A toy rocket is launched from a platform 42 feet above the ground at a speed of 91 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 91t + 42, where t is the time in seconds. How high will the rocket be after 3 seconds? HELP ASAP!!

A. 122 feetB. 218 feetC. 93 feetD. 2570 feet

Answer:

(8,4)

Step-by-step explanation:

yes

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.

For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.

Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.

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Final Answer:

The point (0,0) does not satisfy the inequality [tex]y ≥ x^2[/tex] + x - 4, as 0 is not greater than or equal to -4. Additionally, it does not satisfy [tex]y > x^2 + 2x + 1[/tex], as 0 is not greater than 1. Therefore, (0,0) does not meet the conditions of the system of inequalities.

Step-by-step explanation:

The point (0,0) is not a solution to the given system of inequalities. First, considering the inequality [tex]y ≥ x^2 + x - 4[/tex], when substituting x=0 and y=0 into the equation, we find that 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the conditions of the first inequality. Moving on to the second inequality, [tex]y > x^2 + 2x + 1[/tex], substituting x=0 and y=0 results in 0 not being greater than 1.

Consequently, (0,0) fails to meet the requirements of the second inequality as well. In summary, the point (0,0) does not simultaneously satisfy both inequalities, rendering it unsuitable as a solution to the system.

Analyzing solutions to systems of inequalities involves evaluating each inequality independently to ensure the chosen point satisfies all conditions. In this instance, the failure of (0,0) to satisfy either inequality demonstrates that it does not conform to the system's criteria. When dealing with systems of inequalities, it is essential to carefully assess each component to accurately determine the solution set.

No, (0,0) is not a solution to the given system.

The system consists of two inequalities: y ≥ x^2 + x - 4 and y > x^2 + 2x + 1. To check whether (0,0) is a solution, substitute x = 0 and y = 0 into both inequalities. For the first inequality, x^2 + x - 4 becomes -4, and 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the first inequality. Moving on to the second inequality, x^2 + 2x + 1 becomes 1, and 0 is not greater than 1. Hence, (0,0) fails to satisfy the second inequality as well. As a result, (0,0) is not a solution to the system of inequalities.

In summary, by substituting the coordinates of (0,0) into both inequalities, we find that the point does not meet the conditions set by either inequality. Therefore, (0,0) is not a solution to the system. This conclusion is based on the specific values obtained through substitution, demonstrating that the coordinates do not satisfy the given inequalities.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For any triangle, the sum of the measures of the three interior angles is always 180 degrees. An exterior angle is formed by extending one side of the triangle. The sum of the measures of the exterior angle and its corresponding remote interior angles is always 180 degrees. Therefore, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.

Final answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

Explanation:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For example, if one of the remote interior angles of a triangle measures 40 degrees, then the corresponding exterior angle measures 40 degrees as well. The sum of the measures of the other two interior angles would be 140 degrees, making the exterior angle equal to 40 degrees.

Therefore, the correct option that completes the statement is equal to.

The correct answer is:

A=4

B=5

hopes this helps you and future people!

Answer:

a = 4 and b = 5

Step-by-step explanation:

The simplest form of square root of eighty can be written as:

[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]

Now as it is a square root function, we will pair up the four 2's in two pairs.

And will take out [tex]2\times2[/tex] outside the square root.

Making the answer = [tex]2\times2\sqrt{5}[/tex]

or [tex]4\sqrt{5}[/tex]

So, a = 4

and b = 5

ok so original perimeter = 12 +12 + 17 +17 = 58 mm

if dimensions are multiplied by 12:

12*12 = 144 and 17*12 = 204

 new perimeter = 144 +144 +204 +204 = 696 mm

696 / 58 = 12

so the perimeter increased by a factor of 12, answer is A

Answer:

The perimeter is increased by a factor of 12.

Option (a) is correct .

Step-by-step explanation:

Formula

Perimeter of a rectangle = 2 (Length + Breadth)

As given

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

Perimeter of a rectangle = 2 × (12 + 17)

                                         = 2 × 29

                                         = 58 millimeters ²

As given

when the dimensions are multiplied by 12 .

New Length = 12 × 12

                    = 144 millimeter

New Breadth = 17 × 12

                      = 204 millimeter

Thus

New Perimeter of a rectangle = 2 × (144 + 204)

                                         =  2 × 348

                                         = 696 millimeter²

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]

Therefore the perimeter is increased by a factor of 12.

Option (a) is correct .

Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then. 

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute.

Let w be the quarts of water left in the tub.

Let t be the time in minutes.

So, the equation to model this situation is :

Modelling equation: [tex]w=50-2.5t[/tex]

This equation is viable only up to when t is 20 minutes. That will give w = 0. More than 20 minutes is not possible.

Answer:

The land should be recorded in the purchaser's books at : $153,000.

Step-by-step explanation:

Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.

Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.

The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.

To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.

Final answer:

The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.

Explanation:

The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.

Steps to find the nonpermissible value:

Identify the denominator of the expression, which is (Y-3).

Set the denominator equal to zero: Y - 3 = 0.

Solve for y: Y = 3.

Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.