Answer:
x=4
Step-by-step explanation:
Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. x1 + 3x2 = f cx1 + dx2 = g
Answer:
The answer is "[tex]d \neq 3c,[/tex]f and g are arbitrary".
Step-by-step explanation:
The matrix of the device is increased
[tex]\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right][/tex]
Reduce the echelon row matrix
[tex]\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right] \\\\R_1 \leftrightarrow R_2 \\\\\frac{R_2 -1}{C R_1 \to R_2} \sim \left[\begin{array}{ccc} c&d&g\\ 0 & \frac{3c-d}{c}& \frac{cf-g}{c}\\ \end{array}\right][/tex]
Therefore, if 3c[tex]\neq[/tex] 0 is d [tex]\neq[/tex] 3c, the device is valid. Therefore d [tex]\neq[/tex] are arbitrary 3c, g and f.
The values of the coefficients c and d are 1 and 3, respectively
The system of equations are given as:
[tex]x_1 + 3x_2 = f[/tex]
[tex]cx_1 + dx_2 = g[/tex]
From the question, we understand that the system of equations is consistent.
Assume that the system of equations is also dependent, then it means that:
[tex]c =1[/tex]
[tex]d =3[/tex]
[tex]g =f[/tex]
Hence, the values of the coefficients c and d are 1 and 3, respectively
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(a) Complete the table of values for y = 6 - 4x.
Please help ❤️
Answer:
[tex]\boxed{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}}[/tex]
Step-by-step explanation:
Given equation to us is :-
[tex]\implies y = 6 - 4x [/tex]
So , here we can put different values of x in order to get different values of y .
Initial table given to us is ,
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & & & 2&&-6 \\\cline{1-6}\end{tabular}[/tex]
Put x = (-1) :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6 -4(-1) \\\\\implies y = 6 + 4 \\\\\red{\bf\implies y = 10} [/tex]
Put x = 0 :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6-4(0) \\\\\implies y = 6 - 0 \\\\\pink{\bf\implies y = 6 }[/tex]
Put x = 2 :-
[tex]\implies y = 6-4x \\\\\implies y = 6 - 4(2) \\\\\implies y = 6 - 8 \\\\\blue{\bf\implies y = (-2)} [/tex]
Hence the final table would be :-
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}[/tex]
O A. (-2, 1)
O B. (-2,-1)
O c. (-1,-2)
O D. (1.-2)
Answer:
the answer is C -1-2 to the equation
Joanna is building 2 square planter boxes in her garden . Each box is 2 yard wide . What is the total perimeter of the boxes ?
Answer:
16 yards
Step-by-step explanation:
Square: all sides are equalSquare: 4 sides totalPerimeter of square: 2 + 2 + 2 + 22 + 2 + 2 + 2 = 8 yardsPerimeter of second box: 2 + 2 + 2 + 2 = 8 yardsPerimeters in total: 8 + 8 = 16 yardsI hope this helps!
Which set of mixed numbers has a difference less than 1?
A hexagon ABCDEF is shown.
С-115
D
B
145
Angle CDE is twice the size of angle DEF.
Work out the size of angle CDE.
You must show all your working.
E
160°
+
F
Answer:
140
Step-by-step explanation:
115+165+140+90=510
180*4=720 (sum of interior angles of hexagon)
115+165+140+90+x+2x=720
why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x
510+2x+x=720
3x=210
x=210/3
x=70
ANGLE DEF IS 70
so because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140
ANGLE CDE =140
The angle CDE is 140°.
What is a hexagon?
A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.
According to the given problem,
We know,
Sum of the interior angles of a polygon is,
Sum = 180° (n - 2) where n is the number of sides,
Here n = 6 , then
Sum = 180° × 4 = 720°
Let ∠ DEF be x
Therefore ∠ CDE = 2x,
Sum the interior angles,
⇒ 160 + 90 + 145 + 115 + 2x + x = 720
⇒ 510 + 3x = 720 ( subtracting 510 from both sides )
⇒ 3x = 210 ( dividing both sides by 3 )
⇒ x = 70
∠ CDE = 2x
= 2 × 70
= 140°
Hence, we can conclude, in the hexagon, the angle CDE is 140°.
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Factor completely 3x^2+ 2x -1.
O (3x + 1)(x - 1)
O (3x + 1)(x + 1)
O (3x - 1)(x + 1)
O (3x - 1)(x - 1)
Answer:
option C
Step-by-step explanation:
[tex]3x^2+2x-1\\\\=(3x+a)(x+b)\\\\(3b+a)=2\\\\ab=-1[/tex]
and here we think of b=1 and a=-1
so we have
[tex](3x-1)(x+1)[/tex]
-28 = -7(3x +4) + 21x
I think its 1
Step-by-step explanation:
if it ain't my bad
Hamburger-R-Us offers 8 toppings on its made to order burgers. you can order plain or any combination of toppings. How many types of burgers are possible?
Step-by-step explanation:
For every topping, you can either "take-it or leave-it" for your burger. This means there are 2 options for every topping.
Hence number of possible burgers = 2⁸ = 256.
Which of the following represents A U B?
(There's a venn diagram with a box around it
-in the box outside the diagram- 5, 11, 1, and 7
- in the circle labelled "A"- 3 and 9
-in the circle labelled "B"- 2, 4, 8, and 10
-in the middle portion where the circles overlap- 6 and 12)
Answer Choices
{6, 12}
{2, 3, 4, 6, 8, 9, 10, 12}
{1, 5, 7, 11}
{2, 3, 4, 8, 9, 10}
Answer:
Step-by-step explanation:
the area of square Garden is 625 metre square find its length its perimeter and find the cost of fencing it with 5 round at Rs 25 per metre
Answer:
Length=25m
Parameter=100m
5 round cost RS 12500
Step-by-step explanation:
The area of a square
=x²
According to the question the equation is
x²=625
x=√625
x=25
The parameter is
25×4
100 meter
So
1 meter costs 25
100 " " 25×100
2500
1 round = 100 meter
So
5 round cost 2500×5
12500
Max has 5 apples he gives away 2 How many apples does he have left
please awnser asap asap
Answer:
d) 280
Step-by-step explanation:
40320/3=6720
8720/24=280
If Sin theta=3/4,find the value of cos theta
Answer:
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
Given;
Sin θ = 3/4
To calculated Cos θ;
make a sketch of right-angled triangle with following sides;
opposite side = 3
hypotenuse side = 4
then, the adjacent side will be calculated from Pythagoras theorem;
let the adjacent side = b
b² = 4² - 3²
b² = 16 - 9
b² = 7
b = √7
Therefore, Cos θ is now calculated as;
Cos θ = adjacent / hypotenuse
Cos θ = √7/4
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Therefore, [tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Please look at picture
Answer:
32%
The probability according to these results is 32% because 25 people ordered a cold drink. 8 of those were smalls. 8 divided by 25 is 0.32 which is the percentage of a 100% chance aka 32%
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Lucas opened a savings account 20 years ago with a deposit of $3,815.24. The account has an interest rate of 3.3% compounded
quarterly. How much interest has Lucas earned?
a. $3,488.21
b. $3,546.50
c. $3,815.24
d. $3,941.14
Answer:
Interest earned = $3546.50
Option B is correct option.
Step-by-step explanation:
Time t = 20 years
Principal Amount P =$3815.24
Interest r = 3.3% or 0.033
Compounded quarterly n = 4
We need to find How much interest has Lucas earned?
First we need to find the future value in the account after 20 years
The formula used to find future value A is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values of t, r , n and P to find A i.e future value
[tex]A=P(1+\frac{r}{n})^{nt}\\A=3815.24(1+\frac{0.033}{4})^{20*4} \\Simplifying:\\A=3815.24(1+0.00825)^{20*4} \\A=3815.24(1.00825)^{80}\\A=3815.24(1.929)\\A= 7361.74[/tex]
Now finding interest amount by subtracting the initial deposit from the future value
Interest earned = Future Value (A)- Initial Deposit (P)
Interest earned = 7,361.74 - 3815.24
Interest earned = 3546.50
So, Lucas have earned interest = $3546.50
Option B is correct option.
What is the total cost or sale price to the nearest cent?
$65 Jacket; 35% Discount
What is the value of n in the equation below? a^n/a^3=a^9
3
6
12
27
Describe the error in the simplification below.
2^4x2^5 = (2 • 2)4+5
= 49
Answer:
You need to multiply the exponents, then you can multiply the two factors.
Correct answer of the equation:
2^4 x 2^5, multiply exponents
16 x 32, multiply
= 512
Choose the rule to describe the transformation:
D(-3, -4), C(-3, -1), B(0, -4)
to
D '(3, -4), C '(3, -1), B '(0, -4)
a. reflection across the y-axis
b. reflection across y = -x
c. translation: (x,y)LaTeX: \longrightarrow⟶(x + 4, y)
d. reflection across y = x
Answer:
a. reflection across the y-axis
Which is the distance between the points M ( -21, -7)and N ( -5, -7)
Answer:
16
Step-by-step explanation:
becasue from -21 to -5 it's 16 units (-21 - -5= 16).
what is the answer for 5/8 ÷ 1/3
Answer:
15/8
5/8 ÷ 1/3
[Reciprocate the second fraction] =>
5/8 × 3/1
=>15/8
Answer:
1.875
as a fraction 15/8
Or
1 and 7/8
Siri told me.
please help me i dont understand this
Answer:
Step-by-step explanation:
the range is the out put of the function.. what can y be.. in other words
so it's all real numbers... :)
If the point (8,-5) is 6 units above the point P(x, y) and 3 units to the right of it, then what are the coordinates of
the point P(x, y)?
Answer:
(5, -11)
Step-by-step explanation:
We know that (8, -5) is 6 units above and 3 units to the right of point P. Knowing this, let's work backwards by starting from (8,-5) and counting 6 units down and 3 units to the left on the graph.
If you counted correctly, this should place you at the (5, -11). (You can also check your work by counting 6 units up and 3 units to the right from (5, -11) and seeing if you end up at (8, -5).)
Let V(t) represent the values of a bank account, in thousands dollars, t years after the account is opened at the bank. Determine whether each statement below is true
Complete question is;
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.
V(0) = 2 means that the value of the bank account when it is opened is $2000
V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000
V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening
Answer:
Statement 1: True
Statement 2: False
Statement 3: False
Step-by-step explanation:
We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.
This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000
From this little explanation, it's clear that only statement 1 is correct.
The daily output at a plant manufacturing chairs is
approximated by the function
f(L,K) = 453KL 3/5 chairs
where L is the size of the labor force measured in hundreds
of worker-hours and K is the daily capital investment in
thousands of dollars. If the plant manager has a daily budget
of $13,000 and the average wage of an employee is $9.00
per hour, what combination of worker-hours (to the nearest
hundred) and capital expenditures (to the nearest thousand)
will yield maximum daily production?
Complete Question
The daily output at a plant manufacturing chairs is approximated by the function
[tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] chairs
where L is the size of the labor force measured in hundreds
of worker-hours and K is the daily capital investment in thousands of dollars. If the plant manager has a daily budget of $13,000 and the average wage of an employee is $9.00 per hour, what combination of worker-hours (to the nearest hundred) and capital expenditures (to the nearest thousand) will yield maximum daily production?
a)200 worker-hours and $9000 in capital expenditure
b)1100 worker-hours and $3000 in capital expenditure
c)500 worker-hours and $8000 in capital expenditure
d)900 worker-hours and $5000 in capital expenditure
e)600 worker-hours and $6000 in capital expenditure
f)300 worker-hours and $10,000 in capital expenditure
Answer:
d)900 worker-hours and $5000 in capital expenditure
Step-by-step explanation:
From the question we are told that
Daily output at a plant manufacturing chairs is approximated by the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]
Daily budget of $13,000
Average wage of an employee is $9.00 per hour
a) Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (a)
Mathematically solving with L=200 K=9000
[tex]f(L=200,K=9000) = (45\sqrt[3]{9000})200^3^/^5[/tex]
[tex]f(L=200,K=9000) = 45*20.8*24[/tex]
[tex]f(L=200,K=9000) = 22464[/tex]
b)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (b)
Mathematically solving with L=1100 K=3000
[tex]f(L=1100,K=3000) = (45\sqrt[3]{3000})1100^3^/^5[/tex]
[tex]f(L=1100,K=3000) = 45*14.4*66.8[/tex]
[tex]f(L=1100,K=3000) = 43286.4[/tex]
c)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (c)
Mathematically solving with L=500 K=8000
[tex]f(L=500,K=8000) = (45*\sqrt[3]{8000})*500^3^/^5[/tex]
[tex]f(L=500,K=8000) = 45*20*41.63[/tex]
[tex]f(L=500,K=8000) =37467[/tex]
d)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (d)
Mathematically solving with L=900 K=5000
[tex]f(L=900,K=5000) = (45*\sqrt[3]{5000})*900^3^/^5[/tex]
[tex]f(L=900,K=5000) = 45*17.09*59.2[/tex]
[tex]f(L=900,K=5000) =45577.88[/tex]
e)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=600,K=6000) = (45\sqrt[3]{6000})600^3^/^5[/tex]
[tex]f(L=600,K=6000) = 45*18.17*46.4[/tex]
[tex]f(L=600,K=6000) =37974[/tex]
f)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=300,K=10,000) = (45*\sqrt[3]{10,000})*300^3^/^5[/tex]
[tex]f(L=300,K=10,000) = 45*21.5*30.6[/tex]
[tex]f(L=300,K=10,000) = 29704.2[/tex]
Therefore the function f shows maximum at L=900 K=5000
Giving the correct answer to be
d)900 worker-hours and $5000 in capital expenditure
Which expression is equivalent to 2x^3y(x^2y - 3xy^2)?
F. 2x⁵y² - 6x⁴y³
That is the answer.
By means of distribution.
Baseball hat for
$22.90 at 5% sales tax
Answer:I got $21.76
Step-by-step explanation:
;-;
Nick has a box of ornaments that
he uses to decorate his tree each year.
All of them are blue, except for six.
All of them are green, except for six.
All of them are red, except for six.
How many of each colored ornament
does Nick have?
After going through the statement in the question, the number of each colored ornament Nick have is 3.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.
Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
There are three colors.
We can infer that there are 3 ornaments of each color because there are 6 ornaments for each of the other two colors.
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