There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula h, equals, 58, point, 4, plus, 2, point, 3, 2, fh=58.4+2.32f, where hh represents the expected height in centimeters and ff represents the length of the femur in centimeters. What is the meaning of the ff-value when h, equals, 152h=152?

Question

There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula h, equals, 58, point, 4, plus, 2, point, 3, 2, fh=58.4+2.32f, where hh represents the expected height in centimeters and ff represents the length of the femur in centimeters. What is the meaning of the ff-value when h, equals, 152h=152?
Answer
Multiple Choice Answers
The femur length for someone with an expected height of 40.3 centimeters.
The femur length for someone with an expected height of 152 centimeters.
The change in expected height for every one additional centimeter of femur length.
The expected height for someone with a femur length of 152 centimeters.

GPT-4o mini · Answer

To find the meaning of the $ f $-value when $ h = 152 $ in the equation $ h = 58.4 + 2.32f $, we need to determine $ f $ (the femur length) when the expected height $ h $ is 152 cm. 1. Set the equation equal to 152: $$ 152 = 58.4 + 2.32f $$ 2. Subtract 58.4 from both sides: $$ 152 - 58.4 = 2.32f $$ $$ 93.6 = 2.32f $$ 3. Divide both sides by 2.32 to solve for $ f $: $$ f = \frac{93.6}{2.32} \approx 40.34 $$ Now, $ f $ represents the femur length for someone with an expected height of 152 centimeters. Therefore, the correct answer is: **The femur length for someone with an expected height of 152 centimeters.**

Answer

There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula h, equals, 56, point, 7, plus, 2, point, 3, 7, fh=56.7+2.37f, where hh represents the expected height in centimeters and ff represents the length of the femur in centimeters. What is the meaning of the ff-value when h, equals, 170h=170?
Answer
Multiple Choice Answers
The femur length for someone with an expected height of 47.8 centimeters.
The femur length for someone with an expected height of 170 centimeters.
The change in expected height for every one additional centimeter of femur length.
The expected height for someone with a femur length of 170 centimeters.

GPT-4o mini · Answer

To determine the meaning of the $ f $-value when $ h = 170 $ in the equation $ h = 56.7 + 2.37f $, we can follow similar steps as before to find $ f $: 1. Set the equation equal to 170: $$ 170 = 56.7 + 2.37f $$ 2. Subtract 56.7 from both sides: $$ 170 - 56.7 = 2.37f $$ $$ 113.3 = 2.37f $$ 3. Divide both sides by 2.37 to solve for $ f $: $$ f = \frac{113.3}{2.37} \approx 47.7 $$ Now that we have found $ f $, it represents the femur length for someone with an expected height of 170 centimeters. Therefore, the correct answer is: **The femur length for someone with an expected height of 170 centimeters.**

Answer

Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, 2, x
y=
−2x
y, equals, start fraction, 4, divided by, 3, end fraction, x
y=
3
4

x
x
y
y=-2x
y=4/3x
Answer
Attempt 1 out of 2
The number of attempts on this specific problem before you are marked incorrect

Solution:
Submit Answer

GPT-4o mini · Answer

To solve the system of equations given by:

$ y = -3x - 2 $
$ y = \frac{3}{2}x + 7 $

We can set the two equations equal to each other since they both equal $ y $:

\[ -3x - 2 = \frac{3}{2}x + 7 \]

Now, let's solve for $ x $:

First, add $ 3x $ to both sides to get all $ x $ terms on one side:

\[ -2 = \frac{3}{2}x + 3x + 7 \]

Simplify $ 3x $ by expressing it as a fraction to combine with $ \frac{3}{2}x $:

\[ -2 = \frac{3}{2}x + \frac{6}{2}x + 7 \]

\[ -2 = \frac{9}{2}x + 7 \]

Subtract $ 7 $ from both sides:

\[ -2 - 7 = \frac{9}{2}x \]

\[ -9 = \frac{9}{2}x \]

Multiply both sides by $ \frac{2}{9} $ to solve for $ x $:

\[ x = -9 \cdot \frac{2}{9} \]

\[ x = -2 \]

Now that we have $ x = -2 $, we can substitute this value back into either equation to find $ y $. We'll use the first equation:

\[ y = -3(-2) - 2 \]

\[ y = 6 - 2 \]

\[ y = 4 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (-2, 4) \]

Final Answer: $ (-2, 4) $

Answer

Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, 2, x
y=
−2x
y, equals, start fraction, 4, divided by, 3, end fraction, x
y=
3
4

x
x
y
y=-2x
y=4/3x
Answer
Attempt 1 out of 2
The number of attempts on this specific problem before you are marked incorrect

Solution:
Submit Answer

GPT-4o mini · Answer

To solve the system of equations given by:

$ y = -2x $
$ y = \frac{4}{3}x $

we need to set the two expressions for $ y $ equal to each other:

\[ -2x = \frac{4}{3}x \]

Next, we'll solve for $ x $.

First, add $ 2x $ to both sides:

\[ 0 = \frac{4}{3}x + 2x \]

Convert $ 2x $ to a fraction with the same denominator ($ 3 $):

\[ 0 = \frac{4}{3}x + \frac{6}{3}x \]

Combine the $ x $ terms:

\[ 0 = \frac{10}{3}x \]

To solve for $ x $, multiply both sides by $ \frac{3}{10} $:

\[ x = 0 \]

Now that we have $ x = 0 $, we can substitute this value into either equation to find $ y $. Let's use the first equation:

\[ y = -2(0) = 0 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (0, 0) \]

Final Answer: $ (0, 0) $

Answer

What ordered pairs are the solutions of the system of equations shown in the graph below?
x
y
Answer
Attempt 1 out of 2

left parenthesis(
,
right parenthesis) and left parenthesis(
,
right parenthesis)
Submit Answer

GPT-4o mini · Answer

I don't have the ability to see your graph, but I can guide you on how to determine the ordered pairs that represent the solutions of a system of equations based on a graph.

Locate the Intersections: Look for the points where the lines in the graph intersect. These points are the solutions to the system of equations.
Read the Coordinates: Each intersection point will have an $ x $-value and a $ y $-value. Record those values as ordered pairs in the format $ (x, y) $.
Determine all Intersection Points: If there are multiple points where the lines intersect, record all of them as separate ordered pairs.

Example:

If the lines intersect at the points $ (1, 2) $ and $ (3, -1) $, you would write:
- The ordered pairs are $ (1, 2) $ and $ (3, -1) $.

Complete Your Answer:

Once you identify the intersection points on the graph, you can fill in the response boxes with the ordered pairs like:

$ \text{left parenthesis( } a, b \text{ right parenthesis} $ and $ \text{left parenthesis( } c, d \text{ right parenthesis} $.

If you can describe the graph or the equations involved, I can help you identify the intersection points more specifically!

Answer

Which point would be a solution to the system of linear inequalities shown below?
y, is less than, one quarter, x, minus, 4, y, is less than or equal to, minus, 6, x, plus, 6
y<
4
1

x−4y≤−6x+6
Answer
Multiple Choice Answers
left parenthesis, 4, comma, 10, right parenthesis(4,10)
left parenthesis, minus, 4, comma, 5, right parenthesis(−4,5)
left parenthesis, minus, 4, comma, minus, 4, right parenthesis(−4,−4)
left parenthesis, minus, 4, comma, minus, 6, right parenthesis(−4,−6)

GPT-4o mini · Answer

To determine which point would be a solution to the system of linear inequalities:

Inequalities Given:
- $ y < \frac{1}{4}x - 4 $
- $ y \leq -6x + 6 $
Evaluate Each Point: We will test each provided point to see if they satisfy both inequalities.

Testing the Points:

Point (4, 10):
- For $ y < \frac{1}{4}x - 4 $: \[ 10 < \frac{1}{4}(4) - 4 \implies 10 < 1 - 4 \implies 10 < -3 \quad \text{(False)} \]
- Point (4, 10) does not satisfy the first inequality.
Point (-4, 5):
- For $ y < \frac{1}{4}x - 4 $: \[ 5 < \frac{1}{4}(-4) - 4 \implies 5 < -1 - 4 \implies 5 < -5 \quad \text{(False)} \]
- Point (-4, 5) does not satisfy the first inequality.
Point (-4, -4):
- For $ y < \frac{1}{4}x - 4 $: \[ -4 < \frac{1}{4}(-4) - 4 \implies -4 < -1 - 4 \implies -4 < -5 \quad \text{(False)} \]
- Point (-4, -4) does not satisfy the first inequality.
Point (-4, -6):
- For $ y < \frac{1}{4}x - 4 $: \[ -6 < \frac{1}{4}(-4) - 4 \implies -6 < -1 - 4 \implies -6 < -5 \quad \text{(False)} \]

Summary of Findings:

None of the tested points satisfy both inequalities. However, let’s check where they stand in the second inequality to see if any might meet that criterion.

Since the first inequality fails for all points, let's recheck if we can find any satisfying ones.

Continuing the evaluations would include the critical boundaries from both inequalities and checking more thoroughly might yield:

For $y = -6x + 6$ and $y = \frac{1}{4}x - 4$, graph them to check the regions they cover.

Suggestions Based on the Norms:

None directly from the points listed - you might want to retry their evaluations or provide more context if any additional points appear to be worthy of checking against these defined inequalities.

If needed to confirm back with adjustments based on boundaries like slope intersections or chosen scope for other pairs fitting into double linear measures.