A rectangular prism is 4 units by 2 1/2 units by 1 1/2 units. How many cubes with a side length of 1/2 unit will completely fill the prism ?

Answers

Answer 1

Answer: V prism = 4 × (5/2) × (3/2) = 15 units^3;
V cube = (1/2)^3 = 1/8 units^3;
15 ÷ (1/8) = 15 × 8 = 120 cubes;

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After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula? A) 5x^3+2x-4=2x^2 B) x^2-6x-7=2x^2 C) 2x^2-3x+10=2x^2+21 D) 5x^2-3x+10=2x^2

Answers

Answer:

B & D

Step-by-step explanation:

The quadratic formula can be used to solve for x for any quadratic. Recall a quadratic is any function whose highest exponent known as degree is 2. Looking at the answer selections, A has one term with exponent 3. This isn't possible in the formula. Looking at answer C, the term with exponent 2 has the same coefficient on each side of the equal sign. When it is rearranged these will cancel out no exponent of 2 will be in the equation anymore. Only B & D work after being rearranged and simplified

The two equations after simplifying will give quadratic equations are:-

x ²-6x-7=2x² and 5x²-3x+10=2x².

What is a quadratic equation?

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Solving for the quadratic equation:-

Option B:-

x ² - 6x - 7 = 2x²

- 2x² + x ² - 6x - 7 = 0

x ² + 6x + 7 = 0

Option D:-

5x² - 3x + 10 = 2x².

5x² - 2x². - 3x + 10 = 0

3x² - 3x + 10 = 0

Therefore two equations after simplifying will give quadratic equations are- x ²-6x-7=2x² and 5x²-3x+10=2x².

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Darcy wants to buy a new skirt. The price of the skirt is $35.00 and 7% sales tax will be added to the price. Darcy has $40.00 to spend. How much money will Darcy have left after paying for the skirt and the sales tax?

Answers

The value of the skirt with a tax is
$35.00 + ($35.00 x 0.07) = $37.45
He has $40.00 and his change will be
$40.00 - $37.45 = $2.55

There are 32 students in a PE class. Of the students, 1/4 are girls. How many girls are in the class?

Answers

if there are 32 students in the class and 1/4 of them are girls. divide 32 by 4 and you get 8. so 8 of them are girls

There are 8 girls in the class. All you do is divide 32 by 4. In doing so you will get 8. Then plug it in to see if it's true so you would do 8 times 4 which is 32.

What is the surface are of the square