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]
Oscar is selling tickets to a school play. Adult tickets cost $8 and student tickets cost $7. If he collected $245 by selling 34 tickets, how many adult and student tickets did he sell?
Answer:
Adult= 7 tickets
student= 27 tickets
Step-by-step explanation:
Step one:
let adult tickets be x
and students be y
Adult tickets cost $8 and
student tickets cost $7
So
[tex]8x+7y=245-----------1\\\\x+y=34-----------2[/tex]
Step two:
from equation 2
x=34-y
put the value of x in equation 1
[tex]8(34-y)+7y=245\\\\272-8y+7y=245\\\\272-y=245\\\\-y=245-272\\\\-y=-27\\\\y=27[/tex]
put y= 27 in equation 1
[tex]x+27=34\\\\x=34-27\\\\x=7[/tex]
1
For every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of
cornstarch. How many teaspoons of white vinegar are there for every tablespoon of cornstarch?
A. 1
5
В.
C 1
D. 5
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
What is the 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 that, for every 2 teaspoons of white vinegar in a jar of homemade glue, there are 5 tablespoons of cornstarch.
The number of teaspoons of white vinegar are there for every tablespoon of cornstarch = 2/5
= 0.4
Therefore, the number of teaspoons of white vinegar are there for every tablespoon of cornstarch is 0.4.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ6
Determine if the graph of the quadratic equation opens up or down and is wider or narrower than the graph y=x?
y = -x? +2
Answer:
y = -x^2 +2
Step-by-step explanation:
? means like add something in. Like ^2 is what I added in.
https://brainly.com/question/20359398. This is what I learned after this chapter. (Concept.) You can learn about it and get ahead if they'll learn this.
4 1/3 Divided by 1/2
16 liters to quarts (dry measure)
Answer:
16 litres =14.53 US qt dryStep-by-step explanation:
Please mark my answer as a brainliest. ❤❤❤Sam’s height is 1.58 m. His younger brother Tom’s height is 0.4 m less than his height. What is Tom’s height?
A)1.58 m B) 1.54 m C)1.98 m D) 1.18 m
Sam's height= 1.58m
Tom's height= 0.4m less than Sam's
= (1.58- 0.4)m
= 1.54m
Which of the following equations are linear?
Hint: Two of them are linear.
1. y = 7/x
2. y = 3x + 4
3. 3x + 4y = 24
Final Answer: They are all Linear
Steps/Reasons/Explanation:
Question: Which of the following equations are linear?
1. [tex]y = \frac{7}{x}[/tex] Linear
2. [tex]y = 3x + 4[/tex] Linear
3. [tex]3x + 4y = 24[/tex] Linear
Because a linear equation is an equation of a straight line, it means that the degree of a linear equation must be 0 or 1 for each of its variables.
~I hope I helped you :)~
What is the perimeter of a rectangle with a height of 4 units and a length of 21 units?
A 75 units
B 44 units
С 25 units
D 50 units
Answer:
С 25 units
Step-by-step explanation:
hope this help
pick me as the brainliest
Answer:D
Step-by-step explanation:
Given f(x) = 2^x and g(x)=x+1, (fog)(x)=
Answer:
(f ￮ g)(x) = [tex]2^{x+1}[/tex]
Step-by-step explanation:
Substitute x = g(x) into f(x) , that is
(f ￮ g)(x)
= f(g(x))
= f(x + 1)
= [tex]2^{x+1}[/tex]
Answer:
B
Step-by-step explanation:
Find the area and perimeter of the original planned patio and the new planned patio. MIT HINDI MT Luis decided to make the patio 2 feet longer. The drawing shows his new plans for the patio. New planned patio 8 feet 10 feet 2 feet
Answer:
original
perimeter - 36 feet
area - 80 square feet
new patio
perimeter - 40 feet
area - 96 square feet
_______ is the highest point in the entire graph.
A. relative maximum
B. absolute maximum
C. relative minimum
D. relative maximum
Answer:
B
Step-by-step explanation:
Will give brainliest
Answer:
B
Step-by-step explanation:
I just know it.
Solve using substitution.
- x - y = -1
X = 2
Answer:
x = 2
y = -1
Step-by-step explanation:
-(2) - y = -1
add 2
-y = 1
divide by -1
y = -1
Acardboard popcom container is shaped like a cone that is 11 inches high and has a radius of 2.5 inches What is the volume of the container? Use 3 14 for pi Round your answer to the nearest hundredth
Answer:
71.99 in³
Step-by-step explanation:
The formula to apply is that of volume of a cone where;
V=π*r²*h/3 --------where V is the volume of the container, r is the radius of the container and h is the height of the container
Given that : π=3.14 , r is 2.5 inches , h= 11 inches then apply values to the container as;
V= 3.14 * 2.5²* 11/3
V= 3.14 * 6.25 * 3.67
V= 71.9948
V= 71.99 in³
Answer:
Volume of Cone= 71.9583
Step-by-step explanation:
Volume of Cone= (1/3)πr²h
Volume of Cone= (1/3)×3.14×(2.5)²×11
Volume of Cone= 71.9583
PLZ ANSWER IF U KNOW THE ANSWER
I need help finding witch one is right
Answer:
I believe it's B!
Step-by-step explanation:
y=mx+b
y intercept is b
slope is m
y intercept is positive 5
slope is down 2 to the right 3
y= -2/3x+5
Answer:
The answer is B.
Step-by-step explanation:
In a slope form equation, y = mx + b where m represents gradient and b is y-intecept. In the graph above, the line shows a negative gradient and the y-intercept is 5. So the possible option is B.
What is this? Please answer with an explanation
Answer:
x=9,30............etc
Step-by-step explanation:
if value of x=9 then
the function
value of f(x)=4
if x=30 then value of function f(x)=27
Select all the expressions that are equivalent to 9 + 7x – 3y.
Answer:
9 – (–7)x – 3y
Step-by-step explanation:
because - * - = +
so 9 – (–7)x – 3y = 9+7x -3y
Proving Triangles Similar CFU
Determine if the triangles are similar. If similar, state how and complete the similarity
statement. If not similar, select N/A for the last two responses.
F
יח
12
18
8
14
10
2
21
Are the triangles similar?
How are they similar?
Complete the similarity statement: AY FN - A
Answer:
yes
they are similar because they are proportionally related
YRW
WILL GIVE BRAINLIEST TO EVER ANSWERS FASTEST WITH CORRECT ANSWER!
Answer:
9,450 feet
Step-by-step explanation:
plz help! will give brainliest!
x^6
When multiplying numbers in exponential form, if the number is the same, you can simply add the exponents:
x^2 * x^4 = x^(2+4) = x^6
For the right triangle shown, which equation is correct?
1. all answers are correct
2. cos(53) = x/16
3. cos(53) = sin(37)
4. sin(37) = 16/x
Answer:
3.37
Step-by-step explanation:
x+37+16+90=180
x+143=180
×=180-143
x = 37
A mercury thermometer records a temperature of 10°F at 9 a.m. If the temperature drops by 3°F every hour, what will be the temperature by 2 p.m.?
Answer:
No
Step-by-step explanation:
At the first game of the Major League Baseball season, a statistician keeps track of every pitch that a player throws during the game. The statistician reported that the mean pitch speed was 80 miles per hour (mph) and the standard deviation of the serve speeds was 10 mph. Assume that the statistician also gave us the information that the distribution of pitch speeds was mound- shaped and symmetric. What percentage of the player's serves were between 80 mph and 100 mph
Answer:
47.725%
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 80 mph
σ is the population standard deviation = 10 mph
For x = 80 mph
z = 80 - 80/10
z =0
Probability value from Z-Table:
P(x = 80) = 0.5
For x = 100 mph
z = 100 - 80/10
z = 2
Probability value from Z-Table:
P(x = 100) = 0.97725
Probability of the player's serves thay were between 80 mph and 100 mph is calculated as:
P(x = 100mph) - P(x = 80 mph)
= 0.97725 - 0.5
= 0.47725
The percentage of the player's serves that were between 80 mph and 100 mph is calculated as:
Converting to percentage:
0.47725 × 100 = 47.725%
PLSSSSSS I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simplify the Expression:
[tex]\sqrt{9a^{2} }[/tex], if a<0
[tex]\sqrt{9a^{2}}=\sqrt{9}\sqrt{a^{2}}=3|a|[/tex]
As [tex]a < 0[/tex], [tex]|a|=-a[/tex], so [tex]3|a|=\boxed{-3a}[/tex]
What is the answer to 3/4x1/7
Answer:0.1072
Step-by-step explanation:
Siri
PLS HELP MY GRADE DEPENDS ON IT
Image is attached below
Answer: the first one
Step-by-step explanation: head math
Estimate 48% of 199o
Answer:
Not sure if this is a typo but
48% of 199=95.52
48% of 1990=955.2
Step-by-step explanation:
Answer: 95.52.
Explanation: First take 199 then do times 48, then you'd get 95.52. Hope that helps!
2/3 of a cake is divided between 6 friends. How much do they each get?
Answer:
4
Step-by-step explanation:
2/3 x6/1
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{6}{1}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{6}[/tex]
To change the ÷ sign to a × sign, swap the denominators and numerators of the second fraction.
[tex]\frac{2}{3}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{2}{18}[/tex]
Directly multiply. Numerators with numerators and denominators with denominators.
[tex]\frac{2}{18}[/tex] = [tex]\frac{1}{9}[/tex]
Divide the fraction by 2 to simplify it.
EMERGENCY PLEASE HELP! Which set of ordered pairs does not represent a function?
A. {(1,2), (7,8)}
B. {(-4,4),(-2,2),(-1, 1)}
C. {(1,1),(1,2)
D. {(-5,-4),(3,6)}
E. {(0,1),(1, 1), (2, 1)}
Answer:
c.
Step-by-step explanation:
The X value 1 is repeated