subtract as indicated. Express your answer as a single polynomial in ste 5(x^(3)+x^(2)-3)-2(2x^(3)-2x^(2))

The lengths of the two legs are 2 centimeters and 9 centimeters.

Let's call the shorter leg of the right triangle x and the other leg y. According to the given information, we can create the following equation:

x = y - 7

Since we know that the hypothenuse is 13 centimeters, we can use the Pythagorean theorem to create another equation:

x^2 + y^2 = 13^2

Substituting the first equation into the second equation, we get:

(y - 7)^2 + y^2 = 13^2

Simplifying and rearranging terms, we get:

2y^2 - 14y - 72 = 0

Using the quadratic formula, we can solve for y:

y = (14 ± √(14^2 - 4(2)(-72))) / (2(2))

y = (14 ± √484) / 4

y = (14 ± 22) / 4

y = 9 or y = -2

Since the length of a leg cannot be negative, we reject the negative solution and take y = 9 centimeters as the length of the other leg. Then, we can use the first equation to find the length of the shorter leg:

x = 9 - 7

x = 2 centimeters

Therefore, the lengths of the two legs are 2 centimeters and 9 centimeters.

Learn more about lengths

brainly.com/question/30100801

#SPJ11

Answer:

The second answer is correct

Step-by-step explanation:

The first image shows nuclear fusion, combining two lighter nuclei to make a helium and a heavy nucleus, and the second image shows nuclear fission, taking a large unstable nucleus and turning it into two lighter nuclei.

A graph of the resulting image after the given triangle is rotated 90° counterclockwise about the origin is shown in the image below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (9, 3) → Ordered pair A' = (-(3), 9) = (-3, 9).

Ordered pair B  = (3, 0) → Ordered pair B' = (-(0), 3) = (0, 3).

Ordered pair C  = (8, 0) → Ordered pair C' = (-(0), 8) = (0, 8).

Read more on rotation here: brainly.com/question/28854313

#SPJ1

This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π.

Complete the statement. y=cos −1x means that x=cos y, for 0≤y≤π

This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π. In other words, if we know the value of x, we can use the inverse cosine function to find the angle y that has a cosine of x. This is useful for solving equations involving cosine, such as finding the angles of a triangle given the lengths of its sides.

Learn more about Cosine

brainly.com/question/29114352

#SPJ11

x² - 7y - 4x²y + 8xy² is standard form of equation.

What are equations, and what different kinds are there?

Equations can be divided into two categories: identities and conditional equations. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.

                     When two expressions are joined together by the equals sign ("="), the result is an equation. A mathematical statement that demonstrates the equality of two mathematical expressions is the definition of an equation.

  8xy²+1x²-4x²y-7y

standard form = 8xy² + 1x² - 4x²y - 7y

                       =  x² - 7y - 4x²y + 8xy²

Learn more about equation

brainly.com/question/29657992

#SPJ1

Step-by-step explanation:

The equation that represents the resale value V (in dollars) of the smartphone as a function of the time t (in years) since it was purchased is:

V = 700e^(-0.2t)

Quinn has 6 dimes and 15 quarters in his pocket.

Let's use a system of two equations to represent the given information:

d + q = 21      (1)   // The number of dimes and quarters adds up to 21

10d + 25q = 435 (2)   // The total value of the coins in cents is 435

where d represents the number of dimes and q represents the number of quarters.

We can use equation (1) to solve for d in terms of q:

d = 21 - q

Substituting this expression for d into equation (2), we get:

10(21 - q) + 25q = 435

210 - 10q + 25q = 435

15q = 225

q = 15

So, Quinn has 15 quarters. Substituting this value into equation (1), we get:

d + 15 = 21

d = 6

So, Quinn has 6 dimes.

Learn more about equation: https://brainly.com/question/10413253

#SPJ11

The solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places

To solve the given trigonometric equation on the interval [0,2π), we need to use the quadratic formula.

First, let us rewrite the equation in terms of x:
2x^2 + 5x + 2 = 0

Next, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

Plugging in the values from the equation:
x = (-(5) ± √((5)^2 - 4(2)(2)))/(2(2))

Simplifying:
x = (-5 ± √(25 - 16))/4
x = (-5 ± √9)/4
x = (-5 ± 3)/4

This gives us two possible values for x:
x = (-5 + 3)/4 = -2/4 = -0.5
x = (-5 - 3)/4 = -8/4 = -2

Now we need to convert these values back to θ by using the inverse cosine function:
θ = cos^-1(-0.5)
θ = cos^-1(-2)

The first value, θ = cos^-1(-0.5), gives us two solutions on the interval [0,2π):
θ = 2π/3 and θ = 4π/3

The second value, θ = cos^-1(-2), does not give us any solutions on the interval [0,2π) because the cosine function only takes on values between -1 and 1.

Therefore, the solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places.

Learn more about Trigonometric

brainly.com/question/29156330

#SPJ11

Radians and degrees are two units of measurement for angles. Each one has its own pros and cons, and the choice between the two largely depends on the situation and personal preference.

Radians:
Pros:
- Radians are the natural unit of measurement for angles in mathematics and physics. They are closely related to the concept of a circle, and many formulas and equations involving angles are simpler when using radians.
- Radians are unitless, which can make calculations easier and more intuitive.
Cons:
- Radians are not as familiar to most people as degrees, and can be harder to visualize and understand.
- Radians can be more difficult to work with when measuring small angles, since they use fractions or decimals instead of whole numbers.

Degrees:
Pros:
- Degrees are the most commonly used unit of measurement for angles, and are more familiar to most people.
- Degrees are easier to work with when measuring small angles, since they use whole numbers instead of fractions or decimals.
Cons:
- Degrees are not the natural unit of measurement for angles, and many formulas and equations involving angles are more complicated when using degrees.
- Degrees require the use of a special symbol (°) and are not unitless, which can make calculations more difficult and less intuitive.

Overall, the choice between radians and degrees deends on the situation and personal preference. Radians are generally more natural and simpler to work with in mathematics and physics, but degrees are more familiar and easier to visualize.

To learn more about radians and degrees from the given link

https://brainly.com/question/30396383

#SPJ11

Therefore , the solution of the given problem of arithmetic mean comes out to be  option A an=3+2(n-1).

The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.

Here,

The following is the formula for the general word "an" in an arithmetic sequence:

=> a = a1 + (n - 1)d

where the first term is denoted by a1, the term number is n, and the common difference is d.

A1 = 3 and A11 = 23 are provided. To determine the common difference, we can use the method for the eleventh term:

=> a11 = a1 + (11 - 1)d

=> 23 = 3 + 10d

=>  d = 2

Inputting this number of d into the general term's formula yields the following results:

=> a = 3 + (n - 1)2

The right response is therefore: an=3+2(n-1).

To know more about arithmetic mean ,visit

brainly.com/question/13000783

#SPJ1

Answer:

You must be really must to answer that paper yho

Answer: Your answer will be [tex]x=7[/tex]

If it's okay, I would like someone to talk to. My email address is jeremiah.mccrocklin06 at symbol g mail . com

obtain the solution using the long division method

Answer:

1. Transitive

2. Reflexive

3. Symmetric

4. Reflexive

5. Symmetric

6. Transitive

The value of n for the given equation 3⁵. 3ⁿ = 3⁸ is n = 3.

Several rules of exponents are presented according to the capacities they possess. The following rule governs multiplication: Add the exponents while maintaining the base's consistency.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing similar bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the base constant.

The given equation is:

3⁵. 3ⁿ = 3⁸

Using the product rule for exponents we have:

3⁽⁵ ⁺ ⁿ⁾ = 3⁸

The above expression can be written as:

5 + n = 8

n = 8 - 5

n = 3

Hence, the value of n for the given expression 3⁵. 3ⁿ = 3⁸ is n = 3.

Learn more about exponents here:

https://brainly.com/question/15993626

#SPJ9

The complete question is:

It is one of the most fundamental curvilinear geometric shapes, a cylinder has historically been thought of as a three-dimensional solid. It is considered a prism with a circle as its base in basic geometry.

the area of mathematics that focuses on the characteristics and connections between points, lines, surfaces, solids, and their higher dimensional equivalents.

We can find the solution this way,

The volume of water in the Cylinder before marbles were dropped in =

The volume of water in the Cylinder After marbles were dropped in -

Volume of marbles

So, we can write it as,

Volume of water before = Volume of water after - Volume of Marbles

To learn more about Volume, visit:

https://brainly.com/question/14197390

#SPJ1

The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.

Let D = (x, y)

Now, We know that;

The midpoint of AC = Mid-point of BD

(-2 + 5)/2 = (x + 3)/2

3 = x + 3

x = 0

(- 3+3)/2 = (y + 2)/2

y = - 2

Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

Learn more about the parallelogram here:

brainly.com/question/1563728

#SPJ9

Answer:

35/40 = (7*5)/(8*5) = 7/8

So the Lions won 7/8 of the games they played.

2) To write a decimal equivalent to 7/8, we can divide 7 by 8 using long division:

0.875

___________

8 | 7.000

- 6.4

_______

60

-56

____

40

-40

____

0

So 7/8 is equivalent to the decimal 0.875.

To write a percent equivalent to 7/8, we can multiply the decimal equivalent by 100:

0.875 * 100 = 87.5%

So the Lions won 87.5% of the games they played.

Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.

Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.

The arithmetic operations were used to arrive at the answer.

The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.

So, the total pounds of fruit bought = 0.5 + 3 = 3.5

Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits  = (x + y)

Hence, the required solution has been obtained.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ1

Answer:

2400

Step-by-step explanation:

144 are seated

94% yet to arrive

6% = 144

Easy method Find the value of 1%

144/6 will be 1%

If 1% =24 then 100% will be 24x 100

Total tickets sold will be 2400

Check: 6% of 2400 is 144

write the equation with both of them = 100

(3x + 50) + (2x + 15) = 100

combine like terms

5x + 65 = 100

subtract

5x = 35

x = 7

the question asks for <JTU = 2x + 15

plug in x = 7

x = 29

EDIT

Answer:

JTU = 29°

Step-by-step explanation:

I'm not sure if this is correct but I got 29°

(3x+50)° + (2x+15)° = 100°

x= 7°

(2x+15)°

((2x7)+15)° = 29°

The equation is true, the point (-1,6) does indeed lie on the line (-3,5).

The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine whether or not the point (-1,6) lies on the line (-3,5), we need to plug in the x and y values of the point into the equation of the line and see if the equation is true.

First, we need to find the slope of the line. The slope is the difference in the y values divided by the difference in the x values:

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

Next, we need to find the y-intercept of the line. We can do this by plugging in one of the points and solving for b:

5 = (1/2)(-3) + b

b = 5 + (3/2) = 13/2

Now we have the equation of the line: y = (1/2)x + 13/2

Finally, we can plug in the x and y values of the point (-1,6) to see if the equation is true:

6 = (1/2)(-1) + 13/2

6 = -1/2 + 13/2

6 = 12/2

6 = 6

To know more about equation of a line click on below link:

https://brainly.com/question/21511618#

#SPJ11

Answer:

3

Step-by-step explanation:

by the help of Prashant chettri

(-3x + 2y + z = 0 )

The equation of the plane passing through the origin and containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) can be found by taking the cross product of the two vectors and using the resulting vector as the normal vector of the plane. The cross product of the two vectors is given by:

\( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \times \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] = \left[\begin{array}{c}(-1)(3) - (1)(0) \\ (1)(3) - (1)(1) \\ (1)(0) - (1)(-1)\end{array}\right] = \left[\begin{array}{c}-3 \\ 2 \\ 1\end{array}\right] \)

Therefore, the equation of the plane is given by:

\( -3x + 2y + z = 0 \)

This is the equation of the plane passing through the origin and containing the two given vectors.

Learn more about vectors

brainly.com/question/29740341

#SPJ11

The fraction of a day that the average fire burns is given as follows:

100%.

The fraction of a day that the average fire burns is obtained applying the proportions in the context of the problem.

For the log cabin, the fraction is given as follows:

1/4.

The average fire burns four times this length, hence the length is given as follows:

4 x 1/4 = 4/4 = 1 = 100% of a day.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)

In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).

Plugging in these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

C(7, 3) = 7! / (3! * 4!)

C(7, 3) = 5040 / (6 * 24)

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, the man can take 35 different combinations of shirts without repetition.

To learn more about combinations here:

https://brainly.com/question/28065038#

#SPJ11

The Surface Area of Container is 954. 56 inch².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

Learn more about Surface Area here:

https://brainly.com/question/29298005

#SPJ1

The equation of the circle centered at (-4,3) with radius 3 is (x + 4)^2 + (y - 3)^2 = 9. Simplifying this equation means to simplify the terms in the equation by using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse.

In this equation, the hypotenuse is the radius, which is 3, and the sides are (x + 4) and (y - 3). Substituting the values into the Pythagorean Theorem, we get (x + 4)^2 + (y-3)^2 = 9, which is the equation of the circle centered at (-4,3) with radius 3. This equation can be simplified further by factoring the terms, which yields (x + 4) (x + 4) + (y - 3) (y - 3) = 9. This is the fully simplified equation of the circle.

Know more about Substituting here

https://brainly.com/question/18330729#

#SPJ11

This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n. To demonstrate the equations using induction, we need to follow three steps: the base case, the induction hypothesis, and the induction step.

1) P(n) : 2 + 4 + 6 + ⋯+ 2n= n(n+ 1), ∀ n∈ℕ.

Base case: For n = 1, the equation becomes 2 = 1(1+1), which is true.

Induction hypothesis: Assume the equation is true for n = k, that is, 2 + 4 + 6 + ⋯+ 2k= k(k+ 1).

Induction step: We need to show that the equation is also true for n = k+1. That is, 2 + 4 + 6 + ⋯+ 2k + 2(k+1)= (k+1)(k+2).

Using the induction hypothesis, we can substitute k(k+1) for 2 + 4 + 6 + ⋯+ 2k:

k(k+1) + 2(k+1) = (k+1)(k+2)

Distributing the (k+1) on the right side of the equation gives us:

k(k+1) + 2(k+1) = k(k+1) + 2(k+1)

This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.

2) ∑i^2= n(n+1)(2n+1)/6, ∀ n∈ℕ.

Base case: For n = 1, the equation becomes 1^2 = 1(1+1)(2(1)+1)/6, which simplifies to 1 = 1, which is true.

Induction hypothesis: Assume the equation is true for n = k, that is, ∑i^2= k(k+1)(2k+1)/6.

Induction step: We need to show that the equation is also true for n = k+1. That is, ∑i^2 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6.

Using the induction hypothesis, we can substitute k(k+1)(2k+1)/6 for ∑i^2:

k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6

Multiplying both sides of the equation by 6 gives us:

k(k+1)(2k+1) + 6(k+1)^2 = (k+1)(k+2)(2(k+1)+1)

Distributing the (k+1) on both sides of the equation gives us:

k(k+1)(2k+1) + 6(k+1)^2 = k(k+1)(k+2)(2k+3)

This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.

For more about equations:

https://brainly.com/question/29657992

#SPJ11

Answer:

c(t) = $85 × (1.09)^t

Step-by-step explanation:

Assuming that the inflation rate remains constant at 9% per year, the cost of the athletic shoes after t years can be determined by multiplying the original cost by the inflation factor for t years, which is given by (1 + 0.09)^t, or 1.09^t. Therefore, the algebraic rule to determine the cost, c(t), of the shoes after t years is:

c(t) = $85 × 1.09^t

Simplifying the expression, we get:

c(t) = $85 × (1.09)^t

where t is the number of years after the original purchase.