A man standing on the edge of a 30 foot tall building throws a ball at a velocity of 25 ft/sec into the air. The function of the ball's height, h (in feet), at t seconds is given. h(t) = -5t² + 25t + 30. How long does it take for the ball to hit the ground? _________ seconds. * 1 point

Answer:

g = 14

Step-by-step explanation:

Using g = 14 we can do 14 x 3 to get 42. Then we can subtract 42 by 5 to get 37.

Answer:

g = 14

Step-by-step explanation:

3g - 5 = 37

    +5    +5

3g = 42

3g/3 = 42/3

g = 14

Answer:

1,1 or -1,3

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

bottom right quadrant is IV

Answer:

It's B

Step-by-step explanation:

Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it

The given sequence is geometric sequence not arithmetic.

An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.

Difference between arithmetic and geometric sequence:

An arithmetic sequence has a constant difference between each consecutive pair of terms

while

A geometric sequence has a constant ratio between each pair of consecutive terms.

Here, we have a sequence 5,10,20.

So a₁ = 5, a₂ = 10, a₃ = 20

Difference = a₃- a₂ = 20 - 0 = 10

                    a₂ - a₁ = 10 - 5 = 5

Since the difference is not constant, therefore the given sequence is not arithmetic.

Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.

Therefore, the sequence is geometric sequence.

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Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.

For instance, to multiply 3/4 by 2:

Put 2 over 1, making it 2/1, to make it a fraction.

To get 1/2, invert 2/1.

To get 3/8, multiply 3/4 by 1/2.

Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.

Hence, 1/4 is equivalent to 3/4 when divided by 2.

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Answer:

b^2 + 2b <= 168

Step-by-step explanation:

The base is b.

The height, h, is 4 in. greater than twice the base, so the height is 2b + 4.

The area of a triangle is bh/2. We replace h with the expression for height.

A = bh/2 = b(2b + 4)/2 = (2b^2 + 4b)/2 = b^2 + 2b

The area is b^2 + 2b.

The area is no more than 168 in.^2, so it is less than equal to 168 in.^2.

b^2 + 2b <= 168

("<=" means "less than or equal to")

Since you don't show the choices, choose an inequality that is equivalent to the one just above.

Answer:

y = √(4x - 8) - 3

Step-by-step explanation:

y = 1/4(x + 3)² + 2

To find the inverse, switch the places of the x and y.  

x = 1/4(y + 3)² + 2

Solve for y.

x - 2 = (1/4(y + 3)² + 2) - 2

x - 2 = 1/4(y + 3)²

4(x - 2) = 4(1/4(y + 3)²)

4x - 8 = (y + 3)²

√(4x - 8) = √((y + 3)²)

√(4x - 8) = y + 3

√(4x - 8) - 3 = (y + 3) - 3

√(4x - 8) - 3 = y

y = √(4x - 8) - 3

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Therefore, each of the 10 braces exerts a force of approximately 6035.25 N.

To calculate the force exerted by each of the 10 braces, we need to consider the horizontal force exerted by the wind and the geometry of the wall and bracing.

Given:

Height of the wall (h) = 17.0 m

Length of the wall (l) = 11.0 m

Number of braces (n) = 10

Horizontal force exerted by the wind (F_w) = 645 N/m^2

First, let's calculate the total area of the wall:

Wall area (A) = h * l = 17.0 m * 11.0 m = 187.0 m^2

Since the net force from the wind acts at a height halfway up the wall, we can consider the force acting on the top half of the wall:

Force on the top half of the wall (F_t) = F_w * (A/2) = 645 N/m^2 * (187.0 m^2 / 2) = 60352.5 N

Next, let's calculate the force exerted by each brace:

Force exerted by each brace (F_brace) = F_t / n = 60352.5 N / 10 = 6035.25 N

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The body of the loop executes two times before the condition is no longer met. So, the correct answer is:
c. 2

Let's examine the given code fragment step-by-step:

1. The variable "x" is initialized with a value of 8.
2. The "while" loop checks if the condition (x / 3) is not equal to 2. If this condition is true, the loop will execute.
3. Inside the loop, the value of "x" is decremented by 1.

Now, let's check how many times the loop will execute:

1. In the first iteration, x = 8. The condition (8 / 3) != 2 is true (2.67 != 2), so the loop executes. Then, x = 8 - 1 = 7.
2. In the second iteration, x = 7. The condition (7 / 3) != 2 is true (2.33 != 2), so the loop executes. Then, x = 7 - 1 = 6.
3. In the third iteration, x = 6. The condition (6 / 3) != 2 is false (2 == 2), so the loop does not execute any further.

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Let's assume that the cube has a side length of "s". Therefore, the volume of the cube would be:

Volume of Cube = s³

Now, the sphere replaces one quarter of the volume of the cube. This means that the volume of the sphere would be one quarter of the volume of the cube.

Volume of Sphere = (1/4) x Volume of Cube

We can use the formula for the volume of a sphere to find its volume:

Volume of Sphere = (4/3) x π x r³

where "r" is the radius of the sphere.

We know that the sphere replaces one quarter of the volume of the cube. Therefore:

(4/3) x π x r³ = (1/4) x s³

Simplifying this equation, we get:

r³ = (1/4) x (3/√(4)) x s³ x (1/π)

r³ = (3/16) x s³x (1/π)

r = (3/16)^(1/3) x s x (1/π)^(1/3)

Now, we can use the formula for the volume of the sphere to find its volume:

Volume of Sphere = (4/3) x πx r³

Volume of Sphere = (4/3) x π x [(3/16)^(1/3) x s x (1/π)^(1/3)]³

Volume of Sphere = (4/3) x π x (27/256) x s³ x (1/π)

Volume of Sphere = (27/64) x π x s³ x (1/π)

Now, we can find the volume of the souvenir piece by subtracting the volume of the sphere from the volume of the cube:

Volume of Souvenir Piece = Volume of Cube - Volume of Sphere

Volume of Souvenir Piece = s³ - (27/64) x π x s³ x (1/π)

Volume of Souvenir Piece = s³ - (27/64) x s³

Volume of Souvenir Piece = (37/64) x s³

Therefore, the volume of the souvenir piece is (37/64) times the volume of the cube.

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Answer:

7.5m

Step-by-step explanation:

Since we are not asked what to look for we can find the maximum height reached by the ball

The ball reaches its maximum height when dh/dx = 0

dh/dx = -2.4x + 6

0 = -2.4x + 6

2.4x = 6

x = 6/2.4

x = 2.5

Get the max height

Recall:

h =-1.2x^2 + 6x ,

h(2.5) = -1.2(2.5)^2 + 6(2.5)

h(2.5) = -1.2(6.25)+15

h(2.5) = -7.5 + 15

h = 7.5

Hence the maximum height reached by the ball is 7.5m

Answer 1/16

Step-by-step explanation:

= 2^-4 / 1

= 2^-4

=1/2^4

=1/16

The simplest form of the given equation 2⁻⁴/4⁰ is 1/16.

A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Given an expression 2⁻⁴/4⁰

simplifying it

=> 2⁻⁴/1

=> 1/ 2⁴

=> 1/16

therefore, the simplest form of the given equation is 1/16.

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Answer:

w = 9 7/10

Step-by-step explanation:

w + 4 1/4 = 13 19/20

Subtract 4 1/4 from each side

w = 13 19/20 - 4 1/4

Get a common denominator of 20

w = 13 19/ 20  - 4 1/4*5/5

w = 13 19/ 20  - 4 5/20

w = 9 14/20

We can simplify

w = 9 7/10

Rewrite the fractions to have the same denominator:

1/4 can be rewritten as 5/20

now you have w + 4 5/20 = 13 19/20

Solve for w by subtracting 4 5/20 from both sides:

W = 9 14/20 which can be rewritten as 9 7/10

answer: 9 7/10

Expkanation:

In a cyclic quadrilateral, the angles opposite each other are supplementary.

3x

From the following three options for running the appropriate t-test, Both Options (2) and (3) could be applicable depending on the specific research question being investigated.

The appropriate t-test to use in this scenario is paired t-test. This test compares before and after values for one type using excel. In this scenario, you would be comparing either the altimeter error of ACME or brand x before adjustment and calibration and after adjustment and calibration to see if there are any differences in the means (performance).

Based on the scenario described, Option 1 is not appropriate because there is no hypothesized population mean to compare against. Therefore, we can exclude this option.

Option 2, comparing one brand against another, could be appropriate if we want to investigate if there are any significant differences in altimeter error between brands. This would be a two-sample t-test.

Option 3, comparing the altimeter error of one brand before and after calibration, could also be appropriate to see if the adjustment and calibration had a significant impact on the altimeter's performance. This would be a paired t-test.

This test is the appropriate test to use because the dependent variable data in this scenario is the ratio and the type of question requires a paired t-test. In this scenario, you are comparing the performance of the two brands before and after adjustment and calibration, which requires paired t-test to answer the research question.

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Answer:

22

Explanation:

The cell phone plan costs $39.99 per month plus $0.18 for each text message.

Let the number of text messages sent or receive = t

The cost, C in a month will be:

If you have at most $44 to spend, it means the cost can be less than or equal to $44.

We then solve the inequality for t.

Since text messages cannot be decimal, the maximum number of text messages that you can send or receive next month is 22.

The height of the tree to 1 dp is 17.6 m

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

To find the height of the tree , trigonometric ratio can be used.

The height of the tree from the eye level is the opposite

The distance between the person and the tree is the adjascent.

Therefore;

tan35° = x/23

x = tan35 × 23

x = 16.1 m

The height of the tree will be;

h = 16.1 + 1.5

= 17.6

Therefore the height of the tree is 17.6m

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The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

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Answer:

Step-by-step explanation:

With what?

Answer:

Step-by-step explanation:

with what question

By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Step-by-step explanation:

You will pay $18 for a item with original price of $20 when discounted 10%. In this example, if you buy an item at $20 with 10% discount, you will pay 20 - 2 = 18 dollars.

Answer:

Volume of a cylinder = 225.80 in³ (Approx)

Volume of cone = 75.29 in³ (Approx)

Step-by-step explanation:

Given:

Volume of sphere = 150 in³

Find:

Volume of a cylinder and a cone

Computation:

Volume of sphere = [4/3]πr³

150 = [4/3][22/7]r³

r = 3.3 in (Approx)

Height = 2(3.3) = 6.6

Volume of a cylinder = πr²h

Volume of a cylinder = [22/7]3.3²(6.6)

Volume of a cylinder = 225.80 in³ (Approx)

Volume of cone = [1/3]πr²h

Volume of cone = 75.29 in³ (Approx)

Answer:

k=2

Step-by-step explanation:

2x+y=1 (1)

(1)×2: 4x+2y= 2

The y-intercept of both lines must be the same as if the y-intercept is different, it will have no solutions instead of infinite solutions. In order to achieve infinite solutions, both lines must be on the same points and have same gradient and same y-intercept.

Hence, k= 2

Answer: k=2

Step-by-step explanation:

If the two equations 2x+y=1, 4x+2y=k have infinite number of solutions, it means that the two equations are dependent and represent the same line. To check this, we can find the ratio of the coefficients of x and y in the two equations:2/4 = 1/2

1/2 = k/1

From the first ratio, we can see that the coefficient of x in the second equation is twice that of the first equation.

Similarly, the coefficient of y in the second equation is twice that of the first equation. Therefore, the second equation is just a multiple of the first equation.Solving the first equation for y, we get y = 1-2x. Substituting this into the second equation, we get:4x + 2(1-2x) = k

4x + 2 - 4x = k

2 = k

Therefore, the value of k is 2.

A:  10x + 8 = 3(x – 2)

    10x + 8 = 3x – 6

    7x =  – 14

    x = -2

The equation will be changed into = f(x)= 32

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

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Answer:

The answer to your question is simply just 9.

The solution of the system equation are x = -1 and y = 6.

The solution of the system equation is calculated as follows;

7x + 4y = 17 -------- (1)

3x - 2y = -15 -------- (2)

Solve the equation using elimination method as follows;

3: 21x + 12y = 51   ------ (3)

7: 21x - 14y = -105  ------ (4)

Subtract (3) from (4);

-26y = -156

y = 156/26

y = 6

The value of x is calculated as;

7x + 4y = 17

7x + 4(6) = 17

7x + 24 = 17

7x = 17 - 24

7x = -7

x = -7/7

x = -1

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Solution of a system of equations involving quadratic functions, required to calculate the values of the variables that satisfy both equations simultaneously.

Write down the equations in standard form.

A quadratic equation can be written in the form ax² + bx + c = 0, where a, b, and c are constants.

Similarly, a system of quadratic equations can be written in the form.

a₁x² + b₁x + c₁= 0

a₂x² + b₂ x + c₂ = 0

Rearrange one of the equations so that one of the variables is expressed in terms of the other.

Then substitute this expression into the other equation to obtain a single quadratic equation in one variable.

Solve the resulting quadratic equation using any of the available methods.

Such as factoring, completing the square, or using the quadratic formula.

Once you have found the values of the variables.

Substitute them back into one of the original equations to find the corresponding values of the other variables.

Check the solutions by plugging them into both equations and verifying that they satisfy both equations.

If the two equations do not have any real solutions, then the system has no real solutions.

If the two equations have infinitely many solutions, then the system is dependent.

And one of the equations is a multiple of the other.

Here, the solution set is given by the equation of the dependent line.

If the two equations have a unique solution, then the system is independent.

And the solution set is given by the coordinates of the intersection point of the two graphs.

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