the area of a rectangle is 15x^2y^5. if the length is 5xy^3, what is the width?

Answer:

its A if you are taking the unit test

Step-by-step explanation:

Answer:

Line segment: E

Plane: D

Perpendicular lines: B

Line: A

Parallel lines: C

Step-by-step explanation:

This middle school mathematics question asks for matches between geometric terms and their definitions. Line segments have two endpoints, planes extend infinitely without thickness, perpendicular lines intersect at 90 degrees, lines extend indefinitely in two directions, and parallel lines never intersect.

Explanation:

In the field of mathematics, particularly in geometry, we often deal with various foundational elements such as lines, line segments, planes, and the relationships between them. To understand these concepts, it is essential to know their definitions and how they relate to each other.

A line segment is best described as a part of a line that has two distinct endpoints. This means a line segment is contained and does not extend infinitely in any direction. An example of this is the edge of a ruler, which begins and ends at specific points. The correct match for a line segment in the provided list is E) part of a line that has two endpoints.

A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions. It's similar to a vast sheet of paper with no edges. It is defined by at least three noncollinear points and is often represented in drawings as a four-sided figure, but it continues without end. The correct definition for a plane is D) a flat surface that extends infinitely and has no thickness.

Perpendicular lines are two lines that intersect at an angle of 90 degrees. The point where they cross forms right angles, and the two lines are always at the same distance from each other at this point. The definition of perpendicular lines is B) two lines that intersect at 90° angles.

Regarding a line, it is an undefined term in geometry that represents a straight path that extends infinitely in both directions with no thickness. It is comprised of an infinite number of points. A simple description of a line is A) a series of points that extend in two directions without end.

Lastly, parallel lines are lines in the same plane that do not intersect, no matter how far they are extended on either side. This is because they are always the same distance apart, maintaining a consistent separation across their entire length. The correct match for parallel lines is C) lines that lie in the same plane and do not intersect.

Robin's basket is heavier than Ted's basket by 2 ounces.

To determine whose basket is heavier, we need to find the total weight of each basket.

Ted's basket contains 5 apples, each weighing 8 ounces. Therefore, the total weight of Ted's basket is 5 * 8 = 40 ounces.

Robin's basket contains 6 apples, each weighing 7 ounces. Therefore, the total weight of Robin's basket is 6 * 7 = 42 ounces.

Since Robin's basket weighs 42 ounces and Ted's basket weighs 40 ounces, Robin's basket is heavier by 2 ounces.

Final answer:

The total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.

Explanation:

To find the total interest, we need to use the formula:

Interest = Principal × Rate × Time

Given that the principal is $32,000, the interest rate is 6.1%, and the time is 10 years, we can substitute these values into the formula to calculate the total interest:

Principal: $32,000

Rate: 6.1%

Time: 10 years

Interest = $32,000 × 0.061 × 10 = $19,520

Therefore, the total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.

Answer:

One Gallon

Step-by-step explanation:

One Imperial gallon is 4.54 litres so in that case the gallon is greater but one US gallon is only 3.79 litres so in that case the litres is bigger. ... or 1 gallon =1/. 22 =4.545 liters. so one gallon is greater than 4 liters.

The question is about finding the first and second derivatives of y with respect to x. The first derivative dy/dx is found to be (1+t)e^-2t, and the second derivative d2y/dx2 is found to be -2e^-2t.

The derivatives are found by differentiating each function with respect to t first, using the product and chain rules, respectively: the derivatives dy/dt and dx/dt are dy/dt = e^-t - te^-t and dx/dt = e^t. Then, dy/dx can be found as (dy/dt)/(dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t(1+t))/(e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.

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Answer:

C. 14

Step-by-step explanation:

I just answered it correct

The fractions (48/72) and (6/9) are proportional as, (8/8)(6/9) is equal to (48/72).

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, A fraction 48/72.

Now, If we simplify the fraction by factoring out some common terms we'll have,

24/36.

= 12/18.

= 6/9.

So, They are proportional.

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The value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Right ∆ with Hypotenuse is x, Opposite is 10

Reference angle  = 30°.

We need to find the value of x

Since we are given a reference angle with opposite length, and we are to find the hypotenuse length, x, apply the following trigonometric ratios formula:

sin(theta)=opposite side/hypotenuse

Plug in the values into the equation

sin 30 = 10/x

1/2=10/x

Apply cross multiplication

x=20

Hence, the value of x is 20 when right triangle is with the hypotenuse labeled x , one angle has a measure of thirty degrees, and the opposite leg has a length of ten.

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Answer:$352.16

Im in a rush so cant add explaination

Answer: The simplified form will be

[tex]\frac{1}{(x+3)(x+4)}[/tex]

Step-by-step explanation:

Since we have given that

[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}[/tex]

We need to simplify the above expression, we get that

[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}\\\\=\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\[/tex]

Now, we first factorize the quadratic equation:

[tex]x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x-3)\\\\=(x+3)(x-2)[/tex]

Similarly,

[tex]x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)[/tex]

So, it will become

[tex]\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\\\=\frac{x+1}{(x+3)(x-2)}\times \frac{x-2}{(x+4)(x+1)}\\\\=\frac{1}{(x+3)(x+4)}[/tex]

Hence, the simplified form will be

[tex]\frac{1}{(x+3)(x+4)}[/tex]

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{6 \dfrac{19}{25}}[/tex]

[tex]\mathsf{= \dfrac{6\times25 + 19}{25}}[/tex]

[tex]\mathsf{= \dfrac{150 + 19}{25}}[/tex]

[tex]\mathsf{= \dfrac{169}{25}}[/tex]

[tex]\mathsf{= 169 \div 25}[/tex]

[tex]\mathsf{= 6.76}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{6.76}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]