The solution for the linear system will be , x(t) = 4 c₁e^t + 4 c₂e^t and
y(t) = -c₂e^t + c₂(1 - t)e^t .
The solution is given by ,
matrix | x y | = c₁ .v . e^λt + c₂( w + v.t ) e^λt
Given that the matrix has repeated eigenvalue with eigenvector generalized vectors ,
λ = 1 with eigenvector v = [ 4 , -1 ] and generalized vectors w =[ 0,1 ].
then the solution will be,
c₁ [ 4 , 1 ] e^t + c₂[ 0 , 1] + [ 4 , -1 ] )e^t
therefore,
x(t) = 4 c₁e^t + 4 c₂e^t
y(t) = -c₂e^t + c₂(1 - t)e^t
Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.
Matrix multiplication, for example, depicts the combination of linear maps.
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Find the probability that if 10 different-sized washers are arranged in a row, they will be arranged in order of size. Use a graphing calculator and round the answer to six decimal places. The probability of the washers arranged by size is ______.
The probability of the washers arranged by size is 2.755731 ( six decimal places).
Probability
Probability is simply the possibility of something happening. When we are unsure about the outcome of an event, we can discuss the probabilities of various outcomes . Statistics is the study of probability-governed events.We can arrange them in 10! = 3628800 different ways.
There is only one way to arrange them in size order.
The washers arranged by size have a probability of
1/3628800 = 2.75573192
≈ 2.755731 (six decimal places)
Therefore, The probability of the washers arranged by size is 2.755731
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Use the rational zeros theorem to list all possible rational zeros of the following.
h(x)= 7x^4+7x^3-2x^2-5x-5
All the possible rational zeros of h(x) are given as follows:
±1/7, ± 5/7 ± 1, ± 5.
What is the rational zero theorem?The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 7.Constant term of -5.The factors are given as follows:
Factors of 7: {1,7}.Factors of 5: {1,5}.Then the zeros are given as follows:
±1/7, ± 5/7 ± 1, ± 5.
As:
1/7 is the division of 1 by 7.5/7 is the division of 5 by 7.1 is the division of 1 by 1.5 is the division of 5 by 1.More can be learned about the rational zeros theorem at https://brainly.com/question/28782380
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Helppp pleaseee it’s due today pleasee
Answer:
4
6
y=4x+6
Step-by-step explanation:
check the attached file
Evaluate the expression for the given value of the variable 4c - 3. C= -2
Answer:
-11
Step-by-step explanation:
4c - 3 Substitute -2 for c
4(-2) - 3
-8 - 3
-11
Answer:
-11
Step-by-step explanation:
We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.
4c - 3 ⇒ 4(-2) - 3
Now, we can simplify this.
-8 - 3 = -11
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noemi strings together x green beads at $0.75 each with 3 blue beads at $0.30 each. she makes a bracelet that averages $0.60 per bead. choose an equation to model the situation.
The equation to model on this situation is :
0.6 = (0.75x + 0.9)/(x + 3)
Noemi makes bracelets averaging $0.60 per bead, so we need to write an equation that models this average bead cost. This can be found by dividing the total bead cost by the number of beads used.
1. The total cost of a bead can be found by multiplying the price of each type of bead by the number used and adding these values together.
So:
Total Cost = 0.75x + 3*0.3
= 0.75x + 0.9
2. Total number of beads = x + 3
3. Thus, the average cost is:
(0.75x + 0.9)/(x + 3)
4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:
0.6 = (0.75x + 0.9)/(x + 3)
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information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of fDegree 3; zeros: 5,-4i
The remaining zeros of Degree of f will be = -5 and 4i
According to the given question,
We can see that the given degree is = 3
∴ This means that there are 3 roots ( zeros )
We can conclude from the above statement that,
The number of roots = The degree that is given in the question.
For example, if the question gives the degree = x
Then the roots will also be = x
This question follows the complex conjugate root theorem,
This theorem states that the if there are complex roots with real coefficients then the root of its polynomial, will also be its complex conjugate.
The resultant conjugate of,
⇒ 5 = -5
⇒ -4i = +4i
Therefore, the remaining zeros of Degree of f will be = -5 and 4i
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what the value of the question
Answer: [tex]14\sqrt 2[/tex]
Step-by-step explanation:
Consider square ABCD. What is the angle of rotation about the center that maps AB to BC?
Recall that rotations are counterclockwise.
The angle of rotation is 90 degrees.
What is a square?
In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.
The angle of rotation about the center that maps AB to BC is 90 degrees.
If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.
The angle of rotation that maps AB to BC is the angle through which the square was rotated.
Hence, the angle of rotation is 90 degrees.
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Which expression shows how much greater the volume of the larger cube is than the volume of the smaller cube?
option D
Given;
larger cube edge length - 3x+2 units
smaller cube edge length - 2x-1 units
We know that volume of a cube = (Edge of the cube)3
volume of larger cube = (3x+2 )³
=27x³+8 +54x²+36x
volume of smaller cube=(2x-1)³
=8x³-1 -12x²+6x
Volume difference = volume of larger cube -volume of smaller cube
volume difference =( 27x³+8+54x²+36x)-(8x³- 1 - 12x²+6x)
= 19x³+9+66x²+30x
=19x³+66x²+30x+9
Hence volume of larger cube is greater by (19x³+66x²+30x+9)
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Leon Starr purchased 55 shares of stock at
$41.09 per share. His online stockbroker charged him
a $15.99 commission. What is the total amount that he
paid for the stock?
Total amount paid for the stock:
Answer: $2,275.94
Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:
41.09(55)
41.09 x 55
That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!
Solve the system if we x-3y=0 and 3x-6y=9 by combining the equations.
Step-by-step explanation:
Hope u get it x=3×3
x=9
It didn't include in the photo
Translate the verbal expression into an algebraic inequality, solve and graph your answer:
The quotient of a number and -3 plus 5 is at least 12.
The complete answer for the verbal expression into an algebraic inequality is [tex]\frac{n}{-3} +5 \geq 12[/tex] .
What are inequality?
In arithmetic, the relationship between 2 values that are not equal is outlined by inequalities. difference means that not equal. Generally, if 2 values don't seem to be equal, we tend to use “not equal (≠)”.
Main body:
First, let's call "a number": n
"The quotient" means we are dividing.
Therefore, "the quotient of a number and -3" can be written as:
n÷ -3
now we need to add 5 to the expression ,
[tex]\frac{n}{-3} +5[/tex]
The quotient of a number and -3 plus 5 is at least 12.
so the expression found out till is equal to at least 12 which means sign used is " ≥"
Hence , the complete answer is [tex]\frac{n}{-3} +5 \geq 12[/tex] .
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Period:
9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?
10) Pedro goes to 70 % of the basketball teams games. If the basketball team plays 20 games, how many did he go to?
11) Your bill at a restaurant comes to $ 24.00. You want to leave a 15% tip. What is your final bill?
12) Monica wants to buy a bag of Taxis for $13.50. If the store is having a discount of 20% off, how much is she spending?
13) How much interest is earned on $ 100 at 70 % for 9 years?
14) How much interest is earned on a $42 investment at 5 % for three years?
The percent of increase Maria walked if found as the 50%.
Explain the term percent increase?The amount that a percentage has increased over time is expressed as a percent increase.One would need to figure out the difference between the initial value and the final value, subtract to determine the precise sum of the drop, in order to arrive at this amount.The formula for the percentage increase is given as;
Percent increase = Increase / original number x 100
original number = 20 miles
Increase = 30 miles - 20 miles
Increase = 10 miles
So,
Percent increase = 10 / 20 x 100
Percent increase = 50%
Thus, the percent of increase Maria walked if found as the 50%.
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The correct question is-
9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?
55]
Evaluate the expression a² + b ÷ 3 for each set of given values. Enter each number in the provided box.
a = 4, b=3 |
a=2,b=21
a = 3, b = 6
Evaluating the expression a² + b ÷ 3 for each set of given values we have
a = 4, b=3, and a² + b ÷ 3 = 17a=2, b=21, and a² + b ÷ 3 = 11a = 3, b = 6, and a² + b ÷ 3 = 11How to evaluate the expressionsThe expressions are evaluated using substitution as done below
for a = 4, b=3
substituting the the values of a and b
= a² + b ÷ 3
= 4² + 3 ÷ 3
= 16 + 1
= 17
For a=2, b=21
substituting the the values of a and b
= a² + b ÷ 3
= 2² + 21 ÷ 3
= 4 + 7
= 11
For a = 3, b = 6
substituting the the values of a and b
= a² + b ÷ 3
= 3² + 6 ÷ 3
= 9 + 2
= 11
substituting the values yielded the results as 17, 11 and 11
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Can anyone help?! I have no clue how to do this geometry.
Answer:
Step-by-step explanation:
Angle E = W =119 degree
Angle V = 360-105-59-119
Angle V = 77
As DEFG = VWXY
There for D = V
So angle D = 77
Angle G = 360 -77-59-119
Angle = 105
Answer:
119 degree
Step-by-step explanation:
Any similar polygons have:
1- congruent corresponding angles
2- proportional corresponding sides
Here the question asking about measure of angle E.
The easiest way to find the corresponding angles by comparing the polygons names DEFG and VWXY, the 1st letter in both are D and V, that means these two angles are corresponding and congruent. Same for the 2nd letter in both are E and W, that means angle E is congruent to angle W which is 119 degree.
Done
NO LINKS!! Please help me with this problem. Part 1gg
Answer:
Graph A
Step-by-step explanation:
Given piecewise function:
[tex]f(x)=\begin{cases}9+x, \;\;\:\:x\leq3\\x^2+3,\;\;x > 3\end{cases}[/tex]
To graph the given piecewise function:
Draw the line y = 9 + x for the domain (-∞, 3].Draw the curve y = x² + 3 for the domain (3, ∞).The line y = 9 + x is a straight line with a positive gradient.
It crosses the x-axis at (-9, 0) and crosses the y-axis at (0, 9).
Therefore, the only graph that shows the line y = 9 + x is the first graph.
Use the drawing tools to form the correct answer on the graph.
A buoy marks a channel for boat navigation and bobs up and down with the motion of the wave
the buoy above sea level, in feet, after t seconds.
The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is f(t) = 2cos (∏/4 t).
f(t) will be lowest when cos (∏/4 t) is lowest.
The value of cosine lies between -1 to 1.
When cos (∏/4 t) = -1, f(t) has lowest value.
Solve the equation cos (∏/4 t) = -1
cos (∏/4 t) = -1
∏/4 t =cos ⁻¹ (-1)
∏/4 t = (2n + 1)∏
t = (2n + 1)4 where n is a whole number.
The value of the function is lowest at t = 4, 12, 20.
The lowest points are (4,-2), (12,-2),(20,-2) etc.
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Answer: (4, -2) (12,-2)
Step-by-step explanation:
What is the area of this triangle?
Enter your answer in the box.
units?
Answer:
Below
Step-by-step explanation:
If you turn it sideways and use the y-axis portion as the base (4) , you can see height = 5
Area = 1/2 * b * h = 1/2 * 4 *5 = 10 units^2
What is the possible value of a positive, even integer that's shaped like a 4?
Answer: It's not possible for a positive, even integer to have a specific shape, such as the shape of a 4. This is because integers are abstract mathematical concepts that represent whole numbers and do not have any physical properties, such as shape. Additionally, even integers are simply integers that are divisible by 2, and do not have any specific shape associated with them.
If you're asking about a specific number that has the shape of a 4, such as the number "4" written in a specific way, it's important to note that the value of a number does not depend on its physical appearance. For example, the number 4 written as "4" and the number 4 written as "IV" (the Roman numeral for 4) are both the same number, and have the same value.
In △QRS , point A is between points Q and R, point B is between points R and S, and AB¯¯¯¯¯∥QS¯¯¯¯¯ .
QA=23 cm , QR=41 cm , and RS=123 cm .
What is RB ? HURRY!!!!
Answer:
RB = 54 cm--------------------------------
Since AB and QS are parallel, the segment AB divides QR and SR proportionally.
QR/AR = SR/BRAs QR = QA + AR we get:
41/(41 - 23) = 123/ RB41/18 = 123/RBRB = 123*18/41RB = 54Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.
Two triangles are similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles.
If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures. Consider a hula hoop and the wheel of a cycle, the shapes of both these objects are similar to each other as their shapes are the same.
Triangle is a three-sided polygon. The condition for the similarity of triangles is;
i) Corresponding angles of both the triangles are equal, and
ii) Corresponding sides of both the triangles are in proportion to each other.
Properties of the triangle:
1-Both have the same shape but sizes may be different
2-Each pair of corresponding angles are equal
3-The ratio of corresponding sides is the same
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Marisol needs to purchase AT LEAST 55 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Marisol purchase with $19.00 at the Party Palace?
The combination of streamers and balloons at the Party Palace will be 21 and 34, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Marisol necessities to buy Somewhere around 55 party enrichments. The Party Castle charges $0.50 per beautiful decoration and $0.25 per expansion, including the charge.
Let 'x' be the number of decorative streamers and 'y' be the number of balloons. Then the equations are given as,
0.50x + 0.25y = 19 ...1
x + y = 55 ...2
From equations 1 and 2, then we have
0.50x + 0.25(55 - x) = 19
0.25x = 5.25
x = 21
The value of y is given as,
21 + y = 55
y = 34
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A water tank initially contained 70 liters of water. It is then drained at a constant rate of 2.5 liters per minute.
How many minutes have passed, m, when the tank contains 47 liters? Round to the nearest tenth.
The time taken to drain 23 liter at the rate of 2.5 liters per minute=9 minutes.
What is the concept of pipes and cistern?A cistern is a tank used to hold liquids, usually water, and it contains inlet and outlet pipes so it can fill up or empty itself. A pipe is a segment of a hollow cylindrical object used to transport water from one location to another. The cistern or tank typically has pipes attached to it so that they may be filled and emptied. Part of the tank evacuated in an hour is equal to 1/y if it takes y hours to completely empty it. If a pipe can completely fill and drain a tank in x and y hours, respectively. The net portion of the tank will be filled in one hour when both pipes are opened simultaneously, assuming y>x, by the formula (xy) = (xy) / (y-x).
70 liters of water were initially present in a water tank.
2.5 liters of water were drained every minute.
The tank holds 47 liters before water is added, thus 70-47 =23 liters.
Therefore,23/2.5=9.2 is the time it takes to drain 23 liters at the rate of 2.5 liters per minute.
Taking 2.5 liters per minute to fill a 23liter container takes 9.2minutes.
Water filled in a certain amount of time is equal to the water filling rate in minutes.
Taking 2.5 liters per minute to drain a 23liter container will take 9 minutes.
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he button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.
Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.
nodes in an influence diagram represent part of the model
The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell
The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.
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In a storage locker, there are 15 large boxes and 26 small boxes. The large boxes each weigh 24 pounds. The small boxes each weigh 16 pounds. How much do all of the boxes weigh altogether?
Answer:
864
Step-by-step explanation:
Find composition of A and B
A ={(1;2);(-3;0);(4;7)}
B ={(2;1);(0;3);(4;-3)}
A o B=
The composition of A and B represents by the set A o B = {(2,2),(4,0)}
What is a set of ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given sets are
A = {(1,2), (-3,0), (4,7)}
B = {(2,1), (0,3), (4,-3)}
The inputs of B are 2, 0, and 4.
The outputs of B are 1, 3, and -3.
The inputs of A are 1, -3, and 4.
The outputs of A are 2, 0, and 7.
The composition can be written as A o B = A(B(x)
A(B(2)) = A(1) = 2
A(B(0)) = A(3) = not valid [Since 3 is not an input of A].
A(B(4)) = A(-3) = 0
The composition is {(2,2), (4,0)}.
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If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the ramp is 23 feet long, what angle (in degrees) does the ramp make with the ground?
Answer:
≈20.35°
Step-by-step explanation:
height = 8
hypotenuse =23
angle is x
sin(x) =8/23
[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°
x is about ≈20.35°
The ramp makes an angle of approximately 20.86 degrees with the ground.
Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,
we need to find the angle ramp make with the ground.
To find the angle that the ramp makes with the ground, we can use the sine function.
The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.
In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).
Let's calculate the angle:
sin(angle) = opposite/hypotenuse
sin(angle) = 8/23
To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:
angle = arcsin(8/23)
We can find the approximate value of the angle:
angle ≈ 20.86 degrees
Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.
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I could really use some help I got 10 mins left on quiz please help
The value of x in the problem is 0
Given that PQR is a straight line
In this problem PQ+QR=PR
The value of PQ is 9
The value of QR is not given but given an equation 2x+3
And QR is x+12
So PQ+QR=PR
9+2x+3=x+12
12+2x=x+12
2x-x=12-12
x=0
Therefore, the value of x in the problem is 0
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evaluate the six trigonometric functions at 11pi/3. (give an exact answer, not a decimal approximation.)
The six trigonometric functions at 11π/3 are as follows-
sin (11π/3) = -[tex]\sqrt{3}[/tex]/2
cos (11π/3) = 1/2
tan (11π/3) = -[tex]\sqrt{3}[/tex]
cot (11π/3) = -1/[tex]\sqrt{3}[/tex]
sec (11π/3) = 2
cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]
Let us evaluate the six trigonometric functions at 11π/3 as follows -
11π/3 can be written as (6π+5π)/3 = 2π + 5π/3.
a. sin (11π/3) = sin (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= sin (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, sin is negative in the 4th quadrant.
= -sin (π/3)
= -[tex]\sqrt{3}[/tex]/2
Hence, sin (11π/3) = -[tex]\sqrt{3}[/tex]/2
b. cos (11π/3) = cos (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= cos (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, cos is positive in the 4th quadrant.
= cos (π/3)
= 1/2
Hence, cos (11π/3) = 1/2
c. tan (11π/3) = tan (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= tan (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, tan is negative in the 4th quadrant.
= -tan (π/3)
= -[tex]\sqrt{3}[/tex]
Hence, tan (11π/3) = -[tex]\sqrt{3}[/tex]
d. cot (11π/3) = 1/ tan (11π/3)
Hence, cot (11π/3) = - 1/ [tex]\sqrt{3}[/tex]
e. sec (11π/3) = 1/ cos (11π/3)
Hence, sec (11π/3) = 2
f. cosec (11π/3) = 1/ sin (11π/3)
Hence, cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]
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An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. If there is clear evidence that this proportion is less than 0.10, she will accept the shipment. To reach a decision, she will test the hypotheses H0: p = 0.10 versus Ha: p < 0.10. To do so, she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck. Only 8 of the potatoes sampled are found to have major defects. What is the value of the large-sample z statistic?
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. If there is clear evidence that this proportion is less than 0.10, she will accept the shipment. To reach a decision, she will test the hypotheses H0: p = 0.10 versus Ha: p < 0.10. To do so, she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck. Only 8 of the potatoes sampled are found to have major defects. Compute the value of the large-sample z statistic. What is the P-value for this hypothesis test?
P-Value for the hypothesis test will be of z = 1.9065
The P-value for conducting the right-tailed test H0 : μ = 3 versus HA : μ > 3 is the probability that we would observe a test statistic greater than t* = 2.5 if the population mean
μ really were 3. Recall that probability equals the area under the probability curve. The P-value is therefore the area under a tn - 1 = t14 curve and to the right of the test statistic t* = 2.5. It can be shown using statistical software that the P-value is 0.0127
The P-value, 0.0127, tells us it is "unlikely" that we would observe such an extreme test statistic t* in the direction of HA if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P-value, 0.0127, is less than
α
= 0.05, we reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ > 3.
Note that we would not reject H0 : μ = 3 in favor of HA : μ ≠ 3 if we lowered our willingness to make a Type I error to α = 0.01 instead, as the P-value, 0.0254, is then greater than
α= 1.9065.
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