Answer:
Infinitely solution exists,
Required solution is, [tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
Step-by-step explanation:
We have the given equations:
[tex]x_1+2x_2+8x_3=8[/tex]
[tex]x_1+x_2+4x_3=4[/tex]
Here, the augmented matrix is :
[tex]\left[\begin{matrix}1&2&8&8\\1&1&4&4\end{matrix}\right][/tex]
Now, find the echelon form of the augmented matrix.
[tex]=\left[\begin{matrix}1&2&8&8\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_2-R_1}[/tex]
[tex]=\left[\begin{matrix}1&0&0&0\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_1+2R_2}[/tex]
Therefore, [tex]x_1=0[/tex]
[tex]-x_2-4x_3=-4[/tex]
[tex]\Rightarrow x_2=4(1-x_3)[/tex]
Let [tex]x_3=t[/tex], then the required solution is
[tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]
if 1ninch represents 22 miles on a map then how many miles will represent 2240 miles
Answer:
Step-by-step explanation:
you have to divide
Answer:
101.8181...
Step-by-step explanation:
I divided heres how.
1 inch equals 22 miles
2240 miles
2240/22=101.8181...
Hope this helps you.
Aubrey buys 2 souvenirs during each day of vacation. Write an equation that shows the relationship between the days of vacation x and the number of souvenirs bought y.
Write your answer as an equation with y first, followed by an equals sign.
Answer:
2X = Y
Step-by-step explanation:
To determine the equation that will allow to establish the amount of souvenirs bought by Aubrey (Y), taking into account that for each day of vacation (X) buys 2 souvenirs, the following must be taken into account:
The number of days (X) must be multiplied by 2. Thus, if you buy 2 souvenirs per day and your vacation lasts 4 days, you will have bought 8 souvenirs (4 x 2). Thus, the value of Y is equal to 2X, that is:
2X = Y
Use the Commutative Property to write an expression equivalent to –5d + 12.
Step-by-step explanation:
[tex]\huge\bold\purple{ equivalent\: of \: -10d+24 }[/tex]
Answer:
767657
Step-by-step explanation:
#6* #6 Multiples Σ > Which answer choice has ONLY multiples of a. 7, 14, 21, 35, 56 b. 7, 21, 27, 35, 49 c. 7, 14, 28, 43, 56 d. 7, 21, 28, 49, 53
Answer:
A
Step-by-step explanation:
B) No 27 is a multiple of 3 alone.
C) No 43 is prime. If you replaced it with 42 all would be well.
D) N 53 is prime.
A) everything is divisible by 7.
Use the drop-down menus to complete the statements to match the information shown by the graph
Answer:
Produce per pound costs less than meat per pound because the slope of the graph for meat is greater than that of the graph for produce.
The slope of the graph tells you the unit rate in dollars per pound .
Devon is five years younger than Sydney the sum of their ages is 57 what is Sydney
Answer:
Sydney is 31 years old.
Step-by-step explanation:
LET age of Devon be x years
and let age of Sydney be y years
if x=y-5-------(i)
x+y= 57 (sum)
Using (i)
(y-5)+y=57
2y=62
y=31
Find the distance between the points (3,5) and (12,2).
?
Answer:
9.48
Step-by-step explanation:
Answer:
3√10 or about 9.49 units.
Step-by-step explanation:
To find the distance between any two points, we may use the distance formula given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let (3, 5) be (x₁, y₁) and (12, 2) be (x₂. y₂). By substitution:
[tex]d=\sqrt{(12-3)^2+(2-5)^2[/tex]
Evaluate:
[tex]d=\sqrt{(9^2)+(-3)^2[/tex]
Square:
[tex]d=\sqrt{81+9}[/tex]
Simplify:
[tex]d=\sqrt{90}=\sqrt{9\cdot10}=\sqrt{9}\cdot\sqrt{10}=3\sqrt{10}\approx9.49[/tex]
The distance between (3, 5) an (12, 2) is 3√10 or about 9.49 units.
3(5 +4) + 4 – 2 •4
I need help please!
Answer:
23
Step-by-step explanation:
PEMDAS states that you must do parenthesis first:
(5+4)=(9)
Then Multiplication:
3(9)=27
2*4=8
Then addition and subtraction right to left:
27+4-8
31-8
23
simplify the expression 9(h - 1)
Answer:
9h - 9
Step-by-step explanation:
9(h - 1)
distribute
(9 * h) + (9 * - 1)
9h + (9 * - 1)
9h + -9
9h - 9
Answer:9h-9
Step-by-step explanation:
4. (LT 1.1) The perimeter of the rectangle below is 40 feet. Its length and width are
given in terms of x. Find the length and width of the rectangle.
3x
2x + 5
Answer:
Length, L = 9 feet.
Width, W = 11 feet.
Step-by-step explanation:
Given the following data;
Perimeter = 40 feet
Length = 3x
Width = 2x + 5
The perimeter of a rectangle is given by the formula;
P = 2(L + W)
40 = 2(3x + 2x +5)
40 = 2(5x + 5)
40 = 10x + 10
10x = 40 - 10
10x = 30
x = 30/10
x = 3
Now, to find the length;
Length, L = 3x
Substituting into the equation, we have;
Length, L = 3*3
Length, L = 9 feet
To find the width;
Width, W = 2x + 5
Substituting into the equation, we have;
Width, W = 2(3) + 5
Width = 6 + 5
Width, W = 11 feet.
Find the slope and the y-intercept of the line.
5x-2y = -4
Write your answers in simplest form.
slope:
Undefined
X
y-intercept: |
?
Answer:
Slope 'm' = [tex]\frac{5}{2}[/tex]
And y-intercept = 2
Step-by-step explanation:
Slope-intercept form of a line is given by the equation,
y = mx + b --------(1)
Here, m = slope of the line
b = y-intercept
Given equation is,
5x - 2y = -4
2y = 5x + 4
y = [tex]\frac{5}{2}x+2[/tex]
By comparing this equation with equation (1),
Slope 'm' = [tex]\frac{5}{2}[/tex]
And y-intercept = 2
trops have 3 eyes
Bops have 2 eyes
there are 31 eyes altogether
haw many trops were there ?
how many bops were there ?
Answer:
3 trops
11 bops
Step-by-step explanation:
3×3=9
11×2=22
22+9=31
Plz help brainlest if correct
Answer:
Help with what....????
Step-by-step explanation:
[tex]3/5 of 5/9\\[/tex]
Answer:
⅓
Step-by-step explanation:[tex] \frac{5}{9} \times \frac{3}{5} [/tex]
[tex] = \frac{1}{3} \times \frac{1}{1} [/tex]
[tex] = \frac{1}{3} [/tex]
Checking:[tex] \frac{1}{3} \div \frac{3}{5} [/tex]
[tex] = \frac{1}{3} \times \frac{5}{3} [/tex]
[tex] = \frac{5}{9} [/tex]
#CarryOnLearning
Hey there!
When you see the word “of” in mathematical statement, it usually means “multiply” (aka Multiplication)
“3/5 of 5/9”
3/5 • 5/9
MULTIPLY the NUMERATORS (TOP NUMBERS) from each other & also MULTIPLY the DENOMINATORS (BOTTOM NUMBERS) from each other!
3(5) / 5(9)
3(5) = 15 ⬅️ NUMERATOR
5(9) = 45 ⬅️ DENOMINATOR
15/45
The GCF (Greatest Common Factor) for both of your numbers is: 15.. so DIVIDE both the NUMERATOR and DENOMINATOR from 15
15 ÷ 15 / 45 ÷ 15
15 ÷ 15 = 1 ⬅️ NUMERATOR
45 ÷ 15 = 3 ⬅️ DENOMINATOR
Answer: 1/3 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Myra can fill 18 glasses with 2 containers of tea. How many glasses can she fill with 3 containers?
Answer:
one container has 18/2 = 9 glasses so 3 will have (9)(3) = 27 glasses
Step-by-step explanation:
please help due in 10 mins!!
Answer:
Step-by-step explanation:
C
(X)=x3-22x2+157x-360
Answer:
Step-by-step explanation:
x1 = x2 = 6
x3 = 10
this is it im pretty sure
S641591 is a hacker don’t trust em
Answer:
welp ok
Step-by-step explanation:
Answer:
ok done
Step-by-step explanation:
Solve by elimination
5x+6y= -10
3x-2y= -6
[tex]x = - \frac{2(5 + 3y)}{5} [/tex]
Solving for Y.[tex]y = - \frac{5(2 + x)}{6} [/tex]
Second equation:Solving for X.[tex]x = \frac{2(y - 3)}{3} [/tex]
Solving for Y.[tex]y = \frac{3(2 + x)}{2} [/tex]
A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:
769 691 699 730 711 765 702 718 719 712 768 688 757
695 768 735 709 758 708 693 736 700 687 772 715
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)
Answer:
A.
mean = 724.2
Median = 715
Mode = 768
B.
Range = 85
Standard deviation = 29.30
C.
Interval = [665.6, 782.8]
Step-by-step explanation:
Number of samples n = 25
Summation X= 769 + 691 + 699 +730+711+ 765+ 702 718 +719 +712+ 768 +688 +757+695 768 +735 +709 +758 +708+ 693 +736 700+ 687 +772 +715 = 18105
A.
1. Mean = 18105/25
= 724.2
2. Median is the middle value when arranged from the least value to the highest = 715
3. Mode is the number with the highest frequency = 768 (occured two times)
B.
1. Range = highest value - lowest value
Highest value = 772
Lowest value = 687
772-687 = 85
2. Standard deviation = √(X-barX)²/n-1
= √20604/25-1
=√858.5
= 29.30
Please check attachment for the full calculation of the standard deviation
C.
Interval
[Mean - 2(sd), mean + 2(sd)]
= [724.2-2x29.3, 724.2+2x29.3]
=[665.6, 782.8]
The number of books that Jordan has read is greater than 22.
HELP PLSS
Answer:
x>22
Step-by-step explanation:
What is the tangent ratio for D
How to solve 52+ 58+ q=180 for q.
Answer:
70
Step-by-step explanation:
180 - 52 - 58 = q
q = 70
hope this helps...
Jack work after school. Each day he is paid a set amount, plus an hourly wage.
Answer:
What's the question? :)
Step-by-step explanation:
I need help with these two questions ASAP thank you.
Answer:
There isn't a clear answer
Step-by-step explanation:
4 Alz(CO3)3
Do u multiple the 4 with the stuff in the parentheses ?
Answer:
a total of 56 atoms
Step-by-step explanation:
Aluminum carbonate is the compound
Yes, you multiply what is inside the parentheses times 4 and also times 3. That is:
8 atoms of Al
36 atoms of Oxygen
and
12 atoms of Carbon
giving a total of 56 atoms
I WILL GIVE BRAINLIEST PLZ ANSWER DUE IN A FEW MINUTES
What is every factor of 116
Answer:
1,2,4,29,58,116
Step-by-step explanation:
Prime factorization 116=2x2x29
hey guys i need help plz will give brainlist
Step-by-step explanation:
Effective resistance in the 30Ω and 40Ω parallel circuit = 1 / (1/30 + 1/40) = 120/7 Ω.
20Ω + 10Ω = 30Ω
Effective resistance in the 50Ω and (20Ω + 10Ω) parallel circuit = 1 / (1/50 + 1/30) = 75/4 Ω.
Now we can add the resistances up:
Effective resistance for circuit
= 120/7 Ω + 75/4 Ω = 1005/28 Ω.
Hence I = V / R
= 9.0V / (1005/28 Ω) = 0.25A. (2s.f.)
find the value of x ?!??
Answer:
x=4
Step-by-step explanation:
Pentagon's sum of interior angle is 540°
let's add all the given degrees
100+20x+16x+16+140+160-5x=540
Collect like terms
100+16+140+160+20x+16x-5x=540
416+31x=540
31x=540-416
31x=124
x=124/31
x=4```
the equation of function is y=4x+5 what is the value of y when x=3?
Answer:
y=17
Step-by-step explanation:
y=4x+5
change x to 3
y=4(3)+5
y=12+5
y=17
The required value of y is 17 when x=3 for the given equation y = 4x + 5.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The equation of function is given in the question, as follows:
y = 4x + 5
We have to determine the value of y when x=3 for the above equation.
As per the question, we have
y = 4x + 5
Substitute the value of x = 3 in the above equation,
y = 4(3) + 5
y = 12 + 5
y = 17
Thus, the required value of y is 17.
Learn more about the equations here:
brainly.com/question/10413253
#SPJ6