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Sauron
2 days ago
5

Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation. Who found

the correct equation and solution? Why is the other person incorrect?
5 times the difference of a number and 20 is the same as half the sum of 4 more than 4 times a number.

Mathematics
1 answer:
Inessa [3.9K]2 days ago
3 0
Kevin, since the problem states a number (x) minus 20, and given that 20 is mentioned later, it indicates that it is the second number involved here.
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iven: C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the
Leona [4166]

Answer:

For a clearer understanding, refer to the attached figure:

Step-by-step breakdown:

1. According to the unique line postulate, only one line segment can be created: BC

This is because a single line can only connect two distinct points.

2. Utilizing the definition of reflection, reflect BC across l.

To identify the line segment reflected over l, we will apply the reflection definition.

3. Based on the reflection definition, C remains as its own image and A represents the image of B.

The reflection definition states that a figure is transformed into a mirror image around a line. Thus, CD serves as the perpendicular bisector of AB, which makes A and B equidistant from D, producing their mirror images.

4. Because reflections maintain length, we find that AC = BC

In a reflection, the figure transforms to create a mirror image, ensuring the lengths remain unchanged.

8 0
1 day ago
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There are seven boys and five girls in a class. The teacher randomly selects three different students to answer questions. The f
Svet_ta [4321]

The likelihood of selecting one girl is calculated as \frac{5}{12}. This is based on having 5 girls within a total of 12 students, and the probability of an event can be expressed as: \frac{\text{# of things you want}}{\text{# of things are possible}}.

Using the same reasoning, for the next student, we have reduced the number of students by 1, leading to 11 possible outcomes instead of 12, giving us:\frac{7}{11}, which represents the probability of selecting a boy as the second choice.

Lastly, the probability of choosing a girl for the third selection follows the same logic and is given as:\frac{4}{10}.

However, we must combine these individual probabilities to determine the likelihood of this specific sequence of selections occurring:

\frac{5}{12}*\frac{7}{11}*\frac{4}{10}=\frac{140}{1320}

This simplifies to:

\frac{7}{66}

4 0
8 days ago
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Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc
Leona [4166]

To address this problem, let's start by formulating the general motion equation along the vertical direction.

This gives us:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

  • g: gravitational acceleration
  • vo: initial velocity
  • h0: starting height

For the first individual:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second individual:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

When both individuals reach the identical altitude, the following holds:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rearranging results in:

\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50

\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21

\frac {19} {12} * t = 29

Solving for time:

t = 29 (\frac {12} {19})\\t = 18.31s

Result:

The two window washers reach the same height after 18.31 seconds.

6 0
16 days ago
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If mc008-1.jpg, what is f(5.9)?
PIT_PIT [3919]
The inquiry is as follows: given f(x) = 3 [ x - 2 ], what is the value of f(5.9)? The options available are: 9, 10, 11, and 12. To solve for f(c) when c is any real number, simply substitute x with c in the equation. Thus, f(5.9) = 3 [ 5.9 - 2 ] = 3 [ 3.9 ]. We recognize that [ 3.9 ] simplifies to 3, leading to 3 * 3 = 9. Therefore, the final answer is 9.
6 0
11 days ago
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What is the following sum? 2 (RootIndex 3 StartRoot 16 x cubed y EndRoot) + 4 (RootIndex 3 StartRoot 54 x Superscript 6 Baseline
Leona [4166]

Response:

a on edge

Detailed explanation:

I completed the cumulative examination.

3 0
10 days ago
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