A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...

Answer:

Important information like the common difference, 1st term, the # of terms; the last term must be included to find the sum of a series.

Answer:

Refer graph attached below

Step-by-step explanation:

Given equation  [tex]x^2-4=5[/tex]

We have to  Solve the given equation  [tex]x^2-4=5[/tex] graphically.

We first solve the given equation [tex]x^2-4=5[/tex]

Consider the given equation [tex]x^2-4=5[/tex]

Adding 4 both sides, we have

[tex]\Rightarrow x^2-4+4=5+4[/tex]

Simplify, we get,

[tex]\Rightarrow x^2=9[/tex]

[tex]\Rightarrow x^2-9=0[/tex]

To plot the graph let [tex]x^2-9=y[/tex] be the equation

It will be a parabola with vertex (0,9).

Refer graph attached below

Answer:

Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]

Now, calculate first [tex](f+g)(x)[/tex] ;

[tex](f+g)(x) = f(x) + g(x)[/tex]

Substitute the given values we have;

[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]

Combine like terms;

[tex](f+g)(x) =5x+5[/tex]

Let y = [tex](f+g)(x)[/tex]

Then, we have y = 5x+5

Now, Graph the equation of the line y =5x +5

Using slope intercept form: An equation of line is given by :

y = mx +b ; where m is the slope of the line and b is the y-intercept.

On comparing we get;

m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)

Now, find the intercepts of the equation: y=5x+5;

x-intercepts: The graph or line crosses the x-axis i.,e

Substitute y = 0 and solve for x;

0 = 5x +5

Subtract 5 on both sides we get;

-5 = 5x

Divide both sides by 5 we get;

x = -1

x-intercepts= = (-1, 0)

Similarly for y-intercept:

Substitute the value of x= 0 and solve for y;

y = 5(0)+5

y = 5

y-intercepts = (0, 5)

Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.

Answer:

The value of x is 1.6

Step-by-step explanation:

We have been given that triangle CDF ∼ triangle MKP.

Therefore, the ratio of the corresponding sides are equal.

Hence, we have

[tex]\frac{DC}{MK}=\frac{CF}{MP}[/tex]

Plugging the known values, we get

[tex]\frac{9}{1.8}=\frac{8}{0.x}[/tex]

Cross multiplying, we get

[tex]9x=8\times1.8[/tex]

Divide both sides by 9

[tex]x=\frac{8\times1.8}{9}[/tex]

Simplifying, we get

[tex]x=8\times10.2\\\\x=1.6[/tex]

The value of x is 1.6

Answer:

What was the answer?!?!!?!? >-<

Answer:

(the square root of 2 minus the square root of 6) / 4

52 weeks per year

 biweekly means she gets paid every 2 weeks

 so 52/2 = 27

22500/27 = 833.33 each paycheck

The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:

d + 4 = 0

d = -4

Evaluating when d = -4:

d^4 + 2 * d^2 + 5 * d − 10

= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10

= 256 + 2 * 16 – 20 – 10

= 256 + 32 – 30

= 258

Therefore basing on the remainder theorem, the remainder would then be:

Remainder = 258 / (d + 4)                             ---> Answer

In scientific notation, 0.00001 is equal to 1 × 10⁻⁵.

Scientific notation is a way of expressing very big or very small numbers conveniently and with the appropriate number of significant figures.  The general expression for the scientific notation is shown below:

M × 10ⁿ

M is a number that is greater than or equal to 1 but less than 10 and n is the number of times you have to multiply M by 10 to get the number.

The value of n can be easily determined by looking at the decimal point and counting the number of times it is moved to the left or to the right until a proper value of M is obtained.

The steps are as follows:

        NOTE: If the decimal point was moved to the left, then the

                    exponent n  will be written as positive (+x).

                    If the decimal point was moved to the right, then the

                   exponent  n will be written as negative (-x).

Applying the steps to the problem:

STEP 1: 0.00001

The decimal point is four places away from the digit 1.

STEP 2:  To get a number M that is greater than or equal to 1 but less than 10, the decimal point must be moved five places to the right and placed after the digit 1. (000001 or 1)

STEP 3: Since the decimal point was moved five places to the right, the exponent should have a magnitude of 5 and a negative sign. (1 × 10⁻⁵)

Keywords: scientific notation, exponential notation

Scientific notation is a form that can be used to represent very large or very small numbers

The option that gives the correct representation of 0.00001 is scientific notation (standard form) is the option;

Reason:

Required: To convert 0.00001 to a power of 10

Solution:

The method to convert a decimal to a scientific notation is given by moving the decimal point to the right of the first significant digit then multiply the result by 10 raised to the negative of the number of places the decimal point is moved

Where;

a = The number having only one digit to the left of the decimal point

b = The number of places the decimal point is moved (b is positive moving left and negative for moving right)

The given decimal number is 0.00001

Therefore, the decimal can be moved 5 places to the right to give;

0.00001 = 1.0 × 10⁻⁵ = 10⁻⁵

Learn more here:

https://brainly.com/question/17478191

If Marisol has a gross annual pay of $50,000 and receives total employee benefits of 14.5% of her gross annual pay, then you can find how many benefits she receives, using proportion:

[tex] \$50,000 - 100\%,\\ \$x - 14,5\% [/tex].

Then

[tex] \dfrac{50000}{x} =\dfrac{100}{14.5} ,\\\\ x=\dfrac{50000\cdot 14.5}{100}=500\cdot 14.5=7250 [/tex].

In total she will receive $50,000+$7250=$57250.

Answer: $57250.

[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]. Option d is correct.

Simplification is defined as the solution making tendency to expressions.

Here,  expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]

Multiply the whole power 3 in the square bracket.
Gives,
⇒[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  

Thus, [tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex].

Learn more about simplification here:
https://brainly.com/question/8675627

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Final Answer:

The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).

Step-by-step explanation:

In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).

Given that the point [tex]$(r, \theta)$[/tex]  in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:

[tex]\[ x = r \cos(\theta) \][/tex]

[tex]\[ y = r \sin(\theta) \][/tex]

For the given point $(7, 5)$, we have:

[tex]\[ x = 7 \cos(5) \][/tex]

[tex]\[ y = 7 \sin(5) \][/tex]

Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:

[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]

[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]

We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:

[tex]\[ x' = -2r \sin(\theta) \][/tex]

[tex]\[ y' = 2r \cos(\theta) \][/tex]

Now, if we substitute the values of [tex]$r$[/tex]  and [tex]$\theta$[/tex] from the given point (7, 5):

[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]

[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]

Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.

Answer:

Option A is correct.

Step-by-step explanation:

We are given that, the model for the depreciating value of a semi-truck is,

[tex]y = A_{O}(0.83)^x[/tex]

1. It is required to find the value of the truck initially i.e. when x= 0.

So, substituting x= 0, we have,

[tex]y = A_{O}(0.83)^0[/tex]

i.e. [tex]y = A_{O}\times 1[/tex]

i.e. [tex]y = A_{O}[/tex]

Since, the graph passes through the point (0,70,000).

Thus, we get, [tex]A_{O}=70,000[/tex]

Hence, the initial value is 70,000.

2. It is required to find the value of the truck initially i.e. when x= 50,000

That is, when x= 0, the value of y= 50,000.

Graphically, it means that the graph would cut y-axis at the point (0,50,000).

Thus, the y-intercept would be at 50,000.

Change in the initial value will not have any affect on the rate of the graph.

So, from the above, we get,

Option A is correct.

Answer: So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 0.64 feet.

Step-by-step explanation:

Since we have given that

Area of Pam 's picture frame which is square in shape = 3 sq. ft.

As we know the formula for "Area of square ":

[tex]Area=Side^2\\\\3=Side^2\\\\\sqrt{3}\ ft=Side[/tex]

So, Perimeter of square frame would be

[tex]Perimeter=4\times side\\\\Perimeter=4\times \sqrt{3}\\\\Perimeter=6.93\ ft[/tex]

Radius of Meg's circular frame = 1 foot

So, Circumference of circular frame would be

[tex]2\pi r\\\\=2\times \dfrac{22}{7}\times 1\\\\=\dfrac{44}{7}\\\\=6.29\ ft[/tex]

So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 6.93-6.29=0.64 feet.