Table of Values

Question

x ya yb
0 0 3
1 2 3.5
2 4 4
Which of the following systems of linear equations does the table of values represent?

(1 point)
Responses

{y=2xy=3x+1/2


{y=1/2xy=2x+3


{y=2xy=1/2x+3

{y=2x+3y=1/2x

Answer 1

To match the table of values with the correct system of linear equations, we can analyze the data provided:

The table shows values for \( x \), \( ya \), and \( yb \):

\[ \begin{array}{|c|c|c|} \hline x & ya & yb \ \hline 0 & 0 & 3 \ 1 & 2 & 3.5 \ 2 & 4 & 4 \ \hline \end{array} \]

Let's analyze the values for \( ya \) and \( yb \) to determine the equations.

For \( ya \):

1. When \( x = 0 \), \( ya = 0 \).
2. When \( x = 1 \), \( ya = 2 \).
3. When \( x = 2 \), \( ya = 4 \).

The points are (0, 0), (1, 2), and (2, 4). This suggests a linear relationship, and we can find the slope:

\[ \text{slope} = \frac{2 - 0}{1 - 0} = 2 \]

Using point-slope form \( y = mx + b \):

• The slope \( m = 2 \) and it passes through the origin (0,0). Thus, the equation for \( ya \) is:

\[ ya = 2x \]

For \( yb \):

1. When \( x = 0 \), \( yb = 3 \).
2. When \( x = 1 \), \( yb = 3.5 \).
3. When \( x = 2 \), \( yb = 4 \).

The points are (0, 3), (1, 3.5), and (2, 4).

Calculating the slope:

\[ \text{slope} = \frac{3.5 - 3}{1 - 0} = 0.5 \] \[ \text{slope} = \frac{4 - 3.5}{2 - 1} = 0.5 \]

Using point-slope form \( y = mx + b \):

• The slope \( m = 0.5 \) and it has a y-intercept \( b = 3 \). Thus, the equation for \( yb \) is:

\[ yb = 0.5x + 3 \]

Now, putting these two results together, we can express the system of equations for \( ya \) and \( yb \):

\[ \begin{align*} ya &= 2x \ yb &= 0.5x + 3 \ \end{align*} \]

Comparing this to the given options, we identify:

The correct representation from the responses is:

\[ {y = 2x, y = \frac{1}{2}x + 3} \]

Thus, the last option is:

\[ {y = 2x, y = \frac{1}{2}x + 3} \]

Answer 2

Question
Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?(1 point)
Responses

{y=5x−10y=3x −10
enlarged left brace start layout first row y equals 5 x minus 10 second row y equals 3 x minus 10 end layout

{y=10+5xy=10+3x
enlarged left brace start layout first row y equals 10 plus 5 x second row y equals 10 plus 3 x end layout

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=10−5xy=10−3x

Answer 3

To determine which system of equations represents the egg-drop project scenario, we need to establish the equations describing the height of the egg over time based on the fall rates.

Given Information:

• The eggs are dropped from a height of 10 feet.
• One egg falls at a rate of 5 feet per second.
• The other egg falls at a rate of 3 feet per second.

Variables Defined:

• Let \( x \) represent the time in seconds.
• Let \( y \) represent the height of the egg (in feet).

For Each Egg:

1. Egg falling at 5 feet per second:

   • The height decreases by 5 feet for every second that passes.
   • Starting from a height of 10 feet: \[ y = 10 - 5x \]

2. Egg falling at 3 feet per second:

   • The height decreases by 3 feet for every second that passes.
   • Starting again from a height of 10 feet: \[ y = 10 - 3x \]

System of Equations:

Thus, the system of equations representing the situation is: \[ \begin{align*} y &= 10 - 5x \ y &= 10 - 3x \end{align*} \]

Analyzing Responses:

Now we will check the provided options to find a match:

1. {y = 5x - 10, y = 3x - 10}
2. {y = 10 + 5x, y = 10 + 3x}
3. {y = -5x, y = -3x}
4. {y = 10 - 5x, y = 10 - 3x}

The correct representation is:

\[ {y = 10 - 5x, y = 10 - 3x} \]

Therefore, the correct answer is the last option: \[ {y = 10 - 5x, y = 10 - 3x} \]

Answer 4

In which phase do cells rest?(1 point)
Responses

interphase
interphase

prophase
prophase

anaphase
anaphase

metaphase

Answer 5

Cells rest primarily during interphase. This phase of the cell cycle is important for cell growth, DNA replication, and preparation for cell division. Interphase consists of three sub-phases: G1 (first gap), S (synthesis), and G2 (second gap).

During interphase, the cell is not actively dividing but is metabolically active, carrying out various functions to prepare for mitosis or meiosis.

So the correct answer is:

interphase.

Answer 6

Which of the following correctly orders events during mitosis?(1 point)
Responses

The nuclear membrane dissolves. Microtubules organize the chromosomes. The mitotic spindle attaches to chromosomes.
The nuclear membrane dissolves. Microtubules organize the chromosomes. The mitotic spindle attaches to chromosomes.

Microtubules organize the chromosomes. The nuclear membrane dissolves. The mitotic spindle attaches to chromosomes.
Microtubules organize the chromosomes. The nuclear membrane dissolves. The mitotic spindle attaches to chromosomes.

The mitotic spindle attaches to chromosomes. Microtubules organize the chromosomes. The nuclear membrane dissolves.
The mitotic spindle attaches to chromosomes. Microtubules organize the chromosomes. The nuclear membrane dissolves.

The nuclear membrane dissolves. The mitotic spindle attaches to chromosomes. Microtubules organize the chromosomes.

Answer 7

The correct order of events during mitosis, particularly in the prophase stage, is as follows:

1. The nuclear membrane dissolves (this occurs during prophase).
2. Microtubules organize and form the mitotic spindle.
3. The mitotic spindle attaches to chromosomes (specifically at the kinetochores).

Now let's analyze the provided options:

1. The nuclear membrane dissolves. Microtubules organize the chromosomes. The mitotic spindle attaches to chromosomes.

2. Microtubules organize the chromosomes. The nuclear membrane dissolves. The mitotic spindle attaches to chromosomes.

3. The mitotic spindle attaches to chromosomes. Microtubules organize the chromosomes. The nuclear membrane dissolves.

4. The nuclear membrane dissolves. The mitotic spindle attaches to chromosomes. Microtubules organize the chromosomes.

The accurate sequence based on mitosis events is:

• The nuclear membrane dissolves.
• Microtubules organize to form the mitotic spindle.
• The mitotic spindle attaches to the chromosomes.

Thus, the first option is correct:

The nuclear membrane dissolves. Microtubules organize the chromosomes. The mitotic spindle attaches to chromosomes.

Answer 8

In what phase of mitosis do chromosomes split into sister chromatids?(1 point)
Responses

anaphase
anaphase

telophase
telophase

cytokinesis
cytokinesis

prophase

Answer 9

The phase of mitosis in which chromosomes split into sister chromatids is anaphase.

During anaphase, the sister chromatids are pulled apart by the spindle fibers and move toward opposite poles of the cell. This separation marks a crucial step in ensuring that each new daughter cell will receive an identical set of chromosomes.

So the correct answer is:

anaphase.

Answer 10

Which type of stem cell is able to differentiate into any cell type, including extraembryonic placental cells?(1 point)
Responses

pluripotent cells
pluripotent cells

multipotent cells
multipotent cells

totipotent cells
totipotent cells

embryonic cells

Answer 11

The type of stem cell that is able to differentiate into any cell type, including extraembryonic placental cells, is referred to as totipotent cells.

Totipotent cells can develop into any cell within an organism, as well as the tissues needed to support the embryo, such as the placenta. This ability exists in the earliest stages of embryonic development.

Therefore, the correct answer is:

totipotent cells.