2b (squared) + 3b (squared) - 3b

Answer:

The equation gives only the total vertical distance traveled by the firework or maximum height reached by the firework

Step-by-step explanation:

Given;

A function that models the fireworks vertical distance with no respect to time,x, as;

f(x)=-16x^+96x+112

The equation gives only the total vertical distance traveled by the firework, it does not account for the position of the firework at a particular time.

Thus, with the given function we can only estimate the maximum height reached by the firework.

Answer:

um 8??

Step-by-step explanation:

According to the question we have the correct option is "f(x) = x² + 2". the correct option is D) . The following functions are even functions:x² - 5 x² + 2 Even functions are those functions in which f(-x) = f(x).

The following functions are even functions:

x² - 5 x² + 2. Even functions are those functions in which f(-x) = f(x).

It means, if the value of x is changed to -x, and if the new function is the same as the original function, then that function is said to be an even function.

For example, take f(x) = x² + 2.

Therefore, f(-x) = (-x)² + 2. = x² + 2.

Hence, the function is even and the answer is "f(x) = x² + 2" alone.

Therefore, the correct option is "f(x) = x² + 2".

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The slope of the passing line through the origin is 112.5°.

The slope of a line is given as a tangent ratio.

In this case we have the angle, so the slope would be given as

      tan(7π/8).

Therefore,

The angle the line makes with the horizontal is given in radians here:

                     7π/8

In this degrees, we can use:

180° = π radians

1 radian = 180°/π

5π/8 radians = 5π/8 × 180° /π

                     =5π/8 × 180°/π

                     =112.5°

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Answer:

20

Step-by-step explanation:

Answer: The answer is option C: $17,925.00.

Step-by-step explanation: Using the simple interest formula:

I = Prt

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We can find the interest earned over the 6 years:

I = P * r * t = $15,000 * 0.0325 * 6 = $2,925

Adding the interest to the principal, we get the balance at the end of the 6 years:

Balance = Principal + Interest = $15,000 + $2,925 = $17,925

Therefore, the answer is option C: $17,925.00.

Answer:

The slope is \(\frac{5}{2}\) (5/2)

Step-by-step explanation:

Key skills needed: Subtraction, Division, Slope Formula

1) So to find the slope here, we use the slope formula.

Given 2 points \((x_1, y_1)\) and \((x_2, y_2)\)

To find the slope you do: \(\frac{y_2-y_1}{x_2-x_1}\)

2) So in this case, the 2 points are (-1,-2) and (1,3)

3) We can use the slope formula to find the slope

Now we do \(\frac{y_2-y_1}{x_2-x_1}\)

This would be: \(\frac{3-(-2)}{1-(-1)}\)

If you are subtracting -2, that means you add 2. If you are subtracting -1, then that means you add 1.

This means ---> \(\frac{3+2}{1+1}\)

3+2 is 5, and 1+1 is 2 so your slope would be \(\frac{5}{2}\) (5/2)

Hope you understood and have a nice day!! :D

Answer:

+2

Step-by-step explanation:

The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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Answer:

20/21

Step-by-step explanation:

40 /42  =  20 /21

(Decimal: 0.952381)

The round-off errors when measuring the distance that a long jumper has jumped are uniformly distributed between 0 and 5.8 mm.

To round values to 4 decimal places, we need to consider the range of possible values between 0 and 5.8 mm.

When rounding a measurement, we look at the digit in the fifth decimal place. If it is 5 or greater, we round up the fourth decimal place. If it is less than 5, we keep the fourth decimal place as it is.

Let's consider some examples to better understand this process:

1. If the measured distance is 2.3457 mm, the digit in the fifth decimal place is 7, which is greater than 5. Therefore, we round up the fourth decimal place to 2.3458 mm.

2. If the measured distance is 4.9999 mm, the digit in the fifth decimal place is 9, which is greater than 5. Again, we round up the fourth decimal place to 5.0000 mm.

3. If the measured distance is 3.2142 mm, the digit in the fifth decimal place is 2, which is less than 5. In this case, we keep the fourth decimal place as it is, resulting in 3.2142 mm.

By following this rounding process, we can round off the measured distances to 4 decimal places, taking into account the uniformly distributed round-off errors between 0 and 5.8 mm.

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

The probability that the cycle time exceeds 65 minutes given that it exceeds 55 minutes is 1/3.

To solve this problem, we can use conditional probability. We know that the cycle time for trucks hauling concrete is uniformly distributed between 50 to 70 minutes. Let X be the cycle time in minutes.

So, P(X > 65 | X > 55) = P(X > 65 and X > 55) / P(X > 55)

We can simplify the numerator as P(X > 65 and X > 55) = P(X > 65) since if X is greater than 65, it is also greater than 55. Using the formula for the uniform distribution, we get:

P(X > 65) = (70 - 65) / (70 - 50) = 1/4

Similarly, we can calculate the probability of X being greater than 55:

P(X > 55) = (70 - 55) / (70 - 50) = 3/4

Putting these values in the conditional probability formula, we get:

P(X > 65 | X > 55) = (1/4) / (3/4) = 1/3

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Answer:

Step-by-step explanation:

Consider the rule  

C

−

A

−

S

−

T

or All Slow Turtles Crawl for this type of problem.

Both of these rules indicate in which quadrant the trigonometric function is positive. In all quadrants except the first, only 1 out of the three trigonometric functions are positive; the other two are negative.

Quadrant 1: All are positive

Quadrant 2: Sine is positive

Quadrant 3: Tangent is positive

Quadrant 4: Cosine is positive

The acronym and the expression mentioned above are meant to facilitate your ability to remember these. Beware, though that C-A-S-T starts in the 4th quadrant and then goes to the 1st, 2nd and finally the 3rd, while "All Slow Turtles Crawl# goes from 1st to 4th.

Now, back to the problem at hand.

If cosine is positive, then we are already limited to 2 quadrants: IV and I. However, in quadrant I, all the functions are positive, and the problem says that sin is negative in this case. This leaves us one option: quadrant IV.

Answer:

-258

Step-by-step explanation:

Answer:

the length of RS to the nearest tenth of a foot is 240.6ft

Answer:

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

x =  − 2  −  ln ( 6 )/ ln ( 4 )

Decimal Form:

x = −3.29248125 …

Hope this helps!

Answer: y = 5x + 70

Step-by-step explanation:

The equation t + 14 = 5 simplifies to t = -9. Therefore, the rescue center needs 9 more terrariums.

To solve the equation t + 1 + 3 + 5 + 5 = 5, we need to add up the number of terrariums needed for each pixie frog and set it equal to the total number of terrariums available.

t + 1 + 3 + 5 + 5 = 5

Simplifying the left side, we get:

t + 14 = 5

Subtracting 14 from both sides, we get:

t = -9

Since we cannot have a negative number of terrariums, this means that the rescue center needs 9 more terrariums.

To verify this answer using substitution, we can replace t with 9 and see if the equation holds true:

9 + 1 + 3 + 5 + 5 = 23

Since the total number of terrariums needed is 23 and the rescue center only has 3, this verifies that they need 9 more terrariums.

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Complete question:

An animal rescue group in Africa is taking care of 5 injured baby pixie frogs. They plan to release them back into the wild when they are healthy. Each pixie frog needs its own terrarium. One of the rescue volunteers checks and sees that there are only 3 terrariums. Solve the equation t 1 3 5 5 to find how many more terrariums, t, the rescue center needs. How many more terrariums does the rescue center need? How can you use substitution to verify that your answer is correct?

d. The sum of a Rational number and

Irrational number is always Irrational

y=-2x(squared)+3x-7

the 2x is squared

hope that helped

Answer:

0.45 miles per minute and 6.75

Step-by-step explanation:

27/60=0.45<-- Miles per minute

0.45x15=6.75<--Miles in 15 minutes

Hope this helps pls give brainliest

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

The points are given as (10, 1) and (9, -4)

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is calculated as

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have

d = √[(10 - 9)^2 + (1 + 5)^2]

Evaluate

d = √37

Hence, the exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

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In the given boundary-value problem, we are asked to set up the set of equations required to solve the problem using the finite difference method. The equation is y" = 2x²y + xy + 2, and we are given the boundary conditions y(1) = -1 and y(4) = 4.

To solve the problem using the finite difference method, we can approximate the second derivative y" using the central difference formula: y" ≈ (yₙ₊₁ - 2yₙ + yₙ₋₁) / h². Substituting this approximation into the original differential equation, we obtain the finite difference equation: (yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2.

For the given boundary conditions, y(1) = -1 and y(4) = 4, we can use these values to form additional equations. At x₀ = 1, we have the equation y₀ = -1. At xₙ = 4, we have the equation yₙ = 4.

In summary, the set of equations required to solve the boundary-value problem by the finite difference method, with the given boundary conditions, would be:

(y₂ - 2y₁ + y₀) / h² = 2x₁²y₁ + x₁y₁ + 2,

(y₃ - 2y₂ + y₁) / h² = 2x₂²y₂ + x₂y₂ + 2,

...

(yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2,

y₀ = -1,

yₙ = 4.

These equations form a system of equations that can be solved numerically to obtain the solution to the boundary-value problem.

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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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