Solve for x and graph the solution on the number line below.

The rules of the patterns are 3 + 3x and 6 + 6y

The patterns are given as:

For pattern x, we have the following highlights:

Start = 3

Rule = Add 3

This means that the nth term of pattern x is:

Pattern x = 3 + 3x

For pattern y, we have the following highlights:

Start = 6

Rule = Add 6

This means that the nth term of pattern y is:

Pattern y = 6 + 6y

For pattern x, set x = 0, 1, 2 and 3

So, we have

3 + 3x = 3 + 3(0) = 3

3 + 3x = 3 + 3(1) = 6

3 + 3x = 3 + 3(2) = 9

3 + 3x = 3 + 3(3) = 12

For pattern y, set y = 0, 1, 2 and 3

So, we have

6 + 6x = 6 + 6(0) = 6

6 + 6x = 6 + 6(1) = 12

6 + 6x = 6 + 6(2) = 18

6 + 6x = 6 + 6(3) = 24

Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern

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Answer:

61500

Step-by-step explanation:

1/3 = 3/15

2/5 = 6/15

1 - 3/15 - 6/15 = 6/15

6/15 = 24600

24600 ÷ 6 × 15 = 61500

Answer:

92250

Step-by-step explanation:

Forming algebraic equation and solving:

Let the income  = x

Amount spent on housing = (1/3) of the income

                                             [tex]\sf = \dfrac{1}{3}x[/tex]

Amount spent of daily expenditure = (2/5) of the income

                                                          [tex]\sf =\dfrac{2}{5}x[/tex]

Income = Savings + housing expenditure + daily expenditure  

Income - housing expenditure - daily expenditure = savings

[tex]\sf x - \dfrac{1}{3}x-\dfrac{2}{5}x=24600\\\\\\\dfrac{x*15}{1*15}-\dfrac{1*5}{3*5}x-\dfrac{2*3}{5*3}x = 24600\\\\\\[/tex]

            [tex]\sf \dfrac{15}{15}x-\dfrac{5}{15}x-\dfrac{6}{15}x = 24600\\\\\\\dfrac{(15 -5 - 6)}{15}x = 24600[/tex]

              [tex]\sf \dfrac{4}{15}x = 24600[/tex]

                 [tex]\sf x = 24600 *\dfrac{15}{4}\\\\ x = 6150*15[/tex]

Income = 92250

The value that will be equivalent to the expression will be 5625³.

It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.

The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:

= (3² × 5⁴)³

= (9 × 625)³

= 5625³

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Answer:

243

Step-by-step explanation:

-9^2 = -9 * -9 = 81

81 * 3 = 243

The best possible ways to compare least crowded place are options A and D

Given that,

Antonio is comparing the crowdedness at three different sports events. Our aim to find the least crowded sporting event. Here we use square meter as measurement for population. So it is pretty obvious that a place is less crowded when people in that region are less in number. So the option A is correct which is less people per square meter. Similarly, option D is also correct because if a person have more square meters then it is clear that the region is less populated .

Therefore, the options A and D are the go-to ways to compare the least crowdedness in the sporting events.

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Answer:

The things that you need to pick are option A and option D. Trust me on this, I did the exact same question and I got is correct. Also please please please pick me as Brainliest... or y'know don't... and then feel bad.

The mattress has a total cost of  $24.28

From the question, the given parameters are:

Cost of a mattress = $74.95

Markdown = 70%

Sales tax in oak grove = 8%

Using the sales tax and the markdown, the total cost for the mattress is calculated using

Total cost of mattress = Cost of a mattress * (1 + Sales tax) * (1 - Markdown )

Substitute the known values in the above equation

So, we have the following equation

Total cost of mattress = 74.95 * (1 + 8%) * (1 - 70%)

Evaluate the products

Total cost of mattress = 24.28

Hence, the total cost of the mattress is $24.28

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The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

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yes, it is the same than 3:2. And we can not simplify it more

Answer: C : y = 3/2 - 4

Step-by-step explanation:

Find the Slope (Slope Formula)

(4,2) (6,5)

m = (5-2)/(6-4)

m = 3/2

Find "b"

y = mx + b (Slope intercept form)

2 = 3/2(4) + b

2 = 6 + b

-4 = b

Answer:

width < 13

Step-by-step explanation:

let width of the rectangle = x

length = 8 + 2x

according to the question,

8+2x < 34

2x < 34-8

2x < 26

x < 13

Considering the area of the rectangular lot, the width of the walkway is of 3.9 feet.

Considering a rectangle of length l and width w, we have that the area and the perimeter are given as follows:

In the context of this problem, for the garden and the walkway, the dimensions are given as follows:

Considering that the area is of 238 square feet, we can solve for the width of the walkway as follows:

15(12 + w) = 238

12 + w = 238/15

12 + w = 15.9.

w = 15.9 - 12

w = 3.9 feet, which is the width of the walkway.

Since the area is in square feet, the length and the width are in feet.

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Answer:

  16,400 ft

Step-by-step explanation:

You want to know the number of feet in a 5 km race, rounded to the nearest hundred. You are given conversion factors 5280 ft = 1 mi = 1.61 km.

Unit conversion can be done by multiplying by a conversion factor whose numerator is equal to its denominator, and that cancels unwanted units, replacing them with units you want.

  [tex]5\text{ km}=5\text{ km}\times\dfrac{5280\text{ ft}}{1.61\text{ km}}\approx16397.5\text{ ft}\approx\boxed{16,\!400\text{ ft}}[/tex]

__

Additional comment

Both of the given conversions are equal to 1 mile, so their ratio is 1. We put feet on top of the fraction, because that is the unit we want. The km value is in the denominator so the km units in numerator and denominator cancel.

The conversion for km is 1 mi = 1.609344 km (exactly). The actual conversion to ft will give 16,404 76/381 ft. This has a very long repeating decimal fraction.

Answer:

4x² + 29x + 7 = (4x + 1)(x + 7)

Step-by-step explanation:

Like terms are terms with same variable and same power.

       Perimeter = sum of all the sides

                         = 3x² + 1 + 15x + 6 + x² + 14x

                         = 3x² + x² + 15x + 14x + 1 + 6

Combine like terms,

                        = 4x² + 29x + 7

Factorize:

        Sum = 29

  Product = 4*7 = 28

   Factors = 1 , 28    {28 + 1 = 29 & 28*1 = 28}

Rewrite the middle term using the factors,

                           = 4x² + x + 28x + 7

                           = x(4x + 1) + 7(4x + 1)

                           = (4x + 1)(x + 7)

Answer:

x=71 y=109

Step-by-step explanation:

Answer:

lie on a certain vertical straight line

Step-by-step explanation:

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics.

Answer: x = 58

Step-by-step explanation:

The angles are alternating interior angles. This means that the angles are equal.

So x = 58

Answer:

I think it's because the triangle sides are isometrics so that's why the sides are equal

Answer:

a opened because a closed means that number ond more

Step-by-step explanation:

The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Θ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]

a ) We assume that the length until the first flaw follows an exponential distribution.

Probability density function of exponential distribution:

f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]

The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.

The probability is the integral over the corresponding interval:

the further calculation has been shown in fig. attached

since equation was not possible to write here

b) We assume that the length until the first flaw follows an exponential distribution.

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Answer:

D

Step-by-step explanation:

2d + 8y = 20

y = 2

substitute y = 2 into the other equation

2d + 8(2) = 20

2d + 16 = 20 ( subtract 16 from both sides )

2d = 4 ( divide both sides by 2 )

d = 2

solution is (2, 2 )

answer-> D. (2,2)

Given,

2d + 8y = 20  .............................................(Equation i)

y = 2 .............................................................(Equation ii)

substituting y = 2 in equation i, we get

2d + 8(2) = 20

2d + 16 = 20

2d = 20 - 16

2d = 4

d = 2

Hence the correct answer would be option D. (2,2)

We have used the substitution method to solve the given system of linear equations.

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Answer:

No solution

Step-by-step explanation:

2- 3x + 4 + x = -2x + 1

2  -3x  + 4 + x = -2x + 1

6  -3x + x = -2x + 1

6  -3x + x = -2x + 1

6  -2x = -2x + 1

6  -2x = -2x + 1

move -2x to the right by adding 2x on both sides

6  -2x = -2x + 1

+2x         +2x

6  =  + 1

is 6 equal to 1?

No, so No solution

We have the next formula to calculate the volume of the cylinder

where

r is the radius

h is the height

in our problem

r=3in

h=9in

we substitute the values

the volume round to the nearest tenth is V=254.5 in ^3

Give to each part of the fraction a variable (a letter)

Numerator: n

Denominator: d

the denominator of a fraction is two more than the numerator:

both numerator and denominator are increased by ten, the simplified is 9/10:

Use the equation above to find the value of n:

As n is equal to 8 find the value of d:

The original fraction is:

From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.

We are to find how many hours will a customer use the bike per dollar.

This can also be likened to calculating miles per gallon.

if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.

So, hours per dollar is also a division problem too.

(9 hours)/($38)

= 9/38

= 0.2368

= 0.24 hours per dollar (to the nearest hundredth)

The area of the circle is 201 m².

So, the area of the circle:

We know that 4a = 2πr, now calculate r as follows:

Rounding off: 8m

Area of circle:

Rounding off: 201 m²

Therefore, the area of the circle is 201 m².

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If I stated 2 * - 3    OR  -10/-5  then the factor/quotient and its sign is given by -6 and 2

What is a quotient in math?

The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient

What is quotient formula?

The quotient formula is given as follows: Dividend ÷ Divisor = Quotient (if the remainder is zero) The general formula for any division problem is given by: Dividend ÷ Divisor = Quotient + Remainder.

2 * -3 = -6  or -10/-5= 2

Thus the quotient is -6 and 2

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If one of the daughters marries a non-bald man and they have a son, the chance that the son will become bald as an adult is 0%

If the couple has a daughter, the chance that she will become bald as an adult is 0%

In the question, we have been given that the neither the father nor the mother is bald, and out of the four children only one son is bald, but the other son and the two daughters are not bald, now we solve the following:

Part a

A chance that the son will become bald as an adult:

If the daughter has no bald gene (XX), and she marries a non bald man then there is 0% chance that the son will become bald as an adult because neither the mom nor the dad has the baldness gene

Part b

The chance that she will become bald as an adult:

If the daughter having a bald gene ([tex]X^{b} X[/tex]) marries a non bald (XY)man then also there is a 0% chance that the daughter will be bald as an adult. As the baldness is a recessive trait, for the daughter to be bald she needs to have two baldness gene( one from father and one from mother). And since this is not the case the daughter might have baldness gene but the phenotype will be non-bald.

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The value of the greater integer will be 10.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The algebraic expression is,

'' An integer is subtracted from 8 times the next consecutive integer, the difference is 71.''

Now,

Let a number = x

Then, Its consecutive number = (x + 1)

So, We can formulate;

⇒ 8 (x + 1) - x = 71

Solve for x as;

⇒ 8x + 8 - x = 71

⇒ 7x + 8 = 71

⇒ 7x = 71 - 8

⇒ 7x = 63

⇒ x = 9

Thus, The value of greater number = x + 1

                                                      = 9 + 1

                                                       = 10

Therefore, The value of the greater integer will be 10.

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Answer:

Simplifying

7 + 2x = 4x + -3

Reorder the terms:

7 + 2x = -3 + 4x

Solving

7 + 2x = -3 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

7 + 2x + -4x = -3 + 4x + -4x

Combine like terms: 2x + -4x = -2x

7 + -2x = -3 + 4x + -4x

Combine like terms: 4x + -4x = 0

7 + -2x = -3 + 0

7 + -2x = -3

Add '-7' to each side of the equation.

7 + -7 + -2x = -3 + -7

Combine like terms: 7 + -7 = 0

0 + -2x = -3 + -7

-2x = -3 + -7

Combine like terms: -3 + -7 = -10

-2x = -10

Divide each side by '-2'.

x = 5

Simplifying

x = 5