In the equation |x| = b, if b>0, then how many solutions are there for x?
O Zero
O Two
O Can't be determined without more information
O One

The correct option is (C) The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Given that the following table represents  the linear function f(x), and the equation represents the linear function g(x) :

x                   0                     2                          4

f(x)                1                      9                         17

and g(x) = 3x + 1 .........(1)

We have to compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

From the graph, we note that (0, 1), (2, 9) and (4, 17) are three points on the line graph of function f(x).

We know that, the slope of any line having two points (a, b) and (c, d) on it is given by

m = d-b/c-a

So, the slope of the line of f(x) is

m = 9-1/2-0

m = 8/2

⇒ m = 4

Since the line of f(x) passes through the point (0, 1), so its equation will be

f(x) -1 = m(x-0)

⇒ f(x) -1 = 4(x-0)

⇒ f(x) -1 = 4x

⇒ f(x) = 4x+1 ........... (2)

The slope-intercept form of the equation of a line is y = mx + c, where m is the slope and c is the y-intercept of the line.

Comparing equation (2) and (1) with the slope-intercept form, we get

slope of f(x) = 4  and  y-intercept of f(x) = 1 and

slope of g(x) = 3  and  y-intercept of g(x) = 1.

Thus, the slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Option (C) is CORRECT.

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The simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .

For Example : 5y,2y are like terms .

In the given question 1/2 / ( x² - y²) - 5/2(x² - y²) the first term is a complex fraction,

[tex]=\frac{\frac{1}{2} }{(x^{2}-y^{2} ) } -\frac{5}{2(x^{2} -y^{2}) }[/tex]

Simplifying the complex fraction we get ,

= 1/2(x² -y²) -5/2(x² -y²)

= 1/(2x² - 2y²) -5/(2x² -2y²)

On further simplifying

= 1/2x² -1/2y²- 5/2x²  +5/2y²

On combining the like terms of x² and y².

= 1/2x² - 5/2x² -1/2y²  +5/2y²

taking LCM of like terms as 2x² and 2y².

=(1-5)/2x²+(-1+5)/2y²

= (-4)/2x² + 4/2y²

=-2/x² + 2/y²

Therefore , the simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

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Answer:

8:30 a.m.

Step-by-step explanation:

The total time it takes for Lyle to reach his friend's house is 720/80 + 1 + 0.25 * 2, which is 9 + 1.5 = 10.5 hours

The latest possible time that Lyle would be able to leave his house to reach on time is 8:30 a.m.

The solution of the given system of equations is (1, 3)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

y = 4 - x    ....... (1)

3x + y = 6  ....... (2)

To use elimination method, add x to both sides of equation (1)

x + y = 4 ....... (3)

Substract equation (3) from equation (2)

3x + y = 6

x + y = 4   –

2x       = 2

 x       = 1

Substitute x = 1 into equation (1)

y = 4 - x

  = 4 - 1 = 3

Thus the solution is (1,3)

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Answer: x = -10

Step-by-step explanation:

Answer:

(- 10, 10 )

Step-by-step explanation:

6x + 5y = - 10 ( subtract 6x from both sides )

5y = - 10 - 6x → (1)

3x + 5y = 20 → (2)

substitute 5y = - 10 - 6x into (2)

3x - 10 - 6x = 20

- 3x - 10 = 20 ( add 10 to both sides )

- 3x = 30 ( divide both sides by - 3 )

x = - 10

substitute x = - 10 into (2) and solve for y

3(- 10) + 5y = 20

- 30 + 5y = 20 ( add 30 to both sides )

5y = 50 ( divide both sides by 5 )

y = 10

solution is (- 10, 10 )

Answer:

y = 3x + 1

y = -x + 5

Step-by-step explanation:

Take the system of equations and substitute (1 ,4) in any one of the equations. If both the sides are justified, then (4,1) is the solution to that pair of equations.

  1) y = -3x  - 1   ---------(I)

     y = -x + 5

Substitute (1,4) in equation (I)

        4 = -3*1 - 1

        4 = -3-1

        4 ≠ -4

So, (1, 4) is not a solution.

2) y = 3x + 1   ---------------(II)

   y = - x + 5

Substitute (1 ,4) in equation (II)

      4 = 3*1 + 1

       4 = 3 + 1

       4 =  4

(1 ,4) is the solution for this system of equation.

Answer:

780 ≥ 58.53x + 566.83

Step-by-step explanation:

He has $780 that he can spend, so the total must be less than or equal to 780.

Let x = number of biking outfits.

Costs:

Bicycle: $490.50

Reflectors: 4 × $14.98 = $59.92

Gloves $16.44

Outfits: $58.53x (The cost of x outfits is 58.53x)

The total he spends is:

490.5 + 59.92 + 16.44 + 58.53x =

= 58.53x + 566.86

This total has to be less than or equal to $780.

58.53x + 566.86 ≤ 780

This can be written as

780 ≥ 58.53x + 566.83

The term is 0.04

The geometric sequence given is

0.004, __, 0.4, 4....

Now let us find the value of r which is the factor between the terms, called the common ratio.

r = [tex]\frac{0.04}{0.004}[/tex] = [tex]\frac{0.4}{0.04}[/tex]

 = 10

General form= [tex]a_{n}[/tex] =[tex]a_{1}[/tex]×[tex]r^{n-1}[/tex]

The geometric series

           [tex]a_{n}[/tex] = 0.004× [tex]10^{n-1}[/tex]

Therefore to find the second number of the sequence is

          [tex]a_{2}[/tex]  = 0.004 × [tex]10^{2-1}[/tex]

               = 0.004 × 10

               = 0.04

Therefore the missing term of a geometric sequence is 0.04.

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Answer:

Option 2 [tex]x[/tex] = 15, [tex]y[/tex] = 3

Step-by-step explanation:

Vertical angles are equivalent. Thus [tex]4x+10y[/tex] = 90. To solve for [tex]x[/tex], we set [tex]6x[/tex] = 90, since adjacent angles equal 180. This gives us 15 as x. Plugging 15 into the first equation we get that y is equal to 3.

Answer:

Point form:

(2, 9)

Equation form:

x = 2,y = 9

Step-by-step explanation:

marshal just stoopid.. that simple

anyway marshal divided it by 100 instead of 104, the answer of it divided by 104 is 243.547509615

The sum of an infinite geometric series is twice its first term then the common ratio(r) be 1/2.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

Given: S = 2a₁

a₁ be the first term

r be the common ratio

Let the equation be S = a₁/1-r

2a₁ = a₁/1-r

substitute the values in the above equation, we get

2 = 1/1-r

2 - 2r = 1

2r = 1

The value of r = 1/2

Therefore, the common ratio(r) be 1/2.

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Answer: 22

Step-by-step explanation: 143 divided by 6.50 = 22, therefore our answer is 22

Answer:

i think the answer may be possibly 86%

The slope of the given problem is 14

It is a problem of linear regression Line

y = a +by

where a = ∑Y - b ∑X / N  

and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)  

      Month(X) Temperature (y)  X²              XY

               1                   42                        1                  42

               2                  56                        4                 112

               3                  70                         9                210

               4                  84                        16               336

Total        10               252                     30               700

Number of observation (n) = 4

So, b = 4(700) - (10)(252) / ( 120 - 10²)

         = 2800-2520/20

        = 280/20

         = 14

b = 14

Now a=  252 - (14)10/ 4

          =112 /4

         = 28

So, The linear regression line is

         y= 28 + 14x

Slope = 14

The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.

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We can see that there is no element which is common Hence, they are mutually exclusive events.

Let A be the event of getting a sum of 7 on dice.

Let B be the events of getting a sum of 6 on dice.

A={ (1,6), (2,5), (3,4), (4,3), (5,2) }

B = { (1,5) , (2,4), (3,3),  (4,2), (5,1), }

Mutaullty exclusive events are those when there is no common event between two events.

Where there is empty set of intersection.

But we can see that there is no element which is common

So, n(A∩B) = ∅

Hence, they are mutually exclusive events.

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The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

As given in the question,

Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]

Simplify the given two rational expressions by factorizing them,

[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]

Restriction on the variables is given by  x≠ -5,  x≠ -1.

Therefore, the  simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]  is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5,  x≠ -1.

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Answer:

Needs alot of steps which you can try

Step-by-step explanation:

Sum of interior angles=exterior angle

Eg, left side 60°+90° = the exterior (big angle outside triangle)

All of the lines are straight so you can find angles using (angles on a straight line) so 180°- the angle known when your solving

There is also opposites angles which are equal, you can search it up

We have proved that , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

It is given that XY ║ WZ and XW ║ YZ.

We have to prove that ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX.

What is the SSS rule of congruency of triangles ?

SSS axiom states that if two triangles have three pairs of congruent sides, then the triangles are congruent.

As per the question ;

XY ║ WZ and XW ║ YZ

So , using this data we can conclude that ;

XY = XW and WZ = YZ

The two triangles are ΔXWZ and ΔZYX

So ,

XY = XW (from given data)

and

WZ = YZ (from given data)

and

XZ = XZ (common)

∴ Both triangles are congruent to each other ;

i.e.,

ΔXWZ ≅ ΔZYX

by using the SSS axiom.

Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

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Solving the problem with the arithmetic progression, the 32nd term of the sequence is 558.

Arithmetic progression is a sequence of numbers in which the next term is depicted by adding a fixed number 'd' to the preceding term. The series is in arithmetic progression.

We all know the formula for arithmetic progression is,

aⁿ = a + ( n-1 ) d

where d = difference between two corresponding terms, n = no. of term, a = first term

We have to find the 2nd term, and it's, a³⁸ = 3 + ( 38 - 1)( 18 - 3 ) = 3 + 37× 15 = 3 + 555 = 558.

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From the given vertices, the area of the polygon is 28.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

First, you should plot the points, then see image 1.

From the figure, it is possible to see that the bases ( AB and CD) = 5-3=2

and heights (AC and BD) =-7-(-7)=7+7=14. Thus,

A= B*H= 2*14=28

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   For numbers 5 and 20 the value of the geometric mean of these numbers is

Gm (5, 20) = 10

      The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

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The amount of you swam is +15 feet and your friend swam is -6 feet.

Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.

The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.

It is given that you move the forward that means you move in positive direction.

So, you move forward means you move +15 feet.

It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.

So, your friend moves backward means he move -6 feet.

Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.

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On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is  5y²/6 +2y/15.

In an algebraic expression Like terms are  defined as those terms that have same variable and that variable has the same power .

For Example : 5a,9a are like terms .

In the given question

=y²/2 +y/3 +y²/3 -y/5

On combining the like terms , one with y² and other with y.

We get;

=y²/2 +y²/3 +y/3  -y/5

Taking LCM of like terms with y² as "6"

and LCM of like terms with y as "15".

We get ;

=(3y²+2y²)/6 +(5y-3y)/15

=5y²/6 +2y/15

Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is  5y²/6 +2y/15.

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244140625 x^{54} value of the Algebraic functions .

What is Algebraic functions?

Evaluate the exponent

= [tex]\frac{5^{7} . 125^{3} }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{78125 . 125x^{3} }{25^{2} } . x^{54}[/tex]

Multiply the numbers

= [tex]\frac{78125 . 1953125 }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{152587890625}{25^{2} } . x^{54}[/tex]

Cancel terms that are in both the numerator and denominator

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= 244140625 x^{54}

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The total of Sam's liabilities are $5225.

A liability is an obligation of an individual towards his creditors arising out of some transactions. Bank loans, credit card bills, accounts payable , accrued expenses are examples of liabilities.

Given that Sam has a car that is worth $8,500. However, he still owes $4,750 on the car. He also has $1,500 in his savings account, a comic book collection worth $900 and owes $475 on his credit card.

Irrespective of his assets and savings Sam still owes $4750 on the car and $475 in his card card , therefore these are his liabilities.

Total liabilities of Sam = $4750+$475 = $5225

Therefore, total of Sam's liabilities are $5225

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Answer -

1/2x + 5 = 7

1x/2 + 5 = 7

1x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 2.5/2 = 7

X = 4

Answer:

24

Step-by-step explanation:

3a/6 = 12

3a = 6 * 12

3a = 72

a = 72/3

a = 24

Check:

3*24/6 = 12

72/6 = 12

Answer:

Solutions below.

Step-by-step explanation:

a) To solve this question, we can use the formula.

Average Cost per Bracelet = Total Price ÷ Number of Bracelets.

Toy Barn

Average Cost = $5.40 ÷ 6 = $0.90 per bracelet

Dollar Deals

Average Cost = $10.50 ÷ 11 = $0.95 per bracelet (rounded off to 2 decimal places)

b) The better deal comes with a lower price per bracelet, in this case, Toy Barn has a better deal.