There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
The matrix is:
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
The system of equations' equivalent augmented matrix is
[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]
The following matrix has been reduced and transformed into a set of equations.
x(1) + x(3) = 0
Subtract x(3) on both side, we get
x(1) = -x(3)
x(1) = -t
x(2) = 0
Let x(3) = t
[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
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The complete question is:
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
(x1, x2, x3) =
Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is given by E(t)=2600−50t.
Part 1) Terry started at an elevation of 2,600 ft.
Part 2) The elevation is decreasing by 50 feet per second.
we have
E(t) = 2600 -50t
where
E(t) is Terry's elevation in feet
t is the time in seconds
Part 1) For t=0
substitute the value,
E(0) = 2600 -50(0)
E(0) = 2600
therefore
The equation says us that Terry started at an elevation of 2,600 ft
Part 2) we have
E(t)=2600−50t
This is the equation of the line in slope-intercept form.
The slope m is equal to, m = -50 ft/sec
The slope is negative because is decreasing
therefore
The elevation is decreasing by 50 feet per second.
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In the two units of company, the employees in unit one are 650 and monthly salary is N2750, the employees in unit two are 700 and monthly salary is N2500 then the combined arithmetic mean is
Answer:
2620
Step-by-step explanation:
Use the distributive property to rewrite the expression 5(n+9)
Choose the ratio that is equivalent to this one 2/9
Add.
4 2/8+ 9 4/8
Please help me. Thank u
:)
The solution of the addition of term is; 43/4
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given terms as;
4 2/8+ 9 4/8
We have to add the terms, so first convert into normal fraction.
4 2/8 = 10/8
9 4/8 = 76/8
Now add;
10/8 + 76/8
= 86/8
= 43/4
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Answer:
13 6/8
Step-by-step explanation:
If bookshelf A is 3 feet long and bookshelf B is 4 feet long, what is the length of bookshelf C?If bookshelf A is 3 feet long and bookshelf B is 4 feet long, what is the length of bookshelf C?
A. 5 feet is the length of bookshelf C.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
this is a Pythagorean theorem problem, and it involves right triangles.
If this is the case, then we can use the formula: a² + b² = c².
In this case, it gives us the values of a and b,
so we have 3² + 4² = c².
This is equal to 9 + 16 = c², and further simplified, 25 = c².
So we can then find the square root of 25,
written as √25, which would equal 5,
as 5² = 5 * 5,
and 5 * 5 = 25.
So therefore your answer would be A. 5 feet.
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5. An equilateral triangle is shown below.
Determine the AREA of the triangle.
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
[tex]altitude=\sqrt{8^2-4^2} =4\sqrt{2^2-1^2} =4\sqrt{3} \\area~of~triangle=\frac{1}{2} \times base \times altitude\\=\frac{1}{2} \times 8 \times 4\sqrt{3} \\=16\sqrt{3} \\\approx 27.7 ~in^2[/tex]
What is the answer to this equation X-5<4
Answer:
Just add 5 to the other side
Step-by-step explanation:
x < 9
suppose a pipe containing water with 0.2 kg of sugar per liter runs into a tank filled with 400 liters of water currently containing 10 kg of sugar. the flow from the pipe enters the tank at 10 liters per minute. the solution is kept thoroughly mixed and drains from the tank at the same rate. setup and solve an initial value differential equation.
An initial value differential equation is S(t) = 10 * e^(-0.005t).
Sugar Amount Differential EquationThe initial value differential equation for the amount of sugar in the tank can be modeled as:
dS/dt = (0.2 kg/L) * 10 L/min - (S/400 L) * 10 L/min
where S is the amount of sugar in the tank in kg and t is the time in minutes.We can solve this equation using separation of variables:dS/S = -0.005 dt
Integrating both sides:ln(S) = -0.005t + C
Using the initial condition that S = 10 kg at t = 0:ln(10) = C
So the solution is:S(t) = 10 * e^(-0.005t)
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What number has 1 ten thousand, the same number of thousands as ten thousands, 8 more hundreds than thousands, 7 fewer tens than hundreds, and 1 more than tens?
Answer: 11,923
Step-by-step explanation:
For the following exercises, determine whether the relation represents a function. {(a, b),(b, c),(c, c)}
The relation {(a, b), (b, c), (c, c)} does not represent a function because for the input value "c", there are two possible output values, "c" and "c". In a function, for each input value, there can only be one output value.
The vertical line test may be used to assess whether or not a relation is a function by looking at its graph.
If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.
To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.
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5.___________________means if an event happens by chance
Fill in the blank: when you build a sumif or countif formula, the first part of the formula in parentheses is the_______ A. Criteria B. Cndition C. Operator D. Range
The Range is the first component of the formula in parentheses.
What is Range
The range in statistics is the difference between the highest and lowest values for a specific data collection. For instance, if the given data set has the values 2, 5, 8, 10, and 3, the range will be 10 - 2 = 8.
It is possible to think of the range as the distance between the highest and lowest observation as a result. The consequence is known as the scope of observation. The breadth of statistics reflects the diversity of observations.
The first component of a sum or count calculation that is enclosed in the parenthesis is the Range.
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13. A rectangle is 3 feet wide and has an area of 438 square feet. What is the
perimeter of the rectangle?
Answer:
Below
Step-by-step explanation:
L x W = 438
L = 438/W
L = 438/3 = 146 ft
then perimeter = 3 + 3 + 146 + 146 = 298 ft
Answer:
It should be 146
Concord Pizza's checkbook balance is $1,799.59. The bank statement has a balance of $2,314.22. Interest earned on the statement was $35.50. With checks outstanding of $504.13 and a monthly service charge of $25.00, the reconciled balance is:
The reconciled balance would be:
$2,314.22 (bank statement balance) + $35.50 (interest earned) - $504.13 (checks outstanding) - $25.00 (monthly service charge) = $1,820.59
A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually sells for
$6.00 per pound. The cheaper brand sells for $3.00 per pound. How much of each type should be mixed in order to
have 20 pounds of coffee that is worth $4.50 per pound?
The amount of each type that should be mixed in order to have 20 pounds of coffee mixture that is worth $4.50 per pound is: 10 pounds $6.00 Gourmet coffee, 10 pounds $3.00 Cheap brand.
How to find the mixtures of coffee?Gourmet coffee $6.00 ---- x pounds
Cheap brand $3.00 --- 20 - x pounds
Mixture $4.50 ---- 20
Total 20 pounds6 x + 3 ( 20 - x ) = 4.50 × 20
6 x + 3 ( 20 - x ) = 90
6 x + 60 - 3 x = 90
Collect like terms
6 x - 3 x = 90 -60
3 x = 30
x = 10
Cheap brand
20-x pounds
20-10
=10 pounds $3.00 Cheap brand
Therefore 10 pounds and 10 pounds should be mixed.
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Find the solution set of the system of linear equations represented by the augmented matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x3 = t and solve for x1 and x2 in terms of t.)
leftbracket3.gif 2 1 −1 3 rightbracket3.gif
1 −1 1 0
0 1 2 1
(x1, x2, x3) =
The solution set of the system of linear equations is (x1, x2, x3) = (3/2, 3/2, −1/4).
We can solve this system of linear equations using Gaussian elimination method.
Step 1: Add the first row to the second row:
leftbracket3.gif 2 1 −1 3 rightbracket3.gif
1 −1 1 0 2
0 1 2 1
Step 2: Subtract 2 times the second row from the third row:
leftbracket3.gif 2 1 −1 3 rightbracket3.gif
1 −1 1 0 2
0 0 4 −1
Step 3: Divide the third row by 4:
leftbracket3.gif 2 1 −1 3 rightbracket3.gif
1 −1 1 0 2
0 0 1 −1/4
Step 4: Subtract the third row from the first row:
leftbracket3.gif 2 1 −1 3 rightbracket3.gif
1 −1 0 −1/4 7/4
0 0 1 −1/4
Step 5: Add 4 times the second row to the first row:
leftbracket3.gif 2 0 −5/4 3 rightbracket3.gif
1 0 1 −1/4 −1/4
0 0 1 −1/4
This echelon form gives us the solution:
x3 = −1/4
x2 = 7/4 + x3 = 7/4 − 1/4 = 3/2
x1 = 3 − x2 = 3 − 3/2 = 3/2
So, the solution set of the system of linear equations is (x1, x2, x3) = (3/2, 3/2, −1/4).
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what are the coordinates of the point on the directed line segment from (1,5) to (6,10) that portions the segment into a ratio of 3 to 2?
Answer:
The answer is point (4,8)
Step-by-step explanation:
The horizontal (x) distance between the given points is 6-1 = 5.
If the horizontal distance is 5, then because the ratio of the given points is 3 to 2, we can say that 3/5 of 5 is 3. The horizontal distance between (1,5) and (x,y) is 3, so x = 4.
We can do the same with the vertical (y) distance, which is 10-5 = 5.
Again, 3/5 of 5 is 3, so y = 5+3 = 8
Answer: the point is (4,8).
CHECK: We can check this result by finding the distances between the given points to (4,8), and calculating the distance.
Distance between (1,5) and (4,8) = √18 = 3√2
Distance between (6,10) and (4,8) = √8 = 2√2
The ratio between the distances is 3:2, so the solution checks out.
Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Each month, the interest for the current balance is calculated as:
$3,287.90 * 14.5% / 12 = $48.22
How Do Interest Rates Work?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
The new balance after each payment is:
$3,287.90 + $48.22 - $1,200.00 = $2,147.12
Repeat the calculation until the balance is zero:
Month 1:
Balance: $3,287.90
Interest: $48.22
New Balance: $2,147.12
Month 2:
Balance: $2,147.12
Interest: $31.14
New Balance: $1,178.26
...
Month 26:
Balance: $0.00
So, it takes 26 months to pay off the credit card, and the total amount paid including interest is $31,622.68.
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Please help! Image below…
Answer:
In order in which the boxes appear in the sentences
[tex]\textsf{y-intercept \;\;\boxed{28000}}\\\\\textsf{this represents dollar value for a car that is $\boxed{0}$ years old}\\\\\textsf{Slope of the regression line is $\boxed{-4900}$}[/tex]
Step-by-step explanation:
Double-Declining-Balance Depreciation
A building acquired at the beginning of the year at a cost of $107,600 has an estimated residual value of
$4,300 and an estimated useful life of 4 years. Determine the following.
rate
(a) The double-declining-balance
(b) The double-declining-balance depreciation for the first year
%
C
A method of accounting known as the double declining balance (DDB) maintenance method entails depreciating some assets at a rate that is twice that of straight-line depreciation. As a result, depreciation increases during the initial year of possession and decreases thereafter.
When is double dropping balance permissible?When to apply the twofold decreasing balance technique of depreciation When you buy assets that depreciate more rapidly in the first few years, the optimal scenario for using double reducing balance depreciation is that situation. The asset that lost value the most in the first few years of ownership is a car.
a) Straight-Line Depreciation Percent = 100% / 4 years = 25% / year
Depreciation Rate = 2 x 25% = 50% / year
b) Depreciation for a Period = 50% x Book Value at Beginning of the Period
Depreciation for Period 1 = 50% x $107,600 = $53,800
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In ΔOPQ, q = 75 cm, mm∠O=113° and mm∠P=18°. Find the length of o, to the nearest centimeter.
The length of o to the nearest centimeter is 91 cm.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We have the law of sine of triangles, which is stated as,
a / sin A = b / sin B = c / sin C
where a, b and c are the sides opposite to the angles of the triangle A, B and C respectively.
Given, In ΔOPQ, m ∠O=113° and m ∠P=18°.
m ∠Q = 180° - (m ∠O + m ∠P)
= 180° - (113° + 18°)
= 49°
q / sin Q = o / sin O
o = (q / sin Q) (sin O)
= (75 / sin 49°) (sin 113°)
= (75 / 0.7547) (0.9205)
= 91.476 cm
≈ 91 cm
Hence the length of o is 91 cm.
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Answer: 91 is the answer on dlta
SHOW WORK! PLEASE EXPLAIN! Thank you
Answer:
Below
Step-by-step explanation:
Calculate the unit price of $ per ounce of the 4 options to find the smallest
$2 / 4 = .50 per ounce
4.25 /8 = .53
6/12 = .50
6.75/18 = .375 per ounce <=====cheapest
The city is building a rectangular parking lot. The city wants the width of the parking lot to be 8 yards. The area of the parking lot must be at most 80 square yards. (These are city regulations.) Write an Inequality that describes the possible lengths (in yards) of the parking lot.
Use l for the Length of the rectangular parking lot.
Answer:The area of the parking lot is length * width. If the width of the parking lot is 8 yards, the area of the parking lot can be represented by the inequality:
Area <= 80
length * 8 <= 80
To get the possible lengths of the parking lot we need to divide both sides by 8:
length <= 10
Therefore, the inequality that describes the possible lengths of the parking lot (in yards) is:
length <= 10 yards
The possible lengths of the parking lot is any value less than or equal to 10 yards.
Step-by-step explanation:
System A
-2x-y+4=0
2x+y=4
System B
3x-y=6
3x+y=6
O The system has no solution.
The system has a unique solution:
(x, y) = (D
O The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
O The system has a unique solution:
(x, y) = D
The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
The correct statement regarding the equation is that A. the equation has no solution.
How to explain the equation?It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, the equation will be illustrated thus:
-2x - y + 4 = 0 .... i
2x + y = 4 ... ii
From equation i
-2x - y = -4
2x + y = 4
Add both equation will give 0.
The equation has no solution.
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need assistance with This Math question here I’ll give you brainliest
Answer:
A. (3 + 4)² - 9
Step-by-step explanation:
She must add 3 and 4 first but in order to do so she must put them in brackets thus correctly following the order of operations
Answer:
(3 + 4)² - 9
3 + 4 first so that goes in brackets
The result is squared so the ² goes outside the brackets
Finally, subtract 9 so that goes after
The perimeter of a rectangular parking lot is 190 meters. The width is one-fourth the length. Write a system of equations for this scenario, but do not solve
The linear equation for this scenario will be 2(x + x/4)=190 where x=Length.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Perimeter of rectangle=2 (length + Breadth)
Given Perimeter=190
Let length=x
then Breadth will be = x/4
Hence, the perimeter will form linear equation given below
2(x + x/4)=190
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Please help me with this question.
The area of the shaded region is given as follows:
70 cm².
How to obtain the area of the shaded region?The area of a triangle is given by half the multiplication of the base and of the height of the triangle.
For the triangle, the area is of 30 cm², while the height is of 6 cm, hence the base is obtained as follows:
0.5 x 6 x b = 30
3b = 30
b = 30/3
b = 10 cm.
Considering the side length of 10 cm², the area of the square is given as follows:
10² = 100cm².
The area of the shaded region is given by the subtraction of the area of the square by the area of the triangle, hence:
100 - 30 = 70 cm².
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A coin flips 200 times. Heads 96 Tails 104
Find the first and second derivative of the following function in terms of the parameters
c1 and c2.
y=c1x + c2x5
y′=
y″=
Find a linear second-order differential equation
F(x, y, y′, y″) = 0
for which
y = c1x + c2x5
is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y′ and ypp for y″.)
On solving the provided question, we can say that the derivative will be y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
what is derivative?The derivative of a function with real variables in mathematics gauges how sensitively the function's value will change in response to changes in its arguments. Calculus's fundamental tools are derivatives. Differentiation (in mathematics, the rate of change of a function with respect to a variable) (in mathematics, the rate of change of a function with respect to a variable). Calculus and differential equation problem-solving depend heavily on derivatives. Finding the "slope" of a specific function is the definition of "derivative" or "taking a derivative" in calculus. Because it is often the slope of a straight line, the slope should be enclose in quotations. While applying to practically every function, derivatives are measures of rate of change.
Linear second-order differential equation F(x, y, y′, y″) = 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
differential equation
y = c₁x + c₂x⁴ ...(i)
Differentiating equation (i)
y¹ = c₁(1) + c₂ ( 4 x³ ) ...(ii)
Differentiating equation (ii)
y¹¹ = c₂ ( 12 x² )
12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹
x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
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