Answer:
Minimum Values:
x = 0, y = 1, z = 3
Maximum Values:
x = 7 , y = 11 , z = 47
Step-by-step explanation:
FOR MINIMUM VALUES:
0<= x <= 7
It is clear from the above inequality that the minimum value of x must be 0.
y>= 1
This inequality shows that the minimum value of y must be 1. Using these minimum values of x and y to get the minimum value of z:
z = 2x + 3y
z = (2)(0) + (3)(1)
z = 3 (Minimum)
FOR MAXIMUM VALUES:
0<= x <= 7
It is clear from the above inequality that the maximum value of x must be 7.
x + y <= 11
To calculate maximum value of y we can use the minimum value of x in this inequality:
0 + y <= 11
y <= 11
Hence, the maximum value of y is 11.
Using these maximum values of x and y to get the maximum value of z:
z = 2x + 3y
z = (2)(7) + (3)(11)
z = 47 (Maximum)
solve the matrix and prove that it is equal 0
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
[tex] \tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}[/tex][tex] \underline{ \underline { \text{To \: Find}}} : [/tex]
[tex] \sf{ {A}^{2} - 5A+ 22I= 0}[/tex][tex] \underline{ \underline{ \text{Solution}}} : [/tex]
The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by [tex] \sf{ {A}^{T}} [/tex]. Again , Interchange it's rows and columns in order to find ' A '.
[tex] \tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}[/tex]
Now , LEFT HAND SIDE ( L.H.S )
[tex] \tt{ {A}^{2} - 5A+ 22I}[/tex]
Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.
⟼ [tex]\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}[/tex]
⟼ [tex]\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]
⟼ [tex]\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]
⟼ [tex] \begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]
⟼ [tex]\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]
⟼ [tex]\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}[/tex]
⟼ [tex]\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}[/tex]
⟼ [tex] \sf{0}[/tex]
RIGHT HAND SIDE ( R.H.S ) : 0
L.H.S = R.H.S [ Hence , proved ! ]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Answer:
Step-by-step explanation:
\underline{ \underline{ \text{Given}}} :
\begin{gathered} \tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}\end{gathered}
\underline{ \underline { \text{To \: Find}}} :
\underline{ \underline{ \text{Solution}}} :
The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by \sf{ {A}^{T}}
. Again , Interchange it's rows and columns in order to find ' A '.
\begin{gathered} \tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}\end{gathered}
Now , LEFT HAND SIDE ( L.H.S )
\tt{ {A}^{2} - 5A+ 22I}
Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.
⟼ \begin{gathered}\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered}\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered}\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered} \begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered}\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered}\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}\end{gathered}
⟼ \begin{gathered}\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}\end{gathered}
⟼ \sf{0}0
RIGHT HAND SIDE ( R.H.S ) : 0
I need help, I need to find the value of j, thank you
Step-by-step explanation:
[tex] \sin(x) = \frac{8}{10} \\ x = 53.13[/tex]
[tex] \sin(53.13) = \frac{4}{j} \\ j = \frac{4}{ \sin(53.13) } = \frac{4}{0.8} = 5[/tex]
-16(x - 6) -4
B. x > 8
C. x < -4
D. x < 8
s t u p i d study island :') uωu`
Answer:
i think it is c but i am probably super wrong
Step-by-step explanation:
Cody increased the amount of money he saves each week from $40 to $75. By what percentage did Cody increase the amount of money he saves?
Step-by-step explanation:
75-40= 35
[tex] \frac{35}{40} \times 100\% = 87.5\%[/tex]
for each sequence find the first 4 terms and the tenth term
a) n squared +3
b) 2n squared
Answer:
Step-by-step explanation:
Given that:
a) n³
The first 4 terms are;
let assume n = 1
1³ = 1
if n = 2
2³ = 8
if n= 3
3³ = 27
if n = 4
4³ = 64
So, the sequence is 1, 8, 27, 64
The tenth term of this sequence is: 10³ = 1000
b)
2n²
if the first term is 1
then 2(1)² = 2
if n = 2
2(2)² = 8
if n = 3
2(3)² = 18
if n = 4
2(4)² = 32
So, the sequence is 1, 8, 18, 32
The tenth term will be 2(10)² = 200
Anyone want points or brainiest here is a question. What is 4-1!
:D
Answer:
it would 41 amiright?
Answer:
4-1=3
Step-by-step explanation:
hope it helps and have a great day :)
Solve the following system of equations for x using elimination
4x + y = 2
x - y = 3
A. -2
B. 1
C. 3.
D.4
Answer:
A
Step-by-step explanation:
A
Answer:
b 1 ksoeoeskmx
Step-by-step explanation:
ksowoxk374
3x + 2y = 26
y = 5x
Slove the system
Answer = 2
Step-by-step explanation:
3x + 2(5x) = 26
3x + 10x = 26
13x = 26
26 ÷ 13 = 2
Translate the given phrase into an algebraic expression.
Three is subtracted from
g
Answer:
g - 3
Step-by-step explanation:
g- 3
Hope that helps!
Ms. Orozco's class has 8 boys and 12 girls in the class. What is probability of choosing a girl?
Answer:
12/20 = 3/5
Step-by-step explanation:
hope this helps
A side of a square is
8 3/2
inches. Using the area formula A = s^2, determine the area of the square.
Answer:
12 inches
Step-by-step explanation:
once again... drop the answer or ill drop ur ip :)
Answer:
-11x = -48 +15
x = (-48+15) / (-11)
x = -33 / -11
x= 3
hope that help
Step-by-step explanation:
4e88s45etds8sistzerse8rse85t8ss
Mai solved the equation below incorrectly. Identify Mai's error and then solve the equation correctly.
X-9) = {(x + 18)
3x - 3= kx +9
1
4
X-3=9
1
41
-x = 12
X = 48
What was Mai's error?
Answer: Please see explanation column for answer.
x= -36
Step-by-step explanation:
Step 1
from the attachment, Mai's solving is given as
1/3 (1/2x- 9) = 1/2 (x+18)
1/6x-3= 1/2x+9
1/4x-3=9
1/4x=12
x=48
Mai's error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.
Solving correctly, we have that
1/3(1/2x-9) = 1/2(x+18)
1/6x -3= 1/2x+ 9
taking like terms to like terms
1/6x-1/2x= 9+3
(1-3)/6x= 12
-2/6x= 12
-1/3x= 12
multiplying both sides by -3
-1/3x X -3 = 12 X -3
x= -36
PLEASE HELP ME FILE IS ATTACHED
Answer:
Its below in the explanation
Step-by-step explanation:
2^2 = 4 so y=4 and x,y = 2,4
3^2 = 9 and x,y = 3,9
4^2=16 and x,y=4,16
Please give me brainliest
Answer:
2^2 = 4 so y=4 and x,y = 2,4
3^2 = 9 and x,y = 3,9
4^2=16 and x,y=4,16
Step-by-step explanation:
Peter is renting two kinds of rafts for a vacation company. One type seats 3
people and the other seats 5 people. If 53 people are using the vacation
company and he rents 13 rafts, how many of each type of raft does he rent?
Answer:
Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
Step-by-step explanation:
Let [tex]x[/tex] denote the number of rafts seating 3 people and [tex]y[/tex] the number of rafts seating 5 people. The total number of rafts is 13, so [tex]x+y=13[/tex]. We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so [tex]3x+5y=53[/tex].
It's always a good idea to put these equations under each other:
[tex]\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.[/tex]
We can subtract the first equation three times from the second one to obtain [tex](3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7[/tex]
Now, substitute this found value for [tex]y[/tex] into [tex]x+y = 13[/tex] and we see that [tex]x=6[/tex]. We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
At Jonathan's school, there are 30 seventh graders participating in the school play. Of the students in the seventh grade, 60% are not participating in the school play. How many seventh graders at Jonathan's school are not participating in the school play?
Answer:
75
Step-by-step explanation:
If 30 students represent 40% of the class, we can divide 30 by .40 to get 75.
find the y and x intercept for
4x-y=12
Answer:
x intercept: (3,0)
y intercept: (0, -12)
If you get this question right I will give you brainlist
Answer:
I think 99in
Step-by-step explanation:
3x13=39
5x12=60
39+60=99
A large company states in its promotional literature that 74% of its employees have college degrees. Assume this claim is true. If 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?
A. 0.0176
B. 0.4052
C. 0.5948
D. 0.9284
Answer:it is 0.5948
Step-by-step explanation:c
The probability that at least 1 of the selected employees will not have a college degree is 0.594776.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,n is the number of trials or sample size,p is the probability of a single success, andq is the probability of a single failure.Given that 74% of the employees have degrees, therefore, 26% of the employees have no degree.
Now, since we want at least any one of the three people selected to have a degree. Therefore, the probability of everyone having a degree can be written as,
Probability that at least any one of the three people selected to have a degree = 1 - Probability of everyone having a degree
Now, using the binomial distribution we can write,
[tex]\text{Probability} = 1 - [^3C_0\cdot(0.26)^0 \cdot (0.74)^{(3-0)}]\\\\\text{Probability} = 1 - 0.405224 = 0.594776[/tex]
Hence, the probability that at least 1 of the selected employees will not have a college degree is 0.594776.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
#SPJ2
PLEASE HELP ASAP
Which expression is not equal to 1?
A} sin θ csc θ
B} cos θ sec θ
C] tan θ cot θ
D} sin θ cos θ
Answer:
D} sin theta cos theta
Step-by-step explanation:
Edge
Answer:
D
Step-by-step explanation:
Edge2021
Convert to standard form: 3y -17 = 2x
What is it guys?????????
Answer:C
Step-by-step explanation:
Notice that the line is heading downward. This is a clue that it has a negative slope. Think of slope as rise over run. Rise being up or down on the y axis and run being left or right on the x axis. If we start at (0,0) and count down 3 squares and left 4 squares we can see that -3/4 is the slope.
Answer:
A. 3/4
Step-by-step explanation:
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
(-8, -6) (-4, -3)
[tex]\frac{-3 + 6}{-4 + 8} = \frac{3}{4}[/tex]
Maryanne is making roast chicken for dinner. It takes 2 1/2 hours to cook. She plans to eat dinner at 6:00pm. At what time should she put the chicken in the oven?
Answer:
3:30
Step-by-step explanation:
Joey drives his car 80 miles per hour on the highway. Write an equation that relates his distance traveled. (d) to the time elapsed (t).
Answer:
d=80+t? hope that helps not much info in this
Step-by-step explanation:
if you have three apples and john takes 1 how many do you have
Answer:
you got two apple left I hope this helps
2,000 - 61k = 48
In 1962, the population of a bird species was 2,000.
The population k years after 1962 was 48, and k
satisfies the equation above. Which of the following
is the best interpretation of the number 61 in this
context?
Answer:
61 is the rate at which the population changes every year
Step-by-step explanation:
Given
[tex]2000 - 61k = 48[/tex]
Required
Interpret 61
A linear equation has the form:
[tex]y = mk + b[/tex]
or
[tex]b + mk = y[/tex]
Where m is the rate
By comparison:
[tex]mk = -61k[/tex]
[tex]m = -61[/tex]
Hence, 61 represents the rate at which the population changes yearly.
The negative sign implies that the populatiin reduces
WILL MARK YOU BRAINLIEST
Answer:
the second : the angles are congruent and the side lengths are proportional
Which of the following numbers is not between -2.6 and 1.3 on the number line?
0.5
-2.1
1.4
-1.8
Answer:
1.4
Step-by-step explanation:
-2.6---------------1.3
0.5 is between
-2.1 is between
1.4 is not between
-1.8 is between
30 = x + 22
What does x equal to?
Answer:
x = 8
Step-by-step explanation:
30 = x + 22
subtract 22 from both sides
8 = x
Tatiana deposits $600 into a bank account that pays 4.75% interest compounded annually. The expression(1 + 0.0475)t represents the number of dollars in the account after t years for every dollar in the original balance. Which of the following is a reasonable interpretation of the expression 600(1 + 0.0475)t in this context?
A: The amount of interest the account earns after 1 year
B:The amount of interest the account earns after 600 years
C:The amount of money in the account after 1 year
D:The amount of money in the account after t years
Answer:
b
Step-by-step explanation:
Answer:
the answer is d just trust me im doing this test right now
Step-by-step explanation: