How do you find the value for x in the problem?

Answer:

4mph

Step-by-step explanation:

The volume of the prism with the given dimensions is;

V = 12x³ - 30x²

We are given that the formula for the volume of a cube is;

V = Lwh

where;

L is length

w is width

h is height

We are given;

L = (24x² + 6x)/(x -1)

w = 2x - 5

h = (x² - x)/(4x + 1)

This means that;

V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]

Now, let us factorize the terms that can be factorized;

(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]

Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]

Using the factorized terms to get the volume now;

V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]

(x - 1) will cancel out and also 4x + 1 will cancel out to give;

V = 6x * x * (2x - 5)

V = 6x²(2x - 5)

V = 12x³ - 30x²

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The other zero of the parabola with a vertex at (4, -2) and one zero at 1 is 7, determined by the symmetry of the parabola about its vertex.

If a parabola has its vertex at (4, -2) and one of its zeros is 1, we can find the other zero by using the concept of symmetry about the vertex. Since the axis of symmetry for a parabola with a vertical axis goes through the vertex, we know that the x-coordinate of the vertex will be exactly in the middle between the two zeros. The vertex form of a parabola's equation is typically written as y = a(x-h)² + k, where (h, k) is the vertex. In this case, the vertex is (4, -2).

Knowing that one zero is 1, we can determine that the other zero is equidistant from the vertex on the other side. This means that the distance from the vertex x-coordinate (4) to the known zero (1) is 3 units (4 - 1 = 3). So, counting 3 units in the other direction from the vertex's x-coordinate will give us the second zero: 4 + 3 = 7. Thus, the other zero of the parabola is 7.

Given is the Principal amount, P = 1600 dollars.

Given the Annual interest is 7% i.e. r = 0.07

Given the Compounding period is semi-annually i.e. n = 2.

Given is the Time of investment, t = 33 years.

It says to find the Final Value of invested amount in the account after 33 years.

We know the formula for Future Value of Money is given as follows :-

[tex] Future \;\;Value = P*(1+\frac{r}{n})^{nt} \\\\
Future \;\;Value = 1600*(1+\frac{0.07}{2})^{(2*33)} \\\\
Future \;\;Value = 1600*(1+0.035)^{66} \\\\
Future \;\;Value = 1600*(1.035)^{66} \\\\
Future \;\;Value = 1600*(9.684185201) \\\\
Future \;\;Value = 15494.69632 \\\\
Future \;\;Value = 15,494.70 \;\;dollars [/tex]

Hence, the final balance would be 15,494.70 dollars.

Answer:

After 33 years balance in the account  = A= $15494.696

Explanation:

We will applying the compound interest formula.

[tex] A =  P(1 +\frac{r}{n})^{nt} [/tex]  

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years

Given that,

P = $1,600

r = 7%  =  [tex] \frac{7}{100}  [/tex] = 0.07

n = 2 (because of twice in a year)

t = 33 years

A= [tex] 1600(1 + \frac{0.035}{2}) ^{2*33}  [/tex] 

A =[tex]  1600 (1.035)^{66}  [/tex] 

A= $15494.696

Answer: C)  The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.

If the x-coordinate is 7, representing 7 hexagons, the y-coordinate, representing the total number of sides, is 42. This is because each hexagon has 6 sides, and 7 hexagons have 7 * 6 = 42 sides.

To find the y-coordinate when the x-coordinate represents the number of hexagons, and the y-coordinate represents the total number of sides, we need to use the properties of a hexagon. A hexagon has 6 sides.

Given that the x-coordinate is 7, this means there are 7 hexagons. Each hexagon has 6 sides, so to find the total number of sides (which is the y-coordinate), you multiply the number of hexagons by the number of sides each hexagon has:

Thus,

y-coordinate = 7 hexagons * 6 sides per hexagon = 42 sides

Therefore, if the x-coordinate is 7, the y-coordinate is 42.

Area = (L1 + L2)*h/2

Area = 18

L1 + L1 = 6

h = ???

18 = (L1 + L2)*h/2

18 = (6) * h/2 Multiply both sides by 2

36 = 6h Divide by 6

36/6 = h

h = 6

So the square is 6 by 6

Area square = s^2 where s is the side of the square.

Area = 6^2 = 36 

so your answer will be 6^2 = 36 

Answer:

Categorical

Step-by-step explanation:

Take a vote and write it down, take your data and see how the results are.

Final answer:

The transformation is a translation where you subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate. Using this rule, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

Explanation:

The student is asking about a translation transformation in a coordinate plane. Given the original and translated coordinates for point X, we can determine the translation rule by calculating the differences between the coordinates.

The x-coordinate has changed from 6 to 2.8, a decrease of 3.2, and the y-coordinate has changed from -2 to -1.3, an increase of 0.7. Thus, the translation rule is to subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate.

To find the translated coordinates for points Y and Z, we apply the same rule:

In summary, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

To find the translation rule, we used the given coordinates of X and X' to determine a translation vector of (-3.2, 1). Using this rule, the coordinates of Y' are (4.3, 6) and Z' are (4.8, 5).

Given the vertices of triangle XYZ: X(6, -2.3), Y(7.5, 5), and Z(8, 4), and knowing that vertex X when translated has coordinates X'(2.8, -1.3), we need to determine the translation rule.

Hence, the coordinates of the translated points are Y'(4.3, 6) and Z'(4.8, 5).

here is the complete question-Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X` has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.

wouldn't it be 54.5 ?

Answer:

3/23 x 5/23 = 15/529 = 2.84%

Answer:

[tex]12\frac{1}{6}[/tex] cups of punch

Step-by-step explanation:

Peter is making a punch. He mixes :

Orange juice  =  [tex]4\frac{1}{2}[/tex] cups

Ginger ale   =    [tex]1\frac{1}{3}[/tex]

Strawberry lemonade =  [tex]6\frac{1}{3}[/tex]

Now we will add all the mixes

[tex]4\frac{1}{2}[/tex] +  [tex]1\frac{1}{3}[/tex] +  [tex]6\frac{1}{3}[/tex]

Now first we convert all the mixed fractions to improper.

[tex]\frac{9}{2}+ \frac{4}{3}+ \frac{19}{3}[/tex]

Now take LCM of 2,3,3 = 6

= [tex]\frac{27+8+38}{6}[/tex]

= [tex]\frac{73}{6}[/tex] =  [tex]12\frac{1}{6}[/tex]

The total number of cups of puch that peter makes is  [tex]12\frac{1}{6}[/tex]

Peter makes a total of 12 cups and 1/6 cup (or approximately 2/3 cup) of punch by mixing 4 1/2 cups of orange juice, 1 1/3 cups of ginger ale, and 6 1/3 cups of strawberry lemonade.

To find the total number of cups of punch that Peter makes,

need to add together the quantities of orange juice, ginger ale, and strawberry lemonade.

Here are the quantities given:

Orange juice = 4 1/2 cups

Ginger ale = 1 1/3 cups

Strawberry lemonade = 6 1/3 cups

Now, add these quantities together:

4 1/2 cups + 1 1/3 cups + 6 1/3 cups

To add these mixed numbers together, it's helpful to first find a common denominator, which in this case is 6.

Convert 4 1/2 to an improper fraction: 4 1/2

= (2 × 4 + 1)/2

= 9/2

Convert 1 1/3 to an improper fraction: 1 1/3

= (3 ×1 + 1)/3

= 4/3

Keep 6 1/3 as it is since it's already in mixed fraction form.

Now, add the fractions:

(9/2) cups + (4/3) cups + (6 1/3) cups

To add the fractions, first, find a common denominator of 6:

(9/2) cups + (8/6) cups + (19/3) cups

Now, all fractions have a common denominator of 6:

(27/6) cups + (8/6) cups + (38/6) cups

Now, add the fractions:

(27/6 + 8/6 + 38/6) cups

Combine the numerators:

(27 + 8 + 38)/6 cups

Now, add the numerators:

(27 + 8 + 38) = 73

So, Peter makes a total of 73/6 cups of punch. You can also simplify this fraction:

73/6 = 12 1/6

Therefore, Peter makes 12 cups and 1/6 cup (or approximately 2/3 cup) of punch in total.

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Natasha can treat a maximum of 10 people to the movies.

To determine how many people Natasha can treat to the movies, we can set up an inequality equation.

Let's say she wants to treat x number of people.

The amount she spends on tickets is $11x, and the amount she spends on popcorn and candy is $21. Since she can spend under $131, the inequality equation would be:

11x + 21 < 131.

To find the maximum number of people Natasha can treat, we need to solve this inequality:

11x + 21 < 131

11x < 110

x < 10

Natasha can treat a maximum of 10 people to the movies.

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Each time Kate refills her gas tank, she would consume 52 liters since it was stated in the problem that there will always be 3 liters of gas before she refills the tank. It was stated that she refilled her tank for two times which means she was able to consume 104 liters (52 liters x 2). It was stated in the problem as well that Kate uses allot the gas in the tank so she consumed the remaining 3 liters in her tank. This means that the total liter she was able to consume was 107 liters (104 liters + 3 liters). To find the distance she gets in miles, you need to multiply the distance covered per liter to the total liter consumed by Kate. Therefore, she was able to get 856 miles (107 liters x 8 kilometers per liter).