the height of an object dropped from the top of a 320-meter building is given by h(t)= -5t^2+320. how long will it take the object to hit the ground

110/5 = 22, that is the middle number

now use the 2 numbers below that and the 2 numbers above that

so you have 20 + 21 + 22+ 23+24 = 110

the 4th number is 23

To find the number of students in the larger class, set up a system of equations using the given information. Solve the system to find the value of x, which represents the number of students in the larger class. The larger class has 28 students.

To find the number of students in the larger class, we can set up a system of equations. Let's call the number of students in the larger class x, and the number of students in the smaller class y. The problem states that one class has 6 more students than the other, so we can write the equation x = y + 6.

We also know that the two classes have a total of 50 students, so x + y = 50. We can solve this system of equations to find the value of x, which represents the number of students in the larger class.

Using the second equation, we can substitute the value of x from the first equation into the second equation: (y + 6) + y = 50. Simplifying this equation, we get 2y + 6 = 50. Next, subtract 6 from both sides to isolate the variable: 2y = 44. Finally, divide both sides by 2 to solve for y: y = 22. Now, we can substitute this value of y back into the first equation to find x: x = 22 + 6 = 28. Therefore, there are 28 students in the larger class.

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Answer:

(5,32)

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is (5+3)×2-6.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is,

(5+3) × 2 - 6

= 8 × 2 - 6

= 16 - 6

= 10

Hence, The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is (5+3)×2-6.

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Answer:

A

Step-by-step explanation:

on Edge

To find the exact solutions of the given equation 2sec^2x-tan^4x=-1, we can simplify the equation using trigonometric identities and solve for tanx. The solutions are x = pi/3 + n*pi for tanx = sqrt(3), and x = -pi/4 + n*pi for tanx = -1.

The given equation is 2sec^2x-tan^4x=-1. To solve this equation, we need to simplify the trigonometric terms using known identities. The identity sec^2x = 1 + tan^2x can be used here. Substituting this identity into the equation gives us 2(1 + tan^2x) - tan^4x = -1. Simplifying further, we have 2 + 2tan^2x - tan^4x = -1. Rearranging the terms, we get tan^4x - 2tan^2x - 3 = 0.

Now, let's substitute tan^2x with u, giving us the equation u^2 - 2u - 3 = 0. This is a quadratic equation that can be factored as (u - 3)(u + 1) = 0. Solving for u, we have u = 3 or u = -1. Substituting back tan^2x for u, we get tan^2x = 3 or tan^2x = -1. Taking the square root of both sides, we have tanx = sqrt(3) or tanx = -1.

Finally, to find the exact solutions of x, we need to consider the periodic nature of trigonometric functions. Since tanx repeats every pi radians, the solutions are x = pi/3 + n*pi, where n is an integer, for tanx = sqrt(3), and x = -pi/4 + n*pi, for tanx = -1.

Answer: There are 9 kennels containing 3 dogs per kennel.

Step-by-step explanation:

27 divided by 3 = 9

Answer:

The value of given expression is 49.

Step-by-step explanation:

The given expression is

[tex](3+4)^2[/tex]

On solving the parenthesis, we get

[tex](3+4)^2=7^2[/tex]

It can written as

[tex](3+4)^2=7\times 7[/tex]

On multiplication, we get

[tex](3+4)^2=49[/tex]

The simplified value of given expression is 49.

Therefore the required value is 49.

Kirk needs 6 more songs to reach a total of 100, so the integer representing the number of songs he needs is +6.

Kirk needs 6 more songs to have a total of 100 songs for his MP3 player.

The integer to represent how many more songs Kirk needs is +6.

This is because an integer is a whole number (not a fraction or decimal) and can be positive, negative, or zero. In this case, since Kirk is adding songs to reach a total, we use a positive integer.

The +6 indicates that 6 more units (songs, in this context) are needed to reach the goal of 100.

To find Taylor's home street address number, we can determine the value of each digit based on the given information and then calculate the sum.

In this problem, we are given that Taylor's home street address number has five digits.

We also know that two of the digits have values of 60,000 and 300, and the last digit is 9.

The value of each of the other digits is ten times the value of the digit on the right.

Let's break down the information we have:

Putting all the digits together, we get the address number: 60,000 + 300 + 3,000 + 30,000 + 9 = 93,309.

The result is g'(x) = -2x.

Given g(x) =[tex]7 - x^2.[/tex]

Evaluate g(x+h)
=[tex]7 - (x+h)^2[/tex]
= [tex]7 - x^2 - 2xh - h^2.[/tex]

Compute g(x+h) - g(x)
=[tex][7 - x^2 - 2xh - h^2] - [7 - x^2][/tex]
= [tex]-2xh - h^2.[/tex]

Divide by h:
(g(x+h) - g(x)) / h
= [tex](-2xh - h^2) / h[/tex]
= -2x - h.

Take the Limit as h Approaches 0: As h approaches 0, the expression -2x - h approaches -2x.
Therefore, g'(x) = -2x.

So, the derivative of g(x) when h = 0 is -2x.

Answer:

its option C

Step-by-step explanation:

Answer:

a) 8 : 11

b) 8:3

Step-by-step explanation:

Given: The total number of apples in the basket = 11

The number of green apples = 3

Then , the number of red apples = [tex]11-3=8[/tex]

a) The ratio of red apples to all apples in the basket will be :-

[tex]\dfrac{\text{Number of red apples}}{\text{Total apples}}=\dfrac{8}{11}=8 : 11[/tex]

b) The ratio of red apples to green apples will be :-

[tex]\dfrac{\text{Number of red apples}}{\text{Number of green apples}}=\dfrac{8}{3}=8 : 3[/tex]

[tex] \dfrac{y}{-6}+5=9\ \ \ \ |-5\\\\\dfrac{y}{-6}=4\ \ \ \ |\cdot(-6)\\\\y=-24 [/tex]

To solve this problem, what we have to do is to divide the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 + x – 1. Whatever remainder we get must be the value that we have to subtract from the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible by 2 x^2 + x – 1.

By using any method, I used long division we get a remainder of -6.

Therefore we have to subtract -6 from the main equation which results in:

4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2 + x + 1

Answer:38200000 Is the correct answer

Step-by-step explanation:

Answer:

The bus travels 15 miles more per hour than the train.

TTM ;)

Bus covers greater distance per hour as a form of transportation.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)        {Two point - slope form}

x/a + y/b = 1                                         {intercept form}

x cos(β) + y sin(β) = L                           {Normal form}

We have Jared wants a quick trip by bus or train to New York. The bus’s average speed is shown in the graph. The train’s average speed is shown in the table.

Distance covered per hour by the train = m[T] = (135 - 90)/(3 - 2) = 45 miles/hour.

Distance covered per hour by the bus = m[B] = (300 - 0)/(5 - 0) = 300/5 = 60 miles/hour

Therefore, Bus covers greater distance per hour as a form of transportation.

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