Mercy drops a penny into a pond. The penny drops 1.5 inches every second.
How many inches below the surface will it be after 8 seconds? write the problem then evaluate.
Problem: Mercy drops a penny into a pond. The penny drops 1.5 inches every second. How many inches below the surface will it be after 8 seconds?
Evaluation:
The penny drops 1.5 inches every second, so after 8 seconds it will have dropped:
1.5 inches x 8 seconds = 12 inches
Therefore, after 8 seconds the penny will be 12 inches below the surface.
An environmental scientist is measuring changes in the water level of a local stream this table shows the changes she recorded during the last few months
May: 5
June: -3
July: 3.5
August: 1.5
During which month did the water decrease?
The water level of the stream decreased during the month of June, where it recorded a change of -3.
Between which months did the water level change the most?
We can calculate the absolute values of the changes in water level for each month by taking the magnitude of each change. The absolute values of the changes are:
May: 5
June: |-3| = 3
July: 3.5
August: 1.5
The month with the highest absolute change is May, with a change of 5 inches in water level.
So, the water level changed the most between April and May.
The scientist recorded the change in water level in September, and that value was 5 times the amount of August. What is the value for September?
We can use the information given to find the value for September:
If the change in water level for September was 5 times the amount of August, and August had a change of 1.5 units, then we can multiply 1.5 by 5 to find the change for September:
September change = 1.5 x 5 = 7.5
Therefore, the change in water level for September was 7.5 units.
The temperature at 2:00 pm is 27 degrees. At 2:am the temperature has fallen to -4 degrees. What is the difference in temperature from 2:00 pm to 2:am?
A. 27 + (-4)
B. 27 ÷ (-4)
C. 27 - (-4)
Choose the correct problem.
C. 27 - (-4)
Find the difference in temperature. Show work.
The difference in temperature between 2:00 pm and 2:00 am can be found using the problem:
27 - (-4)
When subtracting a negative number, we can rewrite the problem as the addition of the opposite:
27 + 4
Adding these numbers, we get:
31
Therefore, the difference in temperature between 2:00 pm and 2:00 am is 31 degrees.
A hot air balloon is cruising at an elevation of 500 feet above sea level. The pilot turns off the burner and the balloon drops at a rate of 50 feet per minute for 6 minutes. What is the elevation of the balloon?
Choose the correct problem.
A. 500 + (6 x50)
B. -500 - (-6 x 50)
C. 500 + (-50 x 6)
D. -500 + (-50 - 6)
C. 500 + (-50 x 6)
Evaluate the problem. Show work.
To find the elevation of the balloon after 6 minutes of dropping at a rate of 50 feet per minute, we can use the problem:
500 + (-50 x 6)
Multiplying -50 by 6, we get:
-300
Adding that to the initial elevation of 500 feet, we get:
500 + (-300) = 200
Therefore, the elevation of the balloon after 6 minutes of dropping at a rate of 50 feet per minute is 200 feet above sea level.
A valley is 94 feet below sea level. What is the absolute value of the elevation difference between the valley and the sea level? Write the problem and evaluate.
Problem: A valley is 94 feet below sea level. What is the absolute value of the elevation difference between the valley and the sea level?
To find the absolute value of the elevation difference, we need to subtract the valley elevation from the sea level elevation and then take the absolute value:
|sea level - valley elevation| = |0 - (-94)|
Simplifying the expression inside the absolute value, we get:
|0 - (-94)| = |94|
Therefore, the absolute value of the elevation difference between the valley and the sea level is 94 feet.
Donald is 110 feet above sea level. Mickey is 70 feet below sea level. How far apart are Donald and Mickey? Write the problem and evaluate.
Problem: Donald is 110 feet above sea level. Mickey is 70 feet below sea level. How far apart are Donald and Mickey?
To find the distance between Donald and Mickey, we need to add their elevations:
distance = Donald's elevation + Mickey's elevation
Since Mickey is below sea level, we can add a negative value for his elevation:
distance = 110 + (-70)
Simplifying, we get:
distance = 40
Therefore, Donald and Mickey are 40 feet apart.
Plot the following ordered pair points on the coordinate plane by dragging the colored dot to the correct location A (-7, 3 1/2) B (2.5, 5)
I am sorry, but as an AI language model, I don't have the interface/ feature to interact/ visualize or drag and drop points on a graph. However, I can explain how to plot these ordered pairs on a coordinate plane.
To plot the points A(-7, 3 1/2) and B(2.5, 5), we need to first locate the x and y coordinates on the graph.
For point A, the x coordinate is -7 and the y coordinate is 3.5. So, we can move 7 units to the left from the origin (0, 0) on the x-axis, and then move up 3.5 units on the y-axis to locate the point A on the graph.
For point B, the x coordinate is 2.5 and the y coordinate is 5. So, we can move 2.5 units to the right from the origin (0, 0) on the x-axis, and then move up 5 units on the y-axis to locate the point B on the graph.
After locating these two points on the graph, we can connect them with a straight line to visualize their relationship.
Graph the inequality by dragging the correct parts to the number line
I am sorry, but as an AI language model, I don't have the interface/ feature to interact/ visualize or drag and drop parts on a graph. However, I can help you understand how to graph an inequality on a number line.
To graph an inequality on a number line, follow these steps:
1. Identify the variable and inequality symbol in the inequality.
2. Solve the inequality for the variable to get an expression in the form of x < a or x > a, where a is a constant.
3. Plot a point on the number line at the value of a.
4. Shade the portion of the number line that satisfies the inequality.
5. Add an open circle for < and a closed circle for <= or > and >=, if the boundary value is included or not included in the solution set respectively.
For example, let's say we want to graph the inequality 3x - 5 > 7 on a number line.
We start by isolating x:
3x - 5 > 7
Add 5 to both sides:
3x > 12
Divide both sides by 3:
x > 4
Then we plot an open circle at 4 on the number line, and shade to the right of it because x is greater than 4.
Finally, we write x > 4, because x is not equal to 4 in the solution set.
I hope this helps! Let me know if you have any more questions.
what is the solution to the inequality w+7>0
A) w >-14
B) w >-7
C) w > 0
D) w > 7
Show work
To solve the inequality w + 7 > 0, we can isolate the variable w by subtracting 7 from both sides:
w + 7 - 7 > 0 - 7
Simplifying the left side and the right side, we get:
w > -7
Therefore, the answer is B) w > -7.
Which choice below shows these rational numbers in order from least to greatest?
-4.5, 0, -62.25. 63
A. 4.5, -62.25, 0, 63
B. 63, 0, -4.5, -62.25
C. 0, -4.5, -62.25. 63
D. -62.25. -4.5, 0 63
The rational numbers -4.5, 0, -62.25, 63 arranged from least to greatest are:
D. -62.25. -4.5, 0, 63
Solve the inequality
m + 8 (equal to sign) 18
show your work
To solve the inequality m + 8 = 18, we want to isolate the variable m by undoing the addition of 8. To do this, we can subtract 8 from both sides:
m + 8 - 8 = 18 - 8
Simplifying the expression on the left side and the right side, we get:
m = 10
Therefore, the solution to the inequality m + 8 = 18 is m = 10.
Solve the inequality t-5> -2
To solve the inequality t - 5 > -2, we want to isolate the variable t by undoing the subtraction of 5. To do this, we can add 5 to both sides:
t - 5 + 5 > -2 + 5
Simplifying the left side and the right side, we get:
t > 3
Therefore, the solution to the inequality t - 5 > -2 is t > 3.
t - 5 > -2=
Answer
Show your work
Answer: t > 3
To solve the inequality t - 5 > -2, we want to isolate the variable t by undoing the subtraction of 5. To do this, we can add 5 to both sides:
t - 5 + 5 > -2 + 5
Simplifying the left side and the right side, we get:
t > 3
Therefore, the solution to the inequality t - 5 > -2 is t > 3.
write the inequality that represents the statement
Q is no more than 125
Show work
To represent the statement "Q is no more than 125" as an inequality, we can use the less than or equal to symbol (≤).
Q ≤ 125
Therefore, the inequality that represents the statement "Q is no more than 125" is Q ≤ 125.
Write the inequality that represents the statement
H is more that 34
Show work
To represent the statement "H is more than 34" as an inequality, we can use the greater than symbol (>).
H > 34
Therefore, the inequality that represents the statement "H is more than 34" is H > 34.
Find the distance for each segment determined by the two points given
SEGMENT A (3, 4) and B (9,4) SHOW WORK
SEGMENT F (6,0) and G (6,-11) SHOW WORK
SEGMENT C (-10.5, -7.25) and D (18.5, -7.25) SHOW WORK
SEGMENT M (-1.3, -1.3) and N (-1.3 and 3.6) SHOW WORK
We can use the distance formula to find the distance for each segment determined by the two points given. The distance formula is:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
where (x1, y1) and (x2, y2) are the coordinates of the two points.
SEGMENT A:
(x1, y1) = (3, 4)
(x2, y2) = (9, 4)
d = √[(9 - 3)^2 + (4 - 4)^2]
d = √[6^2 + 0^2]
d = √36
d = 6
Therefore, the distance for Segment A is 6 units.
SEGMENT F:
(x1, y1) = (6, 0)
(x2, y2) = (6, -11)
d = √[(6 - 6)^2 + (-11 - 0)^2]
d = √[0^2 + (-11)^2]
d = √121
d = 11
Therefore, the distance for Segment F is 11 units.
SEGMENT C:
(x1, y1) = (-10.5, -7.25)
(x2, y2) = (18.5, -7.25)
d = √[(18.5 - (-10.5))^2 + (-7.25 - (-7.25))^2]
d = √[29^2 + 0^2]
d = √841
d = 29
Therefore, the distance for Segment C is 29 units.
SEGMENT M:
(x1, y1) = (-1.3, -1.3)
(x2, y2) = (-1.3, 3.6)
d = √[(-1.3 - (-1.3))^2 + (3.6 - (-1.3))^2]
d = √[0^2 + 4.9^2]
d = √24.01
d = 4.9
Therefore, the distance for Segment M is approximately 4.9 units.
find the distance for each segment determined by the two points given
A (3, 4)
B (9,4)
To find the distance between two points A(3, 4) and B(9, 4), we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
where x1 and y1 are the coordinates of point A, and x2 and y2 are the coordinates of point B.
Plugging in the coordinates of the points, we get:
d = √[(9 - 3)^2 + (4 - 4)^2]
d = √[6^2]
d = √36
d = 6
Therefore, the distance between points A and B is 6 units.