Solve system of equations given below using both inverse matrix (if possible) and reduced row echelon forms. (20 Points each) a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7 - b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0.

Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

To calculate the distance traveled, we can multiply the speed by the time traveled.

Speed = 1000 miles per hour

Time = 7.5 * 10⁵ hours

Distance = Speed * Time

Distance = 1000 miles/hour * 7.5 * 10⁵ hours

To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:

Distance = 1000 * 7.5 * 10⁵ miles

Distance = 7.5 * 10⁸ miles

Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

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Answer:

 5 , 7 , 8 represent the side of acute angled triangle

Set B with sides 5 , 7 , 8 represent the side of acute angled triangle.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that:

Set of numbers.

Now, We use the following result:

When given 3 triangle sides then to determine if the triangle is acute angled , right angled or obtuse angled.

First find Square all 3 sides, then Sum the squares of the 2 shortest sides and then Compare the sum to the square of the last side.

if sum > Square of last side ⇒ it is Acute Triangle

if sum = Square of last side ⇒ it is Right Triangle

if sum < Square of last side ⇒ it is Obtuse Triangle  

a). 4  , 5 , 7

4² = 16 ,  5² = 25 , 7² = 49

16 + 25 = 41

Hence, 41 < 49

⇒ It is an Obtuse Triangle.

b). 5 , 7 , 8

5² = 25 , 7² = 49 , 8² = 64

25 + 49 = 74

Hence, 74 > 64

⇒ It is an acute Triangle.

c). 6 , 7 , 10

6² = 36 , 7² = 49 , 10² = 100

36 + 49 = 85

Hence, 85 < 100

⇒ It is an Obtuse Triangle.

d). 7 , 9 , 12

7² = 49 , 9² = 81 , 12² = 144

49 + 81 = 130

Hence, 130 < 144

⇒ It is an Obtuse Triangle.

Therefore, Set B with sides 5 , 7 , 8 represent the side of acute angled triangle.

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Answer:

Hey there!

4t(5t)=20t^2

4t(-4)=-16t

5(5t)=20t

5(-4)=-20

Hope this helps  :)

Step-by-step explanation:

This is just a matter of multiplication. 4t x 5t = \(20t^{2}\), so that will be in your first box. 4t x -4 = -16t, so that'll be in your second box. 5 x 5t = 25t, so that will be in your bottom-first box, and 5 x -4 = -20, so that will be in your last one.

Answer:

x=100, hope this helped.

Answer:

7

Step-by-step explanation:

DE corresponds to AB.

37=5x+2

-2 -2

35=5x

7=x

The surface area of the cylinders are: 7794 square units, 904.9 square units,  12804 square units

recall that a cylinder is a three-dimensional solid with two parallel circular bases joined by a curved surface at a fixed distance from the center.  It is considered a prism with a circle as its base and is a combination of two circles and a rectangle

the general formula for the surface area of a cylinder is

SA = 2пr(r+h)

1  SA =2*22/7*20 (20+42)

125.7(62)

SA = 7794 square units

2) SA = 2пr(r+h)

Sssurface rea = 2*3.142*9(9+7)

Surface area = 56.6(16)

Surface area = 904.9 square units

3)   SA = 2пr(r+h)

surface area = 2*3.142*21(21+76)

Surface area = 132(97)

Surface area = 12804 square units

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In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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A gradient vector field of a function f(x,y) is a vector field that points in the direction of the greatest rate of increase of the function. In other words, the gradient vector field is the collection of all the gradient vectors of a function over a given domain.

The gradient vector field of f can be found by taking the partial derivatives of f with respect to x and y and constructing a vector field from these partial derivatives.
Here,

f(x,y) = ysin(xy),so we have

fx(x,y) = y*cos(xy)

fy(x,y) = sin(xy) + xy*cos(xy)

Thus, the gradient vector field of f is given by the vector field
F(x,y) = (y*cos(xy),

sin(xy) + xy*cos(xy))
This vector field can be visualized as a collection of vectors at each point (x,y) in the plane,

where the direction of the vector is determined by the partial derivatives and the magnitude of the vector represents the rate of change of the function in that direction.
Note that the gradient vector field is always perpendicular to the level curves of the function (i.e., the curves where f(x,y) is constant),

since the gradient vector points in the direction of greatest increase and the level curves are the contours where the function is constant.
Overall, the gradient vector field of

f(x,y) = ysin(xy) is

F(x,y) = (y*cos(xy), sin(xy) + xy*cos(xy)),

which is a vector field that represents the direction and rate of change of the function at each point in the plane.

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Answer:

2 head and 1 tail form my side

Answer:

I think the answer is continuous hope this helps

Step-by-step explanation:

Also got subscribe to my YT channel BlxeVxbes

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

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The values of p and q that will make quadrilateral ABCD a parallelogram are: p = 1; q = 2.

Recall that the diagonals of a parallelogram bisect each other to form congruent segments. Therefore, if the image in the attachment is a parallelogram, then the segments formed by the diagonals must be equal to each other.

Therefore, we have:

7p + 1 = 5p + 3

Combine like terms:

7p - 5p = -1 + 3

2p = 2

p = 1

3q + 1 = 2q + 3

Combine like terms:

3q - 2q = -1 + 3

q = 2.

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Answer:

Step-by-step explanation:

Answer

Likes music                         60

    Likes sports   26

    Doesn't like   34

Does not like music           40

70% watch sports   28

Don't watch sports 12

===================================================

Comments

Those that like music  have a total of 60

26 watch sports 60 - 26 = 34 do not watch sports

Those who do not like music are 100 - 60 = 40

Of the 40, 70/100 * 40 do  watch sports = 28

The rest do not                                             12

Answer:

60 34 26

Step-by-step explanation:

I had the test once

If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".

The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.

If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.

p → q

Read this: if p, then q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.

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If two even integers are multiplied, then the product is also even. Hypothesis: Two even integers are multiplied. Hypothesis starts after the word "if". Conclusion starts after the word "then".

The sentence that comes just after the word "if" in a conditional statement is known as the hypothesis. The sentence that comes after the word then in a conditional statement is the conclusion.

If you earn high grades, the portion that follows the "if" is referred to as a hypothesis, and if you get good grades, the part that follows the "then" is referred to as a conclusion.

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.

p → q

Read this: if p, then q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue.

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The area of this house in square meters is 152.24.

To convert square feet to square meters, you can use the conversion factor of 1 square foot = 0.092903 square meters.

A house is advertised as having 1640 square feet under the roof.

So, the area of the house in square meters is:

1640 square feet * 0.092903 square meters/square foot = 152.24 square meters.

Unit Conversion: It is defined as the changing from one quantity unit to another quantity unit followed by the method of division, and multiplication by a conversion factor.

Thus, the area of this house in square meters is 152.24 if the house is advertised as having 1640 square feet under the roof.

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Answer:

Part A:

You are given the amount of money Madison can spend and the price per pound for the potatoes. To find how many pounds Madison can buy, you would need to divide the amount of money she has by the price per pound.

The equation would be Pounds of potatoes = 6.50 / 0.50

Part B:

The only step required to solve the equation from part A is division.

Dividing 6.50 by 0.50 = 13. This means Madison can buy 13 pounds of potatoes.

Answer:

x=2

Step-by-step explanation:

The area of the carpet is 9/10 square meters. Looking at the given options, we can see that only option (A) shows 9/10 square meters as the area of the carpet, so that is the correct answer.

The formula for the area A of a rectangle is: Area is a measure of the size of a two-dimensional surface, such as the surface of a square, rectangle, triangle, or circle. It is typically measured in square units, such as square meters, square feet, or square inches. The formula for calculating the area of a given shape depends on the shape itself.

A = length × width

In this case, the length of the carpet is 9/10 of a meter, and the width of the carpet is 4/5 of a meter.

Multiplying these values, we get:

A = (9/10) × (4/5)

To simplify this expression, we can first reduce the fractions:

A = (9/10) × (4/5)

A = (9/2) × (1/5)

A = (9/10)

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Answer:

Step-by-step explanation:

Square A:

Area = 225 square feet

side *side = 225

        Side =√225

                 \(=\sqrt{15*15}\)

   Side of square A = 15 ft

Square B:

Area = 400 square feet

Side =√400

       = \(\sqrt{20*20}\)

Side of square B = 20 ft

Use Pythagorean theorem for finding the side of Square C.

Side of square A is the altitude ;  side of square B is the base and side of square C will be the hypotenuse

hypotenuse² = base² + altitude²

                      = 15² + 20²

                       = 225 + 400

                       = 625

hypotenuse = \(\sqrt{625} =\sqrt{25*25}\) = 25 ft

Area of square C = 625 square ft

In short,

Area of square C = area of square B + area of square A

                             = 400 + 225

                             = 625 square ft

Answer:

center = \((-4,8)\)

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is \(x^2+y^2+8x-16y+31=0\)

To find: Radius and center of the circle

Solution:

Equation of circle is \((x-a)^2+(y-b)^2=r^2\)

Here, \((a,b)\) is the center and r is the radius.

\(x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2\)

Use formula \((u+v)^2=u^2+v^2+2uv\)

\((x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2\)

On comparing this equation with equation of circle,

center = \((-4,8)\)

Radius = 7 units

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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The break-even quantity is 3 units. The profit for producing 470 units is $5624. 13 units must be produced for a profit of $120.here both cost and revenue are in dollars.

(a) To find the break-even quantity, we set the cost function C(x) equal to the revenue function R(x) and solve for x:

\(11x + 36 = 23x\)

\(36 = 12x\)

\(x = 3\)

Therefore, the break-even quantity is 3 units.

(b) The profit for producing 470 units can be calculated by subtracting the cost from the revenue:

\(Profit = Revenue - Cost\)

\(Profit = R(470) - C(470)\)

\(Profit = 23(470) - (11(470) + 36)\)

\(Profit = 10810 - 5186\)

\(Profit = $5624\)

The profit for producing 470 units is $5624.

(c) To find the number of units that must be produced for a profit of $120, we set the profit equation equal to $120 and solve for x:

\(Profit = Revenue - Cost\)

\($120 = R(x) - C(x)\)

\($120 = 23x - (11x + 36)\)

\($120 = 12x - 36\)

\(12x = 156\)

\(x = 13\)

Therefore, 13 units must be produced for a profit of $120.

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Answer:

a) Median: 9

b) Range: 5

c) Mode: 7

Step-by-step explanation:

The median is the number in the middle.

First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12

The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.

To find the range, you minus the highest number and the lowest number, 12-7=5.

Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.

Hope this helps!!!

Answer:

\(\boxed{\mathrm {Median = 9}}\)

\(\boxed{\mathrm{Range = 5}}\)

\(\boxed{\mathrm{Mode = 7}}\)

Step-by-step explanation:

The observations are:

8,7,12,7,11,10,7,12

In ascending order:

=> 7,7,7,8,10,11,12,12

A) Median => Middlemost no.

Median = 8,10

=> \(\frac{8+10}{2}\)

=> \(\frac{18}{2}\)

Median = 9

B) Range = Highest No. = Lowest No.

RANGE = 12-7

Range = 5

C) Mode => frequently occurring number

Mode = 7

Answer:

Barry: g(x) = 50 + 30x

Larry: f(x) = 90 + 20x

If Locksmith Larry charges $90 for a house call plus $20 per hour. Locksmith Barry charges $50 for a house call plus $30 per hour. Then f(x)=90+20x is one-variable equation for the charges of locksmith Larry

Two or more expressions with an Equal sign is called as Equation.

Given,

Locksmith Larry charges $90 for a house call plus $20 per hour

f(x) represents this situation

f(x) equal to ninety plus twenty times of x

f(x)=90+20x

Locksmith Barry charges $50 for a house call plus $30 per hour

g(x)  represents this situation

g(x) equal to fifty plus thirty times of x

g(x)=50+30x

Here x represents the number of hours

Hence f(x)=90+20x is the one-variable equation for the charges of locksmith Larry

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Answer:

Gretchen

Step-by-step explanation: This is since 14 to 2 is saying that gretchen has 7 times the blue marbles than red

The solution to the expression 4+(−634) is -630

From the question, we have the following parameters that can be used in our computation:

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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Answer:

Pentagon

Step-by-step explanation: