3 cm 3.5 cm 7 cm find the area​

The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.

To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.

(3x³ - x² + 4) + (2x³ - 3x + 9)

Combine the like terms:

(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)

Simplify further:

5x³ - x² - 3x + 13

In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.

Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.

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Answer:

9r+108

Step-by-step explanation:

9 times r, 9 times 12.

9r+ 12 times 9 equals 9r+108

Answer:

Step-by-step explanation

Frist, the area = ab = 30 m^2 and the perimeter = 2(a + b) = 34 m or a + b = 17 m (2). Solving (1) and (2), a = 15 m and b = 2 m. Since it is a rectangle, the dimensions are (all in m) so the answer is: 15, 2, 15, 2.

Answer:

THe kitchen is 8 by 10

Step-by-step explanation:

x = width

y = length

Area = xy = 80 m²

Perimeter = 2x + 2y = 36 m

2x = 36 - 2y

x = 18 - y   substitute into equation 1

(18 - y)(y) = 80

-y² + 18y - 80 = 0    find roots of y by factoring

y² - 18y + 80 = 0

(y - 8)(y - 10) = 0

y = 8, 10

Since xy = 80, then:

x = 80/10 = 8, or, x = 80/8 = 10

Now you have your dimensions: 8 and 10

To check the answers:

8 x 10 = 80 m²

2(8) + 2 (10) = 36 m

Answers are correct!

Answer:

3192

3738

Step-by-step explanation:

So let’s say that 10 years is the variable B so your equation would be

B = 2100 x 5.2%

Well what is 5.2% of 2100

It is 109.2 and 109.2 x B + 2100 = the first question.

The answer is 3192

Now it is the same for the second one

Let C = 15 years

109.2 x C + 2100 = 3738

The amount of money at the end of 25 years is $30480.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = \(A=P(1+\frac{r}{100})^{nt}\)

Given that, periodic deposit =$8000, rate of interest =5.5% and time period = 25 years.

Now, Amount = 8000(1+5.5/100)²⁵

= 8000(1+0.055)²⁵

= 8000(1.055)²⁵

= 8000×3.81

= $30480

Therefore, the amount of money at the end of 25 years is $30480.

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Answer:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

The height of the tree is 2.06 meters to the nearest hundredth of a meter.

To find the height of the tree, we can use similar triangles and the given information. The terms we'll use are Brody's height, tree's shadow, Brody's shadow, and the height of the tree.

1. Brody's height: 1.75 meters

2. Tree's shadow: 27.95 meters

3. Brody's shadow: 23.7 meters away from the tree

Now, let's set up the proportion using similar triangles:

(Brody's height) / (Brody's shadow) = (Height of the tree) / (Tree's shadow)

1.75 / (23.7) = (Height of the tree) / (27.95)

To solve for the height of the tree, cross-multiply and divide:

1.75 * 27.95 = 23.7 * (Height of the tree)

48.9125 = 23.7 * (Height of the tree)

Height of the tree = 48.9125 / 23.7

Height of the tree ≈ 2.06 meters

So, the height of the tree is approximately 2.06 meters to the nearest hundredth of a meter.

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1)  the language L1 is accepted by this PDA.

2) the language L2 is accepted by this PDA.

To draw trans diagram of a PDA for the following languages, we need to proceed as follows:

(1) The language, L1 = {an c bn : n ≥ 0}, can be represented in the form of a PDA as follows:

We can explain the above trans diagram as follows:

Initial state is q0.

Stack is initiated with Z.

We make a transition to q1, upon reading a, push 'X' onto the stack.

We remain in q1 as long as we read 'a' and continue pushing 'X' onto the stack.

The transition is made to q2 when 'c' is read. In q2, we keep on poping 'X' and reading 'b'.

Once we pop out all the Xs from the stack, we move to the final state, q3.

Thus the language L1 is accepted by this PDA.

2) The language L2 = {an b2n : n ≥ 0}, can be represented in the form of a PDA as follows:

We can explain the above trans diagram as follows:

Initial state is q0.

Stack is initiated with Z.

We make a transition to q1, upon reading a, push 'X' onto the stack.

We remain in q1 as long as we read 'a' and continue pushing 'X' onto the stack.

The transition is made to q2 when 'b' is read.

In q2, we keep on poping 'X' and reading 'b'.

Once we pop out all the Xs from the stack, we move to the final state, q3.

Thus the language L2 is accepted by this PDA.

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Answer:

x > 2

Step-by-step explanation:

2(x+5) = 2x + 10 -> 2x + 10 < 4+5x

Subtract 4 from each side.
2x +6 < 5x
Subtract 2x from each side
6 < 3x
2<x

So, x must be > 2

Answer:

--------------------------------------

Initial height is the y-intercept of the line.

Yearly growth rate is the slope.

So we have:

The equation of the line with these constants is:

The factor is the solution of zeros of the equation and x + 2 making it zero therefore x + 2 will be the solution of the given polynomial so option (B) will be correct.

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

Given the polynomial,

x³ + 2x² - 9x - 18

A factor is consist of a solution of zeros of any polynomial.

For example;

x² + 5x + 6 = 0

x(x + 2) + 3(x + 2) = 0

(x + 3)(x + 2) = 0

Here x + 3 and x + 2 are factor and solution is x = -3 and -2

Similarly,

x³ + 2x² - 9x - 18 = 0

The factor must be the solution to this.

By cross-checking option

Option (A) x + 1 = 0 → x = -1

Keeping x = -1

(-1)³ + 2(-1)² - 9(-1) - 18 = -8 ≠ 0 so it is not the factor.

Option (B) (x + 2) = 0 → x = -2

(-2)³ + 2(-2)² - 9(-2) - 18

-8 + 8 + 18 - 18 = 0 = 0 so it will be factor of the polynomial.

Hence " x + 2 will be the solution of the given polynomial".

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Answer:

Step-by-step explanation:

Given,

2x = 81 - x [Vertically opposite angles]

=> 2x + x = 81

=> 3x = 81

=> x = 81 ÷ 3

=> x = 27 (Ans)

Answer:

you may be talking about this! the answer is (A) for this graph!

if not, let me know!

The statement implies that as total cost doubles and the productivity of labor diminishes, the corresponding output increases, but at a diminishing rate. This suggests diminishing returns to labor, where the additional output from each additional unit of labor decreases.

If the total cost doubles, it indicates an increase in the cost of production. In the context of diminishing marginal productivity of labor, this implies that the additional output produced from each additional unit of labor is decreasing.

Therefore, if total cost doubles while the productivity of labor diminishes, it suggests that the corresponding output has increased, but at a diminishing rate. In other words, the increase in total cost is not proportional to a similar increase in output, indicating diminishing returns to labor.

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5.30 % rate of return would you expect on a 5-year treasury security, assuming the pure expectations theory is valid.

To reflect the true cost and purchasing power of money that is borrowed or invested, an interest rate is called a real interest rate that has been adjusted for inflation. The nominal interest rate depicts the cost of money and reflects the state of the market. A good's nominal value is its price in terms of money. Its value in relation to another good, service, or collection of goods is what determines its true worth. Given that it is the current interest rate in the economy, it is frequently referred to as the market interest rate (usually charged by banks and other institutions). Depending on the bank or the type of loans or deposits, this nominal interest rate may be 8%, 10%, or 12%.

Nominal interest rate = Real interest rate + Inflation rate

= 2.5% + 2.8%

= 5.30%

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Answer:

40.5 Units

Step-by-step explanation:

The area of a kite is A = (d1d2) / 2, where d1 and d2 are the diagonals of the kite.

Since the kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.

d1 = 9 units

d2 = 9 units

A = (9units * 9units) / 2

A = 81units² / 2

A = 40.5 units²

Answer:

76.3 cm²

Step-by-step explanation:

step 1

step 2

step 3

step 4

Answer:

8+16+2=28

Step-by-step explanation:

41/2 feet is equivalent to 54 inches. This results in a total of 48 inches from the whole number and an additional 6 inches from the fraction, summing up to 54 inches.

1. To convert feet to inches, you need to know that there are 12 inches in a foot. In this case, you have 4 feet and 1/2 of a foot. To convert the whole number part, 4, you multiply it by 12 since there are 12 inches in each foot. This gives you 48 inches.

2. To convert the fraction, 1/2 of a foot, you first multiply the numerator (1) by 12 to get 12. Then, you divide this result by the denominator (2). Dividing 12 by 2 gives you 6 inches.

3. Finally, you add the inches from the whole number (48 inches) and the inches from the fraction (6 inches) to get the total number of inches. 48 inches + 6 inches equals 54 inches, which is the final conversion for 4 1/2 feet.

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The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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The adding and subtracting complex numbers and polynomials share similarities in terms of their operations and properties, but they also have key differences.

When adding or subtracting complex numbers and polynomials, both operations follow similar rules. In both cases, like terms are combined by adding or subtracting coefficients. Both complex numbers and polynomials can have real and imaginary parts, and these parts are added or subtracted separately.

However, there are notable differences between adding/subtracting complex numbers and polynomials. Complex numbers involve the addition or subtraction of real and imaginary parts, where the real parts are added/subtracted separately and the same goes for the imaginary parts. In contrast, when adding/subtracting polynomials, the coefficients of corresponding terms are directly added/subtracted.

Furthermore, complex numbers have the additional concept of conjugates, where the conjugate of a complex number is formed by changing the sign of its imaginary part. This property is not present in polynomials.

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Answer:

1/2

Step-by-step explanation:

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

28 * 2 = 56.

Answer:

4×+10y-6y=14

4×+4=14

4×=14-4

4×=12

The hypothenuse in the triangle when the sides that are given are ✓39 and 6 is 8.6.

It should be noted that a triangle has three sides and the longest side is the hypothenuse. Based on the information given, it can be seen that we have two sides that we given in the question already.

In this case, the sides that are given are ✓39 and 6 and we wat to find the hypothenuse. This will go thus;

Hypothenuse ² = (✓39)² + 6²

Hypothenuse ² = 39 + 36

Hypothenuse ² = 75

Hypothenuse = ✓75

Hypothenuse = 8.6

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Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99

The graph shows that the rise is 3 and the run is 3, and the hypotenuse is the length between the two points.

let hypotenuse = x

using Pythagorean theorem:

x^2= 3^2 + 3^2

x^2 = 9 + 9

x= sqrt 18

x = 4.2426....

rounding to the nearest 10th:

x = 4.2

Let be x the amount the owner withdrew. Then, we can write and solve the following equation:

Answer

The owner withdraws $2,000.

Answer:

  at x=0 (the origin)

Step-by-step explanation:

The equation for a proportional relationship is ...

  y = kx

The equation of a straight line is ...

  y = kx +b . . . . . for some y-intercept b

Comparing the proportional relation to the relation for a general line, we see that b=0 in the proportional relation. That is, the y-intercept is at y=0, the origin of the Cartesian coordinate plane.

The graph crosses the x-axis at (0, 0), or x=0.

__

Additional comment

In y=kx, the value k is called "the constant of proportionality." It is also the slope of the line on a graph.

In the usual representation of the slope-intercept equation of a line, y=mx+b, the slope of the line is represented by 'm'. In the above, we used 'k' for that purpose, to facilitate comparing the equations.