the week, his odometer reads 88,003. How many miles did Miguel travel that week?
Hey there.
To do this, we simply just subtract. 88,003-87,845
Once we do this, we get 158. Miguel traveled 158 miles that week.
-TheOneandOnly003
Answer:
87,845-88,033= -188 so he traveled 188 miles that week.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
Multiply.
Answer:
Alternative A
Step-by-step explanation:
2x(x² + 2x - 6)
2x³ + 4x² - 12x
I hope I helped you
Answer: A
Step-by-step explanation:
2x(x² + 2x - 6)
= 2x(x²) + 2x(2x) + 2x(-6)
= 2x³ + 4x² - 12x
Tim can eat 7 apples at a time and barry can eat 2 apples at a time . How many more apples can tim eat
Answer: 5
Step-by-step explanation: Take 2 from 7 to get 5
The ratio of the lengths of the corresponding sides of two rectangles is 8:3 . The area of the larger rectangle is 320 ft. What is the area of the smaller rectangle
solve using quadratic equation: 6x^2 + 7x +2=0
35 pts!! Please help this will help me graduate!!!
Consider this system of equations:
-3x + 5y = 22 (equation 1)
20y − 11 = 12x (equation 2)
This system of linear equations represents ___lines.
(A. coincidental B. Intersecting C. parallel)
The system of equation 1 and the equation 20y = 12x + 88 represents___ lines.
(A. coincidental B. Intersecting C. parallel)
Answer:
This system of linear equations represents parallel lines.
The system of equation 1 and the equation 20y = 12x + 88 represents coincidental lines
Step-by-step explanation:
-3x + 5y = 22 (equation 1)
Lets solve the equation for y
Add 3x on both sides
5y= 3x+22
Now divide by 5 on both sides
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of equation 1 is [tex]\frac{3}{5}[/tex]
20y − 11 = 12x (equation 2)
solve for y
Add 11 on both sides
20y = 12x + 11
Divide by 20 on both sides
[tex]y=\frac{12x}{20}+ \frac{11}{20}[/tex]
simplify the fraction
[tex]y=\frac{3x}{5}+ \frac{11}{20}[/tex]
Slope of equation 2 is [tex]\frac{3}{5}[/tex]
Slope of equation 1 and equation 2 are same , so the lines are parallel
This system of linear equations represents parallel lines.
-3x + 5y = 22 (equation 1) and 20y = 12x + 88
Solve both equations for y
-3x + 5y = 22 (equation 1)
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of equation 1 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5
20y = 12x + 88
Divide by 20 on both sides and simplify the fraction
[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]
Slope of 20y=12x+88 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5
Slope and y intercepts are same so the lines are coincidental
The system of equation 1 and the equation 20y = 12x + 88 represents coincidental lines
2) Line segment MK has endpoints at (2, 3) and (5, ?4). Segment M'K' is the reflection of MK over the y-axis. Which statement describes the relationship between MK and M'K'? A)M'K' is twice the length of MKB)M'K' is half the length of MK.C)M'K' is the same length as MK.D)More information is needed to determine the relationship
Answer:
Option C -M'K' is the same length as MK
Step-by-step explanation:
Given : Line segment MK has endpoints at (2, 3) and (5,4)
M'K' is the reflection of MK over the y-axis
By definition of reflection: reflection of point (x,y) across the the y-axis is the point (-x,y)
which implies M'K' has end points (-2,3) and (-5,4)
Now, we find the length of MK
let [tex](x_1,y_1)=(2,3)\\\\(x_2,y_2)=(5,4)[/tex]
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
⇒ [tex]d=\sqrt{(2-5)^2+(4-3)^2}[/tex]
⇒[tex]d=\sqrt{9+1}[/tex]
⇒[tex]d=\sqrt{10}[/tex] ....(1)
Now, we find the length of M'K'
let [tex](x_1^{'},y_1^{'})=(-2,3)\\\\(x_2^{'},y_2^{'})=(-5,4)[/tex]
[tex]d^{'}=\sqrt{(x_2^{'}-x_1^{'})^2+(y_2^{'}-y_1^{'})^2}[/tex]
⇒ [tex]d^{'}=\sqrt{(-2+5)^2+(3-4)^2}[/tex]
⇒[tex]d^{'}=\sqrt{9+1}[/tex]
⇒[tex]d^{'}=\sqrt{10}[/tex] .....(2)
from (1) and (2) we simply show that the length of MK and M'K' is equal
we can also refer the figure attached for reflection of MK and M'K'
therefore, Option C is correct
Answer:
M'K' is the same length as MK.
Step-by-step explanation:
A reflection is a rigid transformation. Rigid transformations do not affect the length of the line segment
A store has a sale on paper cups, 2 packs for $15.00. There are 100 cups in each pack. During the sale, what is the unit price per cup?
15/2=7.5
7.5/100=0.075
0.075$ per cup.
-TheOneandOnly003
The unit price per cup during the sale is calculated by dividing the total cost of $15.00 by the total number of cups (200). The result is $0.075 per cup.
Explanation:To find the unit price per cup during the sale, we must first determine the total amount of cups you are getting for the price. Given that you purchase 2 packs for $15.00, and each pack contains 100 cups, you're buying a total of 200 cups for $15.00. To get the price per cup, you then divide the total price by the total number of cups.
Step 1: Calculate the total number of cups: 2 packs * 100 cups/pack = 200 cups
Step 2: Calculate the price per cup: $15.00 / 200 cups = $0.075 per cup
So, the unit price per cup during the sale is $0.075.
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