A gardener is attempting to put a fence around a rectangular garden. The total length of the fence is 30 feet. The width of the garden is 3 ft longer than the length. What are the length and width of the garden?

Answer:

There are 15 boxes of 10 oz boxes

Step-by-step explanation:

Let the number of boxes of 10 oz = x

and let the number of boxes of 16 oz = y

By the statement

"Total number of boxes sold is 24"

Equation for the statement will be

x + y =24 ---------------(1)

By the  statement

"she collected $97.50 while rate of 10 oz box is $3.50 and rate of 16 oz box is $5.00."

Equation for the statement will be

1.5x + 5y = $97.50 ------------(2)

From equation (1) we put the value of y = 24 - x in equation (2)

1.5x + 5(24 - x) =  97.50

1.5x + 120 - 5x = 97.50

-3.5x = 97.50 - 120

3.5x = 22.50

x = [tex]\frac{22.5}{1.5}[/tex]

x = 15

Therefore, number of 10 oz boxes is 15.

Answer: [tex]g(x)=5^{x-4}[/tex]

Step-by-step explanation:

When a function f(x) is shifted horizontally by n units to the right , the new function will become :-

[tex]g(x)=f(x-n)[/tex]

The given function : [tex]f(x)=5^x[/tex]

Now, if the given function shifted 4 units to the right , then the new function will become :

[tex]g(x)=f(x-4)[/tex]

[tex]g(x)=5^{x-4}[/tex]

Hence, the  function represents a horizontal shift of [tex]f(x)=5^x[/tex] by 4 units to the right will be :-

[tex]g(x)=5^{x-4}[/tex]

Answer:

B −1.3−(4.9+2.6)

Answer:

-1.3-(4.9+2.6)

I

The number must be added to [tex]2\frac{3}{8}[/tex] to make 6 is [tex]3\frac{5}{8}[/tex].

We need to find what we need to add to [tex]2\frac{3}{8}[/tex] to make 6.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

The fraction [tex]2\frac{3}{8}[/tex] can be written as 19/8

Let x be the number added to given fraction, that is

19/8 +x=6

⇒ x=6-19/8

⇒ x= (48-19)/8

⇒ x= 29/8

⇒ x= [tex]3\frac{5}{8}[/tex]

Hence, the number must be added to [tex]2\frac{3}{8}[/tex] to make 6 is [tex]3\frac{5}{8}[/tex].

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Ten less than five times a number cubed in the mathematical from will be 10 - 5x³.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

Ten less than five times a number cubed.

Let the number be 'x'. Then the cube of the number x will be x³.

Then the five times a number cubed will be given as,

5x³

Ten less than five times a number cubed. Then the expression is given as,

⇒ 10 - 5x³

Ten less than five times a number cubed in the mathematical from will be 10 - 5x³.

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The simplified form of [tex]\frac{6}{18}[/tex] is [tex]\frac{1}{3}[/tex].

To simplify the fraction [tex]\frac{6}{18}[/tex], follow these steps:

Find the greatest common divisor (GCD) of the numerator and the denominator. The numerator is 6 and the denominator is 18. The greatest common divisor of 6 and 18 is 6.

Divide both the numerator and the denominator by their GCD.

When we divide the numerator 6 by 6, we get [tex]\frac{6}{6} = 1[/tex].

When we divide the denominator 18 by 6, we get [tex]\frac{18}{6} = 3[/tex].

Write the simplified fraction: After dividing both parts by 6, the fraction [tex]\frac{6}{18}[/tex] simplifies to [tex]\frac{1}{3}[/tex].

Answer:

The rate of riders to cars is 14 divided by 2. So the unit rate is 7 riders per car. Multiply 7 riders by 12 cars to find that 84 riders can fit on the roller coaster at one time.

The expression representing Rose's stamp collection is given by R = (1/2)x - 7. It denotes that Rose's collection is 7 less than half of Van's stamp collection, where x represents the total number of stamps in Van's collection.

Let's denote Van's stamp collection as x. According to the given information, Rose's stamp collection is 7 less than half of Van's stamp collection.

Expression for Rose's stamp collection (R):

R = (1/2)x - 7

Here's the breakdown of the expression:

(1/2)x represents half of Van's stamp collection.

-7 signifies 7 less than half of Van's stamp collection.

This expression encapsulates the relationship between Rose's stamp collection and half of Van's collection, diminished by 7.

5 7/9  - 4 1/3

covert 1/3 to 9ths 3 x 3 = 9 so 1/3 = 3/9

5 7/9 - 4 3/9 = 1 4/9 meters

The prime factorisation of 105 is therefore 3 * 5 * 7.

We can factorize 105 into its prime factors by dividing it by prime numbers up to the point when we can no longer divide it. Here is how it works:

Divide 105 by the following prime number, 3, for a result of 35.

35 divided by the following prime number, 5, yields a result of 7 that is:

35/5 = 7

The seventh prime number has been reached. The prime factorisation of 105 is therefore 3 * 5 * 7.

Thus, 3 * 5 * 7 is the prime factorization of 105.

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The net change in the value of the account, when rounded to the nearest dollar, is $550.

To find the net change in the value of the account, you would sum up the amounts deposited, subtract the amounts withdrawn, and add the interest earned:

Net change = (Deposits - Withdrawals) + Interest earne

Net change = ($500 - $250) + $300

            = $250 + $300

            = $550

Therefore, the net change in the value of the account, when rounded to the nearest dollar, is $550.

The probable question maybe:

"What is the net change in the value of an investment account after depositing $500, withdrawing $250, and earning $300 in interest, when rounded to the nearest dollar?"