In a game
of ice hockey, the hockey puck took 0.6 second to travel 66 feet to the goal line. Determine the
the average speed of the puck in feet per second.

Simplifying the answer

What is Real number ?

The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.

Solve :  u² = -121

putting square root on both side

             √u²  =  √ (-121)

                u   = (-11)

                u   = 11i

Since, there is no real square root of -121

If i is the imaginary unit then i = -1 and we find that

               11i is square root of -121

Hence, the simplify answer for u² = -121 is 11i

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Answer:

L = 1/2(p) - w

Step-by-step explanation:

a) Flip the equation.

2l + 2w = p

b) Add -2w to both sides.

2l + 2w + −2w = p +-2w

2l = p − 2w

c) Divide both sides by 2.

2L/2 = p - 2w/2

L = 1/2(p) - w

Probability of selecting eight letter word without repetition of letter is 0.3016.

There are total 26 letters in English alphabets. A 8 letter Code word is selected. We have to take care of repetition of letters as be are not allowed to repeat the letters.

Any letter being chosen should have an equal probability of 1/26. So, we have a probability of 1 to get a non-repeated letter while choosing the first letter.

For first letter the probability is = 26/26

For second letter the probability is = 25/26

For third letter the probability is = 24/26

For fourth letter the probability is = 23/26

For 5th letter the probability is = 22/26

For 6th letter the probability is = 21/26

For 7th letter the probability is = 20/26

For 8th letter the probability is = 19/26

To get an eight letter code that has no repeated letters, all these events have to occur.

Probability of selecting eight letter word without repetition of letters =  (26/26) (25/26) (24/26) (23/26) (22/26) (21/26) (20/26) (19/26)

Probability of selecting eight letter word without repetition of letters = 0.3016

So, 0.3016 is the probability of selecting eight letter word without repetition of letters.

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The correct options are that the functions share a y intercept of -1 and both functions have a range of all real numbers.

A function may be defined as the expression in which for one input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Real number may be defined as the set of numbers that has integers, rational numbers, and natural numbers. Here, from the graph we can see that both the functions meet on the y-axis at a point (0, -1). Thus, both these functions share a y intercept of -1. Now, both the functions have a certain value of y for a given value of x. Hence, both functions have a range of all real numbers.

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Answer:b n d

Step-by-step explanation:

Answer:

It's basically a quadrilateral, it has no name for it.

Step-by-step explanation:

start off by graphing the points

the number in the front is the x axis and the number after is the y axis

Ex: (-4,3) = (X,Y)/  X is horizontal going left to right & Y is vertical going up and down.

Answer: x = 20

Step-by-step explanation:

The angles are corresponding angles so they are equivalent to each other. To solve for x, we set them equal and then solve for x.

65 = 3x + 5

60 = 3x

x = 20

Answer:

the other person has it right- it's x =20

ANSWER: x = 3

z = 100

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 2i [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3 {x}^{2} + 12 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3{x}^{2} = - 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{12}{3} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x {}^{2} = - 4 [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ (- 1)(4)} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 1} \sdot \sqrt{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = i \sdot2[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 2i[/tex]

[ i represents iota, i² = -1, (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=2i[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2+12=0[/tex]

Factor 3 from the left side of the equation:

[tex]\implies 3(x^2+4)=0[/tex]

Divide both sides of the equation by 3:

[tex]\implies\dfrac{3(x^2+4)}{3}=\dfrac{0}{3}[/tex]

[tex]\implies x^2+4=0[/tex]

Subtract 4 from both sides:

[tex]\implies x^2+4-4=0-4[/tex]

[tex]\implies x^2=-4[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{-4}[/tex]

[tex]\implies x^2=\sqrt{-4}[/tex]

Rewrite -4 as 2² · -1:

[tex]\implies x=\sqrt{2^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies x=\sqrt{2^2}\sqrt{-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies x=2\sqrt{-1}[/tex]

[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]

[tex]\implies x=2i[/tex]

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

Answer:

y = -2x -3

Step-by-step explanation:

To write an equation we need two points that the line cuts through.

we then use the formula: Gradient = Rise/Run

the points chosen are (0,-3) and (1,-5)

Gradient = (-5--3)/(1-0)

= -2

to write the equation we need one known point, gradient and one unknown point say (x,y).

we therefore use the formula for gradient/slope

G = Rise/Run

-2 = y+3/x-0

-2x = y + 3

y = -2x -3

Answer:

y = - 2x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, - 5) ← 2 points on the line

m = [tex]\frac{-5-(-3)}{1-0}[/tex] = [tex]\frac{-5+3}{1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - 2x - 3 ← equation of line

According to the given line, the points are L and M and the segment is LM.

Lines:

The line is defined as the one-dimensional figure, which has length but no width. It is made of a set of points which is extended in opposite directions infinitely.

Given,

Here we have the diagram.

Through the given diagram we have to identify the points and segments from it.

We know that, the points refers the is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape.

Based on this definition , we have two points that L and M in the given diagram.

Next one we have to identify from the graph is segment,

Segment means the part of the line that connects two points.

So, LM is the segment of the line.

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The graph of the linear equation 4x - y = 8, with two points on the line is shown in the image attached below.

If we know the slope, m, of the linear equation, which is the rise of the line over the run of the line, and also know the y-intercept value, b, we can graph a linear equation such that the slope of the line would be the value of m, and the point where the line intercepts the y-axis would be the value of b in the linear equation that is represented as y = mx + b.

Given the linear equation, 4x - y = 8, we can rewrite this in slope-intercept form as y = mx + b:

4x - y = 8

-y = -4x + 8 [subtraction property of equality]

y = 4x - 8 [division property of equality]

The slope, m, is 4, while the graph of the linear equation must intercept the y-axis at y = -8, because the y-intercept of the linear equation is b = -8.

Thus, the graph of 4x - y = 8 is shown below.

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We need to take the derivative, which is:

[tex]f'(x) = 10x + 2[/tex]

and see where it is positive (increasing) and negative (decreasing). We see that [tex]f'(x) = 0 at x = -1/5, f'(x) < 0 for x < -1/5, and f'(x) > 0 for x > -1/5[/tex]. Therefore, we have

f(x) increasing: (-1/5, ∞)

f(x) decreasing: (-∞, -1/5)

Applying the angle relationships, the measures of the numbered angles are:

m∠1 = 145°

m∠2 = 145°

m∠3 = 35°

m∠4 = 35°

m∠5 = 145°

m∠6 = 145°

m∠7 = 35°

The position of angles when a transversal intersects parallel lines determines the type of angle relationships that exist between the angles, and also their measure.

Based on angle relationships, the angle measures in the image are solved as follows:

m∠1 = 180 - 35 [linear pair angle relationship]

m∠1 = 145°

m∠2 = m∠1 [vertical angles]

m∠2 = 145°

m∠3 = 35° [vertical angles]

m∠4 = 35° [corresponding angles]

m∠5 = m∠2 [alternate interior angles]

m∠5 = 145°

m∠6 = m∠5 [vertical angles]

m∠6 = 145°

m∠7 = m∠4 [vertical angles]

m∠7 = 35°

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Answer: Students filled the brick old red depressing building.

Step-by-step explanation:

Answer:

x = 49°

Step-by-step explanation:

x = 49°

since m and n are parallel to each other

with T an oblique vector

forming a Z shape

to make this true

The range of F(x) = 7.4* is all positive real numbers is true

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Currently, the function is

f(x) = 7 x 4^x

Suppose,

y = f(x) = 7 x 4^x.

=> y = 7 x 4^x

Hence,

lny = ln (7 x 4^x).

We obtain using the logarithm equation

Hence,

ln y = ln7 + ln 4^x.

= ln y = ln7 + x ln4 .

Hence,

y equals e^(ln7 + x ln4).

=> y = e^ln7.e^(xln4) (xln4)

Using the exponential formula, we obtain

=> y = 7xln4

Consequently, y=f(x)=7.x.ln4

To determine function f's value (x)

7.x.ln7 = 0

As a result, For all possible values of x (x€R). To date,

=> 7x ≥ 0

=> 7xln4 ≥ 0

Therefore interval notation will be (0,∞)

Notation for set builders:

{y|y>0}

The graph will be plotted as follows if all the values of x (x€R) are used:

Hence, it is true that the range of f(x)=7*4x is all positive real integers.

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Answer:

Yes

Step-by-step explanation:

Because they are consecutive, one is odd and one is even.

The square of an odd number is always odd

The square of an even number is always even

The difference between an odd number and an even number is always odd

Therefore, the difference between any 2 consecutive square numbers is always odd

Answer:License plate numbers in certain state consists of seven characters: The first character is digit (0 through 9) The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore; license plate number in this state can be any string - of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit How many license plate numbers are possible if no digit appears more than once?

Step-by-step explanation: i don't know rm

Width of the box is the dimension which gives the gives maximum value.

Width of the box = 9 cm

Length of the box = 9 cm

Given,

The perimeter of the rectangular bottom of the box = 36 cm

The height of the box = 4 cm

We have to find the dimension which gives maximum value.

Volume = lwh

Perimeter = 2(l + w)

36 = 2l + 2w

l = (36 - 2w)/2

l = 18 - w

Now,

Volume = length × width × height

V = (18 - w) × w × 4

V = 72w - 4w²

Lets find w by using w = -b/2a

That is,

w = -72/2(-4) = -72/-8 = 9

That is,

Width of the box is 9 cm and it is the dimension which gives the maximum value.

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Answer:  12

Step-by-step explanation: Because the absolut value of something will always be positive.

Answer:

The value for |12| is D. 12

The required cubic model would be y = 1 + x³ for the given set of values.

The cubic model function takes the form:

y = a + bx + cx² + dx³,

where a, b, c, and d are real integers that represent the cubic regression model's coefficients As you can see, we simulate how the value of y changes as x changes.

x₁ = -2, y₁ = -7

x₂ = -1, y₂ = 0

x₃ = 0, y₃ = 1

x₄ = 1, y₄ = 2

x₅ = 2, y₅ = 9

Computing the values in the regression models to get the values of coefficients to which the graph has attached.

y = a + bx + cx² + dx³

Fitted coefficients:

a = 1

b = 0

c = 0

d = 1

Cubic model:

y = 1 + x³

Hence, the required cubic model would be y = 1 + x³ for the given set of values.

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Yes, the system of inequalities listed to the represent the wants of the campaign manager are correct

This refers to the term in mathematics that uses some expressions to typify statements.

The following are the statements in inequalities

Considering the question here:

r = each 60-second radio spot

t = 30 seconds of television time

The budget is limited to $48,000 means less than or equal to

The manager wants at least 45 radio spots, but no more than 90

means radio spots from 45 to 90 hence 45≤ r ≤ 90

at least 20 means television spots of 20 and above hence t ≥ 20

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The ages of Victoria and tyee are 72 and 74.

A linear equation is an algebraic equation of the form y=mx+b that only contains a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables. Ax+By=C is the accepted form for two-variable linear equations. Finding both intercepts of an equation in this form is rather simple (x and y). If an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is said to be linear. The point-slope form, standard form, and slope-intercept form are the three primary types of linear equations.

As given

ages are consecutive even integers

Victoria > Tyee

So

Victoria's age = x

Tyee's age = x + 2

x(x + 2) = 80

= x² + 2x - 80

= x²  + 8x - 10x - 80

Hence , the ages are 72 and 74.

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The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2   .

In the question ,

it is given that

the required line is parallel to x [tex]=[/tex] -5

means the line x [tex]=[/tex] -5 , is a vertical line parallel to y axis , it makes an angle of 90° with the x axis .

so , slope will be tan(90°) = 1/0

hence the slope of the required line is 1/0.

The equation of the line passing through point P(-2,6) and with slope = 1/0 , is

y-6 = (1/0)*(x-(-2))

0 = 1 * (x + 2)

0 = x + 2

x = -2

the graph is drawn below .

Therefore , The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2 .

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Answer:

   -6.4, -5 1/2, -5, and -2 6/4.

Step-by-step explanation:

Arranging these negative values in order from least to greatest may be tricky if you are not familiar with your integer rules and operations. However, if you seem to understand, even a little, this way may be helpful to you.

All you need to know is this. positive and negative are opposites. Thus, if, for example, +2 is greater than +1 in positives, then -2 is less than -1 in negatives. So, in other words, think about it this way when you see a negative number, but you are used to positive numbers, just assume that the biggest number on the positive side is the smallest number on the negative side.

Therefore, if we were to use this method, we would result in -6.4, -5 1/2, -5, and -2 6/4. Since it would be the opposite in positives.

686 bottles of 4 liters each can be filled from this cube.

We can solve this problem by following a few steps.

As we know that a cube has 6 surfaces and each surface has a geometrical shape of a square. We also know that each side of a square is the same.

So, the surface area of a square ≡ Side × Side.

Let's assume the side as z

Now, the area of this square ≡ z × z = z²

∴ z² = 19600, as per the question.

We have to solve the equation,  z² = 19600   Or, z = 140   ( by doing root both sides)

Now we know the side of the cube, then the volume of this cube is z³.

As, we know the volume of a cube ≡ side × side × side, as the height of a cube is also identical.

Volume of the cube = 140³ =  2,744,000 cc

1000 cc is considered as 1 liter. Therefore, this cube consists of, 2,744,000/1000 = 2744 liter of water.

Each bottle consists of 4 liters of water. Then we can fill, 2744/4 = 686 bottles of water.

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Answer:

Step-by-step explanation:

Find the amount of time it takes for a beam of light from the Sun to reach Earth.

Hello!

Here are both solutions to your equation.

Fraction Form:

[tex]\frac{37}{100}[/tex]

OR

Decimal Form:

[tex]0.37[/tex]

Hope this helps!

Answer:

the answer is 29