Answer:
[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]
Step-by-step explanation:
Given
[tex]T:R^3->R^2[/tex]
[tex]T(e_1) = (1,2)[/tex]
[tex]T(e_2) = (-4,6)[/tex]
[tex]T(e_3) = (2,-6)[/tex]
Required
Find the standard matrix
The standard matrix (A) is given by
[tex]Ax = T(x)[/tex]
Where
[tex]T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right][/tex]
[tex]Ax = T(x)[/tex] becomes
[tex]Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right][/tex]
The x on both sides cancel out; and, we're left with:
[tex]A = [T(e_1)\ T(e_2)\ T(e_3)][/tex]
Recall that:
[tex]T(e_1) = (1,2)[/tex]
[tex]T(e_2) = (-4,6)[/tex]
[tex]T(e_3) = (2,-6)[/tex]
In matrix:
[tex](a,b)[/tex] is represented as: [tex]\left[\begin{array}{c}a\\b\end{array}\right][/tex]
So:
[tex]T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right][/tex]
[tex]T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right][/tex]
[tex]T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right][/tex]
Substitute the above expressions in [tex]A = [T(e_1)\ T(e_2)\ T(e_3)][/tex]
[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]
Hence, the standard of the matrix A is:
[tex]A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right][/tex]
Sam is baking 10 pies for a school bake sale. He
uses 21 cups of apples for 6 pies. How many
cups of apples will he need in all? Explain
Answer:
Step-by-step explanation:
21/6 = 3.5. This means each pie requires about 3.5 cups of apples. So, 3.5x10 = 35 cups of apples needed overall
Answer:
35 cups of apples
Step-by-step explanation:
BRANLIEST TO CORRECT ANSWER!!!
Which statements describe vascular tissue?
Check all that apply.
The primary purpose of vascular tissue is to support the plant and help it stand upright.
Phloem carries food made during photosynthesis to other parts of the plant.
Phloem contains the chloroplasts.
Xylem moves water and nutrients throughout the plant.
Xylem is the protective, waxy layer on a plant that prevents water loss.
Answer:
Xylem moves water and nutrients throughout the plant.
Answer:
B and D
Step-by-step explanation:
most people in the comments said it was right so I tried it and got it right
Write the following series in sigma notation. 4 +13 +22 + 31 +40 +49 +58
Answer:
Step-by-step explanation:
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
Find the difference.
Need help fast!
Answer:
D
Step-by-step explanation:
18 - 3 = 15
Which value is equivalent to the expression 45?
Answer:
what value are you talking about
Step-by-step explanation:
Answer:
It's 1024
Step-by-step explanation:
Name AT LEAST 3 other words that are a synonym for a ROOT of a polynimal
Answer:
Root of polynomial synonyms: zero, x-intercept
Step-by-step explanation:
Technically in calculus we also call roots critical points of f, but I'm not sure of the obvious 3rd word. Maybe horizontal intercept?
PLEASE HURRY! (And only respond if you know the answer please.)
A Web music store offers two versions of a popular song the size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 2737 MB. How many downloads of the standard version were there?
Answer:
Step-by-step explanation:
If the no of standard version downloads = 230
Then higher version is twice than that = 460
Total = 2.1 x 230 + 4.9 x 460 = 2737
Prove that: 6^7-6^6+6^5 is divisible by 31
15 points!!!
Step-by-step explanation:
[tex]6^7-6^6+6^5=6^{5+2}-6^{5+1}+6^5\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=6^5\cdot6^2-6^5\cdot6^1+6^5\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=6^5\cdot(6^2-6^1+1)=6^5\cdot(36-6+1)=6^5\cdot31\\\\6^7-6^6+6^5=6^5\cdot31[/tex]
therefore it's divisible by 31
[tex](6^7-6^6+6^5):31=(6^5\cdot31):31=6^5[/tex]
[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]6^7 - 6^6 + 6^5[/tex] s
Taking common factors.
[tex]6^5[/tex] (6² - 6 + 1)
[tex]6^5[/tex] (36 - 6 + 1)
[tex]6^5[/tex] x 31
This is divisible by 31.
Thus,
[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.
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Ian invested $90,000 in an account paying an interest rate of 2.6% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 7 years?
Answer:
A≈107902
Step-by-step explanation:
The $107,902 will be in account after 7 years if Ian invested $90,000 in an account paying an interest rate of 2.6% compounded quarterly
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
p = $90,000
r = 2.6% = 0.026
n = 4
t = 7 years
[tex]\rm A = 90,000(1+\dfrac{0.026}{4})^{4\times7}[/tex]
A = $107,901.71 ≈ $107,902
Thus, the $107,902 will be in account after 7 years if Ian invested $90,000 in an account paying an interest rate of 2.6% compounded quarterly.
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Define curvature and state it's formula
Answer:
I am not sure what the formula is, so I apologize for that.
The curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
Step-by-step explanation:
Please give me the correct answer
Answer:
the correct answer is 5 places
Please give me the correct answer
what is the quotient 2 1/5 over negative 1/10
Answer:
25
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
those 2 1/5 divided by 1/10 = -22
hey im dum dum what's 45*23455/76?
Answer:
13887.8289474
Step-by-step explanation:
i used a calculator cuz im dum too lol
Answer:
45*23455/76 = 133887.82894736
Rosabell had 27 posters for the parade, she droppd 19 while marching in the parade. how many does she hav left.
PLEASE HELP ILL GIVE YOU BRAINLIEST
Answer:
78.54
Step-by-step explanation:
So the rounded answer would be 100. I honestly am not 100% sure. I just looked it up. sorry if it is wrong! :c
JK has endpoints located at J(15,-13) and K(-9,27) what are the coordinates of the midpoint JK.
A.(3,7)
B.(12,20)
C.(1,9)
D.(14,18)
Answer:
(3, 7)
Step-by-step explanation:
The formula for calculating the midpoint of two coordinates is expressed as:
M(X, Y) = [x1+x2/2, y1+y2/2]
Given the coordinates J(15,-13) and K(-9,27), the coordinates of the midpoints is expressed as:
X = 15-9/2
X = 6/2
X = 3
Similarly,
Y = y1+y2/2
Y = -13 +27/2
Y = 14/2
Y = 7
Hence the coordinate of the midpoint is at (3, 7)
if a= -2 b = -3 and c = 2
4a-[3b+2c]
Answer:
yess thir correct answer
Select the correct answer from the drop-down menu.
need help fast please!
Answer:
i think its the first one
Step-by-step explanation:
if u subtract it , then it shouldn't be given a + sign at all
it should stay subtraction
have a good day! :)
plz give me brainliest
Answer: -7x to the seventh power+ x
Step-by-step explanation:
I. What is
42% of
18?
need help fast!
Answer:
It is 7.56!
Other:
Brainliest? Thanks!
Eddie's Evergreens sells Christmas trees and wreaths. Trees cost 3 dollars more than 4 times the price of each wreath. It costs $ 99 buy 2 wreaths and 1 tree . How much does each wreath cost? How much does each tree cost?
Answer:
[tex]W = 16[/tex]
[tex]T = 67[/tex]
Step-by-step explanation:
Represent trees with T and wreaths with W
Given
[tex]T = 3 + 4 * W[/tex]
[tex]2 * W + T = 99[/tex]
Solving (a): Cost of W
Substitute 3 + 4 * W for T in the second equation
[tex]2*W + 3 + 4 * W = 99[/tex]
[tex]2W + 3 + 4 W = 99[/tex]
Collect Like Terms
[tex]2W + 4 W = 99 - 3[/tex]
[tex]6W = 96[/tex]
Divide through by 6
[tex]W =\frac{96}{6}[/tex]
[tex]W = 16[/tex]
Hence, each wreath costs $16
Solving (b): Cost of T
[tex]T = 3 + 4 * W[/tex]
Substitute 16 for W
[tex]T = 3 + 4 * 16[/tex]
[tex]T = 3 + 64[/tex]
[tex]T = 67[/tex]
Hence, each tree costs $67
Morgan's way to solve the equation |2x-7| =5 is first to write |x-3.5|=2.5. explain this approach, and then finish the job.
Answer:
Morgan divided 2 throughout the original equation, giving her |x-3.5|=2.5.
x = 6 and x = 1
Step-by-step explanation:
|2x-7|=5 -- divide by 2
|x-3.5|=2.5 and |x-3.5|=-2.5 -- since this is an absolute value equation, we have to consider both positive and negative
x-3.5 = 2.5
x = 6
x-3.5 = -2.5
x = 1
The list shows numbers in order from least to greatest. -34, -2 .-1.5.0.2.3, 10,25 Which is an integer that can be integer on the blank line in the list? 0 -2.5 -2 1 0 -1
Answer:-2
Step-by-step explanation: I think
Answer: -2
Step by step explaination:
To walk to her friend's house, Cristal normally walks 63 yards north and 16 yards east as shown. How many
yards shorter would it be if Julie took the diagonal shortcut, x?
16 yd
63 yd
х
A
(10
Answer:
65 yd
Step-by-step explanation:
The image of this walking path of Cristal is missing, so i have attached it.
From the image attached, we can see that the path "x" is the hypotenuse path a the triangle.
Thus, we can use pythagoras theorem to find the area. Thus;
x² = 16² + 63²
x = √(16² + 63²)
x = √4225
x = 65 yd
Can anyone solve this.
Answer:
x-1+5x+1=180, 6x=180, x=30
Step-by-step explanation:
PLEASE HELP DUE IN 5 minutes
James earns $12 per hour for working at an appliance store. He also earns a weekly bonus of $36 if he makes a total of 7 or more sales during a given week Last week , James made 7 sales and earned a total of $300 for x hours of working at the appliance store . How many hours did James work?
Answer:
22 hours
Step-by-step explanation:
12 per hour.
$36 = 7 sales.
(300-36)/12=22
So 22 hours.
Hope this helps plz hit that crown !!!
James worked for 20 hours.
what is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given here, James earns $12 per hour and weekly bonus of $36 if he makes a total of 7 or more sales during a given week and earned a total of $300 . Let the time that James worked for be x , then we can form an equation;
36 + 12x = 300
⇒ 12x = 240
⇒ x = 20 hours
Hence, James worked for 20 hours.
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4) Bobby made $6 on an item he sold for $40. What is the commission
rate that Bobby receives on items he sells? *
O a. 666.67%
O b. 34%
O c.15%
O d. 2.4%
Answer:
C
Step-by-step explanation:
I solved it. I promise it is the right answer
You need to purchase supplies for an employee appreciation picnic. Your boss gives you the shopping list below and asks that you get the best deal by buying from one grocer, either Quality Groceries or Fresh Market. You call both grocers, and they provide the price information that you put into the table. Which grocer will provide all these picnic supplies for the lowest cost, and what is that cost without sales tax?
Hamburger Patties 50
Hot Dogs 2 dozen
Hamburger Buns 50
Hot Dog Buns 2 dozen
Potato Salad 2 gallons
Ice Cream 5 gallons
Product Quality Groceries Unit Quality Groceries Price per Unit Fresh Market Unit Fresh Market Price per Unit
Hamburger Patties Package of 10 $15.50 Package of 8 $12.40
Hot Dogs Package of 12 $6.23 Package of 10 $4.99
Hamburger Buns Package of 8 $3.79 Package of 8 $3.55
Hot Dog Buns Package of 12 $2.75 Package of 8 $2.55
Potato Salad Gallon $4.33 Gallon $5.55
Ice Cream Gallon $7.55 Gallon $6.99
Answer:
this doesnt make sense is there any type of picture or more explanation on the question? i'll still help :)
Step-by-step explanation:
Which table shows exponential decay?