The number of pizzas eaten at the class party is equal to one-fourth the number of students, plus two more pizzas for the adults. If nine pizzas are eaten, how many students are there?

The length of the side of the original cube in the given scenario is 5 inches.

A cube is a three-dimensional figure with equal sides.

Given that

The length of the edge of a cube = x

Also, one of the sides is increased by 4 inches, and another side is doubled,

so, now the new dimensions are x, x+4, 2x, and the shape is a rectangular prism.

The area of the rectangular prism = 450 sq. inches

base × height × length = 450 sq. inches

x × (x + 4) × 2x = 450

2x³ + 8x² = 450

2x³ + 8x² - 450 = 0

x³ + 4x² - 225 = 0

Substitute x=5  to see that it is a root of the equation,

5³ + 4(5)² - 225 = 125 + 100 - 225 = 0

So, x - 5 is a factor of the equation,

Now,

x³ + 4x² - 225 = (x−5)(x² + 9x + 45) = 0

The roots of the quadratic equation are imaginary as

D = 9² - 4 × 1 × 45 = 81 - 180 = -99

The discriminant is negative, therefore, the roots are not real.

So, the length of the side of the original cube is 5 inches.

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Answer:

If the question is to the center of that circle instead of "any point inside of that circle" then the answer is true.

Step-by-step explanation:

I got it wrong because I didn't read it all but it is true if it is to any point inside of that circle.

The secant of angle A is 13/5 and the secant of angle B is 13/12. Option A is correct.

To find the secant of angle A and angle B, we need to use the reciprocal function of cosine which is secant. The secant of an angle is equal to the reciprocal of the cosine of that angle.

So, if sec A = 13/5, it means that the cosine of angle A is equal to 5/13. Similarly, if sec B = 13/12, it means that the cosine of angle B is equal to 12/13.

 3.1     Pull out like factors :

   -5x - 25  =   -5 • (x + 5) 

 4.1      Solve :    -5   =  0

This equation has no solution.
A a non-zero constant never equals zero.

 4.2      Solve  :    x+5 = 0 

 Subtract  5  from both sides of the equation : 
                      x = -5 

The value of x in 5(2x - 7)=15x-10 is 5

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.  

Here, the Algebraic expressions with variable in x is given :

5(2x - 7)=15x-10

which is solved using properties of multiplication and solving for value x by arranging variables and constant separately aside:

5(2x - 7)=15x-10  

20x - 35 = 15x -10

20x -15x = 35-10

5x = 25

x= 5

Therefore, the value of x in 5(2x - 7)=15x-10 is 5

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Rounding 2.36 to 1 significant figure results in 2, as the first non-zero digit remains unchanged when the subsequent digit is less than 5.

To round 2.36 to 1 significant figure, you look at the first non-zero digit, which is 2. Since the digit following it (3) is less than 5, the number 2 remains unchanged, and any digits after the 3 are dropped. Therefore, the number 2.36 rounded to 1 significant figure is simply 2.

To round 2.36 to 1 significant figure, we look at the digit after the first significant figure. If this digit is less than 5, we round down. If it is 5 or greater, we round up. In this case, the digit after the first significant figure is 6, which is greater than 5, so we round up. The rounded number to 1 significant figure is 2.4.

The total change in Janet's car insurance payment after 44 years is $1320.

To find the total change in Janet's car insurance payment after 44 years, we can use the formula:

Total change = decrease per year × number of years

In this case, the decrease per year is $30 and the number of years is 44. So the expression representing the total change in her payment would be:

Total change = $30 × 44 = $1320

Therefore, Janet's car insurance payment will decrease by $1320 after 44 years.

Answer:  x = 8

−2x − 1 + 3x =7

−2x + −1 + 3x =7

(−2x+3x) + (−1) =7 (Combine Like Terms)

x+ −1 =7

x−1=7

Step 2: Add 1 to both sides.

x−1+1=7+1

x=8

94.2 cm divided by pi which is 3.14 equals to 30 evenly hoped this helped yall out

The volume of the conical cup is approximately 94.25 cm³. This is the amount of water it can hold when full.

To find the volume of the conical paper cup, we'll use the formula for the volume of a cone:

[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]

Where:

- ( V ) is the volume of the cone

- ( pi ) is a constant (approximately 3.14159)

- ( r ) is the radius of the circular base of the cone

- ( h ) is the height of the cone

Given:

- ( r = 3 ) cm (half the diameter)

- ( h = 10 ) cm

Substituting the given values into the formula:

[tex]\[ V = \frac{1}{3} \times \pi \times (3^2) \times 10 \][/tex]

[tex]\[ V = \frac{1}{3} \times \pi \times 9 \times 10 \][/tex]

[tex]\[ V = \frac{1}{3} \times 90\pi \][/tex]

[tex]\[ V = 30\pi \][/tex]

Now, let's calculate the approximate value of [tex]\( \pi \)[/tex] which is 3.14159:

[tex]\[ V \approx 30 \times 3.14159 \][/tex]

V≈94.2477

So, the volume of the conical paper cup is approximately [tex]\( 94.2477 \, \text{cm}^3 \) or \( 94.25 \, \text{cm}^3 \)[/tex] rounded to two decimal places. This is the amount of water the cup can hold when full.

First, find the width by using the perimeter formula for a rectangle, solve the equation, and then calculate the length by adding 6 yards. With both widths, calculate the area. The rectangle's area is 55 square yards.

To solve for the area of the rectangle, we must find its length and width first. The given condition is that the length is 6 yards longer than the width. If we denote the width as w yards, then the length would be w + 6 yards.

Since the perimeter is the sum of all sides, for a rectangle, it can be calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. Substituting the given perimeter (32 yd) and the expressions for length and width, we have:

Now that we have both dimensions, the area of the rectangle can be calculated using the formula A = l × w. Substituting the found values:

Area = 11 yd × 5 yd = 55 yd²

Therefore, the area of the rectangle is 55 square yards.

Answer:

[tex]25x^{2}y^{22}[/tex] is the answer.

Step-by-step explanation:

The given expression is [tex](5xy^{5})^{2}(y^{3})^{4}[/tex].

Now we have to simplify the expression given in the question.

[tex](5xy^{5})^{2}(y^{3})^{4}=(5)^{2}(x)^{2}(y^{5})^{2}(y^{3})^{4}=25x^{2}y^{10}y^{12}=25x^{2}y^{10+12}=25x^{2}y^{22}[/tex]

Therefore the simplified form of the expression will be [tex]25x^{2}y^{22}[/tex]

i don't know the answer can you help me

Answer: 1/2

Step-by-step explanation: 1/2 bc 50 and 50 is like 1/2 and 1/2

Hope this helped ya! :}

Edit: js realized this was 7 years ago-