The perimeter of a rectangle is 84. The length is 10 more than three times the width. Find the length and width.

Signed and unsigned integer expressions differ in how they interpret and represent numerical values. Signed integers can represent both positive and negative values, while unsigned integers can only represent non-negative values.



1. Signed Integer Expressions: Signed integers are capable of representing positive, negative, and zero values. They allocate a bit for the sign, typically using the leftmost bit (the most significant bit). The remaining bits are used to represent the magnitude of the number. The sign bit is set to 0 for positive or zero values and set to 1 for negative values. This representation allows for a wider range of values, but half of the possible bit patterns are reserved for negative numbers, limiting the maximum positive value that can be represented.

2. Unsigned Integer Expressions: Unlike signed integers, unsigned integers do not allocate a bit for the sign. Instead, all bits are used to represent the magnitude of the number, allowing for a wider range of non-negative values. As a result, unsigned integers can represent larger positive values than their signed counterparts. However, they cannot represent negative values or zero, as there is no reserved bit to indicate the sign.

The choice between signed and unsigned integer expressions depends on the specific requirements of a program. Signed integers are typically used when negative values need to be represented or when arithmetic operations may result in negative values. On the other hand, unsigned integers are useful when dealing with quantities that are always expected to be positive, such as array indices or lengths of data structures. It's important to consider the range of values required and the potential impact of overflow or underflow when selecting between signed and unsigned integer expressions.

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π

sec(π4) – trigonometry value

The exact value of trigonometry - sec(π4) is 2√2.

Multiply 2√2 by √2.

2⋅√2⋅2

Combine and simplify the denominator.

2√2

Cancel the common factor of 2.

√2

There are various ways to display the outcome.

Exact Form:

√2

Decimal Form:

1.41421356…

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Answer:

not a real number

Step-by-step explanation:

any negative number under a square root sign, except for 0, isn't real

On evaluating the given roots,

(a) \($-(\sqrt[3]{8}) = -2$\)

(b) \($\sqrt[4]{-81}$\) is not a real number

(a) \($-(\sqrt[3]{8})$\):

The cube root of 8 is the number that, when raised to the power of 3, equals 8. In this case, the cube root of 8 is 2, because \(2^3 = 8\).

Since we have a negative sign in front of the cube root, the result will be the negative value of the cube root of 8.

Therefore, \($-(\sqrt[3]{8}) = -2$\).

(b) \($\sqrt[4]{-81}$\):

The fourth root of a number is the number that, when raised to the power of 4, equals the given number.

In this case, we are looking for the fourth root of -81.

However, the fourth root of a negative number is not a real number. This is because raising a positive number to an even power (in this case, 4) will always result in a positive value, and there is no real number that, when raised to the power of 4, gives a negative result.

Therefore, the fourth root of -81 is not a real number.

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The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-9 + 4)/(30 - 0)

Slope, m = -5/30

Slope, m = -1/6.

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Answer:

The constant of proportionality is:

Step-by-step explanation:

We know that when y varies directly with x, we get

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality

From the graph, it is clear that the point (2/5, 1/2) passes through the line which represents the direct relationship.

so we have the point (2/5, 1/2), and

x = 2/5

y = 1/2

so substituting x = 2/5 and y = 1/2 in the equation

k = y/x

k = [1/2] / [2/5]

k = [1 × 5 ] /  [2 × 2 ]

k = 5/4

Therefore, the constant of proportionality is:

Hi friend! Hope you find this response helpful! :)

0.66666667

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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In general, any symmetrical object will have a net torque of zero if the axis of rotation is through its center of mass.

It seems that the list of examples is missing from your question, so I'll provide a general explanation of situations where the net torque is zero. Please feel free to provide a list of examples for a more specific answer.

A net torque of zero about an axis perpendicular to the page and extending from the center means that the total clockwise torque is equal to the total counterclockwise torque. This can occur when:

1. There are no external forces acting on the system, so there is no torque.
2. The external forces are acting along the line of the axis, causing no rotation and hence no torque.
3. The clockwise and counterclockwise torques cancel each other out, resulting in a net torque of zero.

Some examples of objects that have a net torque of zero about the axis perpendicular to the page and extending from the center of the object are a sphere, a cube, a cylinder, and a cone.

Please provide the list of examples you'd like me to evaluate, and I'll be glad to help you determine which have a net torque of zero.

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Answer:

2. b

3. d

Step-by-step explanation:

I checked it  based on the decimals. 5/8 = 0.625, which is B on the numberline in 2.

5/6 is 0.833, which is D on the numberline in 3

Answer:

x = 6

Step-by-step explanation:

8(-6 + 6x) = 240

Distribute the 8

-48 + 48x = 240

Add 48 to both sides

48x = 288

Divide both sides by 48

x = 6

Answer:

yes

Step-by-step explanation:

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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Solution:

Given:

The angles of a triangle are as shown in the sketch below;

Consecutive even integers are the set of integers such that each integer in the set differs from the previous integer by a difference of 2 and each integer is divisible by 2.

For the three angles to be consecutive even integers, then

Since the three angles are in the triangle, then;

Substituting the value of x into equations (1) and (2) to get the values of y and z,

Therefore, the measure of each angle if the angles are consecutive even integers are;

Answer:

58° , 60° , 62°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the 3 consecutive even integers be n, n + 2, n + 4 , then

n + n + 2 + n + 4 = 180

3n + 6 = 180 ( subtract 6 from both sides )

3n = 174 ( divide both sides by 3 )

n = 58

n + 2 = 58 + 2 = 60

n + 4 = 58 + 4 = 62

the 3 angles are 58° , 60° , 62°

Answer:

301 plates

Step-by-step explanation:

For numbers between 0 and 9, 1 plate was used each.

This means that 10 plates were used.

For numbers between 10 and 99, 2 plates were used for each.

This means that the number of plates used will be:

2 * 90 = 180 plates

For numbers between 100 and 136, 3 plates were used for each.

This means that the number of plates used is:

3 * 37 = 111 plates

The total number of plates used is therefore:

10 + 180 + 111 = 301 plates

301 plates were used in total.

Reason: Replace m with 160 to go from 8m+150 to 8(160)+150

When using PEMDAS or a calculator, that expression simplifies to 1430.

Answer:

Step-by-step explanation:

(a +b)² = a² + b² + 2ab

a = 3a and b = 2.5b

2ab = 2*3a*2.5b = 15ab

15ab is the monomial that needs to be inserted

Answer:

Im Sure its A

Step-by-step explanation:

Answer:

2/2=1

6/2=3

2/2=1 so the fractions are equivalent

2/6 = 1/3

Hope this helps

Step-by-step explanation:

The exponential function given in this problem represents an exponential decay, and it's asymptote is of y = 0.

An exponential function is modeled according to the rule given as follows:

\(y = ab^x + c\)

The parameters of the function are defined as follows:

To verify if the function represents growth or decay, we have to check parameter b as follows:

In the context of this problem, the function is defined as follows:

\(y = 14\left(\frac{1}{2}\right)^x\)

Hence the parameters of the given function are as follows:

a = 14, b = 0.5, c = 0.

Then:

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Answer:

Answer down bellow

Step-by-step explanation:

Q's asked: Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? What is the equation of the asymptote?

Answer: Decay; y = 0

hope this helps

~~Wdfads~~

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Answer:its 5

Step-by-step explanation: cuz

Discounting One Year What is the present value of a $500 payment in one year when the discount rate is 5 percentis b. $476.19.

To find the present value of a future payment, we need to use the formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years.

In this case, we want to discount the $500 payment by one year, so n = 1. The discount rate is 5 percent or 0.05.

Plugging these values into the formula, we get: PV = $500 / (1 + 0.05)^1 = $476.19.

Therefore, the correct answer is b. $476.19.

The present value of a $500 payment in one year when the discount rate is 5 percent is $476.19.

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Answer:

\( \frac{43}{100} \times 27 = \frac{1161}{100} = 11.61\)

\(11.61 \: is \: the \: ans\)

Answer:

11.61

Step-by-step explanation:

% means 100

so we have 43/100

of means multiplication X 27

so we have 43/100x27

and the answer is 11.61

if you want to approximate it is 12

Answer:

0.032%

Step-by-step explanation:

192192/600600600 x 100% = 0.00032 x 100%

0.032%

The volume of a right circular cylinder is an increasing function of the radius at a fixed height. So, the correct answer is option C. The volume is an increasing function because the partial derivative of V with respect to r is given dV/dr=2πrh.

The volume of a right circular cylinder with radius r and height h is given by V=πr^2h. To determine if the volume is an increasing or decreasing function of the radius at a fixed height, we need to find the partial derivative of V with respect to r.
The volume is an increasing function because the partial derivative of V with respect to r is given dV/dr=2πrh.
1. Start with the volume formula: V = πr^2h
2. Differentiate V with respect to r, keeping h constant: dV/dr = 2πrh
3. Since dV/dr is positive (2πrh > 0 for r > 0 and h > 0), the volume is an increasing function of the radius at a fixed height.

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The problem can be expressed in the form

The cost per kg for the potatoes and onions is

15 kg of potatoes and 10 kg of onions will cost

From the question it can be deduced

let the price of potatoes be x and the price of onions be y

The total cost of 4 kg of potatoes and 2 kg of onions is Rs. 350

4x + 2y = 350

If the cost of 3 kg of potatoes is same as the cost of 2 kg of onions

3x = 2y

substituting 2y for 3x in 4x + 2y = 350

4x + 3x = 350

7x = 350

x = 50

solving for y in 3x = 2y

3 * 50 = 2y

2y = 150

y = 75

c. 15x + 10y will cost

= 15 * 50 + 10 * 75

= 1500

the cost will be 1500

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