Use a vertical format to add the polynomials. -8x^(2)-9x-2 8x^(2)+10x-6 6x^(2)-4x+2

Answer:

  2 m

Step-by-step explanation:

You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.

The volume formula for the triangular prism is ...

  V = Bh . . . . the product of the triangle area and the base–base distance

  12.6 = B·4.5

  2.8 = B . . . . . . . area of the triangular base

The area of the triangular base is given by ...

  A = 1/2bh

The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...

  2.8 = 1/2(2.8)h

  2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h

The center height of the tent is 2 meters.

__

Additional comment

If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.

  V = 1/2LWH

  12.6 = 1/2(4.5)(2.8)h = 6.3h

  2 = h . . . . meters

According to the given information product of (3x - 2) and (2z + 6) is 6xz + 18x - 4z - 12.

In mathematics, expressions are also combinations of constants, variables, operators, and function calls that represent mathematical operations or relationships.

Let's start with distributing the first term of the first expression to both terms of the second expression, then distributing the second term of the first expression to both terms of the second expression:

(3x - 2)(2z + 6)

= 3x(2z + 6) - 2(2z + 6)

= 6xz + 18x - 4z - 12

Now, let's use the FOIL method to find the same product:

(3x - 2)(2z + 6)

= 3x(2z) + 3x(6) - 2(2z) - 2(6)

= 6xz + 18x - 4z - 12

As you can see, both methods result in the same product: 6xz + 18x - 4z - 12.

Therefore, according to the given information product of (3x - 2) and (2z + 6) is 6xz + 18x - 4z - 12.

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Answer: 76

Step-by-step explanation:

58 and 18 are both numbers that don't have any variables, so they are like terms, so you just add them together

58+18=76

If you need to break it down a bit more:

50+10=60

8+8=16

60+16=76

Answer: transfers

Step-by-step explanation: now make sure you submit in time.

Answer: 20

Step-by-step explanation:

49 ÷ 245 %

convert the percentage to decimals

49 ÷ 2.455

calculate the product or quotient

20

                   Please give me brainliest

Answer:20

Step-by-step explanation:

Let's denote the number we are looking for as "x".

We can set up the equation:

245% of x = 49

We can convert 245% to the decimal form by dividing by 100:

2.45 * x = 49

To solve for x, we can divide both sides of the equation by 2.45:

x = 49 / 2.45

x = 20

Therefore, 245% of 20 is equal to 49.

The simple interest rate for this loan is 12.4%.

To find the simple interest rate, we can use the formula for simple interest, which is:
Simple Interest = Principal x Rate x Time

In this case, we are given the simple interest (\$496), the principal (\$12,000), and the time (4 months). We can plug these values into the formula and solve for the rate.
\$496 = \$12,000 x Rate x (4/12)

Simplifying the equation, we get:
\$496 = \$4,000 x Rate

Dividing both sides by \$4,000, we get:
Rate = 0.124

To convert this to a percentage and round to one decimal place, we multiply by 100 and round:
Rate = 0.124 x 100 = 12.4%

Therefore, the simple interest rate for this loan is 12.4%.

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The distribution of Sn + Tm is a binomial distribution with parameters (n+m, p).

This can be proved using the fact that the sum of independent binomial random variables follows a binomial distribution with the sum of the number of trials and the same probability of success.



Let X ~ Binomial(n, p) and Y ~ Binomial(m, p) be independent random variables representing the number of heads in the first n coin tosses and the last m coin tosses, respectively.

Then, the sum of X and Y, Z = X + Y, follows a binomial distribution with parameters (n+m, p).

The probability mass function of Z can be written as:

P(Z = k) = P(X + Y = k) = ∑ P(X = i) * P(Y = k-i) for i = 0 to k

Since X and Y are independent, we can write:

P(Z = k) = ∑ P(X = i) * P(Y = k-i) = ∑ (n choose i) * p^i * (1-p)^(n-i) * (m choose k-i) * p^(k-i) * (1-p)^(m-k+i)

Simplifying the above equation, we get:

P(Z = k) = (n+m choose k) * p^k * (1-p)^(n+m-k)

Therefore, Z ~ Binomial(n+m, p).

As a result, the distribution of Sn + Tm has the parameters (n+m, p) of a binomial distribution.

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If the diameter of a cone is 19 yd and the height is 13 yd, the volume of this cone is equal to 1,228 cubic yard.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Radius = diameter/2 = 19/2 = 9.5 cm.

Substituting the given parameters into the volume of a cone formula, we have the following;

V = 1/3 × πr²h

V = 1/3 × 3.14 × 9.5² × 13

Volume, V = 1,228 cubic yard.

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Answer:

  10.81 ft

Step-by-step explanation:

You want the length of the shortest ladder that will reach over a 2 ft high fence to reach a building 6 ft from the fence.

Relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

In the attached diagram, the ladder is show as line segment CD, intersecting the top of the fence at point B. The length of the ladder is the sum of segment lengths BD and CB.

Using the above trig relations, we can write expressions that let us find these lengths in terms of the angle at D:

  sin(D) = AB/BD   ⇒   BD = AB/sin(D)

  cos(D) = BG/CB   ⇒   CB = BG/cos(D)

Then the ladder length is ...

  CD = BC +CB = AB/sin(D) +BG/cos(D)

  CD = 2/sin(D) +6/cos(D)

The minimum can be found by differentiating the length with respect to the angle. This lets us find the angle that gives the minimum length.

  CD' = -2cos(D)/sin²(D) +6sin(D)/cos²(D)

  CD' = 0 = (6sin³(D) -2cos³(D))/(sin²(D)cos²(D)) . . . common denominator

  0 = 3sin³(D) -cos³(D) . . . . the numerator must be zero

Factoring the difference of cubes, we have ...

  0 = (∛3·sin(D) -cos(D))·(∛9·sin²(D) +∛3·sin(D)cos(D) +cos²(D))

The second factor is always positive, so the value of D can be found from

  ∛3·sin(D) = cos(D)

  D = arctan(1/∛3) . . . . . . . divide by ∛3·cos(D), take inverse tangent

  D ≈ 37.736°

  CD = 2/sin(37.736°) +6/cos(37.736°) = 3.51 +7.30 = 10.81 . . . feet

The shortest ladder that reaches over the fence to the building is 10.81 feet.

__

Additional comments

The second attachment shows a graphing calculator solution to finding the minimum of the length versus angle in degrees.

The ladder length can also be found in terms of the distance AD.

  L = BD(1 +BG/AD) = (1 +6/AD)√(4+AD²)

The minimum L is found when AD=∛(BG·AD²) = ∛24 ≈ 2.884.

Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

Since, 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

To determine whether a value of x is a solution to the inequality 13 < 2x+3, we need to substitute the value of x into the inequality and see if it is true or false.

Let's try x = 5. Then: 13 < 2x+3

13 < 2(5)+3

13 < 10+3

13 < 13

This is not true, since 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

Note that if we had found 13 < 13 instead, then we would have concluded that x = 5 is not a solution to the inequality. But since the inequality is strict (i.e., "less than"), we need to have a strict inequality when we substitute the value of x to determine whether it is a solution.

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Answer:

Smaller number = 19

Larger number = 71

x + y = 90

x = 14 + 3y

Step-by-step explanation:

Let y represent the smaller number, and then represent the larger number as x, in terms of y:

Smaller number = y

Larger number = x = 3y + 14

Since the sum of the two numbers is 90, form an equation by adding them together in this notation:

y + 3y + 14 = 90

Simplify the equation:

4y + 14 = 90

4y = 76

y = 19

Therefore the smaller number is 19. Now substitute into the expression for the larger number to find its value:

x = 3(19) + 14 = 71

Now verify the two values sum to 90 like we expect:

19 + 71 = 90

Now we can use what we know to complete the equations, if x = 71:

x + y = 90 (we know they sum to 90)

x = 14 + 3y (as respresented above - multiplying by 3 and adding 14)

Answer:

To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:

the first term of the binomial is y^2 (which is already the case)

the second term of the binomial is -2ky (which corresponds to -36y in the given expression)

the third term of the binomial is k^2 (which corresponds to 81 in the given expression)

To find k, we can use the formula:

k = (1/2)*(-b/a)

where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.

In this case, a = 1 and b = -36, so:

k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18

Therefore, the missing number to create a perfect-square binomial is 18:

(y - 18)^2 = y^2 - 36y + 324

The value of the height function h(-2) is 0.

The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1

To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1

Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2

The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:

For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0

For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1

To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1

Since h1'(0) is negative, h1 has a local maximum at u=0.

The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0

Therefore, the value of the height function h(-2) is 0.

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Answer:

1.4

Step-by-step explanation:

If 6/p =15/3.5

You can cross multiply the equation

6x3.5 =15P

21=15P

Divide both sides by 15

21/15 = P

1.4 =P

The quadratic equation (c+5)²=36 will give c = 1,-11.

A quadratic equation is a type of equation in algebra that involves a variable (usually denoted as "x") raised to the power of 2, or squared. The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants, with a≠0. The goal is to solve for the variable x, which may have one or two possible solutions depending on the coefficients of the equation.

Now,

To solve the equation (c + 5)² = 36:

Taking the square root of both sides of the equation

√(c + 5)² = ±√36

Simplify the left-hand side using the rule that √a² = |a|:

|c + 5| = ±6

Solve for c in each case by subtracting 5 from both sides of the equation:

c + 5 = 6 or c + 5 = -6

Solve for c in each equation:

c = 1 or c = -11

Therefore, the solutions to the equation (c + 5)² = 36 are c = 1 and c = -11.

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The area of the sector outlined by the given arc is 32π square units.

What is the area of the sector?

The area of a sector of a circle with radius r and central angle θ (in radians) is given by the formula:

sector area = (1/2) x r² x θ

The length of an arc of a circle with radius r and central angle θ (in radians) is given by the formula:

arc length = r x θ

In this case, we know that the radius is 8 units and the arc length is 4π units. So we can set up an equation:

4π = 8θ

Solving for θ:

θ = (4π)/8 = π/2

So the central angle is π/2 radians.

The area of a sector of a circle with radius r and central angle θ (in radians) is given by the formula:

sector area = (1/2) x r² x θ

Plugging in the values we know:

sector area = (1/2) x 8² x π/2

sector area = 32π

Therefore, the area of the sector outlined by the given arc is 32π square units.

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We have that, given the equation x^(2)+(144)/(1369)(144)/(1369)=13 , we will have as a solution x = 485/1369

To isolate the variable term and simplify the right, we need to follow the steps below:

Step 1: Subtract the fraction term from both sides of the equation.

[tex]x^2+(144/1369)(144/1369) - (144/1369)(144/1369) = 13 - (144/1369)(144/1369)[/tex]

Step 2: Simplify the right side of the equation by multiplying the fractions and then subtracting from 13.

[tex]x^2 = 13 - (20736/1874161)[/tex]

Step 3: Combine the terms on the right side of the equation by finding a common denominator and subtracting.

[tex]x^2 = (24320661/1874161) - (20736/1874161)[/tex]

Step 4: Simplify the right side of the equation by subtracting the numerators and keeping the common denominator.

[tex]x^2 = (24320661 - 20736)/1874161[/tex]

Step 5: Simplify the fraction on the right side of the equation by reducing to lowest terms.

[tex]x^2 = (24300025/1874161)[/tex]

Step 6: Take the square root of both sides of the equation to isolate the variable term.

[tex]x = \sqrt{(24300025/1874161)}[/tex]

Step 7: Simplify the square root by factoring out any perfect squares.

[tex]x = \sqrt{(485^2)/(1369)}[/tex]

Step 8: Simplify the square root by taking the square root of the perfect squares.

[tex]x = 485/1369[/tex]

Therefore, the solution to the equation is [tex]x = 485/1369[/tex].

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Part A: The height of the container is 5cm.

Part B: The cost of the coffee is $2.83.

Part C: The height of the container is 9cm.

Part D: The cost of the hot chocolate powder is $49.35.

What is volume of cylinder ?

The volume of a cylinder is the amount of space occupied by a cylindrical shape. It is given by the formula:

V = πr²h

where V is the volume, r is the radius of the circular base of the cylinder, and h is the height of the cylinder. The formula is derived by multiplying the area of the circular base (πr²) by the height (h) of the cylinder.

According to the question:
Part A:

Given that the container is a cylinder with a radius of 3cm, we can use the formula for the volume of a cylinder to find the height of the container. The formula for the volume of a cylinder is:

V = πr²h

where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

45π = π(3)²h

Simplifying and solving for h, we get:

h = 5

Therefore, the height of the container is 5cm.

Part B:

The volume of the container is 45π cm³ and the cost of coffee is $0.02 per cubic centimeter. Therefore, the total cost of the coffee is:

Total cost = Volume x Cost per unit volume

Total cost = 45π x $0.02

Total cost = $0.90π

Rounding to two decimal places, we get:

Total cost = $2.83

Therefore, the cost of the coffee is $2.83.

Part C:

Given that the container is a cylinder with a radius of 5cm, we can use the same formula for the volume of a cylinder to find the height of the container. Substituting the given values, we get:

225π = π(5)²h

Simplifying and solving for h, we get:

h = 9

Therefore, the height of the container is 9cm.

Part D:

The volume of the container is 225π cm³ and the cost of hot chocolate powder is $0.07 per cubic centimeter. Therefore, the total cost of the hot chocolate powder is:

Total cost = Volume x Cost per unit volume

Total cost = 225π x $0.07

Total cost = $15.75π

Rounding to two decimal places, we get:

Total cost = $49.35

Therefore, the cost of the hot chocolate powder is $49.35.

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Answer:

Let's start by using variables to represent the number of rows containing 20 vines and 25 vines. Let:

x be the number of rows containing 20 vines

3x be the number of rows containing 25 vines (since there are 3 times as many rows containing 25 vines as there are rows containing 20 vines)

We know that Sarah plants a total of 760 vines, and that each row contains either 20 vines or 25 vines. Therefore, we can write an equation based on the total number of vines:

20x + 25(3x) = 760

Simplifying and solving for x:

20x + 75x = 760

95x = 760

x = 8

So there are 8 rows containing 20 vines, and 3 times as many rows containing 25 vines, or 3(8) = 24 rows containing 25 vines.

Therefore, Sarah planted 8 rows with 20 vines and 24 rows with 25 vines.

Answer:

There are 500 total people. 215 gave blood and 159 helped set up, giving a total of 374. However, since 89 people did both, we counted those 89 people twice. So we subtract 89 to get 285 total volunteers.

500-285=215 did not volunteer

There were 220 people that neither donated nor helped.

To find out how many people neither donated nor helped, we can use the formula for the union of two sets:

  A∪B = A + B - A∩B.

In this case, A is the number of people who donated, B is the number of people who helped, and A∩B is the number of people who both donated and helped.

Plugging in the given values, we get:

  A∪B = 217 + 156 - 93 = 280

This tells us that there were 280 people who either donated or helped. To find out how many people neither donated nor helped, we can subtract this number from the total number of people surveyed:

  500 - 280 = 220

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The final answer in quotient and remainder form is:

(x^(2)+4x-20)÷(x-4) = x+8 with a remainder of 12

To determine the quotient and remainder of the given expression, we can use synthetic division. Synthetic division is a method of dividing a polynomial by a linear factor in the form of x-a. In this case, the linear factor is x-4, so a=4.

Here are the steps for synthetic division:

Write the coefficients of the dividend, x^(2)+4x-20, in a row: 1 4 -20
Write the value of a, 4, to the left of the coefficients.
Bring down the first coefficient, 1, to the bottom row.
Multiply the value in the bottom row by a, 4, and write the result, 4, in the second column of the top row.
Add the numbers in the second column of the top row, 4+4, and write the result, 8, in the bottom row.
Multiply the value in the bottom row by a, 4, and write the result, 32, in the third column of the top row.
Add the numbers in the third column of the top row, -20+32, and write the result, 12, in the bottom row.

The bottom row now contains the coefficients of the quotient, 1 and 8, and the remainder, 12. So the quotient is x+8 and the remainder is 12.

The final answer in synthetic division form is:

4 | 1  4  -20
 |    4   32
 -------------
 | 1  8   12

The final answer in quotient and remainder form is:

(x^(2)+4x-20)÷(x-4) = x+8 with a remainder of 12

So the quotient is x+8 and the remainder is 12.

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Answer:

Okay this is the bi-modal distribution histogram

Answer:

Step-by-step explanation:

Firstline = 33%

Second line = 36%

Answer:

Firstline = 33%

Second line = 36%

Step-by-step explanation:

The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

To find the final amount for an investment P over t years at an annual interest rate of r compounded quarterly, we can use the formula for compound interest:  

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = Final amount

P = Principal (initial investment)

r =  Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time period in years

Here we have

P = $5,000,

r = 6% = 0.06,

n = 4 (since the interest is compounded quarterly), and

t = 5 years.  

Using the above formula

[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]

[tex]A = 5000(1.015)^{20}[/tex]

[tex]A = 5000(1.34985711)[/tex]

[tex]A = $6,749.29[/tex]

Therefore,

The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

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Answer: 10x² + 3x + 4

Step-by-step explanation: I hate math.

The equation of the image is x = 32 - 2y which is dilated by a scale factor of 1/4 about the center.

Dilation is a process for creating similar figures by modifying the dimensions.

To dilate a line by a scale factor of 1/4 about the center, we can first find the coordinates of the center of dilation.

Since no center is given in the problem, we can assume that the center is the origin (0,0).

To find the equation of the image, we need to apply the dilation to the original line. The dilation multiplies all distances by the scale factor, so the image of the point (x, y) is (1/4)x, (1/4)y).

So, the image of line 8 - 2y = x under this dilation is:

8 - 2(1/4)y = (1/4)x

8 - (1/2)y = (1/4)x

32 - 2y = x

Therefore, the equation of the image is x = 32 - 2y.

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Answer: y = x + 8

Step-by-step explanation:

\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]

Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
 T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
 T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
 M=\left[\begin{array}{cc}
   3 & 6 \\
   5 & -2
 \end{array}\right]
\]
and
\[
 M=\left[\begin{array}{cc}
   8 & 4 \\
   5 & 2
 \end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
 M_{1}M_{2}=\left[\begin{array}{cc}
   43 & 2 \\
   -10 & 4
 \end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.

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