The width of a rectangle is 3 inches less than twice the length. If the length of the rectangle is represented by L, write an algebraic expression to represent the width

Final answer:

To find the markup on a pair of hiking boots with a cost of $80 and a 15% markup rate, multiply the cost by 0.15 to get a $12 markup. The selling price would then be $80 + $12, totaling $92.

Explanation:

To calculate the markup for a pair of hiking boots that the store buys for $80 with a markup rate of 15%, first convert the percentage to a decimal by dividing by 100.

Markup rate as a decimal: 0.15

Next, multiply the cost price by the decimal.

Markup amount = Cost price × Markup rate

Markup amount = $80 × 0.15

Markup amount = $12

So, the markup on the hiking boots is $12. To find the selling price, you add the markup to the cost price:

Selling price = Cost price + Markup amount

Selling price = $80 + $12

Selling price = $92

The store would sell the hiking boots for $92.

Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.

Let's use algebra to solve this problem.

Let L be the length of Little Lake Rock in feet, and let B be the length of Lake Big Rock in feet.

We are given two pieces of information:

Lake Big Rock is 1650 ft longer than Little Lake Rock: B = L + 1650.

Together, they are 5273 ft long: B + L = 5273.

Now, we have a system of two equations with two variables:

B = L + 1650

B + L = 5273

We can use the first equation to express B in terms of L and then substitute this expression into the second equation:

B = L + 1650

Now, substitute B in the second equation:

(L + 1650) + L = 5273

Combine like terms:

2L + 1650 = 5273

Subtract 1650 from both sides:

2L = 5273 - 1650

2L = 3623

Now, divide by 2 to find the length of Little Lake Rock (L):

L = 3623 / 2

L = 1811.5 feet

Now that we know the length of Little Lake Rock, we can find the length of Lake Big Rock using the first equation:

B = L + 1650

B = 1811.5 + 1650

B = 3461.5 feet

So, Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.

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Answer:

Recognize that both 0.96 and 0.144 are divisible by 12:

(0.96/12) / (0.144/12) = 0.08 / 0.012.  This reduces to 0.02 / 0.003, or

20/3 or approx. 6.666.

You could also begin by eliminating the decimal fractions.  Mult. 0.96 and 0.144 each by 1000 results in 960/144.

Since both 960 and 144 can be divided evenly by 24, we get 40 and 6.

40/6 = 20/3, or approx. 6.666, as before.

Step-by-step explanation:

Answer:

The answer is 10,560 yards and 6 miles. The 5,280 yards is just from her home to the school. So you multiply it by 2 and divide by 1760.

Step-by-step explanation:

The estimation of 9.9 squared multiplied by 1.79 is 180.

To estimate the value of 9.9 squared multiplied by 1.79, use rounded numbers to simplify the calculation.

First, round 9.9 to 10 and calculate 10 squared, which is 100.

Next, we round 1.79 to 1.8.

Now, we can perform the multiplication:

100 x 1.8 = 180

Therefore, an estimation is 180.

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The value of 9.9 Squared x 1.79 is 175.59

Let's  calculate

[tex]9.9^{2}[/tex]×1.79 let's break it down step by step:

[tex]9.9^{2}[/tex] means 9.9 [tex]\times[/tex] 9.9 multiplied by itself:

9.9×9.9, which equals 98.01

Now, multiply

98.01 × 1.79 = 175.5879

Rounded to a reasonable precision, the value is approximately

175.59

The process involves squaring

9.9 first and then multiplying the result by

[tex]1.79.9.9^{2}[/tex] gives us 98.01 and then that result is multiplied by

1.79 to obtain 175.59.

The explanation illustrates the order of operations: performing the exponentiation before the multiplication. This follows the basic principles of arithmetic, ensuring each step is carried out accurately to arrive at the final result.

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Answer: 3

Step-by-step explanation:

Given : Juanita is making necklaces to give as presents.

She plans to put 15 beads on each necklace. Beads are sold in packages of 20.

To find the least common number of packages she can buy to make necklaces and have no beads left over,  First we need to find the least common multiple of 15 and 20.

Since , [tex]15=3\times5\\\\20=2\times2\times5[/tex]

Then least common multiple of 15 and 20 =[tex]2\times2\times3\times5=60[/tex]

Now, the least common number of packages she can buy to make necklaces and have no beads left over =[tex]\dfrac{60}{20}=3[/tex].

Hence, the least common number of packages she can buy to make necklaces and have no beads left over=3

If Olivia wants to prevent interest capitalization, she must pay the accrued interest each month. That amount is

... I = Prt = $13,100×0.076×(1/12) = $82.97

Over 4 years (48 months), these payments total $82.97×48 = $3982.56.

_____

If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month. Then the amount of interest that will be capitalized at the end of 48 months is ...

... $13,100×((1 +0.076/12)^48 -1) = $4637.01

The difference in these amounts is ...

... $4637.01 -3982.56 = $654.45 . . . . . matches selection a.

Answer:

A

Step-by-step explanation:

654.45

The total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters is,

⇒ 51.44 meters

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

On Saturday she performed in four shows.

Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters.

Now, To find the total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters we can add all the distances,

⇒ 8.05 m + 17.71 m + 14.38 m + 19.35 m

⇒ 51.44 meters

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Just subtract 0.7 from 1.34

y = -2.04

Hope this help

Answer:  The required solution is x = -2.04.

Step-by-step explanation:  We are given to solve the following linear equation :

[tex]0.7+y=-1.34~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation, we must find the value of the unknown variable y.

The solution of equation (i) is as follows :

[tex]0.7+y=1.34\\\\\Rightarrow y=-1.34-0.7\\\\\Rightarrow y=-2.04.[/tex]

Thus, the required solution is x = -2.04.

Answer:

V shape.

Vertex at (4,0)

Intersect with y axis at (0,4)

Step-by-step explanation:

In order to solve this you just ahve to search fo the graph that grows like a V because when you deal with functions that have absolute values you can have negative and positive values for the independent variable but not for the dependent, in this case x is the independent so x will have negative and positive values while Y will only grow in the postives, now the vertex of the function is found where Y=0 so to calculate that you equal the function to 0

y=|x-4|

0=|x-4|

x=4

So the vertex will be at (4,0) and the intersect with the y axis will be located where x=0, so you evaluate the function for 0:

y=|x-4|

y=|o-4|

y=|-4|

y=4

So the intersect with the y axis will be at (0,4).

6 divided by 1/3 equals 6 times 3

6*3 = 18

The lengths of the 1515th board could range from 32.51 feet to 33.49 feet, considering the maximum measurement error of plus or minus one third inch per cut.

To find the possible lengths of the 1515th board, we need to consider the maximum error in each board measurement. Each time a board is cut, there is a maximum error of plus or minus one third inch. So, the 1515th board could be as short as 33 feet minus 1515 multiplied by one third inch, and as long as 33 feet plus 1515 multiplied by one third inch. Simplifying this, the 1515th board could be as short as 32.51 feet and as long as 33.49 feet.

Final answer:

Using algebra, the larger of two supplementary angles, where one is 50 degrees more than the other, is found to be 115 degrees.

Explanation:

To solve for the measure of the larger angle in a pair of supplementary angles, where one angle measures 50 degrees more than the other, we can use algebra. If we let x represent the measure of the smaller angle, then the larger angle will be x + 50 degrees. Since supplementary angles sum up to 180 degrees, we can set up the equation x + (x+50) = 180.

Solving this equation:

Combine like terms: 2x + 50 = 180

Subtract 50 from both sides: 2x = 130

Divide by 2: x = 65

Since x is the measure of the smaller angle, the larger angle measures x + 50, which is 65 + 50 = 115 degrees.

Therefore, the measure of the larger angle is 115 degrees.