Which of the following values are solutions to the inequality −6≤1+3x?

The fireworks take 3 seconds to reach their maximum height, and the maximum height reached is 224 feet.

a) The time it takes for the fireworks to reach their maximum height can be determined by finding the time at which the vertical velocity becomes zero. In the given equation, h = -16t² + 96t + 80, the term with t represents the vertical velocity. By taking the derivative of h with respect to t and setting it equal to zero, we can find the time at which the vertical velocity is zero.

Taking the derivative of h, we get:

h' = -32t + 96

Setting h' = 0, we can solve for t:

-32t + 96 = 0

-32t = -96

t = 3

Therefore, it takes 3 seconds for the fireworks to reach their maximum height.

b) To find the maximum height reached by the fireworks, we can substitute the value of t = 3 into the equation for h and solve for h.

h = -16t² + 96t + 80

h = -16(3)² + 96(3) + 80

h = -144 + 288 + 80

h = 224

The maximum height reached by the fireworks is 224 feet.

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The instantaneous rate of change of a function is the derivative of the function at a specific point. The average rate of change of a function on an interval is the difference between the values of the function at the endpoints of the interval divided by the length of the interval. We can use these definitions to find the points where the instantaneous rate of change of f equals the average rate of change of f on the interval [0, sqrt(pi)].

First, we need to find the derivative of f(x). Using the Fundamental Theorem of Calculus, we get:
f'(x) = 2x  sin(x^2)

Next, we need to find the average rate of change of f on the interval [0, sqrt(pi)]. This is given by:
average rate of change = (f(sqrt(pi)) - f(0)) / (sqrt(pi) - 0) = (sin(pi^2) - sin(0)) / sqrt(pi) = 0 / sqrt(pi) = 0

Now we need to find the points where the instantaneous rate of change of f equals the average rate of change of f.

This means we need to solve the equation:

2x sin(x^2) = 0

This equation has two solutions: x = 0 and x = sqrt(pi/2). However, only the second solution is in the closed interval [0, sqrt(pi)]. Therefore, there is only one point in the closed interval [0, sqrt(pi)] where the instantaneous rate of change of f equals the average rate of change of f.

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Therefore the solution of the given problem is  product of the equation is 3\(x^{3}\) + 12x.

The equals sign (=) must appear in an equation. You can think of an equation as having a left and a right side since there will be a mathematical expression on either side of it. Consider an equation to be a set of scales. Although you can use different amounts on either side, for it to be solved, each side must be equally balanced .An unknown will always be present in an algebraic equation. This is symbolized by a symbol, such x, y, or z.

Here,

We must calculate the product of 3x(\(x^{2}\) + 4).

In light of the query

Follow all of the instructions listed below to obtain the equation's product.

Equation; 3x(\(x^{2}\) + 4).

Then,

The product of the equation is,

=>3x(\(x^{2}\) + 4).

=>3\(x^{3}\) + 12x

Therefore the solution of the given problem is  product of the equation is 3\(x^{3}\) + 12x.

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Answer:

Step-by-step explanation:

x^2 + 4x - 5 = 0

-4/2 + (sqrt(16 - 4(1)(-5)))/2

-2 + (sqrt(16+20)/2

-2 + (sqrt(36)/2

-2 + 6/2

-2 + 3

-2 + 3 = 1

-2 - 3 = -5

The exponential function y = 990(0.95) represents exponential decay with a 5% decrease per unit increase in x.

The given exponential function is y = 990(0.95). To determine whether it represents growth or decay, we need to examine the base of the exponent, which is 0.95 in this case.

When the base of an exponential function is between 0 and 1, such as 0.95, it represents exponential decay. This means that as x increases, the corresponding y-values decrease exponentially.

To calculate the percentage rate of decrease, we can compare the base (0.95) to 1. A decrease from 1 to 0.95 represents a difference of 0.05. To convert this difference into a percentage, we multiply by 100.

Percentage rate of decrease = 0.05 * 100 = 5%

Therefore, the given exponential function y = 990(0.95) represents exponential decay with a rate of 5% decrease per unit increase in x. This implies that for each unit increase in x, the y-value will decrease by 5% of its previous value.

It's important to note that the rate of decrease remains constant throughout the function. As x increases, the value of y will continue to decrease by 5% with each unit increase.

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Answer:

There are 11 pigs and 17 chickens.

Step-by-step explanation:

Lets let

p = number of pigs

c = number of chickens

Assuming each animal has only one head, then

p + c = 28

And assuming that pigs have four feet and chickens have two feet:

pig feet = 4p

that is, 4 feet for each pig, and



chicken feet = 2c

right? two feet per chicken.



All the feet are:

4p + 2c = 78

Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.

Multiply p+c=28 times -2.

-2p + -2c = -56

then add the whole equation to the other equation. Do this adding vertically, from top to bottom.

-2p + -2c = -56

4p + 2c = 78

_____________

2p = 22

Divide by 2 to solve

p = 11

There are 11 pigs.

Remember,

p + c = 28

11 + c = 28

subtract 11

c = 17

There are 17 chickens.

The value of angle A and B are 60° and 120° respectively.

It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.

Therefore A = D

B = C

When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:

ABK = 30°

Also, KBC = 90°

Therefore, B = 30° + 90° = 120°

A = D = 180° - 120° = 60°

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Complete question:

Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4

Find: mA and mB.

Answer:

X = 12

Step-by-step explanation:

8(12) = 96

Given the fraction,

The required mixed number is,

Answer:

the answer to the second one is c im pretty sure

Step-by-step explanation:

Answer:

x= 38

y= 71

Step-by-step explanation:

The triangle shown in the figure is an isosceles triangle, a triangle having two sides equal.

The two sides marked with a "dash" are said to be equal.

If we label off the triangle as ABC with AD being the extended length (containing 108°).

We'll get,

AB = AC

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

*Property*

"If two sides of a triangle are equal their corresponding base angles are equal too."

=> ∠BAC = ∠BCA . . . . (¡)

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

From the figure, ∠BCA is equal to y.

*Property*

"Two angles on a straight line sum up to 180°"

∠BAC can be found out by subtracting 109° from the straight angle (180°).

=> ∠BAC = 180 - 109

=> ∠BAC = 71°

Substituting these values in eqn. (¡):

71 = y

Hence, the value of y is 71°

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

*Property*

"The exterior angle(angle on the extended side) of a triangle is equal to the sum of it's interior opposite angles."

Here,

=> 109 = x + 71

=> 109 - 71 = x

=> x = 38°

Hence, the value of x is 38°.

The lines y = 2 and x = 4 are neither parallel nor perpendicular.

The given lines are y = 2 and x = 4.

The line y = 2 is a horizontal line because the value of y remains constant at 2, regardless of the value of x. This means that all points on the line have the same y-coordinate.

On the other hand, the line x = 4 is a vertical line because the value of x remains constant at 4, regardless of the value of y. This means that all points on the line have the same x-coordinate.

Since the slope of a horizontal line is 0 and the slope of a vertical line is undefined, we can determine that the slopes of these lines are not equal. Therefore, the lines y = 2 and x = 4 are neither parallel nor perpendicular.

Parallel lines have the same slope, indicating that they maintain a consistent distance from each other and never intersect. Perpendicular lines have slopes that are negative reciprocals of each other, forming right angles when they intersect.

In this case, the line y = 2 is parallel to the x-axis and the line x = 4 is parallel to the y-axis. Since the x-axis and y-axis are perpendicular to each other, we might intuitively think that these lines are perpendicular. However, perpendicularity is based on the slopes of the lines, and in this case, the slopes are undefined and 0, which are not negative reciprocals.

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Answer

23 computer

Step-by-step explanation:

if he sold 20 computers he would make 2100 which then he would need 240 more dollars to reach his goal and to find the answer you would then divide 240 by 80.

Answer:

Where is the list?

Step-by-step explanation:

The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

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We are expected to land on each color 20 times in 180 spins

Probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

probability of landing any color on any given attempt is 1/9 or 0.11, since all colors are different,  the probability for each is the same.

if you multiply the probability by 180 you will find the amount of time you will expect to land on each color

Hence, 1/9 x 180 = 20times

Hence are expected to land on each color 20 times in 180 spins

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The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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9514 1404 393

Answer:

  150

Step-by-step explanation:

The increase is by the factor 5/3, so the increased number is ...

  90×(5/3) = 150

90 increased in the ratio 5 : 3 is 150.

The front view of the figure is figure A.

Normal surfaces exist surfaces that stand at 90° to each other.

Hidden lines exist utilized to display surfaces that stand not directly visible. All surfaces must be displayed in all sights. If an edge or surface exists obstructed from sight by another feature, it stands drawn utilizing a hidden line.

The front view of the figure is figure A.

Therefore, the correct answer is option A.

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The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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Answer:

Devante is 23 and Savannah is 32.

Step-by-step explanation:

We can set up a system of equations.

s - savannah's age

d - devante's age

s = d + 9

s + d = 53

Now we can substitute (d + 9) for s in the second equation.

(d + 9) + d = 53

2d + 9 = 53

2d = 46

d = 23

To find Savannah's age, we just add 9 to Devante's age. (plugging in 23 for d)

23 + 9 = 32

s = 32

Answer:

a) 646 truck loads

b) $36, 430

Step-by-step explanation:

Since we need to transport 4520 tons of cement and each mixer can carry 7 tons, the total number of loads = 4520 / 7 =645.71 rounded up to 646 loads (Answer a)

b) The first 30 truck loads will cost $85 per load so total cost = 85 x 30 = $ 2,550

The remaining (646-30) truck loads cost $55 per load so cost for the remaining tuck loads after the first 30 = (646-30) x 55 = 616 x 55 = $33,880

Total cost = 33,880 + 2,550 = $36, 430

The kinetic energy will the ball acquire from the bat is 2× 10² J

According to the question

Bat stays in contact for 5.0 X 10⁻³ and the ball travels at a speed of 2.0 X 10⁴.

An object's kinetic energy is the power it has as a result of motion. It is explained as the amount of effort required to move a mass-based body from rest to the indicated velocity.

The body keeps its kinetic energy, which it acquired during acceleration, unless its speed changes.

A mass m object moving at a speed v has kinetic energy 1/2 mv² according to classical mechanics.

Favg= -1/2 MV²

K= -1 2 ( 5.0 x 10⁻³)²

K = - 1/2 ×25 × 10⁻⁶

K = 2× 10² J

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Answer:

1.3c - 10

Step-by-step explanation:

( 5.2c - 7.35 ) + ( - 3.9c + 2.65 )

= ( 5.2c - 7.35 ) - ( 3.9c + 2.65 )

= 5.2c - 7.35 - 3.9c + 2.65

= 5.2c - 3.9c - 7.35 + 2.65

= 1.3c - 10

1. make the + and - sign become only one, which will be - as when + and -, it will be -

2. take out the values from their brackets

3. arrange the values so like terms with the like terms, and in this case c and c, constant with constant

4. solve the equation and you will get the answer

Answer:

The old apple revels in its authority.

Answer: D: x/2 = 45; x = 90

Step-by-step explanation:

half of a number is 45:

x/2 = 45

.: x = 90

Your answer is D

Answer:

D

Step-by-step explanation:

The probability of winning the Mega Millions jackpot is 1 in 258,890,850. We can see that the probability of winning the Mega Millions jackpot is much smaller than in probability of being struck by lightning in a year

To win the Mega Millions jackpot, you need to correctly select 5 different numbers from a pool of 75 numbers, and one additional number from a pool of 15 numbers. The total number of possible combinations is given by the product of the number of combinations for each drawing, which is (75 choose 5) * 15 = 258,890,850.

Comparing this probability to the probability of being struck by lightning in a year, which is estimated to be 1/960,000 by the National Weather Service, we can see that the probability of winning the Mega Millions jackpot is much smaller. In fact, it is more than 270 times smaller than the probability of being struck by lightning in a year.

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