Two in-line skaters, Nell and Kristin start from the same point and skate in the same direction.Nell skates at 8 mile per hour and Kristin skates at 10 miles per hour. if they can keep up the pace for 4.5 hours, how far apart will they be at the end of the time?

Answers in bold:

Problem 4) Shift 6 units left, 1 unit down

Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.

The graphs are below.

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Explanation:

In problem 4, the parent function is y = x^2

Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.

Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.

So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.

I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.

---------------------------------

For problem 5, the parent function is y = |x|

Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.

The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).

Answer:

4.  Translated 6 units left and 1 unit down.

5.  Translated 3 units right and stretched vertically by a factor of 2.

Step-by-step explanation:

Transformations

[tex]\textsf{For $a > 0$}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Parent function:

[tex]f(x)=x^2[/tex]

Translated 6 units left:

Add 6 to the x-variable of the function:

[tex]\implies f(x+6)=(x+6)^2[/tex]

Translated 1 unit down:

Subtract 1 from the function:

[tex]\implies f(x+6)-1=(x+6)^2-1[/tex]

Parent function:

[tex]f(x)=|x|[/tex]

Translated 3 units right:

Subtract 3 from the x-variable of the function:

[tex]\implies f(x-3)=|x-3|[/tex]

Stretched vertically by a factor of 2:

Multiply the function by 2:

[tex]\implies 2f(x-3)=2|x-3|[/tex]

The required possible side length of the tablecloth is 11ft x 11ft.

A square is for sided regular polygon, where the length of all sides is identical and the angle between the adjacent side is 90°.

Given the following parameters

Area of fabric =121 ft² of fabric.

She wants to make a square tablecloth for her dining room table.\

Area of the square = a²

121 = a²

a = √121

a = 11 ft

Thus, the required possible side length of the tablecloth is 11ft x 11ft.

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Answer:a

a

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{xa + xb=47} \atop {4xa + 5xb=200}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable xa from the first equation, you obtain:

xa= 47 - xb

Substituting this expression in the second equation you get:

4×(47 -xb) + 5xb= 200

Solving:

4×47 - 4xb + 5xb= 200

188 - 4xb + 5xb= 200

- 4xb + 5xb= 200 - 188

xb= 12

Remembering that xa= 47 - xb. you get: xa=47 - 12 → xa= 35

Finally, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

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Answer: So that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

Step-by-step explanation:

Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

Step-by-step explanation:

The formula for circumference when the diameter is given is C = π • d

C = circumference

π = pi

d = diameter

So to find the circumference plug in the number (18 - diameter).

C = π • 18

C = 56.5486677646

If needed to round to nearest ...

tenth = 56.5

hundredth = 56.55

However, if the directions say to use 3.14 for π (pi) then the answer would be different.

C = 3.14 • 18

C = 56.52

Hope this helps :)

If a > b then;

a + -b = a positive number

If b > a then;

a + -b = a negative number

If both addends are positive or if the positive addend has a greater absolute value than the negative addend, the sum will be positive. If both addends are negative or if the negative addend has a greater absolute value than the positive addend, the sum will be negative.

Answer:

3.1kg

Step-by-step explanation:

4.7+5.6+6.4+2.8+3.5+4.4+4.5 = 31.9

4.375 x 8 = 35

35 - 31.9 = 3.1

[tex]3 \cdot 3^2 + 8 : 2 - (4+3) =[/tex]

[tex]3 \cdot 3^2 + 4 - 7=[/tex]

[tex]3 \cdot 9 +4 -7=[/tex]

[tex]27 + 4 - 7 = 24[/tex]

==axel134==

Answer: -4/7

Step-by-step explanation:

the formula for the slope is rise/run

or (y-y1)/(x-x1)

we can apply this concept like this:

7-(-7)=7+7=14

-4-4=-8

since -8 is the rise and 14 is the run, the slope is -8/14

simplify to -4/7

Answer:

the gcf of 41 and 48 would be 1

Answer: 1

Step-by-step explanation:

41      48

 /\       /\

1 * 41  1 * 48

Answer: 5/8 + 3/4 = 11/8 = 1 3/8 = 1.375

Step-by-step explanation:5/8+ 3/4= 5/8+ 3 · 2/4 · 2 = 5/8+ 6/8= 5 + 6/8 = 11/8

Answer: Incorect answer

Step-by-step explanation:

5/8X3/4 =11/8 =1 3/8=1.375

Answer:

5 5/8 pounds

Step-by-step explanation:

I added the fractions and got that

Answer:

[tex]c=\frac{bd}{ad+b}[/tex]

Step-by-step explanation:

By isolating the term c, we are trying to arrive at the equation c= ____.

[tex]a=b(\frac{1}{c}-\frac{1}{d} )[/tex]

Divide both sides by b:

[tex]\frac{a}{b}= \frac{1}{c}-\frac{1}{d}[/tex]

Add [tex]\bf{\frac{1}{d}[/tex] to both sides:

[tex]\frac{1}{c} =\frac{a}{b} +\frac{1}{d}[/tex]

Rewriting the right-hand side as a single fraction:

[tex]\frac{1}{c} =\frac{a(d)}{b(d)} +\frac{1(b)}{d(b)}[/tex]

[tex]\frac{1}{c} =\frac{ad+b}{bd}[/tex]

Find the expression of c:

[tex]1\div\frac{1}{c} =1\div\frac{ad+b}{bd}[/tex]

[tex]\bf{c=\frac{bd}{ad+b}[/tex]

Additional:

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Answer:

[tex]c=\dfrac{bd}{ad+b}[/tex]

Step-by-step explanation:

Given equation:

[tex]a=b\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

Divide both sides by b:

[tex]\implies \dfrac{a}{b}=\dfrac{b}{b}\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

[tex]\implies \dfrac{a}{b}=\dfrac{1}{c}-\dfrac{1}{d}[/tex]

Add 1/d to both sides:

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}-\dfrac{1}{d}+\dfrac{1}{d}[/tex]

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}[/tex]

[tex]\textsf{Simplify the left side by applying the fraction rule} \quad \dfrac{p}{q}+\dfrac{r}{s}=\dfrac{ps+qr}{qs}:[/tex]

[tex]\implies \dfrac{ad+b}{bd}=\dfrac{1}{c}[/tex]

Cross multiply:

[tex]\implies c(ad+b)=bd[/tex]

Divide both sides by (ad + b):

[tex]\implies \dfrac{c(ad+b)}{ad+b}=\dfrac{bd}{ad+b}[/tex]

[tex]\implies c=\dfrac{bd}{ad+b}[/tex]

Complex fraction 4²/₃ + 1/3 – 4¹/₃ = 2/3

A fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.

Some steps to solve a fraction -

Step 1: Write the factors of numerator and denominator.

Step 2: Determine the highest common factor of numerator and denominator.

Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.

For example -

4²/₃ + 1/3 – 4¹/₃

= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3

= 14/3 + 1/3 – 13/3

= (14 + 1 - 13)/3

= (15 - 13)/3

= 2/3

Hence , in the mathematics problem can be solved by using the fractions.

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The 95% confidence interval for p is (0.333, 0.480).

If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.

The formula for calculating the confidence interval is expressed as shown below;

CI = p±Z * √p(1-p)/n±0.5/n

Where Z is the z-score at 95% confidence

p is the sample proportion

n is the sample size

Given that n = 144, p = 0.7 and z-score at 95%  

CI = 1.645 (from z table)

Now Substituting this values;

CI = p ± 1.645*√0.7(1-0.4)/144 ±0.5/n

CI = 0.4 ± 1.645*√0.7(0.6)/144 ± 0.5/144

CI = 0.4 ±1.645 * √0.24/144 ± 0.00347

CI = 0.4 ±1.645 * 0.04087± 0.00347

CI = 0.4±0.06723±0.00347

CI =(0.333, 0.480)

Hence, The 95% confidence interval for p is (0.333, 0.480).

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The value of the x in the linear equation of the midpoint is a 3.85.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Midpoint is the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.

From the given information:

Given K is the midpoint of GH, GK = 5x - 3,and GH = 2x + 24

As the midpoint the both equation are equal to the each other.

Then

GK = GH

5x - 3 = 2x + 24

5x+2x = 24+3

7x = 27

x = 27/7

x = 3.85.

So, The value of the x in the linear equation of the midpoint is a 3.85.

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Answer:

Conditional Probability

Step-by-step explanation:

Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

Answer:

9

Step-by-step explanation:

because 8 gallons of lemonade will stand on charge $1.00 will add and answer will be 9

Step-by-step explanation:

use fog

3(1/3x-3)+9

=x

use gof

1/3(3x+9)-3

=x

we can see that both results give us x hence they are inverse

The least natural number that has exactly 6 factors and is not divisible by 2 is 75.

It should be noted the factors of 75 include 1, 3, 5, 15, 25, and 75.

Therefore, it should be noted that 2 isn't among the factors based on the information given in the question.

Therefore, the least natural number that has exactly 6 factors and is not divisible by 2 is 75.

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Answer:

This is a one to one function

Step-by-step explanation:

From the function, we know that f(x) = x - 7 is a linear graph.

Using horizontal line test

the graph is one to one if the horizontal line only cross the graph at one point

The point that is 1/3rd of the distance from (-4.5,0) to (0,9) is (-3,3).We use a formula similar to the midpoint formula for finding the point.

We have been given two points (-4.5,0) and (0,9), we have to find the point is on the line formed by these two points and is 1/3rd away. We don't need to find the distance between these two points to find the asked point. We have to use a formula that is similar to finding the midpoint of a line. For two points (a,b) and (x,y) the midpoint is ([tex]\frac{a+x}{2} ,\frac{b+y}{2}[/tex]).We used equal parts of the two points to find the midpoint, for 1/3rd we will be using uneven parts of the two points.

[tex]x_{1} =\frac{2}{3} (-4.5)+\frac{1}{3} (0)=-3[/tex]

[tex]y_{1} =\frac{2}{3} (0)+\frac{1}{3} (9)=3[/tex]

Therefore the point that lies 1/3rd of the distance from (-4.5,0) and (0,9) is (-3,3).

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Using Descartes's Rule of Signs:

There are four positive real zeros P can have.

There are zero negative real zeros P can have.

Descartes' rule of sign is used to determine the number of positive and negative real zeros of a polynomial function.

We have,

P(x) = 2[tex]x^{4}[/tex] - 7x³ + x² - 18x + 3

We have to look at the sign of the coefficient

Here,

  2[tex]x^{4}[/tex] - 7x³  +  x²  -  18x + 3

(+)---(-)(-)---(+)(+)--(-)(-)---(+)

There are 4 variations so there are 4 positive real zeroes.

For finding negative real zeroes we Put x = -x.

P(-x) =  2[tex]x^{4}[/tex] + 7x³ + x² + 18x + 3

   2[tex]x^{4}[/tex]  +  7x³  +  x²  +  18x  +  3

(+)---(+)(+)----(+)(+)--(+)(+)-- --(+)

There are no variations so there are zero negative real zeroes.

Thus,

a) Using Descartes's Rule of Signs, we know that there are four positive real zeros P can have.

b) Using Descartes's Rule of Signs, we know that there are zero negative real zeros P can have.

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https://sis-union.tnk12.gov/scripts/wsisa.dll/WService=wsUNIStu/seplog01.w

Step-by-step explanation:

Answer:

(2,3)

Step-by-step explanation:

[tex]y=(2)^{2}-1=4-1=3[/tex]

when x = 2, y = 3

Hope this helps

The  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

According to the given question.

We have a equation of a line y-3= 4(x+8).

Here, we have to find the slope of a line y-3= 4(x+8) and a point on the line.

Since we know that, the equation of a lines through a point (x1, y1) is given by y - y1  = m(x - x1), where m is the slope of the line.

And the equation of slope intercept form for a line is y = mx + c.

So, compare the given equation of line y-3= 4(x+8) with the standard equation of line y - y1  = m(x - x1)  which passes through the point (x1, y1), we get

point ( -8, 3) on line y-3= 4(x+8).

Now, the slope intercept form of the line y-3= 4(x+8) is

y - 3 = 4x + 32

⇒ y = 4x + 32 + 3

⇒ y = 4x + 35

Thereofore, the slope of the line y-3= 4(x+8) is  4.

Hence, the  slope of the line y-3= 4(x+8) is  4 and (-8, 30 is a point on line y - 3 = 4(x + 8).

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