The length of a rectangle is 4 ft longer than it’s width. If the perimeter of the rectangle is 28 ft, find it’s area.

Answer:

They are called equivalent expressions since they are two expression that equal the same thing.

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Let the number of half dollars be x,

number of quarters = x + 2

amount of half dollars = 0.5x

amount of quarters = 0.25(x + 2)

= 0.25x + 0.5

total amount = 0.5x + 0.25x + 0.5

= 0.75x + 0.5

0.75x + 0.5 = 11.75

0.75x = 11.25

x = 15

number of quarters = x + 2

= 15 + 2

= 17

There are 17 quarters and 15 half dollars.

That is the correct graph that represents

{3y≥x−9 3x+y>−3

hope i helped =D

we have

[tex]3y\geq x-9[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the solid red line

See the attached figure N [tex]1[/tex]

[tex]3x+y> -3[/tex] ----> inequality B              

The solution of the inequality B is the shaded area above the dotted blue line

See the attached figure N [tex]2[/tex]

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

See the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure

The range of normal body temperatures for a camel throughout the day is from 34°C to 40°C, inclusive.

To represent the range of normal body temperatures for a camel throughout the day, we'll use an absolute value inequality. Given that the normal body temperature is 37°C and it varies by up to 3°C, we can express this as:

|T - 37| ≤ 3

Where T represents the temperature of the camel throughout the day. This inequality ensures that the temperature remains within 3 degrees above or below the normal body temperature of 37°C.

To solve this inequality, we'll consider two cases:

1. When T - 37 is positive:

T - 37 ≤ 3

T ≤ 40

2. When T - 37 is negative:

-(T - 37) ≤ 3

-T + 37 ≤ 3

-T ≤ -34

T ≥ 34

Combining the two cases, the range of normal body temperatures for a camel throughout the day is 34°C to 40°C.

Alex broke 3 glasses during the unpacking of the glasses.

As mentioned in the question, Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The total amount earned for 576 glasses is given as,
= 576 × 0.05
= $28.80.

Amount earned = $22.71
Amount paid by Alex for the broken glass = $28.80 - $22.71 = 6.09
Total glass broked = 6.09 / 1.98 ≈ 3

Thus, Alex broke 3 glasses during the unpacking of the glasses.

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The Sinclair family lives 28,512 feet away from Southside Middle School, calculated by multiplying 5.4 miles by the number of feet in one mile, which is 5,280 feet.

The Sinclair family lives 5.4 miles from Southside Middle School. To convert this distance from miles to feet, we use the conversion factor that 1 mile is equal to 5,280 feet. To find the distance in feet, we multiply the number of miles by the number of feet in one mile:

5.4 miles  imes 5,280 feet/mile = 28,512 feet.

Therefore, the Sinclair family lives 28,512 feet away from Southside Middle School.

Final answer:

To find the intersection points of the curve r(t) with the paraboloid z = x^2 + y^2, we substituted the parametric forms into the equation and solved for t, yielding the points (0, 0, 0) and (2, 0, 4).

Explanation:

The student is asking about the intersection points of a curve r(t) with a paraboloid defined by z = x2 + y2. To find these points, we must substitute the parametric forms of x, y, and z from the curve into the equation of the paraboloid and solve for t.

Given the curve r(t) = ti + (4t - t2)k, we can identify the components of the curve as x(t) = t and z(t) = 4t - t2. The y-component is missing, which implies that y = 0. Now, substituting x(t) into the paraboloid equation, we get:

z = x2 + y2

4t - t2 = t2 + 02

By solving for t, we can determine the intersection points. Simplifying the equation, we get:

0 = 2t2 - 4t

Which gives us the solutions t = 0 and t = 2. Substituting these back into r(t) gives the intersection points (0, 0, 0) and (2, 0, 4).

Answer:

The unit rate is 235 calories per hour.

Step-by-step explanation:

General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate.

Unit rate means we have to find the calories burned in 1 hour.

Hence, calories burned in 1 hour = [tex]\frac{470}{2}= 235[/tex]

Answer :

The unit rate is 235 calories per hour.

The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.

The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.

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Answer: answer is (-19/2,-5)

Step-by-step explanation:

The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].

To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.

In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).

In interval notation, we can express this as:

[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]

This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.

For more such questions on domain

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7,746.90 times x  = 7,901.84

 divide both sides by x

 x = 7,901.84 / 7,746.90

x = 1.020000258

 round to 1.02