I CAN SOLVE PROBLEMS.
5. Create an equivalent expression using the
additive inverse property.
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6. Divide
debelow and determine if it will
terminate or repeat

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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Answer:

, volume = [(3√3)/2]a2h cubic units

Step-by-step explanation:

The formula for the volume of a hexagonal prism is, volume = [(3√3)/2]a2h cubic units where a is the base length and h is the height of the prism.

Answer:

The place value of 1 in 1,234,567,890 is 1,000,000,000.

Answer:

In the ones place there is a 0.

Step-by-step explanation:

Answer:

x = 21

Step-by-step explanation:

(4x+11°) = (5x-10)

4x + 11 = 5x - 10

-x + 11 = -10

-x = -21

x = 21

Answer:

Step-by-step explanation:

1)Move all x terms to one side

11° = x - 10°

2)Move all constant terms to the other side

11° + 10° = x - 10° + 10°

21° = x

So the solution to the equation is x = 21°.

The rate of change is \(\frac{3}{2}\).

A function contains input and output.

It describes the relationships between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

The output is 3

The input is 1

We have,

From the graph,

The coordinates are:

(-2, 0) and (2, 6)

Now,

The rate of change.

= \(\frac{(6 - 0)}{(2 + 2)}\)

= \(\frac{6}{4}\)

= \(\frac{3}{2}\)

Thus,

\(\frac{3}{2}\) is the rate of change.

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Answer:

6 5/6 miles

Step-by-step explanation:

4 1/2 + 2 1/3

4+2=6

1/2+1/3

3/6+2/6=5/6

6 5/6 miles

No, \(4x^{2} +8=12\) is not a linear equation

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

No, \(4x^{2}+8=12\\4x^{2} -4=0\)is not a linear equation because An equation is said to be linear if the maximum power of the variable is consistently 1.

This is a quadratic equation, because quadratic equation has a maximum power of 2.

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Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, Gregg cut 4 sections of pizza dough.

Answer:

First Option: y = 1/2x + 8

Step-by-step explanation:

for lines to be parallel they must have the same slopes

The least possible value of n, where the product of 180 and the positive integer n is a perfect cubic number is 150.

so, by the question,

n×180 is a perfect cube

on the prime factorization of 180, we get

180 = 2²×3²×5

so the number should be

n = 2 × 3 × 5² =150

when we multiply both of them we get

180×n = (2²×3²×5)×(2 × 3 × 5²)

          = (2³×3³×5³)

          =(2×3×5)³

          =(30)³

          =27000

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By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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Answer:

Walmart

Step-by-step explanation:

It is given that,

Jonathan wants to buy his whole basketball team new clothes.

On Amazon there is a sell for 11 shirts for $145.23

The cost of 1 shirt on amazon:

\(C=\dfrac{145.23}{11}=\$13.20\)

On Walmart sell for 23 shirts for $212.19.

The cost of 1 shirt on Walmart:

\(C=\dfrac{212.19}{23}=\$9.225\)

Cost of 1 shirt on Amazon is $13.20 and on Walmart is $9.225. It is clear that on Walmart it is better to buy for $9.225.

Because ,

The given figure is parallelogram and as we know that , a parallelogram has two congruent triangles . Now by the given figure the pair two sides are equal and a opposite angle is equal . So we can say the the two triangles are congruent by SAS congruency .

Answer:

there are 5 red marbles in the jar

Step-by-step explanation:

I think this is the answer

The original cost of the car was $12,935.74 (rounded to the nearest $100).

(a) To find the depreciation rate for a car that originally cost $20,000 and is worth $12,000 after 4 years, we can use the formula:

\(C = (1 - r)^n * C_0\)

where C is the value of the car after n years, C_0 is the original cost of the car, and r is the yearly depreciation rate.

Plugging in the values given, we get:

\(12,000 = (1 - r)^4 * 20,000\)

Solving for r, we get:

\(1 - r = (12,000/20,000)^(1/4) = 0.8185\)

r = 1 - 0.8185 = 0.1815

The depreciation rate for the car is 18.2% (rounded to the nearest tenth of a percent).

(b) To find the original cost of a car that has a yearly depreciation rate of 11% and is worth $10,000 after 2 years, we can use the same formula:

\(C = (1 - r)^n * C_0\)

Plugging in the values given, we get:

\(10,000 = (1 - 0.11)^2 * C_0\)

Solving for C_0, we get:

\(C_0 = 10,000 / (0.89)^2 = $12,935.74\)

The original cost of the car was $12,935.74 (rounded to the nearest $100).

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To find ƒ[A], we need to determine the image of the set A under the function ƒ.

Given A = {3k : k ∈ N}, we can substitute each element of A into the function ƒ(n) = {k ∈ N: knɅk is odd} to find the corresponding images.

Let's evaluate ƒ[A]:

ƒ[A] = {ƒ(n) : n ∈ A}

For n = 3k (where k ∈ N), we have:

ƒ(3k) = {m ∈ N : mɅ(3k) is odd}

To find the values of m that satisfy the condition, we need to consider the parity of 3k and m. Since 3k is always odd, m must also be odd for mɅ(3k) to be odd.

Therefore, ƒ(3k) = {m ∈ N : m is odd} = 2N (the set of all even numbers).

Hence, ƒ[A] = 2N (the set of all even numbers).

Now let's find ƒ^(-1)[ƒ[A]], which represents the preimage of ƒ[A] under the function ƒ.

ƒ^(-1)[ƒ[A]] = {n ∈ N : ƒ(n) ∈ ƒ[A]}

Since ƒ[A] = 2N, which consists of all even numbers, the preimage of ƒ[A] under ƒ will be the set of all natural numbers.

Therefore, ƒ^(-1)[ƒ[A]] = N (the set of all natural numbers).

In summary:

ƒ[A] = 2N (the set of all even numbers)

ƒ^(-1)[ƒ[A]] = N (the set of all natural numbers)

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(a) The eigenvalues are λ1=3+2√2 and λ2=3-2√2 and the eigenvectors are y(t) = c1 e^λ1 t v1 + c2 e^λ2 t v2. (b) The real-valued solution to the initial value problem is y1(t) = -5e^{(3-2\sqrt{2})t} + 5e^{(3+2\sqrt{2})t}y2(t) = -10\sqrt{2}e^{(3-2\sqrt{2})t} - 10\sqrt{2}e^{(3+2\sqrt{2})t}.

Given, The linear system y'=[−35−23]y

Find the eigenvalues and eigenvectors for the coefficient matrix. v1=[ , and λ2=[v2=[]

Calculation of eigenvalues:

First, we find the determinant of the matrix, det(A-λI)det(A-λI) =

\begin{vmatrix} -3-\lambda & 5 \\ -2 & 3-\lambda \end{vmatrix}

=(-3-λ)(3-λ) - 5(-2)

= λ^2 - 6λ + 1

The eigenvalues are roots of the above equation. λ^2 - 6λ + 1 = 0

Solving above equation, we get

λ1=3+2√2 and λ2=3-2√2.

Calculation of eigenvectors:

Now, we need to solve (A-λI)v=0(A-λI)v=0 for each eigenvalue to get eigenvector.

For λ1=3+2√2For λ1, we have,

A - λ1 I = \begin{bmatrix} -3-(3+2\sqrt{2}) & 5 \\ -2 & 3-(3+2\sqrt{2}) \end{bmatrix}

= \begin{bmatrix} -2\sqrt{2} & 5 \\ -2 & -2\sqrt{2} \end{bmatrix}

Now, we need to find v1 such that

(A-λ1I)v1=0(A−λ1I)v1=0 \begin{bmatrix} -2\sqrt{2} & 5 \\ -2 & -2\sqrt{2} \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix}

= \begin{bmatrix} 0 \\ 0 \end{bmatrix}

The above equation can be written as

-2\sqrt{2} x + 5y = 0-2√2x+5y=0-2 x - 2\sqrt{2} y = 0−2x−2√2y=0

Solving the above equation, we get

v1= [5, 2\sqrt{2}]

For λ2=3-2√2

Similarly, we have A - λ2 I = \begin{bmatrix} -3-(3-2\sqrt{2}) & 5 \\ -2 & 3-(3-2\sqrt{2}) \end{bmatrix} = \begin{bmatrix} 2\sqrt{2} & 5 \\ -2 & 2\sqrt{2} \end{bmatrix}

Now, we need to find v2 such that (A-λ2I)v2=0(A−λ2I)v2=0 \begin{bmatrix} 2\sqrt{2} & 5 \\ -2 & 2\sqrt{2} \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}

The above equation can be written as

2\sqrt{2} x + 5y = 02√2x+5y=0-2 x + 2\sqrt{2} y = 0−2x+2√2y=0

Solving the above equation, we get v2= [-5, 2\sqrt{2}]

The real-valued solution to the initial value problem {y1′=−3y1−2y2, y2′=5y1+3y2, y1(0)=2y2(0)=−5

We have y(t) = c1 e^λ1 t v1 + c2 e^λ2 t v2where c1 and c2 are constants and v1, v2 are eigenvectors corresponding to eigenvalues λ1 and λ2 respectively.Substituting the given initial values, we get2 = c1 v1[1] - c2 v2[1]-5 = c1 v1[2] - c2 v2[2]We need to solve for c1 and c2 using the above equations.

Multiplying first equation by -2/5 and adding both equations, we get

c1 = 18 - 7\sqrt{2} and c2 = 13 + 5\sqrt{2}

Substituting values of c1 and c2 in the above equation, we get

y1(t) = (18-7\sqrt{2}) e^{(3+2\sqrt{2})t} [5, 2\sqrt{2}] + (13+5\sqrt{2}) e^{(3-2\sqrt{2})t} [-5, 2\sqrt{2}]y1(t)

= -5e^{(3-2\sqrt{2})t} + 5e^{(3+2\sqrt{2})t}y2(t) = -10\sqrt{2}e^{(3-2\sqrt{2})t} - 10\sqrt{2}e^{(3+2\sqrt{2})t}

Final Answer:y1(t) = -5e^{(3-2\sqrt{2})t} + 5e^{(3+2\sqrt{2})t}y2(t) = -10\sqrt{2}e^{(3-2\sqrt{2})t} - 10\sqrt{2}e^{(3+2\sqrt{2})t}

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Answer: Not similar

Step-by-step explanation:

They are telling you that you have a Side and a Side that are similar.  The sides of the smaller triangle are multiplied by 2 to get the larger triangle, but you need a 3rd element for it to be similar.  You have SS but you need another side or angle for it to be similar

Not similar

When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×\(10^{1735}\)

There are a total of 444\(C_{444}\) (or 6.64 x \(10^{847}\)) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x \(10^{906}\)) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x \(10^{847}\) x 5.34 x \(10^{906}\)

3.53 x \(10^{1735}\)

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The volume of Uranus having a diameter of 50724000 m is 6.829 x 1022 m3.

Volume is defined as the quantity of the three-dimensional space occupied by a closed three-dimensional figure. In the case of any object, volume is measured in cubic units. In cases of solid objects, their volume is measured in cubic units of length, such as meters, centimeters, etc.

To calculate the volume of spherical objects, viz. for a planet (assuming it is an ideal sphere in shape), the following formula is applied:

Volume (V) = 4/3  π\(R^{3}\) cubic units

where R = radius and π  = 3.14, a mathematical constant.

It is given that the diameter ( D ) of Uranus = 50724000 m.

Therefore radius ( R ) = D/ 2 = 50724000 m/ 2 = 25362000 m.

Therefore volume of planet Uranus = 4/3 π\(R^{3}\).

Substituting  π by 3.14 and R by 25362000m, we get

Volume = 6.829 x 1022 \(m^{3}\)

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Answer:

4/15 is the answer my guy

Step-by-step explanation:

5/3 x 4/25= 20/75 simplified is 4/15

The surface area of the glass sculpture in the shape of a right square prism can be represented by the equation 10s^2, where s represents the side length of the base square.

A glass sculpture in the shape of a right square prism is shown. The base of the sculpture's outer shape is a square. To find the surface area of the sculpture, we need to calculate the area of each face and then add them together.

To calculate the surface area, we can use the formula: Surface Area = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

Since the base of the sculpture is a square, we know that the length (l) and width (w) are equal. Let's call this side length s.

To find the surface area, we can substitute the values into the formula:
Surface Area = 2s^2 + 2s*h + 2s*h.

Since the sculpture is a right square prism, we can assume that the height (h) is also equal to the side length (s).

Substituting the values:
Surface Area = 2s^2 + 2s*s + 2s*s.

Simplifying the equation:
Surface Area = 2s^2 + 4s^2 + 4s^2.

Combining like terms:
Surface Area = 10s^2.

So, the surface area of the glass sculpture in the shape of a right square prism can be represented by the equation 10s^2, where s represents the side length of the base square.

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The probability that the sum of the two randomly selected numbers is at least 7 is 12/21, which simplifies to 4/7 or approximately 0.571.

To find the probability that the sum of two randomly selected numbers from the set {1, 2, 3, 4, 5, 6, 7} is at least 7, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.

Let's consider the favorable outcomes:

1. Selecting 4 and 3: There are two ways to choose these numbers: (4, 3) and (3, 4).

2. Selecting 5 and 2: There are two ways to choose these numbers: (5, 2) and (2, 5).

3. Selecting 6 and 1: There are two ways to choose these numbers: (6, 1) and (1, 6).

4. Selecting 7 and any number: There are six ways to choose the second number: (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), and (7, 6).

Therefore, the total number of favorable outcomes is 2 + 2 + 2 + 6 = 12.

Now let's consider the total number of possible outcomes:

We are selecting two numbers from a set of seven, which can be done in C(7, 2) ways (7 choose 2). This can be calculated as follows:

C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21.

So, the total number of possible outcomes is 21.

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Answer:

where are the options

Step-by-step explanation:

Answer: The answer is THE FUNCTION HAS THREE DISTINCT REAL ZEROS

Step-by-step explanation:

I’m pretty sure I still need to check if I got it right

Answer:

z : 6

Step-by-step explanation:

points: (2,-8) and (4, 6)