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Answer:

y= 1

3(3) - 5(1) = 4

9 - 5 = 4

5(3) + 1 = 16

15 + 1 = 16

Answer:

please see photo belowabove for detailed explanation

Step-by-step explanation:

The maximum height reached by the object is 12.5 feet.

The vertex of a parabola is the point where the curve changes direction, and is located at the minimum or maximum point of the quadratic equation. If the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents a minimum value. If the coefficient is negative, the parabola opens downwards and the vertex represents a maximum value.

To find the maximum height reached by the object, we need to find the vertex of the parabola.

The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x² term, and b is the coefficient of the x term in the quadratic equation that represents the parabola.

In this case, the equation is of the form y = ax² + bx + c, where y is the height and x is the time. Using the given coordinates, we can set up a system of equations to solve for a, b, and c:

0 = a(1)² + b(1) + c

16 = a(5)² + b(5) + c

0 = a(9)² + b(9) + c

Simplifying each equation, we get:

a + b + c = 0

25a + 5b + c = 16

81a + 9b + c = 0

Solving for c in the first equation, we get c = -a - b. Substituting this into the other two equations, we get:

25a + 5b - a - b = 16

81a + 9b - a - b = 0

Simplifying these equations, we get:

24a + 4b = 16

80a + 8b = 0

Solving for b in the second equation, we get b = -10a. Substituting this into the first equation, we get:

24a + 4(-10a) = 16

4a = 2

a = 1/2

Substituting this value of a into the equation b = -10a, we get b = -5. Finally, substituting a, b, and c = -a - b into the equation for the x-coordinate of the vertex, we get:

x = -b/2a = 5

So the maximum height is achieved at time x = 5, which corresponds to a height of:

y = ax² + bx + c = (1/2)(5)² - 5(5) = -12.5

However, we are looking for the maximum height, so we take the absolute value of this result, which gives:

|y| = 12.5

Therefore, the maximum height reached by the object is 12.5 feet.

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Probability of each case given in the problem will be 0.3327, 0.1033, 0.0922, 0.3367 respectively.

The probability of an occurrence is an indicator of its likelihood. It is most frequently described as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates assurance.

If an event has a higher probability, it is more likely to happen. One can use various mathematical methods or, depending on the situation, divide the number of favourable possibilities by the total number of potential outcomes to calculate the likelihood of an event.

Now for given cases in the problem,

21. Chances that both pupils will enrol in art: divided by the total number of ways there are to select two students from the full group of 50 students, the number of ways to select two students from the 24 art students is equal to= [tex]^{24}C_2 / ^{50}C_2=(\frac{24!}{22!.2!})/(\frac{50!}{48!.2!} )= \frac{24*23}{2} /\frac{50*49}{2} =0.3327[/tex]

22. Chance that both pupils would study music and art: the number of options there are to select two students from the 16 students who are studying both art and music divided by the total number of methods there are to select two students from the 50 students.= [tex]^{16}C_2 / ^{50}C_2=(\frac{16!}{14!.2!})/(\frac{50!}{48!.2!} )=\frac{16*15}{2} /\frac{50*49}{2} =0.1033[/tex]

23. Probability that both students take music but not art is calculated by dividing the total number of possibilities there are to select two students from the 50 students by the number of students in the group of 14 who only take music= [tex]^{14}C_2 / ^{50}C_2=(\frac{14!}{12!.2!})/(\frac{50!}{48!.2!} )= \frac{14*13}{2} /\frac{50*49}{2} =0.0922[/tex]

24. The likelihood that neither student studies music is determined by the number of ways there are to select two students from the 26 students who do not study music divided by the total number of ways there are to select two students from the complete group of 50 students. = [tex]^{26}C_2 / ^{50}C_2= (\frac{26!}{24!.2!})/(\frac{50!}{48!.2!})=\frac{26*25}{2} /\frac{50*49}{2} = 0.3367[/tex]

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Answer:

Exponential

Step-by-step explanation:

From the table :

Hence, the function is :

As the x-value is an exponential value, the function is exponential

Is the function represented by the following table linear, quadratic or exponential?

Linear

Quadratic

Explanation:

Answer:

B. Square the number of the term, n

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

4^2=16

5^2=25

etc.

The magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5

An equation is an expression that shows the relationship between two or more variables and numbers.

The magnitude, m, of an earthquake is:

m = log (I/S)

Where I is the intensity of the earthquake and S is the intensity of a "standard" earthquake. Hence, for an earthquake that is 35 times more intense than a standard earthquake:

m = log (35S / S) = log (35) = 1.5

The magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5

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Answer:

Step-by-step explanation:

[tex]9^{15} = 3^{30} = 205891132094649[/tex]

Step-by-step explanation:

Prob. of at least one heart when drawing 5 cards from a full deck

= 1 - prob(no hearts at all)

= 1 - C(39,5) / C(52,5)

= .7785

Answer: Book has 130 Pages, pages left 52

Step-by-step explanation:

If 3/5 = 78 pages

5/5 = 78/3 ×5/1 = 390/ 3 = 130 pages

Pages left is 130- 78 = 52 Pages

The solution to the given question will be:-

A) If a number, n, divided by 8 equals 2.5, what is n: n = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n: n = 6.35

C) Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy: 9 years

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

A) If a number, n, divided by 8 equals 2.5, what is n?

n / 8 = 2.5

n = 8 x 2.5 = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n?

n  + 6.05 = 12.4

n = 12.4 - 6.05 = 6.35

C)  Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy?

(1 / 4) M[tex]_{age}[/tex] = S[tex]_{age}[/tex]

S[tex]_{age}[/tex]  =  ( 36 / 4)

S[tex]_{age}[/tex]  =  9 years

Therfore the answers are n = 20 ,n = 6.35, S[tex]_{age}[/tex]  =  9 years

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Answer:

x-5y

Step-by-step explanation:

combine the X's and Y's

Answer:

c

Step-by-step explanation:

the ratio is 2/8.

2/8 = 1/4.

a)

8/20 = 2/5 is NOT equal to 1/4.

b)

12/45 = 4/15 is NOT equal to 1/4

c)

6/24 = 1/4 perfect

d)

2/40 = 1/20 is NOT equal to 1/4

The area of the square with the sides 2 1/2 cm will be A=6.25 square cm.

The space covered by the square in the two-dimensional plane will be the area of the square. Square actually covers the area with four equal sides.

The formula for the area of the square will be given as:-

A=Side x Side

A= 2 1/2 x2 1/2

A=5/2x5/2

A=2.5x2.5

A= 6.25 square cm

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Answer:

9 miles

Divide by 1.6

∠JML is a right angle. The correct option is your third option- right

There are different types of angles which include

In the given diagram, we can observe that ∠JML equals 90°

Hence, ∠JML is a right angle. The correct option is your third option- right

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Answer:

50%

Step-by-step explanation:

1 / 2 = 0.5

to turn a decimal to a percent you multiply it by 100

0.5 x 100 = 50%

Answer: The cost of one sweatshirt is $12 and the cost of one short is $14

Step-by-step explanation:

x= sweat shirt cost

y= shorts cost

4x + 10y = 188

9x+2y=276

x= 12, y=14

Answer:

16 and 5

Step-by-step explanation:

Hope that helps! :)

Answer:

71%

Step-by-step explanation:

Here´s how I do average scores

68 to 90

the difference in the numbers is =

90 - 68 (just a tip, subtract the highest number from the lowest number) =

22/2 will give you 11 and the reason I do this is to compare all the other numbers

11 + 68 or 90 - 11 =

79

72 to 85

85 - 72

13/2 = 6.5

72 + 6.5 or 85 - 6.5

78.5

since grades are rounded to the nearest tenth

79 - 79

79%

so he needs a 75% average to pass

79 - 75 = 4

75 - 4 = 71

The minimum score is 71%

Answer:

3.

Step-by-step explanation:

If there were 20 hats, and 4 of them were fedoras, we can conclude that 1/5 of the sent hats are going to be fedoras.

If there are 15 hats, we multiply 15 by 1/5 to get 3.

Hope this helps!

Answer:

bread

Step-by-step explanation:

If you get bad grades study  :v

Answer:

11 and -11

Step-by-step explanation:

This problem can really only be solved either by way of a calculator or simple memorization. In this case, the product (121) is a perfect square root, meaning it has a whole number answer. One square root of 121 is 11. The second square root of 121 is -11.

[tex]\sqrt{121} = 11[/tex]

[tex]\sqrt{121} = -11[/tex]

You can check your work by squaring your answer and seeing whether it equals the product. Remember, a negative number times another negative number results in a positive answer.

[tex]11^{2} = 121[/tex]

[tex]-11^{2} = 121[/tex]

The two square roots of the number 121 are 11 and -11.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of 121, the square root represents the number that, when multiplied by itself, equals 121.

The two square roots of 121 are 11 and -11 because both 11 and -11, when squared, result in 121.

When we calculate 11 × 11, we get 121.

So, 11 is one of the square roots of 121.

Similarly, when we calculate (-11) × (-11), we also get 121. So, -11 is also a square root of 121.

Therefore, the two square roots of 121 are 11 and -11.

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Answer:

0

Step-by-step explanation:

because they are heading in the same direction

Using an inverse rule of three, it is found that Bobby needs to call 18 more people.

This question is solved by proportions, applying a rule of three.The number of people working and the time needed to complete the work are inversely proportional, as more people means less time, thus, instead of cross multiplication, we multiply the lines, which is an inverse rule of three.When Bobby's parents call, with 9 people, they will need 6 hours to finish the job. How many people are needed to finish the job in 2 hours?

The rule of three is:

9 people - 6 hours

x people - 2 hours.

Multiplying by line:

2x  =  6  x  9

x   =   3  x   9

x    =  27

Already has 9 people, in total needs 97, so he needs to call 27 - 9 = 18 more people.

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Based on the calculations, the equation of this line in standard form is equal to 6x - 11y = 13.

Given the following data:

Mathematically, the equation of a line in standard form is given by this formula:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the slope of this line:

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\\\\Slope = \frac{-1\;-\;2}{-4\;-\;1.5}\\\\Slope = \frac{-3}{-5.5}[/tex]

Slope = 6/11.

For the equation of this line, we have:

y - 2) = 6/11(x - 3/2)

y - 2 = 6x/11 - 9/11

11y - 22 = 6x - 9

6x - 11y = -9 + 22

6x - 11y = 13.

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Complete Question:

What is the equation of this line in standard form (1 1/2, 2) (-4, -1)?

The solution to the trigonometry identity is -sin^2(x) + sin(x) + 1 = -sin(x)

In trigonometry functions, the cosecant(csc) appears to be the reciprocal of the sine function.

Given that:

[tex]\mathbf{1- \dfrac{sin^2(x)}{1}+sin(x)=\dfrac{-1}{csc(x)}}[/tex]

[tex]\mathbf{- \dfrac{sin^2(x)}{1}+sin(x)=\dfrac{-1}{csc(x)}}[/tex]

[tex]\mathbf{- \dfrac{sin^2(x)}{2}+sin(x)+ \dfrac{cos^2x}{2}+\dfrac{1}{2}=-sin(x)}[/tex]

[tex]\mathbf{- sin^2(x)+sin(x)+1 = -sin (x)}[/tex]

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Answer:

D. 39

Step-by-step explanation:

1. Anytime you see x, replace it with 3: [tex]3^3+3^2+3[/tex]

2. You can plug this into a calculator or do it manually. [tex]3^3=27, 3^2=9\\[/tex]

3. Now add it all together: 27+9+3=39.

4. D is the answer

Answer:

d) 39

Step-by-step explanation:

Given that,

→ x = 3

Let's solve the problem,

→ x³ + x² + x

→ (3)³ + (3)² + 3

→ 27 + 9 + 3

→ 39 {option d}

Hence, the solution is 39.