If a function is defined by the formula y=1/2x + 3 and its domain is given by the set {-4,0,8}, then which of the following sets gives the function's range?
Answers
Answer:
y = {1, 3, 7}
Step-by-step explanation:
Given
y = ½x + 3
Domain: {-4, 0, 8}
Required
Determine the range of the function
To do this, we simply substitute each value of the domain in the given expression
We start with the first
Substitute -4 for x in y = ½x + 3
y = ½ * -4 + 3
y = -2 + 3
y = 1
Then 0
Substitute 0 for x in y = ½x + 3
y = ½ * 0 + 3
y = 0 + 3
y = 3
Lastly, 8
Substitute 8 for x in y = ½x + 3
y = ½ * 8 + 3
y = 4 + 3
y = 7
Hence, the range of the function is:
y = {1, 3, 7}
Answer:1,3,7
Step-by-step explanation:
Related Questions
The graphs of each group of equations have at least one characteristic in common. Name the characteristics and then graph each group of equations on the same axes to verify your answer.
Wai recorded the length of each string needed for a knitting project. What is the total length of the string needed?
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle) Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? 1.) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles) 2.) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) 3.) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) 4.) Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Write an algebraic expression to represent the phrase below.a number n decreased by 5 please help
Answers
Answer:
c =9.6
Step-by-step explanation:
Answer:
c = 9.6
Step-by-step explanation:
Let's look at our equation; - 4c - 9.6 + 5c = 0. Now we need to collect the like terms which are -4c and 5c.
- 4c - 9.6 + 5c = 0
5c - 4c - 9.6 = 0
We get: c - 9.6 = 0
Now we will add 9.6 on each side to see what c is equal to.
c - 9.6 = 0
+9.6 +9.6
c = 9.6
Yay! We got our answer! Nice job everyone!
strings of lights you use is 14. How many of each type of light do you have?
Answers
Answer:
- 8 short and 6 long strings
Step-by-step explanation:
Let the number of lights are short = s and long = l.
According to question we have:
- s + l = 14
- 5s + 11l = 106
Subtract 5 times the first equation from the second one to solve for l:
- 5s + 11l - 5s - 5l = 106 - 5*14
- 6l = 36
- l = 36/6
- l = 6
Find s:
- s = 14 - 6 = 8
Answer:
A good rule of thumb is 100 lights for every 1.5 feet of tree. However, if you love lights, you may want to double, or even triple, that amount.
Step-by-step explanation:
Just a guess because you gave no answer choices
Answers
Answer:
Step-by-step explanation:
From the information given:
a human brain weighs = 1 kg ; = 1000 grams
Number of cells = 10¹¹ cells
The density of water filled in each cell = 1 g/mL
From above;
the weight of each of the brain cell = total weight of the human brain/the number of cells
the weight of each of the brain cell = 1000/10¹¹
the weight of each of the brain cell = 1 × 10⁻⁸ grams
Now, to calculate the quantity of water in each cell; we have:
= the weight of each brain × density
=
For cube; we know that
1 mL = 1 cm³
Thus:
Recall that; the volume of a cube as well =
where;
x = length of each sides
∴
=
x = 0.0022 cm
Thus, the length of each side of the cell = 0.0022 cm
The surface area of a single cell = x²
The surface area of a single cell = (0.0022 cm)²
The surface area of a single cell = 4.84 × 10⁻⁶ cm²
Therefore, the total surface area of is:
=
=
= 50 m²
Final answer:
If the human brain's cells were cube-shaped and filled with water, each cell would be roughly 21.5 micrometers on a side. If these cells were spread out into a single-cell-thick layer, the total surface area for one side of the layer would be approximately 4.63 square meters.
Explanation:
To answer your question, the human brain has about 1011 cells, each filled with water. Given the total mass of the brain (about 1 kg) and the number of cells, we can calculate the volume of a single cell. The density of water is 1 g/mL or 1,000 kg/m³, so the volume of all the cells (entire brain) is 1 m³. Therefore, the volume of a single cell must be 1 m³/1011 cells, which is approximately 10-14 m³. For a cubical cell, the side length of the cube (a) would be the cube root of this volume, which is approximately 2.15 x 10-5 m or 21.5 micrometers.
To calculate the total surface area for one side of the cell layer, we multiply the area of a single cell by the total number of cells: (2.15 x 10-5)² m²/cell x 1011 cells = approximately 4.63 m².
Learn more about Cell volume here:
#SPJ3
Answers
Let y = f(x)
f(x) = sin x
g(x) = (2x^2 + 3x - 4)
Use the chain rule.
We want y' = f' (g(x)) • g'(x).
y' = cos(2x^2 + 3x - 4) • (4x + 3)
Done.
Answers
Answer:
Step-by-step explanation:
If you construct a 90% confidence interval for the population proportion and a 95% confidence interval for the population proportion, the 95% confidence will have a wider interval. This is because a higher confidence interval will provide more possible values from which the true value will be determined. Therefore, If you want more confidence that an interval contains the true parameter, then the intervals will be wider.
Answers
Answer: 7 (x+4)
Step-by-step explanation: Since the expression asks for 7 times the sum of a number and 4, you would put x + 4 in parentheses since multiplying 7 comes afterwards.