ryan invested 5000 in an account that grows continuously at an annual rate of 2.5%. What will ryan’s investment be worth after 7 years? Round to the nearest cent

Note that in the above sketch, ΔABC ≇ ΔDCA. That is they are NOT congruent. The proof is that ∠ADC which is supposed to be = ∠BAC are not equal. Thus, line AC which is supposed to be equal to Line BC are not equal.

When two triangles are congruent, it means they are exactly the same in terms of their shape and size, so all corresponding sides and angles are equal.

In ΔABC,

Line AB = 8ft
Line BC = 11ft

Line AC = 13.6ft

∠ABC = 90°

∠BAC = 53.97°
∠ACB = 36.03°


As you can see,

Where as, ∠ADC = 62° - given

∠BAC = 53.97°

Also

Where as:

AC (The Hypotenuse ΔABC which is also the Adjacent Side of ΔACD) = 13.6ft

BC (The adjacent side of ΔABC) = 11ft.

Note that in order to prove congruence, at least two angles and one side from both Triangles must be equal (Angle Angle Side Theorem). Or

Two sides and one angle from both Triangles must be equal (Side - Angle - Side).

Or All three angles (Angle - Angle - Angle);
Or All three Sides (Side - Side Side).

In this case, only one side from both Triangles AC is common to both Triangles.

On the basis of the above, therefore, ΔABC ≇ ΔDCA.


The calculations showing how we arrived at the missing sides and angles are given below:


ΔABC:

AC = √(AB² + BC²)
AC = √(8² + 11²)
AC = √(64 + 121)
AC = √(185)
AC = 13.6014705087

AC [tex]\approx[/tex] 13.60

∠ ACB = arcsin (AB/AC)
∠ ACB = arcsin (8/13.6014705087)
= arcsin(0.58817169767505)
∠ ACB = 0.6288 rad converted to degrees

∠ ACB  = 36.03°

Thus, since the sum of Angles in a Triangle is 180°
∠BAC = 180-36.03° -90°
∠BAC = 53.97°


ΔACD


y (AD) = AC / sin(β)
y (AD) =  13.6/ sin(62°)
y (AD)  = 13.6/0.88294759285

AD = 15.40°

CD = √(AD² - AC²)

CD = √(15.4029526893712 - 13.62)

CD = √52.290951550999

CD = 7.23

The outstanding angle in ΔACD is ∠CAD

Since the sum of Angles in a Triangle is 180°

∠CAD = 180 - 90 - 62
∠CAD = 28°

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached Image.

(a) (i) The function f(x) - g(x) is  √(1-x).

    (ii) The function f(x) - g(x) is -x -1   The domain for f-g is all real numbers.
(b) (i) The function  (f-g)(1) = -2

    (ii) The function (f-g)(2) = √(-1). Therefore, (1/2)g(f(2)) is undefined.

(a)

(i) The function f(x) is already given as f(x) = √(1-x). The domain of f is all real numbers for which 1-x is non-negative. Therefore, the domain of f is x ≤ 1.

(ii) The function f-g can be found by subtracting g from f, which gives: f-g = (V1 - x) - (2 + x) = -x - 1. The domain of f-g is the same as the domain of f, which is x ≤ 1.

(b)

(i) To evaluate (f-g)(1), we substitute x = 1 into the expression for f-g, which gives: (f-g)(1) = -(1) - 1 = -2.

(ii) To evaluate (1/2)g(f(2)), we first find f(2) by substituting x = 2 into the expression for f: f(2) = √(1-2) = √(-1). Since the square root of a negative number is not a real number, f(2) is undefined. Therefore, (1/2)g(f(2)) is also undefined.

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The function with the largest rate of change is function a.

The rate of change defines how fast the function grows.

So, the most "vertical" or the one that grows the fastest is the function with the largest rate of change.

By looking at the graph, we can see that the fastest growing (the steepest) one is function a, so that is the correct option.

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We cannot determine if T is a one-to-one linear operator without more information about the values of N, M, and P2

Yes, T: R3 R3 is a one to one linear operator.

Let x, y, z be elements of R3, then T(x, y, z) = (W1, W2, W3), where W1 = 2Nx - 3y + Mz, W2 = x + 3y - P2 and W3 = -x - Ny + z.

To determine if this is a one to one linear operator, we must show that given two inputs, x, y, z and x', y', z' we have that T(x, y, z) = T(x', y', z') implies x = x', y = y' and z = z'.

We can see that W1 = W1', W2 = W2' and W3 = W3' implies that 2Nx - 3y + Mz = 2Nx' - 3y' + Mz', x + 3y - P2 = x' + 3y' - P2' and -x - Ny + z = -x' - Ny' + z'

Expanding the expressions and simplifying, we have that 2N(x - x') - 3(y - y') + M(z - z') = 0, x - x' + 3(y - y') - P2(z - z') = 0 and -(x - x') - N(y - y') + (z - z') = 0.

Since the expressions must be 0 for all inputs x, y, z and x', y', z' these imply that x = x', y = y' and z = z'. Therefore, T: R3 R3 is a one to one linear operator.
A linear operator T: R3 → R3 is one-to-one if and only if the only solution to the equation T(x, y, z) = (0, 0, 0) is (x, y, z) = (0, 0, 0). In other words, the kernel of T is trivial.

Let's substitute the given values of W1, W2, and W3 into the equation T(x, y, z) = (0, 0, 0) and solve for x, y, and z:

2Nx - 3y + Mz = 0

x + 3y - P2 = 0

-x - Ny + z = 0

From the second equation, we can solve for x in terms of y:

x = P2 - 3y

Substituting this into the first equation gives:

2N(P2 - 3y) - 3y + Mz = 0

Simplifying and rearranging terms:

(6N + 3)y = 2NP2 + Mz

y = (2NP2 + Mz)/(6N + 3)

Substituting this back into the equation for x gives:

x = P2 - 3(2NP2 + Mz)/(6N + 3)

Finally, substituting these values of x and y into the third equation gives:

-(P2 - 3(2NP2 + Mz)/(6N + 3)) - N(2NP2 + Mz)/(6N + 3) + z = 0

Simplifying and rearranging terms:

z(6N + 3 - M - 3N) = P2(6N + 3) - 6NP2

z = (P2(6N + 3) - 6NP2)/(6N + 3 - M - 3N)

Now we have expressions for x, y, and z in terms of the constants N, M, and P2. If these expressions are all equal to zero, then the only solution to the equation T(x, y, z) = (0, 0, 0) is (x, y, z) = (0, 0, 0), and T is a one-to-one linear operator.

However, it is not clear from the given information if these expressions are all equal to zero. Therefore, we cannot determine if T is a one-to-one linear operator without more information about the values of N, M, and P2.

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The  percent decrease in student's weight is 15%.

To calculate this, take the difference between his starting and ending weight and divide it by his starting weight. Multiply the result by 100 to express it as a percent.

To find the percent decrease in his weight, we can use the formula:
percent decrease = (original weight - new weight) / original weight * 100

First, let's plug in the given values:
percent decrease = (280 - 238) / 280 * 100

Next, we can simplify the numerator:
percent decrease = 42 / 280 * 100

Then, we can divide 42 by 280 to get 0.15:
percent decrease = 0.15 * 100

Finally, we can multiply 0.15 by 100 to get the percent decrease:
percent decrease = 15%

Therefore, his weight decreased by 15%.

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A. The sand will not fit into the tank because the volume of the sand is higher than that of the container

B. the difference in the volume of the first and second tank is 70in³

C. The measurement of the tank that will hold exactly 375 is 5in × 7in × 10.7 in

A prism is a solid shape that is bound on all its sides by plane faces.

The volume of a prism is expressed as;

volume = base × height

The volume of the tank = 5×7×9

= 315 in³

The volume of the sand is 375 .

Therefore the volume of the sand is greater than that of the tank, this means the sand will not fit into the tank.

B. The height of the second tank = 9+2 = 11

The volume of the second tank = 5×7 × 11 = 385

therefore the difference in the volume of the first and second tank = 385-315

= 70in³

C. If the tank has thesame base, then the height will be

375 = 5× 7 × h

375 = 35h

h = 375/35

h = 10.7 in

therefore the measurement of the tank that will hold exactly 375 is 5in × 7in × 10.7 in

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Therefore, the solution to the system of equations is x = 7 and y = -2.

Answer: x = 7, y =- 2.

a statement describing the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. Comparable is the equation 2x - 4 = 2. The variable x is present in the previous instance.

We are given the following system of equations:

-2x - 9y = 4    ---(1)

-5x - 10y = -15 ---(2)

We can use the method of substitution to solve this system of equations.

From equation (1), we can solve for x in terms of y:

-2x - 9y = 4

-2x = 4 + 9y

x = -2 - (9/2)y ---(3)

Now we can substitute this expression for x into equation (2) and solve for y:

-5x - 10y = -15

-5(-2 - (9/2)y) - 10y = -15

10 + (45/2)y - 10y = -15

12.5y = -25

y = -2

We have found the value of y to be 5. We can substitute this value back into equation (3) to find the value of x:

x = -2 - (9/2)y

x = -2 + (9/2)(2)

x = 7

Therefore, the solution to the system of equations is x = 7 and y = -2.

Answer: x = 7, y = -2.

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This is the final factored form of the original expression. = (4x^(2)-x-265)/((4(x-9)(x+6)))

To find the factored form of (x^(2)-64)/(x^(2)-3x-54)-(x^(2)-81)/(4x^(2)-12x-216), we will first factor each of the expressions in the numerator and denominator.

The factored form of x^(2)-64 is (x+8)(x-8).

The factored form of x^(2)-3x-54 is (x-9)(x+6).

The factored form of x^(2)-81 is (x+9)(x-9).

The factored form of 4x^(2)-12x-216 is (2x-18)(2x+12).

Now, we can substitute the factored forms back into the original expression:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/((2x-18)(2x+12))

Next, we will simplify the expression by canceling out common factors:

((x+8)(x-8))/((x-9)(x+6))-((x+9)(x-9))/(2(x-9)(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2x+12))

= ((x+8)(x-8))/((x-9)(x+6))-(1/2)((x+9)/(2(x+6)))

= ((x+8)(x-8))/((x-9)(x+6))-(1/4)((x+9)/(x+6))

Now, we will find a common denominator and combine the two fractions:

= ((4(x+8)(x-8))-(x+9))/((4(x-9)(x+6)))

= ((4x^(2)-256)-(x+9))/((4(x-9)(x+6)))

= (4x^(2)-x-265)/((4(x-9)(x+6)))

This is the final factored form of the original expression.

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Answer:

they both are right triangle

Step-by-step explanation:

Option A and C will be the correct answers based on the provided statement.

A right triangle's hypotenuse is its longest side, its "opposing" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.

Congruence of the SAS Triangle According to the theorem, two triangles are said to be congruent to one another if they have a single pair of corresponding sides and an incorporated angle that are equal to one another.

The image shows two triangles that are congruent by the SAS Congruence Theorem.

As a result, the following claims satisfy the requirements for two triangles to be regarded as congruent to one another by the SAS Congruity Theorem:

A. the corresponding two sides and the included angle in both triangles are congruent.

C. A pair of two sides that are congruent with the equivalent two sides and angle in the opposite triangle and are parallel to an angle's ray.

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Answer:

m<6 = 78°

Step-by-step explanation:

I hope your drawing of this problem looks somewhat like this:

                                                                ^  t

                                                              /

                                                            /

                                                   1     /    2

<----------------------------------------------------------------------------->   ℓ

                                               3     /    4

                                                    /

                                         5       /    6

<------------------------------------------------------------------------------>  m

                                      7       /   8

                                            /

                                          /

                                        V

Sorry about the terrible drawing, but I hope I got the angle numbers correctly written.

Angles 3 and 6 are are called alternate interior angles.

They are "interior angles" because they are on the inside of lines l and m. They are "alternate angles" because they are on different sides of the transversal, t.

There is a Geometry theorem about this situation.

Theorem:

If parallel lines are cut by a transversal, then alternate interior angles are congruent.

In this case, since the pair of angles 3 and 6 is a pair of alternate interior angles, then by the theorem above, they are congruent.

m<6 = m<3

Since m<3 = 78°, then m<6 = 78°.

Mr. Cortez is comparing the cost to join two different gyms. Gym A charges a $55 registration fee plus $24 per month. Gym B does not charge a registration fee but charges $35 per month. The cost will be the same for both gyms on the 5 months.

What is gym?

A gymnasium or gym is a place where people can exercise indoors. The word is a translation of "gymnasium," which is Greek. They are typically seen in athletic and fitness facilities, in addition to acting as activity and learning spaces in educational institutions. Gym is slang for "fitness centre," which is often a location for indoor entertainment.

Given,

Gym A charges a $55 registration fee and $24 per month

Total charges after 5 months with registration fee= (24*5+55)= $175

Gym B charges $35 per month

Total charges after 5 months= 35*5= $175

Hence the correct answer is the cost will be the same for both gyms on the 5 months.

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The x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.

To find the x value where P(X < x)=0.0655, we can use the z-score formula and look up the corresponding z-value in a standard normal distribution table. The z-score formula is:

z = (x - mean) / standard deviation

Substituting the given values, we get:

0.0655 = (x - 10) / 4

Next, we can look up the z-value that corresponds to 0.0655 in a standard normal distribution table. We find that the z-value is approximately -1.5. Now we can plug this back into the z-score formula and solve for x:

-1.5 = (x - 10) / 4

-6 = x - 10

x = 4

Therefore, the x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.

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The answer is x=26.

To solve the equation x-5=21 using the addition property of equality, we need to isolate the variable x on one side of the equation. The addition property of equality states that if we add the same value to both sides of an equation, the equation will remain true.

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
x-5+5=21+5

Step 2: Simplify both sides of the equation.
x=26

Step 3: Check the solution by substituting the value of x back into the original equation.
26-5=21
21=21

The solution checks out, so the answer is x=26.

In conclusion, the solution to the equation x-5=21 using the addition property of equality is x=26.

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The relative maxima.

To find the relative maxima and minima of the function f(x) = x + 9/x + 5, we need to first find the derivative of the function.

The derivative of f(x) is f'(x) = 1 - 9/x^2.

Next, we need to set the derivative equal to zero and solve for x to find the critical points.

1 - 9/x^2 = 0

9/x^2 = 1

x^2 = 9

x = ±3

So, the critical points are x = 3 and x = -3.

To determine if these are relative maxima or minima, we need to use the second derivative test.

The second derivative of f(x) is f''(x) = 18/x^3.

Plugging in x = 3, we get f''(3) = 18/27 = 2/3, which is positive. This means that x = 3 is a relative minima.

Plugging in x = -3, we get f''(-3) = 18/-27 = -2/3, which is negative. This means that x = -3 is a relative maxima.

Therefore, the relative maxima is at x = -3 and the relative minima is at x = 3.

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Answer:

4:3

Step-by-step explanation:

16:12=8:6=4:3, that is simplest ratio

Answer:

7/10 - 2/5 = 7/10 - 4/10 = 3/10

Step-by-step explanation:

Equalize both denominators, as in 2/5 = 4/10.

The value of (gof)(4) is 9 if the function f(x) is f(x) =[tex]-x^3[/tex], and function g(x) is g(x) = |1/8x-1| option (A) is correct.

It is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predefined domain and range.

from the question:

We have a function:

f(x) = -x³

Plug x = 4 in the f(x)

f(4) = -4³ = -64

Plug the above value in the g(x)

g(f(4)) = |-8-1| = |-9| = 9

Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (a) is correct.

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complete and correct questions

f(x) = -x3

g(x) = |1/8x-1|

What is the value of (gof)(4)?.

A. 9

B. - 1/8

C. -9

D. 1/8

The determinant of a 3x3 matrix can be found using the following formula:
\[ \left|\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}\right| = a(ei - fh) - b(di - fg) + c(dh - eg) \]

In this case, we can substitute the values from the given matrix into the formula:
\[ \left|\begin{array}{ccc} d+b & d & d \\ d & d+b & d \\ d & d & d+b \end{array}\right| = (d+b)((d+b)(d+b) - d^2) - d(d(d+b) - d^2) + d(d^2 - d(d+b)) \]
Simplifying the expression gives:
\[ = (d+b)(d^2 + 2bd + b^2 - d^2) - d(d^2 + bd - d^2) + d(d^2 - d^2 - bd) \]
\[ = (d+b)(2bd + b^2) - d(bd) + d(-bd) \]
\[ = 2bd^2 + 2b^2d + b^3 - bd^2 - bd^2 \]
\[ = b^3 + 2b^2d \]

Therefore, the determinant of the given matrix is \[b^3 + 2b^2d\].

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All of the functions have a constant rate of change since they are linear functions with a slope (rate of change) that is equal to the coefficient of the independent variable. Therefore, all functions have a constant rate of change of their slope.

Option A: y = 6(2) = 12 has a slope of 6, which means it increases by 6 for every unit increase in x.

Option B: y = 2(3) = 6 has a slope of 2, which means it increases by 2 for every unit increase in x.

Option C: y = 3(4) = 12 has a slope of 3, which means it increases by 3 for every unit increase in x.

Option D: y = 4(2) = 8 has a slope of 4, which means it increases by 4 for every unit increase in x.

Therefore, option A has the most rapid rate of change with a slope of 6.

Answer:

the ans the last person gave is very correct

when x=24, y = y(3)/(2).

Given that y is directly proportional to the cube root of (x+3), we can write this relationship as:

y = k * cube root (x+3)

Where k is the constant of proportionality. We can use the given values of x and y to find k:

y(2)/(3 ) = k * cube root (5+3)

y(2)/(3 ) = k * cube root (8)

y(2)/(3 ) = k * 2

k = y(2)/(3 ) / 2

Now we can use this value of k to find y when x=24:

y = k * cube root (24+3)

y = (y(2)/(3 ) / 2) * cube root (27)

y = (y(2)/(3 ) / 2) * 3

y = y(2)/(3 ) * (3/2)

y = y(3)/(2)

Therefore, when x=24, y = y(3)/(2).

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By applying Two-Variable Linear Equation it can be concluded that the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

Two-Variable Linear Equation is a form of relation equal to the algebraic form which has two variables and both are raised to the power of one.

We will use this concept to calculate the amount of each type of investment.

The total amount invested is $10,000, with some going to bonds and some going to certificates of deposit (CDs). According to the question, the amount invested in bonds is to exceed that in CDs by $3,000. We can write this as an equation:

$10,000 = x + y  , where:

x = the amount invested in bonds

y = the amount invested in CDs

We are also told that x = y + $3,000. We can substitute this into the first equation:

$10,000 = x + y

              = y + $3,000 + y

              = 2y + $3,000

         2y = $7,000

           y = $3,500

Now we can substitute this back into the equation for x:

x = y + $3,000

  = $3,500 + $3,000

  = $6,500

So the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.

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The distance traveled by the bullet is 1000 feet.

The distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target:

Distance = Speed x Time

Substituting the given values, we get:

[tex]Distance = 510^6 feet/hour * 210^{-4} hours[/tex]

Simplifying this expression, we get:

Distance = 1000 feet

Therefore, the bullet has traveled 1000 feet before striking the target.

In summary, the distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target. In this case, the distance traveled is 1000 feet.

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A horizontal change of 96ft, there will be a vertical change of 3072ft.

The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line. In other words, the slope is the rise over the run.

If the slope of a line is 32, that means that for every 1 unit of horizontal change, there is a 32 unit vertical change.

So, if the horizontal change is 96ft, we can use the slope formula to find the vertical change:

Vertical change = slope × horizontal change

Vertical change = 32 × 96

Vertical change = 3072

Therefore, for a horizontal change of 96ft, there will be a vertical change of 3072ft.

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The solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16)

To solve the equation (2)/(3)m=(5)/(8), we can use the Division Property of Equality and the Multiplication Property of Equality.

Here are the steps:

1. Start with the original equation: (2)/(3)m=(5)/(8)

2. Multiply both sides of the equation by the reciprocal of (2)/(3), which is (3)/(2): (2)/(3)m * (3)/(2) = (5)/(8) * (3)/(2)

3. Simplify the left side of the equation: m = (5)/(8) * (3)/(2)

4. Simplify the right side of the equation: m = (15)/(16)

5. Check your solution by plugging it back into the original equation: (2)/(3) * (15)/(16) = (5)/(8)

6. Simplify the left side of the equation: (30)/(48) = (5)/(8)

7. Simplify the right side of the equation: (5)/(8) = (5)/(8)

8. Since both sides of the equation are equal, the solution is correct.

So the solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16).

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The maximum number of days she can drive the car is approximately 4 days.

A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven.

She plans to drive 50 miles. She has at most $230 to spend.

Therefore, the maximum number of days that Tallulah can rent the car while staying within her budget can be computed as follows:

Using equations,

y = 0.13a + 61.79b

where

Therefore, she has a budget of 230 dollars and she wants to ride for 50 miles.

230 = 0.13(50) + 61.79b

230 - 6.5 = 61.79b

223.5 = 61.79b

b = 223.5  / 61.79

b = 3.61709014404

Therefore,

b = 4 days

Hence, she can ride maximum of 4 days.

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The three consecutive integers whose sum is 360 are 119, 120, and 121.

To find three consecutive integers whose sum is 360, we can use algebra to set up an equation and solve for the first integer. Let x be the first integer, then the next two consecutive integers will be x+1 and x+2. The sum of these three integers is 360, so we can write the equation:

x + (x+1) + (x+2) = 360

Simplifying the equation gives us:

3x + 3 = 360

Subtracting 3 from both sides gives us:

3x = 357

Dividing both sides by 3 gives us:

x = 119

So the first integer is 119. The next two consecutive integers are 120 and 121. Therefore, the three consecutive integers whose sum is 360 are 119, 120, and 121.

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The perimeter of a table that is 3m long and 2m wide is 10m.

The perimeter includes the total lengths (2 lengths and 2 breadths) of the four sides or the total distance around the rectangle.

For a rectangle, the perimeter can be determined using the following formula:

Perimeter = 2(l + w)

Length of the table = 3m

Width of the table  = 2m

The perimeter of the table = 2(3 + 2)

= 10m

Thus, for a table that has lengths of 3 meters and width of 2 meters, the perimeter is 10 meters.

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10[4-(3-2x)]+4x=3(8x+4)-2   is an identity equation.

To determine whether the equation is a conditional, an identity, or a contradiction, we need to simplify the equation and see if it is true for all values of x, true for some values of x, or false for all values of x.

First, let's simplify the equation:

10[4-(3-2x)]+4x=3(8x+4)-2

10[4-3+2x]+4x=24x+12-2

10[1+2x]+4x=24x+10

10+20x+4x=24x+10

24x-24x=10-10

0=0

Since the equation is true for all values of x, it is an identity equation. An identity equation is an equation that is true for all values of the variable.

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Answer:

Step-by-step explanation: