The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length

Given:

Amount Nicole borrowed = $1100

Annual interest rate = 7%

Duration = 6 months

Let the amount of interest be x

The amount after t years can be calculated using the formula:

The interest that she would pay can be calculated using the formula:

The amount after 6 months is:

Hence, the interest:

Answer: $38.5

Given:

A diver starts at 342 feet below the surface, which means -342 feet.

Now, she swims 237 feet upward.

It shows that she is moving in a positive direction.

So, the current depth of diver is,

The depth is -105 feet, which shows that the diver is still 105 feet below the surface.

Given the value of a and b

To get a+b

Thus

Thus, a + b = -2.1

1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.

2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.

3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.

4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.

5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.

To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.

This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.

6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.

7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.

The function which shows the total manufacturing cost of skateboards as a function of the number of hours is; g(f(h)) = 845h2 + 2,600h + 100.

It follows from the task content that the function which shows the manufacturing cost as a function of the number of hours be determined.

Since, the number of skateboards is given in terms of hours as; f(h) = 325h and;

The manufacturing cost, g is given in terms of the number of skateboards, b manufactured;

The function instance which represents the manufacturing cost as a function of hours is; g(f(h)).

Therefore, we have; g(f(h)) = 0.008(325h)² + 8(325h) + 100.

Hence, the correct function is; g(f(h)) = 845h2 + 2,600h + 100.

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By definition, a relation is a function if each input value (x-value) has one and only one output value (y-value).

In this case, you have the following relation:

Notice that each ordered pair has this form:

Where "x" is the input value and "y" is the output value.

You can identify that each input value has one and only output value. Therefore, you can conclude that this relation is a function.

Hence, the answer is: It is a function.

he slope-intercept form​ is

y = mx + c

here, m = slope of the line and C is intercept on y axis.

The number of significant figures in 10.1 is 3 as there are two digits before the decimal and one digit after the decimal.

The number of significant digit in 100.05 is 5 as there are 3 digits before the decimal and two digits after the decimal.

The number of significant digits in 120 is 2.

The number of significant digits in 129 is 3.

Hence, the correct answers are (A) and (D)digit

You have to determine the cost for 4.5 inches of the construction using the graph.

The height is on the y-axis, and the cost is on the x-axis.

First, locate 4.5 in the y-axis, which is the value in the midpoint between 4 and 5.

Draw a horizontal line until you intersect with the line, then draw a vertical line from the function until the x-axis:

The line crosses the x-axis at the midpoint between values 102 and 127.5 to determine the value at this point you have to average both costs:

The cost of 4.5 inches of construction is $114.5

Answer: x[tex]\leq[/tex]18

Using complete the square method:

at a sale a desk is being sold for 24% of the regular price. the sale price is $182.40 what is the regular price​

we have that

24% ------> represent $182.40

so

Applying proportion

Find out the 100%

Let

x ----> the regular price

182.40/24=x/100

solve for x

x=(182.40)*(100)/24

x=$760

therefore

The function has an end behaviour of x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞

The equation of the polynomial function is given as

q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50

To determine the end behaviour of the function, we calculate

q(∞) and q(-∞)

So, we have

q(∞) = -2(∞)⁸ + 5(∞)⁶ - 3(∞)⁵ + 50

Evaluate the exponents

q(∞) = -2(∞) + 5(∞) - 3(∞) + 50

This gives

q(∞) = -∞ + ∞ - ∞ + 50

q(∞) = -∞

Also, we have

q(-∞) = -2(-∞)⁸ + 5(-∞)⁶ - 3(-∞)⁵ + 50

Evaluate the exponents

q(-∞) = -2(∞) + 5(∞) - 3(-∞) + 50

This gives

q(-∞) = -∞ + ∞ + ∞ + 50

q(-∞) = -∞

Hence, the end behaviour of the graph is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞

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Complete question

Consider the polynomial function q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50

Calculate the end behaviour

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

Answer:

B, C, D and E.

Explanation:

The proof and reasons for each step is given below:

Step 1:

Statement: RSTU is a parallelogram.

Reason: Given

Step 2:

Statement: RS is parallel to TU and RU is parallel to TS

Reason: (B)Definition of a parallelogram

Step 3:

Statement: ∠RSU≅∠TUS and ∠RUS≅∠TSU.

Reason: (C)Alternate Interior angles are congruent

Step 4:

Statement: SU≅US.

Reason: (E)corresponding parts of congruent triangles are congruent.

Step 5:

Statement: Triangle RSU≅Triangle TUS.

Reason: AAS Congruence Theorem

Step 6:

Statement: RS≅TU and RU≅TS

Reason: (D)Opposite sides of a parallelogram are congruent.

The reasons that support the proof are B, C, D and E.

Answer: I belive it would be 4.6 x 10^11 dollars. I hope this helps you :)

Step-by-step explanation:

Answer:it would be 4.6x10^11

Step-by-step explanation:

First option is correct.

For all the sample sizes, the sample mean is close to 6, give or take (

Answer:

- 5/2

Step-by-step explanation:

If the slope of a line is m then the slope of the perpendicular line is -1/m

The slope of y = 2/5 x is 2/5

Slope of perpendicular line = - 5/2

test

some text with formatting

0. primo

1. secondo

2. terzo

• good

• better

• the best

∛

pl

lkp

ok

=)

1) Examining that ratio, we can perform the following:

2) Note that when we multiply that ratio by their conjugates, that yields a difference between two squares. Note that on the top, there is the expanded version of this expression.

Thus, the answer is D

paid price = 24,998

it is the amount that is 1815 less than the sticker price,

so the sticker price or price of the car is x

so x = 24,998 + 1815

x =26,813

so the price of car is x = 26,813.

For the given equation:

In arithmetic progression, 9,15,21,27,33,39 is a₅ and    a₆ .

What is arithmetic progression?

a₁ = 9

a₂ = 15

a₃ = 21

Notice that a₂ - a₁ = 6 and a₃ - a₂ = 6

We can deduce that aₙ₊₁ = aₙ + 6

We can test this on the 4th term : a₄ should equal  21  + 6 = 27

Since this checks out we can say that the sequence is an arithmetic progression with a common difference of 6.

a₅ = 27 + 5 = 33

and

  a₆ = 33 + 6 = 39

7,0,-7,-14

find the common difference by substracting any term in the sequence from the term that comes after it.

 a₂ - a₁  = 0 - 7 = -7

 a₃ - a₂ = -7 - 0 = -7

 a₄ - a₃ = -14 - -7 = -7

the difference of the sequence is constant and equals the difference between two consecutive terms.

  d = -7

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Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.

So, let's list which areas we need:

- We need the lateral areas of the external parts, which are 4 rectangles.

- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.

- We need the interior aread, which is the same as the lateral area of a cylinder.

For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.

The area of each of them is:

Since we have 4, the total exterior lateral area is:

For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.

First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:

The area of a circle given its radius is:

So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:

We deal with π later on.

For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.

the circumference of a circle is:

The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:

So, the total surface area is the sum of all of these:

Now, we just need to evaluate:

So, the lateral area is approximately 3.15 m².

Given:

The function f(x) = 3cos(x) - 2.

Required:

What are the minimum and maximum value of function?

Explanation:

To check maximum and minimum value of function.

First derivate the original function.

After putting first derivative equal to zero, critical points can be found.

Then, do second deritvative to check points of maxima and minima.

The critical points at which second derivative greater than zero. Point will be of minima.

The critical points at which second derivative less than zero. Point will be of maxima.

So,

Now, do second derivative test for maximum and minimum points

Answer:

Given:

Points that lie on the same line.

Opposite rays

The formal way of writing a logarithm is the following:

Where "a" is the base of the logarithm and "b2 is the argument.

If "a = 10", then the base is not written, like this:

In the case that the base is the constant number "e" then the logarithm is called a "natural logarithm" and it is written as follows:

Answer:

From the solution the largest possible integer value of x is;

Explanation:

Given the inequality;

To solve, let's add 1 to both sides of the inequality;

then let us divide both sides of the inequaty by -1.

Note: since we are dividing by a negative number the inequality sign will change.

Therefore, From the solution the largest possible integer value of x is;

The given equation is

If we subtract 0.6 on each side, we get

Therefore, the given expression is equivalent to B.

If we multiply the given equation with 3, we get

Therefore, the given expression is equivalent to C.

At last, if we subtract 0.6 and 4 on each side, we get

Therefore, the given expression is equivalent to E.