find the equation of the passing through p(4,6) which is parallel to the line with equation 4x-2y+6=0

The expected age for one of the passengers on the train is 7.1 years. This can be explained by following steps:

Following are the calculation for the expected age given  

½ = 6 years old  

1/10 = 7 years old

1/5 = 8 years old  

1/5 = 9 years old

With the help of the above information, expected age can be calculated as follows:  

Expected age = ½*6+1/10*7+1/5*8+1/5*9

 = 6/2+7/10+8/5+9/5

 =3+0.7+1.6+1.8

 = 7.1

Therefore, the correct answer is 7.1 years old.

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The length of the rectangle is 12 yards and the width is 6 yards. The problem is solved with algebra using the formulas for the perimeter of a rectangle and given relation between the length and width.

This problem involves the use of algebra in solving geometrical problems. The question provides information about the perimeter and the relationship of length to width using algebraic expressions. To find the length and the width, we can use the formulas for the perimeter of a rectangle (P=2L + 2W) and the given width (W=2L-18).

Let L represent the length. Then, 2L+W=18 represents the width. Setting 2L + 2W equal to the given perimeter of 36, we get 2L + 2(2L - 18) = 36.

Solving this equation gives: L = 12, and substituting L=12 into W=2L - 18, we get: W=6. Hence, the length is 12 yards and the width is 6 yards.

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Answer:   [tex]x-2y+7=0[/tex]

Step-by-step explanation:

Given : The  line[tex]L_1[/tex] has equation [tex]2x + y = 8[/tex]

In intercept form : [tex]y =-2x+8[/tex]

The slope of [tex]L_1[/tex] =-2    [in intercept form equation of line [tex]y =mx+c[/tex], m is slope ]

Let p be slope of  [tex]L_2[/tex]

We know that when two lines are perpendicular then the product of their slopes is -1.

[tex]\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}[/tex]

The equation of line having slope 'm' and passing through (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Then , equation of line  [tex]L_2[/tex] will be :-

[tex](y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7[/tex]

Answer:

A

Step-by-step explanation:

The pair of equations that would correctly calculate their compound interests are:

Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10

Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P (1+r/n)^(nt)

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

For Veronique, we have:

A = 1000(1 + 0.05/1)⁷ = $1,407.10

For Lily, we have:

A = 1800(1 + 0.09/1)⁷ = $3290.47

To calculate the compound interest for each account, we subtract the principal amount from the final amount:

For Veronique:

Interest = A - P = $1,407.10 - $1,000 = $407.10

For Lily:

Interest = A - P = $3,290.47 - $1,800 = $1,490.47

Therefore, the pair of equations that would correctly calculate their compound interests are:

Veronique's interest = A = 1000(1 + 0.05/1)⁷ - 1000 = 407.10

Lily's interest = 1800(1 + 0.09/1)⁷ - 1800 = 1,490.47.

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So, water decreases by 12 gallons EVERY minute.

How much water will decrease in 60 minutes?

[tex]12*60=720[/tex] gallons

So, the volume changes by 720 gallons in 60 minutes.

ANSWER: Volume decreases 720 gallons in 60 minutes.

Answer:

decreasing linear

Step-by-step explanation:

Answer:

Stu estimated correctly by rounding up.

He ordered enough brick.

The exact area is [tex]228.75[/tex] square feet

Step-by-step explanation:

we know that

the area of the patio is equal to

[tex]A=bh[/tex]

In this problem we have

[tex]b=12.5\ ft, h=18.3\ ft[/tex]

substitute in the formula

[tex]A=12.5*18.3=228.75\ ft^{2}[/tex]

[tex]228.75\ ft^{2}< 247\ ft^{2}[/tex]

The sum of three consecutive integers where the last integer is z is 3z - 3.

The sum of three consecutive integers can be derived using the concept of arithmetic series. For instance, if z represents the last of the three consecutive integers, we know that the numerals preceding it are z-1 and z-2. Hence, the sum of these three integers would be (z-2) + (z-1) + z.

Simplifying this, we get 3z - 3 which corresponds to option c.)3z-3 in the question's list.

Remember, an important aspect of sequences and series is that the numbers are arranged in a specific order.

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The equation of the line that passes through (0, 5) and (−1.5, 1) is y = 8/3 x + 5

The equation can be represented as follows:

y = mx + b

where

m = slope

b = y-intercept

lets find the slope

(0, 5)  (−1.5, 1)

m = 1 - 5 / -1.5 - 0 = - 4 / -1.5 ≈  8 / 3

we multiplied the numerator and denominator by 2

b = 5, b is the value of y when x = 0.

Therefore, the equation will be as follows:

y = 8/3 x + 5

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Answer:

a). it is an Infinite Sequence.

b). This sequence is Geometric Progression.

c).  [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]                              

Step-by-step explanation:

Given: A Sequence 2a , 2a²b , 2a³b² , [tex]2a^4b^3[/tex]

To find: a). Given Sequence is finite or infinite

             b). Pattern of the sequence

             c). Sixth term

a). Since, there is no detail about no. of terms of the sequence.

     Therefore, It implies it is an Infinite Sequence.

b). Given 1st term = 2a  ,  2nd term = 2a²b , 3rd term = 2a³b²

    First we find the difference of 1st and 2nd term

    d = 2a²b - 2a  ⇒  d = 2a (ab - 1)

    Now, Difference of 2nd and 3rd term,

    d = 2a³b² - 2a²b = 2a²b (ab - 1)

So, This Sequence is not a Arthematic Progression.

Now, we find the ratio of 2nd term to 1st term,

[tex]r\:=\:\frac{2a^2b}{2a}\,=\,ab[/tex]

Ratio of 3rd term to 2nd term,

[tex]r\:=\:\frac{2a^3b^2}{2a^2b}\,=\,ab[/tex]

Since, the ratio is common.

This sequence is Geometric Progression.

So, Pattern is next term of this sequence has 1 more in  power of a and b

⇒ [tex]nth\,term\,of\,this\,GP\,=\,2a^{n}b^{n-1}[/tex]

c). [tex]6th\,term\,of\,this\,GP\,=\,2a^{6}b^{6-1}[/tex]

    [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]

Therfore, a). it is an Infinite Sequence.

               b). This sequence is Geometric Progression.

              c).  [tex]6th\,term\,of\,this\,GP\,=\,2a^6b^5[/tex]