A flyer is spread by people at a large conference. Within one hour, the first person gives a stack of flyers to six people. Within the next hour, those six people give a stack of flyers to six new people. If this pattern continues, which summation can be used to calculate the number of people who receive a stack of flyers, not including the initial person, in the first five hours?
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n minus 1
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 1 (6) Superscript n minus 1
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n
Sigma-Summation Underscript n = 1 Overscript 4 EndScripts 1 (6) Superscript n

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Step-by-step explanation:

The parallel lines have:

The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y = 5x + 4

∴ m = 5 and b = 4

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = 5

- Substitute the value of the slope in the form of the equation

∴ y = 5x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The parallel line passes through point (-1 , 2)

∴ x = -1 and y = 2

∵ 2 = 5(-1) + b

∴ 2 = -5 + b

- Add 5 to both sides

∴ 7 = b

- Substitute the value of b in the equation

∴ y = 5x + 7

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

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Answer:

The fence is 18.9 ft long.

Step-by-step explanation:

If you were to create a diagonal line from corner to corner with a square that is 10x16ft, you would have a triangle with 2 known sides and an unknown value. In this case, because you are making a 90° triangle, you can use Pythagorean Theorem:

a^{2} + b^{2} = c^{2}

10^{2} + 16^{2} = c^{2}

100 + 256 = c^{2}

356 = c^{2}

√356 = c

18.9 = c

The length of the fence that Justin needs to split the garden diagonally is approximately 18.9 feet (rounded to the tenth of a foot).

To split the rectangular garden diagonally using a fence, you would be creating two right triangles with the fence as the hypotenuse. You can use the Pythagorean Theorem to find the length of the fence.

The Pythagorean Theorem states: [tex]\(c^2 = a^2 + b^2\)[/tex], where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In this case, the rectangular garden has dimensions of 10 feet and 16 feet, so a = 10 and b = 16. Let c be the length of the fence.

Now, use the Pythagorean Theorem to find c:

[tex]\[c^2 = 10^2 + 16^2\][/tex]

[tex]\[c^2 = 100 + 256\][/tex]

[tex]\[c^2 = 356\][/tex]

Now, take the square root of both sides to find c:

[tex]\[c = \sqrt{356} \approx 18.9\text{ feet}\][/tex]

So, the length of the fence that Justin needs to split the garden diagonally is approximately 18.9 feet (rounded to the tenth of a foot).

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Answer:

2 years are the 18.2% of 11 years.

Step-by-step explanation:

For calculating what percentage of 11 years is 2 years, we have to do the following calculations:

Fraction used to represent the question = 2/11

Now, we divide 2 by 11, where 2 is the dividend and 11 the divisor:

2/11 = 0.1818....

Converting 0.1818 to percentage:

0.1818 * 100 = 18.2% (Rounding to the nearest tenth)

2 years are the 18.2% of 11 years.

Maximum number of rides Alex can go is 23

Solution:

Given that Alex mom gave him $ 45 to spend

Admission to the fair was  $ 7, and each ride costs $1.50

From given question,

The amount of money spent on admission to the fair and on a number of rides which each cost $ 1.50, must be at most $ 45

"At most $ 45" means $ 45 exactly or less

Let "x" be the number of rides Alex takes up

[tex]7 + 1.50 (x) \leq 45[/tex]

[tex]1.50x + 7 \leq 45[/tex]

This is the required inequality

To find the maximum number of possible rides, solve for  x

[tex]1.50x + 7 \leq 45\\\\1.50x\leq 45 - 7\\\\1.50x\leq 38\\\\x \leq 25.33[/tex]

Thus maximum number of rides he can go is 23

Answer:

t=3

Step-by-step explanation:

6t= 36+7-25

t=18/6

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for&a\geq0\\-a&for&a<0\end{array}\right\\\\|x-4|=\left\{\begin{array}{ccc}x-4&for&x-4\geq0\to x\geq4\\-(x-4)&for&x<4\end{array}\right[/tex]

[tex](1)\ x<4\\\\-(x-4)-5=3(x-1)\qquad\text{use the distributivep property}\\\\-x-(-4)-5=3x+(3)(-1)\\\\-x+4-5=3x-3\qquad\text{combine like terms}\\\\-x+(4-5)=3x-3\\\\-x-1=3x-3\qquad\text{add 1 to both sides}\\\\-x-1+1=3x-3+1\\\\-x=3x-2\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-2\\\\-4x=-2\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-2}{-4}\\\\x=\dfrac{1}{2}\in(1)[/tex]

[tex](2)\ x\geq4\\\\x-4-5=3(x-1)\\\\x+(-4-5)=3x-3\\\\x-9=3x-3\qquad\text{add 9 to both sides}\\\\x-9+9=3x-3+9\\\\x=3x+6\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x-3x=3x-3x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3\notin(2)[/tex]

Answer:

a

Step-by-step explanation:

Answer:

[tex](x^3-11x^2+ 22x + 40)\div (x-5)=(x^2-6x-8)[/tex]

Step-by-step explanation:

When dividing [tex](x^3-11x^2+ 22x + 40)[/tex] by [tex](x-5),[/tex]

1. Multiply [tex](x-5)[/tex] by [tex]x^2[/tex] and subtract the result from [tex](x^3-11x^2+ 22x + 40)[/tex] to eliminate [tex]x^3:[/tex]

[tex](x^3-11x^2+ 22x + 40)-x^2(x-5)\\ \\=x^3-11x^2+22x+40-x^2+5x^2\\ \\=-6x^2+22x+40[/tex]

2. Multiply [tex](x-5)[/tex] by [tex]-6x[/tex] and subtract the result from [tex]-6x^2+22x+40[/tex] to eliminate [tex]-6x^2:[/tex]

[tex]-6x^2+22x+40-(-6x)(x-5)\\ \\=-6x^2+22x+40+6x^2-30x\\ \\=-8x+40[/tex]

3. Multiply [tex](x-5)[/tex] by [tex]-8[/tex] and subtract the result from [tex]-8x+40[/tex] to eliminate [tex]-8x:[/tex]

[tex]-8x+40-(-8)(x-5)\\ \\=-8x+40+8x-40\\ \\=0[/tex]

So,

[tex](x^3-11x^2+ 22x + 40)\div (x-5)=(x^2-6x-8)[/tex]

x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = [tex]\frac{1}{5}[/tex]

∵ Tim can finish the job in 6 hours

∴ The rate of Tim = [tex]\frac{1}{6}[/tex]

∵ Sam can finish the job in x hours

∴ The rate of Sam = [tex]\frac{1}{x}[/tex]

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

∴ [tex]\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}[/tex]

To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

   numerators of each fraction

∴ [tex]\frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}[/tex]

Add the numerators and put the sum over 30 x

∵ [tex]\frac{11x+30}{30x}=\frac{1}{2}[/tex]

- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

∴ 22 x + 60 = 30 x

- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

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Answer:

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The equation is -12/c=6

by solving for c you get,

-12/c=6

Then multiply both sides by the LCM c to get, -12=6c

Divide both sides by 6 to get,

-12/6=6c/6

-2=c

Verification:

-12/-2=6 since when a negative number divides a negative number the answer is a positive value

65 student tickets were sold

Solution:

Given that movie theater sells student tickets for $ 6 and adults for $ 8

Let "s" be the number of student tickets sold

Let "a" be the number of adult tickets sold

Cost of 1 student ticket = $ 6

Cost of 1 adult ticket = $ 8

Given that theater sold 140 tickets

Number of student tickets sold + number of adult tickets sold = 140

s + a = 140 ------ eqn 1

The theater generated $ 990

number of student tickets sold x Cost of 1 student ticket + number of adult tickets sold x Cost of 1 adult ticket = 990

[tex]s \times 6 + a \times 8 = 990[/tex]

6s + 8a = 990 ------ eqn 2

Let us solve eqn 1 and eqn 2 to find values of "s" and "a"

From eqn 1,

s = 140 - a ----- eqn 3

Substitute eqn 3 in eqn 2

6(140 - a) + 8a = 990

840 - 6a + 8a = 990

2a = 150

a = 75

Substitute a = 75 in eqn 3

s = 140 - 75

s = 65

Therefore 65 student tickets were sold

Answer:

Explanation:

1. Using the minimun number of sheets  of paper in the interval [300, 400]

a) Cost: $ 2.00 / 100 sheets

b) 300 sheets / day × $ 2.00 / 100 sheets = $ 6.00 / day

c) Approimately 20 school days per month:

2. Using the maximum number of sheets of paper in the interval [300, 400]

a) Cost: $ 2.00 / 100 sheets

b) 400 sheets / day × $ 2.00 / 100 sheets = $ 8.00 / day

c) Approimately 20 school days per month:

3. Middle value:

Calculate the middle value between $160.00 and $120.00

Thus, the answer is the option A.

Answer:

40

Step-by-step explanation:

80% of the test = 32 questions

100% of the test = x questions

Cross multiply

80*x = 100 * 32   Combine the right

80x = 3200         Divide by 80

x = 3200/80

x = 40

There are 40 questions on the test.

Answer:

Here Two triangles BDE and BAC are similar as mentioned

So, According to Similarity of triangles theorem

BE/BC = DE/AC

4/16= x/20

1/4 = x/20

x= 20/4

x=5

Answer:

-9.4, -0.5, 0.75, 1.25, 7/4

Step-by-step explanation:

These are the values of all the numbers in order.

Have a good day!!!

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, convert them into decimal form and mark these points on a line between appropriate integers. Hence, the points are -2.25 (between -2 and -3), -0.5 (between 0 and -1), 0.75 (between 0 and 1), and 1.25 and 1.75 (between 1 and 2).

To plot the given numbers -0.5, 7/4, 1.25, 0.75, -9/4 on a number line, we first need to convert them all into the same form. Converting everything into decimals, we have -0.5, 1.75 (which is 7/4), 1.25, 0.75, and -2.25 (which is -9/4).

Start by drawing a straight horizontal line and mark the points for integers. For example, if the numbers range from -3 to +2, mark these integers on your line. Next, find the points that correspond to the decimal numbers. Suppose you've marked the numbers from -3 to 2, your plot would look like the following:

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Balancing of equations as shown in the attached document requires that the number of atoms, of an element, on the left of the equation is equivalent to the number of the atoms of the same element on the right of the equation. This is in observation of the conservation of mass rule of thermodynamics. Mass and energy cannot be destroyed nor created, it can only be transformed from one form to another. In this case, mass remains the same in the system since this is a chemical reaction- only the bonds between atoms are being rearranged.

Answer:

Part a) The equation for the volume of the film canister is

[tex]32\pi=\pi r^{2}(8)[/tex]

Part b) The radius of the film canister is [tex]2\ cm[/tex]

Step-by-step explanation:

The complete question is

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius of the circular base

h is the height of the cylinder

we have

[tex]V=32\pi\ cm^3[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

[tex]32\pi=\pi r^{2}(8)[/tex]

[tex]32\pi=8\pi r^{2}[/tex]

Simplify

Divide by 8π both sides

[tex]4=r^{2}[/tex]

square root both sides

[tex]r=2\ cm[/tex]

The equation for the volume of the film canister is V = 3.142 × r² × 8.

Use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height.

Substitute the given values into the formula to calculate the volume.

For a given height of 8 centimetres, the volume formula becomes V = 3.142 × r² × 8.

Answer:

Maximum time the teacher should allow for the whole test should be = 55 minutes

Step-by-step explanation:

Number of easy questions in the test = 50

Number of hard questions in the test = 20

Time for each easy question = 30 seconds = [tex]30\ sec\times\frac{1\ min}{60 sec}=0.5\ min[/tex]    

[As 1 minute = 60 seconds]

Time for each hard question = 1 minute 30 seconds = [tex]1\ min+(30\ sec\times\frac{1\ min}{60 sec})=1\ min+0.5\ min=1.5\ min[/tex]

Using unitary method to find duration of whole test.

If 1 easy question takes = 0.5 minutes

Then, 50 easy questions will take = [tex]50\times 0.5\ min[/tex] = 25 minutes

If 1 hard question takes = 1.5 minutes

Then, 20 hard questions will take = [tex]20\times 1.5\ min[/tex] = 30 minutes

Total time for the test will be = [tex]25\ min+30\ min[/tex] = 55 minutes

Answer: 4.75x + 525

Step-by-step explanation:

4.75 times x (the square feet) plus 525

Answer:

x = 1 is not part of the domain

Step-by-step explanation:

The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve

x - 1 = 0 ⇒ x = 1 ← restricted value

The number x = 1 is not part of the domain of the function g(x) = (x+2)/(x-1) because setting x to 1 would result in division by zero, which is undefined. Thus, x = 1 is an asymptotic value and is excluded from the domain.

The number that is not part of the domain of the function g(x) = \frac{x+2}{x-1} is x = 1. Knowing that the domain of a function includes all the values that x can take on for which the function is defined, we can identify values that are not in the domain by looking for any values that would cause the function to be undefined. In the case of g(x), since it involves a division by x-1, we need to make sure that the denominator does not equal zero since division by zero is undefined in mathematics.

To find out when the denominator is zero, we set x-1 = 0 and solve for x. The solution is x = 1, which means that x cannot be 1, since it would make the function undefined. Therefore, x = 1 is not part of the domain of g(x).

As described in FIGURE 4.4 from OpenStax under a CC BY 4.0 license, functions like y = \frac{1}{x} have asymptotes or limits that indicate values that are not part of the domain. g(x) has a similar characteristic, where x = 1 is an asymptote.

Answer:

3x² - 12x - 36

= 3(x - 6)(x + 2)

Step-by-step explanation:

3x² - 12x - 36      Find any common factor. All terms are divisible by 3.

= 3(x² - 4x - 12)    Find two numbers that sum to -4 and whose product is -12. Replace -4 with these two numbers.

= 3(x² - 6x + 2x - 12)   Group the terms splitting from the middle

= 3( (x² - 6x) + (2x - 12) )   Find the common factor in each group.

= 3( x(x - 6) + 2(x - 6) )      The groups have a common factor (x - 6).

= 3( (x - 6)(x + 2) )           Remove the extra brackets

= 3(x - 6)(x + 2)             Fully factored

Answer: [tex]x=26[/tex]

Step-by-step explanation:

When parallel lines are cut by a transversal several angles are formed.

A pair of non-adjacent angles located outside the parallel lines and on opposite sides of the transversal are called  "Alternate Exterior angles".

By definition, they are congruent, which means that they have equal measure.

In this case, you can identify that [tex](5x+7)\°[/tex] and [tex](8x-71)\°[/tex] are Altermate Exterior angles.

Then, you can write the following equation:

[tex]5x+7=8x-71[/tex]

Finally, you must solve for "x" in order to find its value. This is:

[tex]7+71=8x-5x\\\\78=3x\\\\x=26[/tex]

Final answer:

The final line of Mariana's work would show identical sides after simplification, resulting in an equation like 0 = 0 or x = x, indicating an infinite number of solutions.

Explanation:

If Mariana solved a linear equation and found that it had an infinite number of solutions, the final line of her work would show that both sides of the equation are identical after simplification. For instance, if the original equation was 2x + 3 = x + x + 3, upon simplifying both sides, she would end up with x + x = x + x, which is an identity (indicating that any value for x would satisfy the equation). Therefore, the final line could have been a simplified equation that resulted in a statement like 0 = 0 or x = x after all terms cancel out.

Answer:

The required points of the given line segment  are ( - 3, - 7 ).

Step-by-step explanation:

Given that the line segment CD whose midpoint M is ( 1, - 1 ) and point D is ( 5, 5 ), then we have to find point C of the line segment CD-

As we know that-

If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex] ) and  ([tex]x_{2}, y_{2}[/tex]  then the mid points C are-  

C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )

Here,

Let C ( x, y ), D ( 5, 5 ) with midpoint M ( 1, -1 )-

then by the midpoint formula-

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

On comparing x coordinate and y coordinate -

We get,

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

( x + 5 = 2, y + 5 = - 2 )

( x = 2 - 5,  y = -2 - 5 )

( x = - 3,  y = -7 )

Hence the required points  C are (- 3, - 7 ).

We can also verify by putting these points into Midpoint formula.

Answer:

It's asking for simplifying expression with the given value.

Step-by-step explanation:

3x^4 - x + 4; x = 3

3(3)^4 - (3) + 4

3(81) - 3 + 4

243 - 3 + 4

243 + 1

244

Answer:

Step-by-step explanation:

2) 3x⁴ - 25x³ + 27 =   3(2)⁴ - 25(2)³ + 27  = 3*16 - 25*8  +27 = 48 - 200 + 27

= -125

3) 20s⁴ + 24s³ + 4s = 20(1)⁴ + 24(1)³ + 4(1)

= 20 + 24 + 4 = 48

4) 6m⁴ - 4m +20 =  6(4)⁴ - 4(4) +20

= 6*256 - 16 + 20= 1536 - 16 + 20

=1540

5) - 7p⁴ - p + 9 = -7(-2)⁴ - (-2) +9 = -7*16 + 2 +9 = -112 + 2 + 9 = - 101

6) 6a⁷ - a³ + a = 6(-1)⁷ - (-1)³ + (-1) = 6*(-1) - (-1) - 1 = -6 + 1 - 1 = -6

A. side AB = 38/3 units B.m∠VYX =77°

Step-by-step explanation:

A.A rhombus has its four sides equal. This means side AB=side CD

Given that AB=5x+1 and CD=2x+8  equate the two sides to find value of x as;

5x+1=2x+8

collect like terms

5x-2x=8-1

3x=7

x=7/3

side AB = 5x+1

AB= 5*7/3 +1

AB=35/3 +1

AB=35/3 +3/3 = 38/3

B.

The diagonals of a rhombus intersect to form 90°

Hence

(3n²-0.75)°=90°

3n²=90°+ 0.75°

3n² =90.75° -----dividing by 3 both sides

n² =90.75°/3 =30.25°

n²=30.25°

n=√30.25°

n=5.5°

so angle Z =90°

and angle ZVW =(9n+2)°

∠ZVW = (9*5.5 +2 )° =51.5°

In a rhombus all four sides are equal, thus side VY = YX.This means triangle VYX is an isosceles triangle.

Hence angle ∠YVZ=∠WVZ =51.5°, and because VYX is an isosceles triangle then ∠YXV =51.5° so

∠VYX= 180°-(51.5°+51.5°)

          =180°-103°=77°

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Answer:

Step-by-step explanation:

Put the equation in the form y = mx + b.

Plot the y-intercept, (0,b).

Use the slope to find another point on the line.

Connect the two points in a straight line.

Hey!

I'm also getting 11.4, do you think you're wrong or is it saying so? I have also calculated the answer 11.4.

I believe you aren't wrong, but we will make sure.

12 Divided by 100 times 95, you get 11.4, I believe you're correct!

Please give me any updates and let me know if you need any extra help.

Answer:

x=-5/2, -3

Step-by-step explanation:

2x^2+11x+15=0

factor out the trinomial

(2x+5)(x+3)=0

zero property,

2x+5=0, x+3=0

2x=0-5=-5, x=-5/2

x=0-3=-3