Answers
Answer: C. [tex]B=\left[\begin{array}{ccc}1\\3\\-5\end{array}\right][/tex]
Step-by-step explanation: I got this right on Edmentum.
Several operations such as addition, subtraction, multiplication, etc. can be performed on matrices. The value of matrix B is:
[tex]B =\left[\begin{array}{c}1&3&-5\end{array}\right][/tex]
Given that:
[tex]A =\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right][/tex]
[tex]AB =\left[\begin{array}{c}24&-46&-2\end{array}\right][/tex]
Let matrix B be:
[tex]B =\left[\begin{array}{c}a&b&c\end{array}\right][/tex]
The product of A and B is as follows:
[tex]\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right] \times\left[\begin{array}{c}a&b&c\end{array}\right][/tex]
Multiply the rows of A to the column of B. So, we have:
[tex]AB =\left[\begin{array}{ccc}2a+4b-2c\\4a-5b+7c\\2a+7b+5c\end{array}\right][/tex]
This means that:
[tex]\left[\begin{array}{ccc}2a+4b-2c\\4a-5b+7c\\2a+7b+5c\end{array}\right] = \left[\begin{array}{c}24&-46&-2\end{array}\right][/tex]
By comparison, we have:
[tex]2a + 4b - 2c = 24[/tex] --- (1)
[tex]4a - 5b + 7c = -46[/tex] --- (2)
[tex]2a + 7b + 5c = -2[/tex] --- (3)
Multiply (1) and (3) by 2
[tex]2a + 4b - 2c = 24[/tex] --- (1)
[tex]4a + 8b - 4c = 48[/tex] ----- (5)
[tex]2a + 7b + 5c = -2[/tex] --- (3)
[tex]4a + 14b + 10c = -4[/tex] ---- (6)
So, we have:
[tex]4a - 5b + 7c = -46[/tex] --- (2)
[tex]4a + 8b - 4c = 48[/tex] ----- (5)
[tex]4a + 14b + 10c = -4[/tex] ---- (6)
Make 4a the subject in each of the equations
[tex]4a = -46 + 5b - 7c[/tex]
[tex]4a = 48 - 8b + 4c[/tex]
[tex]4a = -4 - 14b - 10c[/tex]
[tex]4a = 4a[/tex]. So, we have:
[tex]-46 + 5b - 7c = 48 - 8b + 4c[/tex] and [tex]-46 + 5b - 7c = -4 - 14b - 10c[/tex]
Simplify both expressions
[tex]-46 + 5b - 7c = 48 - 8b + 4c[/tex]
[tex]5b + 8b - 7c - 4c = 48 + 46[/tex]
[tex]13b - 11c = 94[/tex]
[tex]-46 + 5b - 7c = -4 - 14b - 10c[/tex]
[tex]5b+14b - 7c + 10c = 46-4[/tex]
[tex]19b + 3c = 42[/tex]
Make c the subject
[tex]c = \frac{42 -19b}{3}[/tex]
Substitute [tex]c = \frac{42 -19b}{3}[/tex] in [tex]13b - 11c = 94[/tex]
[tex]13b - 11 \times (\frac{42 - 19b}{3}) = 94[/tex]
Multiply through by 3
[tex]39b - 11 \times (42 - 19b) = 282[/tex]
Open bracket
[tex]39b - 462 + 209b = 282[/tex]
Collect like terms
[tex]39b + 209b = 282+462[/tex]
[tex]248b = 744[/tex]
Solve for b
[tex]b = \frac{744}{248}[/tex]
[tex]b = 3[/tex]
Solve for c
[tex]c = \frac{42 -19b}{3}[/tex]
[tex]c = \frac{42 - 19 \times 3}{3}[/tex]
[tex]c = \frac{-15}{3}[/tex]
[tex]c = -5[/tex]
Solve for a in [tex]4a = -4 - 14b - 10c[/tex]
[tex]4a = -4 - 14 \times 3 - 10 \times -5[/tex]
[tex]4a = 4[/tex]
Divide by 4
[tex]a = 1[/tex]
Recall that matrix B is:
[tex]B =\left[\begin{array}{c}a&b&c\end{array}\right][/tex]
Hence, the value of matrix B is:
[tex]B =\left[\begin{array}{c}1&3&-5\end{array}\right][/tex]
Read more on matrix operations at:
https://brainly.com/question/16956653
Related Questions
2(4 + 7) − 8 ÷ 2 whats the answer
Answers
Answer:
your answer is 18 look below for an explanation!
Step-by-step explanation:
please just trust me i know for a fact its right plz leave a thx and may i please have brainliest?
because 2(4+7)= 8+14= 22. 8/2= 4. 22-4=18.
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned $220 in interest. Set up a systems of linear equations to model the amount of money invested and the interest earned.
Answers
Answer:
x + y = 6000
0.03x + 0.05y = 220
Step-by-step explanation:
Given that :
Total principal amount = $6000
Account A:
Let principal = x
Rate = 3% = 0.03
Account B:
Let principal = y
Rate = 5% = 0.05
Interest earned at after one year = $220
Amount invested :
x + y = 6000
Simple interest = principal x rate x time
Interest earned
(x * 0.03 * 1 ) + (y * 0.05 * 1) = $220
0.03x + 0.05y = 220
Hellppppp I will mark brainliestttt
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Answer:
1/4
Step-by-step explanation:
Which one? (The first answer gets Brainly) (HAS TO BE CORRECT)
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Answer:
Cytoplasm
Step-by-step explanation:
Answer:
Cytoplasm
Step-by-step explanation:
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Answer:
3.62
Step-by-step explanation:
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Answer:
362/ 100 or 3 62/100
Step-by-step explanation:
HELP IM CONFUSED I WASNT AT SCHOOL
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For the second one the distance is 6
Correct me if I’m wrong
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Answers
Answer:
why? also the answer is 1.6y+y-4/15y+7/6y=21/3
We move all terms to the left:
1.6y+y-4/15y+7/6y-(21/3)=0
Domain of the equation: 15y!=0
y!=0/15
y!=0
y∈R
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
We add all the numbers together, and all the variables
1.6y+y-4/15y+7/6y-7=0
We add all the numbers together, and all the variables
2.6y-4/15y+7/6y-7=0
We calculate fractions
2.6y+(-24y)/90y^2+105y/90y^2-7=0
We multiply all the terms by the denominator
(2.6y)*90y^2+(-24y)+105y-7*90y^2=0
We add all the numbers together, and all the variables
(+2.6y)*90y^2+(-24y)+105y-7*90y^2=0
We add all the numbers together, and all the variables
105y+(+2.6y)*90y^2+(-24y)-7*90y^2=0
Wy multiply elements
-630y^2+105y+(+2.6y)*90y^2+(-24y)=0
We get rid of parentheses
-630y^2+105y+(+2.6y)*90y^2-24y=0
We add all the numbers together, and all the variables
-630y^2+81y+(+2.6y)*90y^2=0
Step-by-step explanation:
Which values could be the values of x and y?
Answers
Answer:
1 3/4, 9 1/4
Step-by-step explanation:
continue the pattern
Plz solve ill give brainliest to the first correct answer
Answers
Answer:
-3
Step-by-step explanation:
......................
Janka si vložila 3200 eur na termínovaný účet s 1,2 úrokovou mierov koľko bude mať po 1 roku
Answers
Answer:
the present value is 3,162 euros
Step-by-step explanation:
The computation of the present value is shown below:
As we know that
Future value = Present value × (1 + rate of interest)^number of years
3,200 euros = Present value × (1 + 0.012)^1
3,200 euros = Present value × 1.012^1
Present value is
= 3,200 euros ÷ 1.012
= 3,162 euros
Hence, the present value is 3,162 euros
The fraction 2 5/8 is equivalent to which of the following decimal numbers? pls help ill mark you the brainlyest
A 2.58
B 2.625
C 2.63
D 2. 6
Answers
The fraction of 2 5/8 is equivalent to the decimal form of 2.625.
Why:
5/8 equals 0.625 so by adding this to 2, you get the final sum of 2.625! :)
When 20 is subtracted from five times a number, the result is the same as when 18 is added to three times the number. What is the number?
Answers
Answer:
Number is 19
Step-by-step explanation:
denote the number by x.
the line says:
5x - 20 = 18 + 3 x
Subtracting 3x form both sides
2x - 20 = 18
adding 20 to both sides
2x = 38
dividing both sides by 2
x = 19
Answer:
19
Step-by-step explanation:
let n = the number
5n - 20 = 18 + 3n
combine like terms in one of four different ways
2n = 38
n = 19
The least common denominator of[tex]\frac{1}{6} and \frac{5}{12}[/tex] is 12.
TrueFalse
Answers
Determine the intercepts of the line.
y = -9. – 14
x-intercept:
y-intercept:
Answers
Y-intercept= -23
On a coordinate plane, a vector has an origin (0, 0) and terminal point (8, 7).
Which description of the vector shown is correct?
The magnitude is 15, and the direction angle is approximately 49°.
The magnitude is 15, and the direction angle is approximately 41°.
The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 49°.
The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.
Answers
Answer:
D. The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.
Step-by-step explanation:
The correct description of the vector is that the magnitude is √(113) and therefore the direction angle is 41°.
What is the magnitude of the vector?The magnitude of the vector is the length of the vector which can be calculated from the coordinate of its endpoint.
Let (x1,y1) and (x2,y2) are the coordinate of the two endpoints of a vector V.
The magnitude of the vector= |V|= √(y2-y1)²+(x2-x1)²
We have,
Origin of vector = (0,0)
And,
Terminal point = (8, 7)
Here,
a = 8 and b = 7
Now,
To find the magnitude of the vector, we are going to use;
Formula, |v| = √(a² + b² )
|v| = √(8² + 7² )
|v| = √(64 + 49)
|v| = √113
So, the magnitude of the vector is √113.
Now,
Direction angle is find out using ;
Θ = tan ⁻¹ (b / a)
So, Here,
Θ = Angle Direction
Now,
Θ = tan ⁻¹ (7 / 8)
Θ = 41°
Therefore, the proper description of the vector is that the magnitude is √(113) and also the direction angle is 41°.
Learn more about the magnitude of the vector here:
https://brainly.com/question/27708309
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20+20 helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
40
Step-by-step explanation:
20+20=40 C:
A box of chocolates contains five milk chocolates, three dark chocolates, and fourwhite chocolates. You randomly select a chocolate. It is a milk chocolate or a dark chocolate.
Answers
Answer:
you randomly select and eat three chocolates
Answer:
there is a 5/12 chance its a milk chocolate and a 1/4 chance it's dark chocolate it's more likely chance it's a milk chocolate
Step-by-step explanation:
Natalie walked 3/5 mile in 1/2 hour . how fast did she walk in miles per hour
Answers
Answer:
(6/5) mph
Step-by-step explanation:
A vector in standard position has its terminal point at (7, –4). What is the magnitude of the vector?
Answers
Answer:
Square root of 65
Step-by-step explanation:
Edge
The magnitude of the vector will be 8.0622 units.
What exactly is a vector?A vector is a quantity with a magnitude, and direction that follows the law of vector addition.
Given data;
u = (7, –4)
The magnitude of the vector is, R found as;
[tex]\rm R = \sqrt{7^2+(-4^2)} \\\\ R = \sqrt {65} \\\\ R = 8.0622 \ units[/tex]
Hence the magnitude of the vector will be 8.0622 units.
To learn more about vectors, refer;
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Guys please this has been stressing me out lately and my cousins want me to go to the park but I can’t
Answers
Answer:
1. 42.90
10. 23
11. 36.75
12. 55
14. 16.25
Step-by-step explanation:
I'm sorry I don't know the rest.
Substitute 7 for xand evaluate the expression below.
9x-2x
Answer here
Answers
Answer:
The answer to this equation is 49
Step-by-step explanation:
9x-2x
9×7=63
2×7=14
63-14=49
I got 24 miles for each kind of gas in my car which one of the following is a equivalent radio of miles to gallons.
A. 48 to 2
B. 2 to 48
C. 1 to 24
D. 3 to 240
Answers
I believe that the answer is B
what is y=1/2x-10 Help me
Answers
1. In a class there are 2 boys to every 3 girls. How many girls would be in the class if there are 12 boys? (set up a proportion and solve, think about what two things you have and put them one over the other)
2. A boat traveled 27 miles in 2 hours. At this rate how many miles would the boat travel in 0.5 hour? (set up a proportion and solve)
3. Joe uses 6 grams of coffee beans to make 24 ounces of coffee. How many grams of coffee beans would be used for 288 ounces of coffee? (this problem has ounces but it also gives you three numbers already)
4. A recipe says to use 3 cups of flour for 48 cookies. How many cups of flour would be used to make 72 cookies?
5. A man walks 4 miles in 1.5 hours. How many hours would it take the man to walk 10 miles?
6. It costs $22.50 for 5 pounds of salmon. How much would it cost for 8 pounds of salmon?
Answers
Answer:
1. 12 boys,
5. 15 hours
6. 36
Im not so sure on the others, Gl!
-5+12+6x=7x-10+53+3x
Answers
Answer:
x=-9
Step-by-step explanation:
For brainliest :)
Oml i need more characters
There :)
Answers
Answer:
Imfaooooooo
Step-by-step explanation:
Hope this helps or brightens your day! Please consider marking brainliest! Always remember, your smart and you got this! -Alycia :)
Answer:
characters for what?
anyways....I need brainiest! :P
Can someone help I’ll give you the brainlyst
Answers
Answer:
Step-by-step explanation:
the rate per window is the slope or the uniform amount that the y values increase by
we can see that company A increases 25$ per window
we can see company B increases 40$ per window
and company C increases 35$ per window
so company B charges more per window because it has the greatest slope
Can some one please help me with these problems
Answers
Answer:
yes
Step-by-step explanation:
ok
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse functions
Answers
Answer:
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Step-by-step explanation:
Given
[tex]a(d) = 5d - 3[/tex]
Solving (a): Write as inverse function
[tex]a(d) = 5d - 3[/tex]
Represent a(d) as y
[tex]y = 5d - 3[/tex]
Swap positions of d and y
[tex]d = 5y - 3[/tex]
Make y the subject
[tex]5y = d + 3[/tex]
[tex]y = \frac{d}{5} + \frac{3}{5}[/tex]
Replace y with a'(d)
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
Prove that a(d) and a'(d) are inverse functions
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex] and [tex]a(d) = 5d - 3[/tex]
To do this, we prove that:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Solving for [tex]a(a'(d))[/tex]
[tex]a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})[/tex]
Substitute [tex]\frac{d}{5} + \frac{3}{5}[/tex] for d in [tex]a(d) = 5d - 3[/tex]
[tex]a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3[/tex]
[tex]a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3[/tex]
[tex]a(a'(d)) = d + 3 - 3[/tex]
[tex]a(a'(d)) = d[/tex]
Solving for: [tex]a'(a(d))[/tex]
[tex]a'(a(d)) = a'(5d - 3)[/tex]
Substitute 5d - 3 for d in [tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}[/tex]
Add fractions
[tex]a'(a(d)) = \frac{5d - 3+3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d}{5}[/tex]
[tex]a'(a(d)) = d[/tex]
Hence:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Q2. 81 = 3k
PLEASE HELP !!
Answers
Answer:
27
Step-by-step explanation: