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\sqrt[3]{15x-1} + \sqrt[3]{13x+1} =4\sqrt[3]{x}
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The one side of rectangle is 11 feet and other side is 19 feet.

Step-by-step explanation:

Given,

Area of rectangle = 209 square feet

Let one side of rectangle = w

other side of rectangle = 2w-3

Area of rectangle = One side * other side

[tex]209=w*(2w-3)\\209=2w^2-3w[/tex]

[tex]0=2w^2-3w-209\\2w^2-3w-209=0[/tex]

[tex]2w^2+19w-22w-209=0\\w(2w+19)-11(2w+19)=0\\(2w+19)(w-11)=0[/tex]

Either;

2w+19=0        =>2w=-19

Or,

w-11=0            => w=11

As length cannot be negative, therefore,

One side of rectangle = 11 feet

Other side of rectangle = 2w-3 = 2(11)-3 = 22-3 = 19 feet

The one side of rectangle is 11 feet and other side is 19 feet.

Keywords: rectangle, area

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Answer:

y=3

Step-by-step explanation:

Add the y and divide

7y=21

21/7=3

y=3

Answer:135,136,137

Step-by-step explanation:

408 divided by 3=136

136-1=135

136+1=137

135,136,137

The largest number of the three consecutive even numbers that sum to 408 is 138.

The problem is a classic arithmetic sequence problem in mathematics, where a common difference exists between each number. For consecutive even numbers, this difference is 2. If the sum of three consecutive even numbers is 408, we can form the equation 3n+6=408 (since the first number is 'n', the next is 'n+2', and the following is 'n+4'). Solving this equation gives us n=134, hence the sequence of numbers is 134, 136 and 138. The largest number in this sequence is 138.

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You would have to sell approximately 52 bracelets per week in order to pay your fee.

190 ÷ 3.60 = 52.7

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

To determine the profit you make from selling glow sticks at the Star Wars convention, you can calculate the profit per unit and the total profit considering the costs and selling price.

Here are the key values:

Cost per glow stick: $2.02

Fixed weekly fee for the booth: $190

Selling price per glow stick: $3.60

Now, let's calculate the profit per unit:

Profit per unit = Selling price per unit - Cost per unit

Profit per unit = $3.60 - $2.02 = $1.58

This means you make a profit of $1.58 for each glow stick you sell.

To find the total profit, you need to consider how many glow sticks you sell. Let's assume you sell 'x' glow sticks. Your total profit can be calculated as:

Total Profit = Profit per unit × Number of Units Sold

Total Profit = $1.58x

Now, you need to take into account the fixed weekly booth fee of $190. So, your total profit after deducting the booth fee will be:

Total Profit - Booth Fee = $1.58x - $190

This is your net profit after covering both the cost of the glow sticks and the booth fee. The actual profit you make will depend on how many glow sticks you manage to sell at the convention.

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Answer:

Step-by-step explanation:

a) The maximum number of houses Sam can build in 24 hours is 8, so the constraint is in construction, not decoration. For each small house Sam constructs, he makes $10/3 = $3.33 per hour of work. For each large house Sam constructs, he makes $15/5 = $3.00 per hour. The most money is to be made by building only small houses.

Sam should make 8 small houses and 0 large houses in 24 hours.

__

b) If Sam works 8-hour days, then he can complete at most 80 small houses. The constraint remains in construction, so the answer is the same: build only small houses.

_____

If Sam works more than 16 2/3 hours per day, he can build 100 large houses or more, so the constraint moves to decoration. The decorator makes more money by decorating large houses, so all the effort should go to construction of large houses.

If Sam works between 10 and 16 2/3 hours per day, the best revenue will come from some mix. The problem statement is unclear as to how many hours Sam works in 30 days.

Answer:

it's already simplified :) your welcome

Answer:

1,500

Step-by-step explanation:

75•20

Answer:1500

Step-by-step explanation: 75 times 20 = 1500

The garden view hotel is 235 feet tall

Step-by-step explanation:

The given is:

We need to find the height of the garden view hotel

Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet

∵ The height of the garden view hotel = x feet

∵ The height of the plaza hotel = y feet

∵ The height of the garden view hotel is 17 less than twice the

    height of the plaza hotel

- That means x is less than 2 × y by 17, equate x by the difference

   of 2 × y and 17

∴ x = 2y - 17 ⇒ (1)

∵ Their combined height = 361 feet

∴ x + y = 361

- Find y in terms of x by subtraction x from both sides

∴ y = 361 - x ⇒ (2)

Substitute y in equation (1) by equation (2)

∵ x = 2(361 - x) - 17

- Simplify the right hand side

∴ x = 722 - 2x - 17

- Add like terms

∴ x = 705 - 2x

- Add 2x to both sides

∴ 3x = 705

- Divide both sides by 3

∴ x = 235

The garden view hotel is 235 feet tall

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The height of the Gardenview Hotel is 235 feet, which we found by first creating a system of equations using the information given and then solving by substitution.

To find the height of the Gardenview Hotel, let's create a system of equations based on the information given. Let G be the height of the Gardenview Hotel and P be the height of the Plaza Hotel. We are told that the Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel, which we can express as G = 2P - 17. Additionally, we know their combined height is 361 feet, so G + P = 361.

Now we can solve the system of equations step by step:

Substitute the expression for G from the first equation into the second equation: (2P - 17) + P = 361.

Combine like terms: 3P - 17 = 361.

Add 17 to both sides of the equation: 3P = 378.

Divide both sides of the equation by 3 to find the height of the Plaza Hotel: P = 126.

Now use the value of P to solve for G using the first equation: G = 2(126) - 17.

Simplify to find the height of the Gardenview Hotel: G = 252 - 17.

Thus, the height of the Gardenview Hotel is 235 feet.

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

Answer:

The total pieces of cake are 24

Step-by-step explanation:

Linear equations

It's a relation between one or more variables and or numbers, connected with the equal sign. An example is 4x-5=7, or 2(x+y)=7-(x-y)

This problem can be easily solved without the use of equations, but we are required to.

We know Mindy and Troy combined ate 9 pieces of cake, we also know that Mindy ate 3 pieces of cake. It leaves 6 pieces to Troy. Since Troy ate 1/4 of the whole cake, then

[tex]\displaystyle \frac{1}{4}X=6[/tex]

Where X is the number of pieces of cake

Solving for X

[tex]X=(4)(6)=24\ pieces[/tex]

Answer:

120 mg

Step-by-step explanation:

750 ml       300mg

300 ml         x mg

750 / 300 = 300 / x

x = (300 x 300) / 750 = 120 mg

Answer:

It sold for $9.20 more in 1992 than in 1982.

It sold for $20.70 in 1992.

Step-by-step explanation:

The price in 1982 was $11.50.

The price increased by 80% of $11.50.

We need to find 80% of $11.50.

To find a percent of a number, multiply the percent by the number.

80% of $11.50 =

= 80% * $11.50

= 0.8 * $11.50

= $9.20

It sold for $9.20 more in 1992.

The price in 1992 is the original price of the belt plus the amount of increase.

$11.50 + $9.20 = $20.70

It sold for $20.70 in 1992 than in 1982.

I'm not an expert at this but the answer should be 13.9 or 14

Final answer:

The length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.

Explanation:

In order to find the length of an arc made by an 80° central angle in a circle with a 10 ft. radius, we need to use the formula for the circumference of a circle. The formula for the circumference is C = 2πr, where C is the circumference and r is the radius. In this case, the angle is 80°, so we need to find the fraction of a full circle that the angle represents. Since a full circle is 360°, the fraction is 80/360 = 2/9. Therefore, the length of the arc is 2/9 times the circumference of the circle with a 10 ft. radius.

To find the circumference of a circle with radius 10 ft., we can use the formula C = 2πr. Plugging in the value of the radius, we get C = 2π(10) = 20π ft. Since the length of the arc is 2/9 times the circumference, the length of the arc is (2/9)(20π) ft. Simplifying, we get (40/9)π ft. This is approximately 13.96 ft. Therefore, the length of the arc made by an 80° central angle in a circle with a 10 ft. radius is approximately 13.96 ft.

Step-by-step explanation:

the farmer plants 0.4 of the total field which is 2.3 acres

⇒0.4×2.3= 0.92 acres

now draw a grid of area 2.3 acres and in that area shade 0.92 acres.Use a proper scale to draw the grid. It will a be pictorial representation of the proper and its solution.

Answer:

1) $250

2) $200 + $50x

Step-by-step explanation:

1)

$200 (start up fee) + $50 * ( 1 month ) = $200 + $50 = $250

2)

$200 (start up fee) + $50 * ( x months ) = $200 + $50x

Hope this helps :)

Answer:

The number is 8.

Step-by-step explanation:

Write an equation then solve by isolating the variable.

let x be the number

4x + 15 = 47  Subtract 15 from both sides

4x = 47 - 15

4x = 32     Divide both sides by 4

x = 32/4

x = 8

Therefore the number is 8.

Answer:

8

Step-by-step explanation:

Answer:

C) 12(8+3)

Step-by-step explanation:

Answer:C) 12(8+3)

Step-by-step explanation: i took the test

Answer:

see the explanation

Step-by-step explanation:

Verify the range of each quadratic function

case 1) we have

[tex]f(x)=(x-4)^2+5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (4,5)

The range is the interval [5,∞)

[tex]y\geq 5[/tex]

case 2) we have

[tex]f(x)=-(x-4)^2+5[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (4,5)

The range is the interval (-∞,5]

[tex]y\leq 5[/tex]

case 3) we have

[tex]f(x)=(x-5)^2+4[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (5,4)

The range is the interval [4,∞)

[tex]y\geq 4[/tex]

case 4) we have

[tex]f(x)=-(x-5)^2+4[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (5,4)

The range is the interval (-∞,4]

[tex]y\leq 4[/tex]

Answer:

The required probability is  given by, 0.9919.

Step-by-step explanation:

Let, X be the random variable denoting the no. of pages among those 4 pages which Julia writes where she makes no spelling mistake.

clearly,

X [tex]\sim[/tex] Binomial (4, 0.7)

So,      P(X = x) = [tex]^4C_{x} \times (0.7)^{x} \times (0.3)^{(4 - x)}[/tex]

                            [when  x = 0, 1, 2, 3, 4]

                         = 0 otherwise

According to the question, we are to find out  P(X ≥ 1) .

Now, P(X ≥ 1)

     = 1 - P(X = 0)

     = [tex] 1 - (^4C_{0} \times (0.7)^{0} \times (0.3)^{4})[/tex]

     = [tex] 1 - 0.0081[/tex]

     = 0.9919

So, the required probability is  given by, 0.9919

The probability that Julia will have no spelling mistakes on at least one of the pages is approximately 99.19%.

To determine the probability that Julia will have no spelling mistakes on at least one of the four pages she writes, we can first find the probability that she will make at least one spelling mistake on all four pages and then subtract this from 1.

The probability that there will be a spelling mistake on a page:

= 1 - 0.7 = 0.3.

Since the probability of a spelling mistake on each page is independent, we can multiply the probabilities for the four pages together.

The probability of at least one mistake on all four pages:

= 0.3 x 0.3 x 0.3 x 0.3 = 0.3⁴= 0.0081.

The probability that there will be no spelling mistakes on at least one page

= 1 - 0.0081 = 0.9919 or about 99.19%.

So, the probability is 99.19%.

Answer:

25

Step-by-step explanation:

If a two digit number is a multiple of 5, then it ends with 0 or with 5.

If a two digit number ends with 0, then the number of ones is 0 and the number of tens must be 3 less that is impossible.

Hence, this two digit number must end with 5. If it ends with 5, then the number of ones is 5 and number of tens must be 5 - 3 = 2.

Therefore, the number is 25.

The question is about two-digit numbers that are multiples of 5 and have fewer tens than ones. Numbers such as 15, 25, 35, 45, 50, 65, 75, 85, and 95 satisfy these conditions.

The subject of this question is a mathematical problem solving task regarding two-digit numbers and their properties. The most important criteria are that the number is a multiple of 5 and has less tens than ones. First, multiples of 5 are numbers that end in 0 or 5. Secondly, having less tens than ones implies that the digit in the ones place must be greater than the digit in the tens place.

An example of a number that fulfills these conditions would be 15. Here, the digit in the ones place (5) is greater than the digit in the tens place (1). Also, 15 is a multiple of 5 because it can be divided by 5 without leaving a remainder.

However, 15 is just one of many possible answers. Other numbers that satisfy these conditions are: 25, 35, 45, 50, 65, 75, 85, and 95.

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Answer:

10.32

Step-by-step explanation:

10.31988

the 9 makes the 1 to a 2 so...

10.32

Answer:

4x-19/3

Step-by-step explanation:

1/2(8x+4)+1/3(9-34)

8/2x+4/2+9/3-34/3

4x+2+3-34/3

4x+5-34/3

4x-19/3

Answer:

3x+5

Step-by-step explanation:

search for the best and accurate answers

Answer:

30,000 cm^2.

Step-by-step explanation:

The area  = 3*1 = 3 square meters.

There are 100^2 = 10,000 cm^2 in a square meter

So the area in square centimeters is 3 * 10,000 = 30,000.

Answer:

The option " The sum has degree of 6 , but the difference has a degree of 7 " is correct.

Step-by-step explanation:

Given that the sum and difference of the polynomials [tex]3x^5y-2x^3y^4-7xy^3[/tex] and [tex]-8x^5y+2x^3y^4+xy^3[/tex]

[tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)[/tex]

[tex]=3x^5y-2x^3y^4-7xy^3-8x^5y+2x^3y^4+xy^3[/tex]

[tex]=-5x^5y+0-6xy^3[/tex]

[tex]=-5x^5y-6xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3+(-8x^5y+2x^3y^4+xy^3)=-5x^5y-6xy^3[/tex]

In the simplified sum of the polynomials [tex]-5x^5y-6xy^3[/tex]  we have the degree is 6

[tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)[/tex]

[tex]=3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3[/tex]

[tex]=11x^5y-4x^3y^4-8xy^3[/tex]

Therefore [tex]3x^5y-2x^3y^4-7xy^3-(-8x^5y+2x^3y^4+xy^3)=11x^5y-4x^3y^4-8xy^3[/tex]

In the simplified difference of polynomials [tex]11x^5y-4x^3y^4-8xy^3[/tex] we have the degree is 7

Therefore the option " The sum has degree of 6 , but the difference has a degree of 7 " is correct

Answer:

The sum has a degree of 6, but the difference has a degree of 7.

Step-by-step explanation:

Answer:

For question 9: Angle 1= 20, angle 2= 70, angle 3= 70, angle 4= 20, angle 5= 20, angle 6= 70, and angle 7= 70.

Step-by-step explanation:

Answer:

Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did

Step-by-step explanation:

Let

x ----> number of hours worked by Jolianne

t ----> number of hours worked by Andrew

we know that

The number of hours worked by Jolianne multiplied by $10 per hour plus $27 saved must be equal to the number of hours worked by Andrew multiplied by $8

The linear equation that represent this situation is

[tex]10x+27=8t[/tex] ----> equation A

[tex]x=\frac{t}{2}[/tex] -----> equation B

substitute equation B in equation A

[tex]10(\frac{t}{2})+27=8t[/tex]

so

Andrew's table and equation is correct

Jolianne's table and equation are not correct, because Andrew did not work twice as many hours as she did

Answer:

the answer is B :)

Step-by-step explanation:

Answer:

b. Shift left 3 units

Step-by-step explanation:

You're given

y = √(x + 3)

y = √(x - (-3))

y = √(x - amount_shifted)

amount shifted = -3

so shifted 3 units and the negative means it's shifted to the left