Answer: the number of students that were surveyed is 40
Step-by-step explanation:
Let x = total number of students that were surveyed about their favorite colors
1/4 of the students preferred red.
This means that the number of students that preferred red is 1/4 × x = x/4
1/8 of the students preferred blue.
This means that the number of students that preferred blue is 1/8 × x = x/8
The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes
x - (x/4 + x/8) = x - 3x/8 = 5x/8
3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8
if 15 students prefer green, then
3x/8 = 15
3x = 120
x = 120/3 = 40 students
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
There are two <em>true</em> statements:
- When the function is composed with r, the <em>composite</em> function is V(t) = (1/48) · π · t⁶.
- V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.
<h3>How to use composition between two function</h3>
Let be <em>f</em> and <em>g</em> two functions, there is a composition of <em>f</em> with respect to <em>g</em> when the domain of <em>f</em> is equal to the range of <em>g</em>. In this question, the <em>domain</em> variable of the function V(r) is replaced by substitution.
If we know that V(r) = (4/3) · π · r³ and r(t) = (1/4) · t², then the composite function is:
V(t) = (4/3) · π · [(1/4) · t²]³
V(t) = (4/3) · π · (1/64) · t⁶
V(t) = (1/48) · π · t⁶
There are two <em>true</em> statements:
- When the function is composed with r, the <em>composite</em> function is V(t) = (1/48) · π · t⁶.
- V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.
To learn on composition between functions: brainly.com/question/12007574
#SPJ1
Collect like terms
(2x-x) + (9+3)
Simplify
x+12
now, a line perpendicular to that one, will have a "negative reciprocal" slope, thus
