A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.

Answer:

Option 1

Step-by-step explanation:

Find 2 numbers that multiply to give 16 and sum to give +8 :

These numbers are 4 and 4

Now split +8x into +4x and +4x and factor each part :

x²+4x+4x+16 = 0

x(x+4)+4(x+4) = 0

Keep 1 bracket and the terms outside the brackets make their own :

(x+4)(x+4) = 0

(x+4)²  = 0

Therefore answer will be Option 1

Hope this helped and have a good day

Answer:

Option A

Step-by-step explanation:

  In a arithmetic sequence, difference between any two consecutive term is constant.

  a₁ = 9  & d = 7

         t₁ = 9

         t₂ = a₁ + d

             = 9 + 7

             = 16

         t₃ = t₂ + d = 16+ 7

            = 23

        t₄ = t₃ + d

            = 23 + 7

            = 30

        t₅ = t₄ + d

           = 30 + 7

           = 37

9,16,23,30,37,.......

The equation which can be used to determine x, the number of players the team can bring to the

tournament is 1353 = 943.50 + 31.50x and x = 13 players

1353 = 943.50 + 31.50x

1353 - 943.50 = 31.50x

409.50 = 31.50x

x = 409.50 / 31.50

x = 13 players

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a) As the constants are equal, the situation represents a proportional relationship.

b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constants for each situation are:

k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.

Since the constants are equal, the situation represents a proportional relationship.

The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

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I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )

As per inequality, it means that the value of x can be less than or equal to y.

Inequality in Mathematics

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤, or ≥ are used to denote an inequality, when the two expressions aren't always equal.

Type of Inequality

The given expression, x <= y denotes the type of inequality where the possible values of x are either less than y or equal to less. The value of x cannot be greater than y in any case.

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The points are (7, 13/3).

Lets simplify the equation,

The equation of first line: y = 1/3 x + 2

the equation of second line: y= 4/3x - 5

Solve the system of equations by elimination,

Multiply equation A by -4 both sides

-4y = -4(1/3x +2)

-4y = -4/3x-8

After eliminating the equation we get,

y = 13/3

So now have to find x

13/3 = 1/3x + 2

Lets multiply above by 3
x = 13-6

x = 7.

Hence the points are (7, 13/3)

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Answer:

B

Step-by-step explanation:

What is the solution to the system of equations?

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

The percentage error of the given estimation is 17.7%.

The percentage error of any estimation is calculated as:

Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.

In the question,

The estimated value is given to be 40 marbles.

The actual value is given to be 34 marbles.

We are asked to find the percentage error of this estimation.

We know that:

Percentage error = {(|Actual Value - Estimated Value|)/Actual Value}*100%.

Substituting the values, we get:

Percentage error = {(|34 - 40|)/34}*100%,

or, Percentage error = 6/34*100%,

or, Percentage error = 17.6470 % = 17.7% (Rounding to the nearest tenth, that is, up to one decimal place).

Thus, the percentage error of the given estimation is 17.7%.

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Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

Answer:

49 different ways

Step-by-step explanation:

If there are seven roads that lead to the top, you have seven possible choices to go to the top of the hill.

Then, to come back to the start, you also have seven possible choices (seven roads), and you can pick any road.

So, if you have seven ways to go up and seven ways to go down, the number of different ways of going to the top and coming back is the product of these numbers of possible choices.

N(total) = N(up) * N(down)

N(total) = 7 * 7

N(total) = 49 different ways

Brainliest pls and tysm!

Answer:

0.0000000006

Step-by-step explanation:

0.6 * (0.1)^9 = 0.0000000006

Answer:

Step-by-step explanation:

B: 1, 16, 81

WHY?

Set A is perfect squares from A to 100:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100

Set A = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Set C is perfect fourths

1^4 = 1

2^4 = 16

3^4 = 81

4^4 = 254 (This is greater than 100)

Set C = 1, 16, 81

Hope this helps :)

The product of two numbers when doubled, the product of these larger numbers is 35,732

let

product of x and y = 8933

x × y = 8933

2x × 2y = 8933

4xy = 4(8933)

4xy = 35,732

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Answer: 22 ft

Step-by-step explanation:

Using the mean concept, the ratio of the number of female attendants to the number of male attendants was of 3.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem:

Hence:

[tex]\frac{1200f + 800m}{f + m} = 900[/tex]

1200f + 800m = 900f + 900m

100m = 300f

[tex]\frac{f}{m} = 3[/tex]

Hence the ratio was of 3.

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The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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The value of the indefinite integral is

Given:- The integration of   is given whose lower limit is  and upper limit is .

To Find:- We have to find the value of the integration of   is given whose lower limit is  and upper limit is .

By using the concept of indefinite integral it will be solved.

According to the problem,

Therefore, the value of the indefinite integral is .

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The are of the triangle is mathematically given as

a=62.4in^2. This is further explained below.

Generally, the equation for the area is  mathematically given as

a= 0.5(base X height)

Therefore

a= 0.5 (10.4 x 12)

a=62.4in^2

In conclusion, The area of the triangle is

a=62.4in^2

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Step-by-step explanation:

18z+10z+40z+5+1=360

68z+6=360

68z=360-6

68z=364

z≈5.353

Answer:

I am pretty sure that it is 625.

Answer:

Step-by-step explanation:

please make sure you indicate  whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

Option C

Kindly award branliest

Step-by-step explanation:

Tn = n(n + 1)

T1 = 1(1 +1) = 1(2) = 2

T2 = 2(2+1) = 2(3) =6

T3 = 3(3 + 1) = 3(4) = 12

T4 = 4(4 + 1) = 4(5) = 20

... It obeys

Answer:

A = -8

You're welcome! :)

Answer: a = -8

Step-by-step explanation:

Combine multiplied terms into a single fraction

then find a Find common denominator for the fraction

then Combine fractions with common denominator,

Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,

Multiply the numbers making your equation like this -5a+10=50

subtract 10 by both sides and then you will need to simplify making it

-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8  

The  kind of statistical study the zoologist conducted was D. observational study.

An observational study  serves as a study  whereby the researcher simply observes the subjects without interfering with it.

This is different from carrying out experiment on them or just a theoretical approach.

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CHECK THE COMPLETE QUESTION BELOW:

A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study

Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:

The following identity is used, considering an angle [tex]\theta[/tex].

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem we are given the sine, then the cosine can be found as follows:

[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]

[tex]\cos^2{\theta} = \frac{39}{64}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]

In the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].

The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]

The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]

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Answer:

  2.0 km

Step-by-step explanation:

The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.

The law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Using the given values, we have ...

  c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)

Simplifying the equation, we get ...

  c² = 37.89 -37.8cos(26°) ≈ 3.91559

  c ≈ 1.979 . . . . km

The width of the strait is about 2.0 km.

Using the Factor Theorem to find the function, the correct statement is:

The function is positive on (0,∞).

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

The described roots means that:

[tex]x_1 = 0, x_2 = x_3 = x_4 = x_5 = 2[/tex]

Hence the function is:

f(x) = x(x - 2)^4

(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:

The function is positive on (0,∞).

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