It takes two hours to drive between the towns of Potter and Germantown. It takes 8 hours to make the trip by bicycle. How long will it take for a car and a bicycle to meet, starting at opposite towns at the same time?

Expanding and simplifying the expression gives:

(3x - 2)² = 9x² - 12x + 4

Here we want to expand and simplify the expression below:

(3x - 2)²

First let's expand that, we can rewrite this as:

(3x - 2)² = (3x - 2)*(3x - 2)

We can distribute that product to get:

(3x - 2)*(3x - 2) = (3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2)

Now we can keep simplifying this to get:

(3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2) = 9x² - 6x - 6x + 4

9x² - 6x - 6x + 4 = 9x² - 12x + 4

The simplified expression is:

9x² - 12x + 4

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Answer:

-17/12

Step-by-step explanation:

║5/6 - 7/12║- ║5/3║

= ║10/12 - 7/12║ - ║5/3║

= ║3/12║- ║5/3║

= 3/12 - 5/3

= 3/12 - 20/12

= -17/12

The domain and the range of the function are

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a piecewise function

When combined gives an absolute function

The rule of a function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is greater than the constant term

In this case, it is 0

So, the range is y > 0

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Question

The graph represents the piecewise function:

f(x) =

What is the domain and range of the function

Answer: The equation Y-5 = -7/3(X-3) in standard form is:

3Y - 15 = -7X + 21

Step-by-step explanation:

Answer:

\( \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}\)

Step-by-step explanation:

Here, we have to arrange the polynomial from higher power to lower power.

So, Option C is the correct option

Hope I helped!

Best regards! :D

Answer:

0.078 liters

Step-by-step explanation:

78ml=78/1000L

78ml=0.078ml

Answer:

y + 4 = (16/81)(x - 10)

Step-by-step explanation:

The general formula for a parabola passing through (x, y) and with vertex (h, k) is                  y - k = a(x - h)^2.

Here we are told that x = 1, y = 12, h = 10 and k = -4, which gives us:

                         12 + 4 = a(1 - 10)^2, or

                              16  =  81a

Then a = 16/81, and the desired parabola is

                                  y + 4 = (16/81)(x - 10)

Answer:

Step-by-step explanation:

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.

Answer:

Josh won all the prizes for the contest

Step-by-step explanation:

An equation of the line that began with a y-intercept of (0, 4), shifted up 3 units, and is perpendicular to y = 3/4(x) - 2 is: A. y = -4/3(x) + 7.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, the condition for perpendicularity of two lines is given by m₁ × m₂ = -1. Next, we would determine the slope of this equation that began with a y-intercept of (0, 4):

3/4 × m₂ = -1

3m₂/4 = -1

3m₂ = -4

m₂ = -4/3

In order to determine the new y-intercept, we would translate the equation by shifting it 3 units up:

Translation = y + 3 = 4 + 3 = 7.

Now, we can write this equation in slope-intercept form as follows:

y = mx + c

y = -4x/3 + 7 or y = -4/3(x) + 7.

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Complete Question:

What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?

answer choices:

A. y = -4/3(x) + 7

B. y=-3/4(x)+7

C. y=-3/4(x)+4

D. y =-4/3(x)+4

The amount that you need to save per month to fund the emergency fund would be $ 861. 58.

The discretionary money left per month would be $ 585. 88.

The gross income for the month :

= 17. 50 x 40 per week x 4 weeks a month

= $ 2, 800

The amount left which is realized funds for the month is:

= Gross income - FICA + Federal tax withholding + State tax withholding

= 2, 800 x ( 1 - 26. 15 %)

= $ 2, 067. 80

Five months of realized income for the emergency fund is:

= 2, 067. 80 x 5

= $ 10, 339

The amount to save per month is:

= 10, 339 / 12

= $ 861. 58

The amount left per month for discretionary expenses ;

= 2, 067. 80 - 861. 58 - 620. 24 rent

= $ 585. 88

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Okay, here we have this:

We need to

The ordered pair (3, - 2) is not a solution to the equation 2x - y = 4

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, an equation 2x - y = 4 now if  (3, - 2) is an ordered pair then putting the numerical value of x must satisfy the y value.

when x = 3,

2(3) - y = 4.

6 - y = 4.

- y = 4 - 6.

- y = - 2.

y = 2.

So,  (3, - 2) is not a solution to an equation 2x - y = 4.

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Answer:

80 degrees

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees so we can create the equation 70+30+x=180. This solves out to 80 so x=80 degrees.

For this question, we assume that 2.5% of the thermometers are rejected at both sides of the distribution because they have readings that are too low or too high.

Answer:

The "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees (below which 2.5% of the readings are too low) and 1.96 Celsius degrees (above which 2.5% of the readings are too high).

Step-by-step explanation:

We can solve this question using the standard normal distribution. This is a normal distribution with mean that equals 0, \( \\ \mu = 0\), and standard deviation that equals 1, \( \\ \sigma = 1\).

And because of using the standard normal distribution, we are going to take into account the following relevant concepts:

\( \\ Z = \frac{X - \mu}{\sigma}\) [1]

A positive value indicates that the possible raw value X is above \( \\ \mu\), and a negative that the possible raw value X is below the mean.

From the question, we have the following information about the readings on the thermometers, which is a normally distributed random variable:

It coincides with the parameters of the standard normal distribution, and we can find probabilities accordingly.

It is important to mention that the readings that are too low or too high in the normal distribution are at both extremes of it, one of them with values below the mean, \( \\ \mu\), and the other with values above it.

In this case, we need to find:

Here, we can take advantage of the symmetry of the normal or Gaussian distributions. In this case, the value for the 2.5% of the lowest and highest values is the same in absolute value, but one is negative (that one below the mean, \( \\ \mu\)) and the other is positive (that above the mean).

Solving the Question

The value below (and above) which are the 2.5% of the lowest (the highest) values of the distribution

Because \( \\ \mu = 0\) and \( \\ \sigma = 1\) (and the reasons above explained), we need to find a z-score with a corresponding probability of 2.5% or 0.025.

As we know that this value is below \( \\ \mu\), it is negative (the z-score is negative). Then, we can consult the standard normal table and find the probability 0.025 that corresponds to this specific z-score.

For this, we first find the probability of 0.025 and then look at the first row and the first column of the table, and these values are (-0.06, -1.9), respectively. Therefore, the value for the z-score = -1.96, \( \\ z = -1.96\).

As we said before, the distribution in the question has \( \\ \mu = 0\) and \( \\ \sigma = 1\), the same than the standard normal distribution (of course the units are in Celsius degrees in our case).

Thus, one of the cutoff value that separates the rejected thermometers is -1.96 Celsius degrees for that 2.5% of the thermometers rejected because they have readings that are too low.

And because of the symmetry of the normal distribution, z = 1.96 is the other cutoff value, that is, the other lecture is 1.96 Celsius degrees, but in this case for that 2.5% of the thermometers rejected because they have readings that are too high. That is, in the standard normal distribution, above z = 1.96, the probability is 0.025 or \( \\ P(z>1.96) = 0.025\) because \( \\ P(z<1.96) = 0.975\).

Remember that

\( \\ P(z>1.96) + P(z<1.96) = 1\)

\( \\ P(z>1.96) = 1 - P(z<1.96)\)

\( \\ P(z>1.96) = 1 - 0.975\)

\( \\ P(z>1.96) = 0.025\)

Therefore, the "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees and 1.96 Celsius degrees.

The below graph shows the areas that correspond to the values below -1.96 Celsius degrees (red) (2.5% or 0.025) and the values above 1.96 Celsius degrees (blue) (2.5% or 0.025).

Answer:

  2 +4√2

Step-by-step explanation:

Perhaps you want the simplified form of (6-√8)/(√2 -1).

The denominator can be rationalized by multiplying numerator and denominator by the conjugate of the denominator:

  \(\dfrac{6-\sqrt{8}}{\sqrt{2}-1}=\dfrac{(6-\sqrt{8})(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\dfrac{6\sqrt{2}+6-\sqrt{16}-\sqrt{8}}{2-1}=\boxed{2+4\sqrt{2}}\)

__

Additional comment

The conjugate of the denominator is the same pair of terms with the sign between them changed. The product of the binomial and its conjugate is then the difference of squares. Since the square of a square root eliminates the radical, multiplying by the conjugate has the effect of removing the radical from the denominator.

The same "difference of squares" relation can be used to remove a complex number from the denominator.

  (a -b)(a +b) = a² -b²

In general, the differences of terms of the same power can be factored. This means that denominators with this form can be "rationalized" by taking advantage of that factoring.

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Answer:

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

Simplify the expression in steps:

\(\cfrac{6-\sqrt{8} }{\sqrt{2}-1 } =\)

\(\cfrac{6-2\sqrt{2} }{\sqrt{2}-1 } =\)

\(\cfrac{2(3-\sqrt{2} )(\sqrt{2} +1)}{(\sqrt{2}-1)(\sqrt{2}+1) } =\)

\(\cfrac{2(3\sqrt{2}+3-(\sqrt{2}^2) -\sqrt{2} )}{(\sqrt{2})^2-1 } =\)

\(\cfrac{2(2\sqrt{2}+3-2) }{2-1} =\)

\(\cfrac{2(2\sqrt{2}+1) }{1} =\)

\(4\sqrt{2}+2\)

Answer:

A) 2

Step-by-step explanation:

Start off with the given information. The question states that the x-int. is 4, so you should recognize that there is a point at (4,0). Plug the point into the equation.

k(4) + 2(0) + 8 = 0

Now simplify the equation.

4k + 0 + 8 = 0

Isolate the variable, make sure it's on its own side.

4k = 8

Now get the k by itself to solve the equation. Divide both sides by 4.

k = 2

Answer:

your answer for that problem is 45.6

Answer:

The second choice

Step-by-step explanation:

the equation as to be higher or equal to 1500$  

b im no completly sure

can i get brailiest

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

The Probability of C' based on the information is 0.5.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

Probability that the adult is college educated = 0.5

Probability that adult is Married = 0.4

Probability that the adult is married and educated = 0.24

Probability of C' will be:

= 1 - 0.5

= 0.5

Probability of C U M will be:

= 0.5 + 0.4 - 0.24

= 0.66

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Answer:

347.037461955

Step-by-step explanation:

If you are taking the square root of 120,435. I would just put it into a calculator.

Answer:

\( Cos(C) = \frac{40}{41} \)

Step-by-step explanation:

Ratio of Cos C using the trigonometric ratios formula, would be:

\( Cos(C) = \frac{adjacent}{hypotenuse} \)

Adjacent = BC = 40

Hypotenuse = AC = 41

Plug in the values

\( Cos(C) = \frac{40}{41} \)

After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.

Before moving to solve the equation , let's learn how to solve any algebraic expression:

Step 1: Determine whether the Distributive is necessary.

Property. If so, spread the word!

Step #2: Group similar terms together on either side of the equals symbol.

(meaning: combine all of the similar factors AND

Add up each and every integer (number).

Step #3: Align the variables so that they are all to one side of the equals symbol.

utilizing the inverse process. REMEMBER: No matter what you do

You MUST do to the other side of the equals sign what you did to the one side.

equals (symbol).

Fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

You MUST do anything you do to one side of the equals sign.

the reverse of the equals symbol).

Step #5: Using the variable's ALONE state, isolate it

the opposite process. DO NOT FORGET: No matter what you do to one

You MUST change the other side of the equals symbol to the equals symbol

Given:

2(x + 8)= 2x + 8

2 × x + 2 × 8= 2x + 8

2x+16= 2x+ 8

16= 8

So, x∈∅.

In this equation , the value of x could not be find because variable x is dissolved in itself.

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

Account balance of Ginny after withdrawal = $ 20 .

Given : Ginny's account balance before withdrawal ie . $ 40

            Her withdrawal amount ie . $ 20

To find : account balance after withdrawal

Calculation : Opening balance = $ 40 ie . initially Ginny had $ 40 .

After withdrawal ( taking out ) of $ 20 ,

Ginny has 40 - 20 = $ 20 left .

After adjustment , final amount = $ 20 .

Therefore , account balance of Ginny after withdrawal = $ 20 .

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