10 ÷ (20 ÷ 2² × 5 ÷ 5) × 8 - 2

The volume of the rectangular prism is 22 1/2 m³

A rectangular prism is a three-dimensional object. It is made up of six faces, twelve sides and six vertices.

Volume = length x width x height

2 1/2 x 4 x 2 1/4

5/2 x 4 x 9/4 = 720 / 32 = 22 1/2 m³

Here is the complete question: A rectangular prism has a length of 21/2 meters, a width of 4 meters, and a height of 21/4 meters.

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Answer:

A. 12

B. 3

C. -2

D. -5

Step-by-step explanation:

Verified on edge, just finished it

The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.

Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.

Given:

y = 3x² + 12x + 7

Now writing the equation in vertex form

y = 3x² + 12x + 7

y = 3x(x + 4) + 7

Adding and subtracting 12 on both side

y= 3(x²+ 4x) + 7 -12 + 12

y= 3(x² + 4x + 4) + 7- 12

y= 3(x+ 2)² -5

Now, Comparing it with  y = a(x - h)² + k we get

a= 3

h= -2

and, k= -12

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Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

The explicit rule for this situation is An = 12 + n, where "n" represents the row number.

To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:

A10 = 12 + 10

A10 = 22

So, there will be 22 marbles in the 10th row.

Matching the answers:

Explicit rule: An = 12 + n

Number of marbles in the 10th row: 22

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Tmuch of a head start should the runner on the outside get would be = 2πm.

How to calculate the length of head start for the runner outside?

To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:

The formula for circumferential of circle = 2πr

Circumference of inner circle;

= 2× π×50

= 100π

Circumference of outer circle;

= 2×π×51

= 102π

The length of head start for the runner outside = 102π-100π = 2πm

In order to find the answer, put six and three together to obtain nine, then divide nine in half to get 4.5, and then divide 4.5 by seven to get roughly 0.64.

When translated into a mathematical operation, the phrase "half of the sum of six and three then divided by seven" looks like this: Find the value of the sum of 6 + 3 to get 9 first. Then divide by half, or 4.5, to get the answer. Divide this by seven, and you'll arrive at a result that is roughly 0.64 (rounded to two decimal places).

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The area of the parallelogram is 32 square units.

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:

    |       (3,6)        (11,6)

    |         *-----------*

    |        /           /

    |       /           /

    |      /           /

    |     /           /

    |    *-----------*

    |  (0,2)        (8,2)

    |

Now,

We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.

To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.

Therefore,

The height of the parallelogram is 4 units.

Now,

The area of a parallelogram is given by the formula:

Area = base x height

Plugging in the values we found, we get:

Area = 8 x 4

Area = 32

Therefore,

The area of the parallelogram is 32 square units.

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Answer:

[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]

Step-by-step explanation:

The given expresion is:

(−2x + 4y)(3x − 7y)

We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]

We expand further to obtain:

[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]

[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]

Answer:

[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]

Step-by-step explanation:

We multiply each term in the parentheses, by those of the other parenthesis:

[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]

Now, we simplify.

We have two terms that contain xy:

[tex]=-6x^2+26xy-28y^2[/tex]

Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]

The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.

This refers to a statement or assertion that is made about something, which may or may not be true.

Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.

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The correct answer is -23.

To simplify the given expression, we need to perform the indicated operations and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Given expression: (–5) • (7) – (6) • (–2)

Step 1: Perform the multiplications inside the parentheses.

(–5) • (7) = –35

(6) • (–2) = –12

Step 2: Perform the subtraction operation.

–35 – (–12) = –35 + 12 = –23

Therefore, the simplified expression is:

[tex](-5) \cdot (7) - (6) \cdot (-2) = -35 + (-12) = -23[/tex]

Final answer:

To measure 9/12 or 3/4 of a cup of syrup using a 1/8 cup, fill and level-off the 1/8 cup measuring cup six times. This uses basic fraction multiplication and measurement skills appropriate for middle school mathematics.

Explanation:

To measure light corn syrup using a 1/8 cup measuring cup, you first need to understand the fraction you're working with, which is 9/12 of a cup. Simplifying this fraction gives you 3/4 of a cup (since 9/12 reduces to 3/4 by dividing both the numerator and denominator by 3). Now, since there are 8 portions of 1/8 in a full cup, you need 6 portions of 1/8 (because 3/4 equals 6/8) to measure out 3/4 of a cup of light corn syrup.

To do this, you'll fill the 1/8 cup measuring cup six times and add each portion to your mixture to reach the desired amount of 9/12 or 3/4 of a cup of syrup. This is a simple example of using measurements and fractions to achieve the correct proportions in a recipe or any culinary preparation.

To find the probability of selecting all blue balls, we divide the number of ways to choose 4 blue balls out of 8 by the number of ways to choose 4 balls out of 8 blue balls and 3 white balls.

To find the probability of selecting all blue balls, we need to consider the number of ways we can choose 4 blue balls out of the 8 blue balls in the urn, divided by the total number of ways we can choose 4 balls out of the 8 blue balls and 3 white balls in the urn.

The probability can be calculated as:

P(All blue balls) = (Number of ways to choose 4 blue balls out of 8) / (Number of ways to choose 4 balls out of 8 blue balls and 3 white balls)

Since the balls are selected without replacement, the number of ways to choose 4 blue balls out of 8 is 8 choose 4. The number of ways to choose 4 balls out of 8 blue balls and 3 white balls is 11 choose 4.

Therefore, the probability of selecting all blue balls is P(All blue balls) = (8 choose 4) / (11 choose 4).

The correct answer is actually 60 miles more !!