A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards, find the length of the rectangle.

Answer:

81.6

Step-by-step explanation:

this question is pretty old but I hope this helps people like me trying to find the actual answer unlike the first one.

Answer:

[tex]12[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

For [tex]x=3[/tex] -----> [tex]f(x)=8[/tex]

so

Find the value of k

[tex]f(x)*x=k[/tex]

substitute the value of x and f(x)

[tex]8*3=k[/tex]

[tex]k=24[/tex]

therefore

the equation is equal to

[tex]f(x)=24/x[/tex]

For [tex]x=2[/tex] -------> substitute in the equation and find the value of f(x)

[tex]f(x)=24/2=12[/tex]

To find the total distance David travels during the three days, we add up the distances he travels on each day: m + (m + 35) + 2m = 4m + 35 miles.

To find the total distance David travels during the three days, we need to add up the distances he travels on each day.

On Monday, David travels m miles.

On Tuesday, he travels 35 more than he did on Monday, so he travels m + 35 miles.

On Wednesday, he travels twice the distance he traveled on Monday, so he travels 2m miles.

To find the total distance, we add up the distances on all three days:

Total distance = m + (m + 35) + 2m = 4m + 35 miles.

The expression 3 - 3×6 + 2, following the order of operations, results in -13. There is no need to add unnecessary parentheses or introduce an "invisible" 1; multiplication inherently takes precedence.

The expression should be evaluated according to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's solve the expression step by step:

3 - 3×6 + 2

Step 1: Perform multiplication first, since it precedes addition and subtraction in the order of operations.
3 - (3×6) + 2 = 3 - 18 + 2

Step 2: Proceed with addition and subtraction from left to right.
3 - 18 results in -15, and then adding 2 gives us -15 + 2 = -13.

Therefore, the correct answer to the expression is -13.

There's no need to introduce an "invisible" 1 or to add parentheses around the multiplication, as the multiplication already has precedence over addition and subtraction.

Answer:

  76

Step-by-step explanation:

The last two digits of powers of 36 repeat in a pattern of length 5:

  36^1 mod 100 = 36

  36^2 mod 100 = 96

  36^3 mod 100 = 56

  36^4 mod 100 = 16

  36^5 mod 100 = 76

  36^6 mod 100 = 36

The last two digits of the power 2015 are the same as those of the 5th power: 76.

"The answer is: 50 + 7 x 5 = 85 is correct due to the order of operations.

To understand why 50 + 7 x 5 equals 85, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). According to this rule, multiplication and division are performed before addition and subtraction.

 Let's break down the expression step by step:

1. Identify the multiplication part of the expression: 7 x 5.

2. Perform the multiplication first: 7 x 5 = 35.

3. Now, we have 50 + 35, since we have already computed 7 x 5.

4. Finally, perform the addition: 50 + 35 = 85.

So, following the order of operations, we correctly get that 50 + 7 x 5 equals 85."

7.02 is approximately 10.4 percent of 67.5.

To find what percent 7.02 is of 67.5,

Since we know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We can use a proportion.

Let's call the unknown percent "x."

The proportion would be:

7.02/67.5 = x/100

We can cross-multiply to solve for x:

(7.02 * 100) / 67.5 = x

Simplifying this expression, we get:

x = 10.4

Therefore, 7.02 is approximately 10.4% of 67.5.

Learn more about the percent visit:

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Answer:

Step-by-step explanation:

b=6

The mass of 10,000 peanuts is 4,500 g or 4.5 kg.

The question asks for a reasonable guess for the mass of 10,000 peanuts, given that each peanut has a mass of about 0.45 g. To calculate this, we simply multiply the number of peanuts by the mass of each peanut:

Mass of one peanut = 0.45 g
Number of peanuts = 10,000
Total mass = 0.45 g/peanut x 10,000 peanuts

Now we will carry out the multiplication:

Total mass = 4,500 g

Since we are dealing with a large quantity of peanuts, it is more convenient to express this mass in kilograms:

4,500 g is equivalent to 4.5 kg (since 1 kg = 1,000 g).

Final answer:

To convert 1.375 to a fraction, express it as 1,375/1,000 and simplify by dividing by the greatest common divisor, which is 125, to get 11/8.

Explanation:

To convert the decimal 1.375 to a fraction, we will follow a few steps. First, count the number of decimal places, which in this case is three. This tells us that the denominator of the fraction should be a power of 10; specifically, 1,000. So we write 1.375 as 1,375/1,000. Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 1,375 and 1,000 is 125. When we divide both the top and the bottom by 125, we get 11/8, which is the simplest form of the fraction.

Converting decimals to fractions involves aligning the decimal with the appropriate power of 10 in the denominator and simplifying by finding the greatest common divisor. This systematic approach ensures the representation of the decimal as a simplified fraction, such as 11/8 in the case of 1.375.

To carry out the student's request, you would first raise 'g' to the 7th power to obtain g^7, then subtract 'h' from this result to get the final expression 'g^7 - h'.

To solve the expression mentioned by the student, you need to carry out two mathematical operations in sequence. The first operation is raising 'g' to the 7th power, which can be expressed as g^7. The second operation is subtracting 'h' from the result of the first operation. This can be represented mathematically as g^7 - h.

For example, if g equals 2 and h equals 3, then you would first calculate 2^7 which equals 128. Then you would subtract 3 from 128, yielding an answer of 125.