Find distance between parallel lines given equations in 3d

Answer:

Step-by-step explanation:

The answer is actually B. $160,000; $320,000

The reason for this is because -

$10,000 is the constant, so let a= 10,000.

The investment doubles every 13 years, so let b=2.

Let x= the number of 13-year periods.

The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.

To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).

The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).

After 52 years, the investment's worth would be calculated as follows:

$10,000 × (2^4) = $10,000 × 16 = $160,000

After 65 years, the investment's worth would be:

$10,000 × (2^5) = $10,000 × 32 = $320,000

Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.

Answer:

[tex]10x^4+65x^3-25x^2[/tex]

Step-by-step explanation:

Multiply 5x^2(2x^2 + 13x − 5)

[tex]5x^2(2x^2 + 13x - 5)[/tex]

Multiply 5x^2 inside the parenthesis

[tex]5x^2 * 2x^2 = 10x^4[/tex]

[tex]5x^2 * 13x = 65x^3[/tex]

[tex]5x^2 * (-5) = -25x^2[/tex]

Collect all the terms together

[tex]10x^4+65x^3-25x^2[/tex]

Answer:

Close to 240 times but probably not exactly 240 times

Step-by-step explanation:

Answer:

Step-by-step explanation:

(0.17/365 x30)(6390)

The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To calculate the amount Joan was charged in interest for the billing cycle using the previous balance method, we need to find the average daily balance for the billing cycle, which is calculated as the sum of the daily balances divided by the number of days in the billing cycle.

The daily balance is the balance at the end of each day, and it is calculated by adding new purchases and subtracting payments and credits from the previous day's balance.

In this case,

Joan had a balance of $6390 for the first 3 days of the billing cycle, so her average daily balance for the billing cycle can be calculated as:

((3 x 6390) + (27 x 0)) / 30

= 1917

This means that her average daily balance for the billing cycle was $1917.

To calculate the amount of interest Joan was charged for the billing cycle, we can use the following expression:

Interest = Average Daily Balance x Daily Interest Rate x Number of Days in Billing Cycle

The daily interest rate is calculated as the APR divided by 365 since there are 365 days in a year. In this case, the daily interest rate is:

0.17 / 365

= 0.000465753

So, the expression that can be used to calculate the amount of interest Joan was charged for the billing cycle is:

Interest = 1917 x 0.000465753 x 30

= $26.84 (rounded to the nearest cent)

Therefore,

The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.

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We are given the formula:

V = l w h

and the following values:

l = ?

V = 1344 cm^3

w = 8 cm

h = 12 cm

SO rewriting the formula in terms of l:

l = V / w h

l = 1344 cm^3 / (8 cm * 12 cm)

l = 14 cm

Answer:

d

The answer would be 14

Answer:

(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]

Upon solving the given expression, we get

=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)

=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]

=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

which is the required simplified form of the given equation.

Hence, option A is correct.

Answer:

She ran 5 miles

Step-by-step explanation:

To solve this, we can easily use proportion.

The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.

Using proportion;

Let x = the number of miles Rily  can run

5,280 feet     = 1 mile

26,400 feet    = x

Cross-multiply

5280x = 26,400

To get the value of x, we will divide both-side of the equation by 5280

5280x/5280 = 26400/5280

(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)

x = 26400 / 5280

x=5 mile

Therefore, If Rily ran 26400 feet, then she has ran 5 miles.

We are given a function H(t) that represents the height of a cannon ball after t seconds as:

                  [tex]H(t)=-16t^2+48t+12[/tex]

and a second cannon ball is represented by the function g(t) as:

                       [tex]g(t)=10+15.2t[/tex]

PART A:

  t           0            1             2            3

H(t)        12          44          44           12

g(t)         15.2       25.2      40.4       55.6

Hence, between t= 2 seconds and t=3 seconds the ball will meet

     such that H(t)=g(t)

Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.

and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.

Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.

and the time at which they meet is calculated by solving:

[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]

As t can't be negative.

Hence, we get:

t=2.109 seconds

PART B:

The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.

The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.

To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).

The translation vector is given by:

Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)

Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):

Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)

So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).

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The simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

As we know, the expression can be defined as the combination of constants and variables with mathematical operators.

To begin, either multiply or divide the value in parentheses (32-4), which equals 5.

Add the number in the parentheses once more: 90/[10+5 (always do the parenthesis first) [10+5]= 15.

Finally, divide 90/15 by 6, always keeping that in mind (PEMDAS)

Thus, the simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.

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2x +4 =14

2x =10

x =5

 the number is 5

The length and width of the rectangle are 11 m and 7 m respectively.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

Length of the rectangle is 10 m less  than three times the width,

And area of rectangle = 77 m²

Let the width of rectangle is x m,

Then length of rectangle = 3x -10 m.

The area of rectangle = 77

length × width = 77

x × (3x - 10) = 77

The value of x = 7 satisfy the equation,

Therefore, the width of rectangle is x = 7 m                  

And length of the rectangle is 3x - 10 = 21 - 10 = 11 m

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The Cartesian form of equation is,

3x + 4y = 12

We have to given that,

The parametric equations are,

x = 4 sin² θ

y = 3 cos² θ

Now, Change the parametric equations into cartesian form as,

x = 4 sin² θ

sin² θ = x/4  .. (i)

y = 3 cos² θ

cos² θ = y/3 (ii)

Add equation (i) and (ii),

sin² θ + cos² θ = x/4 + y/3

1 = x/4 + y/3

1 = (3x + 4y)/12

12 = 3x + 4y

3x + 4y = 12

Therefore, The Cartesian form of equation is,

3x + 4y = 12

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