Answer:
Step-by-step explanation:
Given the system of homogeneous equations
x1 + 2x2 - 3x3 = 0 ................. 1
4x1 + 7x2 - 9x3 = 0 ................... 2
-x1 - 3x2 + 6x3 = 0..................... 3
First we will reduce the equation to two equations and two unknowns;
add equation 1 and 3;
2x2-3x2 +(-3x3+6x3) = 0
-x2 + 3x3 = 0
x2 = 3x3 .......... 4
Multiply equation 3 by 4 and add to equation 2;
equation 3 * 4 will give;
-4x1 - 12x2 + 24x3 = 0..................... 5
add equation 5 to equation 2;
7x2-12x2-9x3+24x3 = 0
-5x2 - 15x3 = 0 .......... 6
5x2 = 15x3
x2 = 3x3
Let x2 = k
From equation 4;
k = 3x3
x3 = k/3
substitute x2 = k and x3 = k/3 into equation 1 to get x1 in terms of k
From 1, x1 + 2x2 - 3x3 = 0
x1+2k-3(k/3) = 0
x1 +2k-k = 0
x1 +k = 0
x1 = -k
Writing the answer in vector form will give (x1. x2. x3) = (-k, k, k/3)
k(-1, 1, 1/3)
Hence the answer to the system of equation in vector form is k(-1, 1, 1/3) where k is any constant.
5. There are two kinds of products (called DA and GA) produced in your company every day. Alsothere are two kinds of materials (denoted by A and B) in need One DA costs one unit of A, one unit of B: one GA costs one unit of A, two units of B. You get $3000 when you sell one DA and $5000 for one GA. The supply of the two materials every day is 12,22. a)What is the maximal profit $ b) How many DA and GA should be produced every day to obtain this maximal profit? Number of DA = Number of GA
Answer:
a) $56000b) DA = 2, GA = 10Step-by-step explanation:
Given
DA = A + B ⇒ $3000GA = A + 2B ⇒ $5000Number of A = 12Number of B = 22We can see from the equations that
GA - DA = B ⇒ $2000 andA = $1000 and B = $2000 in terms of profitSo greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.
A + B = 12A + 2B = 22Is the equation set to indicate use of the units A and B
Solving we get
A = 2 and B = 10It this case all the units are used and profit is maximum
2*$3000 + 10*$5000 = $56000Number of DA = 2Number of GA = 10Convert 2.42 to percent
Answer:
242%
Step-by-step explanation:
Answer:
242%
Step-by-step explanation:
Whole numbers are a 100% each, so there's 200%. Tenths are 10% every tenth, so 40%, and hundredths are 1% every hundredth, so 2%.
200+40+2=242%
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16. Find the values of x and y. (2y + 5) (5x - 17) (3x – 11)º
Answer:
x = 26
y = 9
Step-by-step explanation:
(5x - 17)° + (3x - 11)° = 180° (angles in a straight line)
Solve for x
5x - 17 + 3x - 11 = 180
Collect like terms
5x + 3x - 17 - 11 = 180
8x - 28 = 180
Add 28 to both sides
8x = 180 + 28
8x = 208
Divide both sides by 8
x = 208/8
x = 26
Also:
(2y + 5)° + 90° + (3x - 11)° = 180° (angles on a straight line)
Plug in the value of x and solve for y
2y + 5 + 90 + 3(26) - 11 = 180
2y + 5 + 90 + 78 - 11 = 180
Collect like terms
2y + 162 = 180
Subtract 162 from both sides
2y = 180 - 162
2y = 18
y = 9 (dividing both sides by 2)
The maximum speed that an X43A plane can reach is 7,500 miles per hour. At this speed, how many feet
can the X43A travel in 1 second? (1 mile = 5,280 feet)
Answer:
11000 feet/secondsStep-by-step explanation:
This problem requires that we convert from miles per hour to feet per seconds
Given that the speed of the X43A plane is 7500 mph
and that 1 mile = 5,280 feet)
[tex]=\frac{7500miles}{h} *\frac{5280 feet}{mile} \frac{1hour}{3600 seconds} \\\\=\frac{7500*5280}{3600} \\\\=\frac{396*10^5}{3600} \\\\=11000 feet/seconds\\\\=11*10^3feet/seconds\\\\[/tex]
Therefore the speed of the X43A plane in feet per second is 11000
1.) (-18, -20) (18, 16)
2.) (-7, 14) (-11, 4)
3.) (-5, -4) (3, 9)
4.) (13, -8) (-9, -1)
1.) (-18, -20) (18, 16)
m= 1
2.) (-7, 14) (-11, 4)
m= 5/2
3.) (-5, -4) (3, 9)
m= 13/8
4.) (13, -8) (-9, -1)
m= -7/22
A line has a slope of 2 and passes through the point ( -1, 3). Write an equation in slope intercept form
Answer:
y=2x+5
Step-by-step explanation:
The equation of a line in slope intercept form is written as: y=mx +b where m is the slope and b is the y-intercept.
Taking point (-1,3) , m= 2 and imaginary point on the line, (x,y) then ;
m=change is y-coordinates/change in x-coordinate
m=Δy/Δx
m=y-3/x--1
2= y-3 / x+1
2(x+1) = y-3
2x +2 =y-3
2x=y-3-2
2x=y-5
y=2x+5 is the equation.
Answer:b
Step-by-step explanation:
Which statements about opposites are true?
Answer:
The opposite of a negative number is always positive.
Step-by-step explanation:
Answer:
Opposites always have the same absoulute value.
Step-by-step explanation:
^^^^ I don't fully know what type of question you are asking but here is my answer ^^^^
768 pages in 8 days = _____ pages per day
People like having guinea pigs as pets. If a guinea pig can run 14.45 miles in 3.5 hours, then how far can it travel in one hour?
Answer:
4.13 miles
Step-by-step explanation:
i believe
Answer:
4.1285714286
Step-by-step explanation:
Given C=n+15, determine the value of C when n=4
Answer:
19
Step-by-step explanation:
If N=4 and the problem is C= N+15 that means you add 4 to 15 and then get 19 which will be your answer for C. You can also check this by subtracting 19-15 or 19-4!!! I hope this helps!!! Have a great day whom ever you are
The midpoint of RS is M(3,4) One employee is R (5,0) Find the coordinates of the Other endpoint S. ANSWER ASAP PLEASE
Answer:
( 1, 8 )
Step-by-step explanation:
The distance between (5,0) and (3,4) is (-2,4).
As M is the midpoint we add the distance of half the line to it to get the full line.
(3,4) + (-2,4) is (1,8) which is S
the sum of 3 numbers is 114. the second number is 4 times the third the third number is 6 more than the first
Answer:
let the three numbers be x,y,z
X= z-6
Y= 4z
Z= z
Step-by-step explanation:
X+Y+Z=114
hence
=z-6+4z+z=114
=collect like times. X= 20-6=14
= z+4z+z=114+6. Y= 20*4=80
=6z=120. . Z= 20
z=20
Answer:
14 + 20 + 80 = 114
Step-by-step explanation:
Let's begin by representing our 1st number as x.
Then our 2nd number is said to be 6 more than the 1st number, which we can represent as x + 6.
Lastly, our 3rd number is said to be 4 times the 2nd number, which we can represent as 4(x + 6).
Now can write our equation to express the sum of these three numbers as 114 and then solve for x to find the values of these three numbers:
x + (x + 6) + 4(x + 6) = 114
x + x + 6 + 4x + 24 = 114
6x + 30 = 114
6x = 114 - 30
6x = 84
x = 84/6 = 14 (1st number)
x + 6 = 14 + 6 = 20 (2nd number)
4(x + 6) = 4(20) = 80 (3rd number)
We can check our answers by adding these numbers up to see if their sum is 114:
14 + 20 + 80 = 114
34 + 80 = 114
114 = 114
Their sum is 114, so we are confident that our three numbers are correct.
-Hope this helps
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Determine the largest integer value of x in the solution of the following inequality. -3x +1> 7
Answer:
x<1/3
Step-by-step explanation:
The circumference of a circle is 16Pi ft
Area of the circle: 64π ft²
Radius of circle: 8 ft
The circumference formula: C = d · π
We can plug in the values we know.
16π = d · π; We can cancel out the π, as it is on both sides.
d = 16ft; r = 8ft
The area formula: A = πr²
A = 64π ft²
what is 5 1/12 -3 5/12?
Answer:
the answer is -5/6 hope this helps
An assembly line has two inspectors . The probability that the first inspector will miss a defective item is 0.09. If the defective item passes the first inspector, the probability that the second inspector will miss it is 0.08. What’s the probability that a defective item will pass by both inspectors?
Answer:
0.072
Step-by-step explanation:
0.09 × 0.08
Here's the diagram/ explanation
For what x values is the function positive? Select all that apply
Answer:
Option (A)
Option (D)
Step-by-step explanation:
From the graph attached,
Values of function have been plotted on y-axis for every input value of 'x' on x-axis.
Graph clearly states that the function is positive (positive y-values or y > 0) in the two intervals,
-5 < x < 0 and 3.5 < x < 5
Therefore, option (A) and Option (D) will be the correct options.
What is the solution of the following quadratic inequality? x2 – 4x – 21 ≤ 0
Answer:
This is the answer
Answer: B
Step-by-step explanation:
Health insurance helps to protect you from financial loss by _____. a. paying for some or all of your medical costs while you are insured. b. working with medical care providers to minimize or discount the total cost of medical care. c. connecting you with health care representative to help keep you in good medical condition to avoid excessive medical care costs. d. informing you about lectures, classes, and presentations that help inform you about maintaining good medical condition to avoid excessive medical care costs.
Answer:
A: paying for some or all of your medical costs while you are insured.
Step-by-step explanation:
Health insurance helps to protect you from financial loss by: a. paying for some or all of your medical costs while you are insured.
What is health insurance?Health insurance is an insurance coverage that help to cover your medical costs or medical expenses incase of unforeseen circumstance such as:
AccidentIllness etcHealth insurance is important as it help to save cost which means that you will spend less when it come to medical care because you are insured.
Hence, your health insurance company or insurance provider will be responsible for paying for your medical expenses in as far as you are still insured by them.
Inconclusion health insurance helps to protect you from financial loss by: a. paying for some or all of your medical costs while you are insured.
Learn more about health insurance here:https://brainly.com/question/1941778
Subtract.
-4 - 2
Plz help:((
Answer:
The answer is -4-2 = -6
Answer:
-6 is the answer hope that helps
write the product of a number and 21 as an algebraic expression
Answer:
21n=
n-number and since its a number (n) and 21 you would put 21n
Answer:
[tex]\boxed {\tt 21n}[/tex]
Step-by-step explanation:
We want to write the product of a number and 21 as an algebraic expression. Let's define "a number" as the variable n.
We know that "product" means multiplication. The product of a number, n, and 21 is equal to multiplying n and 21.
[tex]n*21[/tex]
21 and n can be flipped due to the commutative property of multiplication.
[tex]21*n[/tex]
[tex]21n[/tex]
The product of a number and 21 is 21n.
Help! ASAP!!!
Use the map shown below to find the distance between cities A and B to the nearest tenth.
Answer:
7.2 units
Step-by-step explanation:
Coordinates of city A = (0, 0)
Coordinates of city B = (6, 4)
Use the distance formula to find the distance between the two cities as follows:
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(0, 0) = (x_1, y_1) [/tex]
[tex] B(6, 4) = (x_2, y_2) [/tex]
Plug in the values into the formula
[tex] AB = \sqrt{(6 - 0)^2 + (4 - 0)^2} [/tex]
[tex] AB = \sqrt{(6)^2 + (4)^2} [/tex]
[tex] AB = \sqrt{36 + 16} = \sqrt{52} [/tex]
[tex] AB = 7.2 [/tex] (nearest tenth)
I am in 9th grade,if you have 889,865x999,786 what doe it equal also yes i am not in virtual school and teacher will not let me use a calculatar
Answer:
889674568890
Step-by-step explanation:
I used a calculator :)
Find a − b when a = −7 and b = 11.
Answer:
-18
Explanation:
a - b
a = -7
b = 11
Insert -7 for 'a' and 11 for 'b'
-7 - 11
= -18
Simplify.
4−16÷4+42
Item 5
Simplify.
4−16÷4+42
Answer:
42
Step-by-step explanation:
16 dividied by 4 is 4
4 minus 4 is 0
and 0 plus 42 is 42
Answer:
45
Step-by-step explanation:
4-16÷4+42
12÷4+42
3+42
45
What is the difference?
77 – 43.6 =
A. 23.3
B. 33.4
O C. 34.6
OD. 44.1
Answer:
B. 33.4
Step-by-step explanation:
77 - 43.6 = 33.4
The digit 5 in which number represents a value of 0.5? The answers are 5.4, 0.059, and 8.513.
Answer:
8.513 is the answer
Step-by-step explanation:
The value of 5 in 0.5 is the tenths place, hence if we look at all other options, the values of 5 are 5(ones place), and 0.05(Hundredth), so the option of 8.513 suits the question's answer. Hope this helped, Thank you.
60 divided (6 1/7 - 1/7) x 4
4. Solve x -- 7 = 25.
A 18
B 32
Answer:
B
Step-by-step explanation:
b okay it b good
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y/-5=1/10
Enter your answer as a reduced fraction.
Answer:
1/2
Step-by-step explanation:
y/-5=1/10
multiply -5 on both sides
y/-5 x -5 - cancels
1/10 x -5/1
1/10 x -50/10 = 5/10 = 1/2
so then its y=1/2