Joan has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $6390, but that was her balance for only the first 3 days of the billing cycle, because she then paid off her entire balance and didn't make any new purchases. If her credit card's APR is 17%, which of these expressions could be used to calculate the amount Joan was charged in interest for the billing cycle?

In rectangle ABCD, the value of x, given that the lengths of the diagonals BD and AC are expressed as 10x + 8 and 9x + 20 respectively, is 12.

In a rectangle, the diagonals are equal in length. This gives us the following equation,

10x + 8 = 9x + 20, where BD and AC represent the lengths of the diagonals respectively.

To solve this for x, we subtract 9x from both sides, which gives: x + 8 = 20. Then, subtracting 8 from both sides of the equation gives: x = 20 - 8 = 12.

So, the value of x that suits this rectangle is 12.

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A circle is defined as all co-planar points equidistant from a given point

A line segment is a piece of a line that has two endpoints.

It is a part of a line with one end point and proceeds on in one direction.

A line refers to collection of line along a straight path proceeding in opposite directions with no endpoints.

Level: Middle school

Subject: Geometry

Topic: Shapes and terms in geometry

Answer:  The slope of the tangent line at the point (3, 2) is [tex]\dfrac[4}{9}.[/tex]

Step-by-step explanation:  We are given to find the slope of the line tangent to the following curve at the point (3, 2).

[tex]3y^2-2x^2=6-2xy~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that the derivative of a function at any given point is equal to the slope of the tangent at that point.

Now, differentiating both sides of equation (i) with respect to x, we have

[tex]\dfrac{d}{dx}(3y^2-2x^2)=\dfrac{d}{dx}(6-2xy)\\\\\\\Rightarrow 6y\dfrac{dy}{dx}-4x=0-2\left(y+x\dfrac{dy}{dx}\right)\\\\\\\Rightarrow 2x\dfrac{dy}{dx}+6y\dfrac{dy}{dx}=4x-2y\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4x-2y}{2x+6y}\\\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{2x-y}{x+3y}.[/tex]

So, at the point (3, 2), we get

[tex]\dfrac{dy}{dx}=\dfrac{2\times3-2}{3+3\times2}=\dfrac{6-2}{3+6}=\dfrac{4}{9}.[/tex]

Thus, the slope of the tangent line at the point (3, 2) is [tex]\dfrac{4}{9}.[/tex]

The slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]) and it can be evaluated by differentiating the given equation of curve.

Given :

To determine the slope of the tangent, differentiation of the given equation of curve is carried out.

Differentiating equation (1) with respect to x.

[tex]\dfrac{d}{dx}(3y^2-2x^2) = \dfrac{d}{dx}(6-2xy)[/tex]

[tex]6y \dfrac{dy}{dx}-4x = 0-2y-2x\dfrac{dy}{dx}[/tex]

Now, further simplification of the above equation gives:

[tex]\dfrac{dy}{dx}(6y+2x)=4x-2y[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x-2y}{6y+2x}[/tex]

Now, at point (3,2) the slope of the tangent will be:

[tex]m = \dfrac{4\times 3-2\times 2}{6\times 2+2\times3}[/tex]

[tex]m = \dfrac{5}{18}[/tex]

So, the slope of the tangent at point (3,2) will be ([tex]5\div 18[/tex]).

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Answer:

D.Non negtaive rational numbers.

Step-by-step explanation:

Given

A store sells self serve frozen yogurt and weight of yogurt taken in ounces.

The function C(w) represents the cost , in dollars .

The given yogurt can be  measured  in gram or kilogram or ounces etc.

The quantity of yogurt can not be negative  because  quantity  is always a positive number . So it can not be a negative number

The quantity is defined as the  amount of  any material or substance .

The quantity is always a positive number . It can not be negative value of a number.

Here, the quantity is taken in ounces  so it is a positive number .

The quantity of any material can be natural number or  positive rational  number .

Hence,the domain for the function C(w)  are non negative rational numbers.

An appropriate domain for the function would be non negtaive rational numbers .

Therefore, the correct answer is option D.

The Answer to the about question rational exponents and radicals is given below.

To solve the first part Let us assume a expression (E) that contains rational exponents

E =  6² / ( 9[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =  6² / ( (3²)[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =  6²  / ( 3[tex]\frac{4}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )

E =   6² / 3[tex]\frac{9}{3}[/tex]

E =   6² / 3³

E = 36/27 = 4/3

E = 4/3

To solve the second part Let us assume a expression (F) that contains radicals.

F = 10 × √(∛(59 +5))

F = 10 × √(∛64)

F = 10 × √(∛(4×4×4))

F = 10 × √4

F = 10 × √(2×2)

F = 10 × 2

F = 20

Thus we have simplified the expression that contains rational exponents and also the expression that contains radicals also.

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To simplify an expression with rational exponents, we multiply the exponents together. To simplify an expression with radicals, we can find the square root of the number.

An expression with rational exponents that can be simplified further is:

To simplify this expression, we can use the rule that states when we raise an exponent to another exponent, we multiply the exponents together. Therefore, (161/4)3/2 = 161/4 * 3/2 = 163/8.

An expression with radicals that can be simplified further is:

To simplify this expression, we can find the square root of 32. The square root of 32 can be simplified as follows: √(32) = √(16 * 2) = √(16) * √(2) = 4√(2).

Actually the real answer is:

-1.

The number 372 rounded to the nearest 100 would be 400.

When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Here, the question said nearest hundred, so I had to look at the value in the tens place which is 7.

Hence, we round up to the next hundred.

So, we get;

372 rounded to the nearest 100 is 400.

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Answer:

Step-by-step explanation:

Given system of linear equations:

y=-1/2x + 4 and

x + 2y=-8.

Let us convert second equation in slope intercept form too.

x + 2y=-8

Subtracting x from both sides, we get

x -x+ 2y=-8-x

2y = -x-8

Dividing both sides by 2, we get

2y/2 = -x/2-8/2

y = -1/2 x - 4.

Let us find slope and y-intercept of each of the equation.

Slope-intercept form of a linear equation is y = mx+b, where m is the slope and b is y-intercept.

On comparing first equation y=-1/2x + 4 by slope-intercept form y = mx+b slope is -1/2 and y-intercept is 4.

For the second equation y = -1/2 x - 4 slope is -1/2 and y-intercept is -4.

Therefore, correct option is 3rd option:

To find the dimensions of the page that will use the least amount of paper, we need to consider the total area of the page and subtract the area of the margins. Set up an equation to represent the given information and solve for the dimensions of the page.

To find the dimensions of the page that will use the least amount of paper, we need to consider the total area of the page and subtract the area of the margins. Let's assume the width of the page is x inches. The total area of the page is then x(x+3) square inches (length times width). The area of the margins at the top and bottom is 2(x+3) square inches (width times depth), and the area of the margins on each side is 3(x) square inches (length times width). We can set up an equation to represent the given information: x(x+3) - 2(x+3) - 3(x) = 64. Simplifying this equation will give us the dimensions of the page that will use the least amount of paper.

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The simplest form of 34 / 710 is 17 / 355.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given that the expression 34 / 710.

Now to write the above expression in simple form, we divide the numerator and denominator by 2

34 / 710 = 34/ 2 ÷ 710 / 2

34 / 710 = 17 / 355

Now the above expression is not easily divisible by any number.

Therefore, The simplest form of 34 / 710 is 17 / 355.

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Answer:

93 and 110 upper fourth

Step-by-step explanation:

Q3 is at 93 and the max number is at 110 so the upper fourth should fall between 93 and 110, the middle half of the responses  will fall between 70 and 93 and the lower fourth of the responses will fall between 40 and 70