Answer:
(
h
∘
f
∘
g
)
(
x
)
is known as a composite function. Here's how composite functions work:
let's say that
x
=
1
. Your function
g
(
x
)
=
1
3
(
x
)
now produces a
y
output of
1
3
, since
g
(
1
)
=
1
3
(
1
)
. Within a composite function, the y-value of one function becomes the x-value of the next, like so:
g
(
1
)
=
1
3
⇒
f
(
1
3
)
=
17
3
⇒
h
(
17
3
)
=
17
Therefore,
(
h
∘
f
∘
g
)
(
1
)
=
17
Based on this, to find the function for
(
h
∘
f
∘
g
)
(
x
)
(combined from right to left, by the way), simply replace
x
in
f
(
x
)
with the function
g
(
x
)
, and replace
x
in
h
(
x
)
with the function of
(
f
∘
g
)
(
x
)
, to get
(
h
∘
f
∘
g
)
(
x
)
.
This, simplified, is equal to
2
x
+
15
, and therefore
(
h
∘
f
∘
g
)
(
1
)
=
2
(
1
)
+
15
=
17
Hope that helps!
D͓̽o͓̽m͓̽a͓̽i͓̽n͓̽: {-6 ≥x͓̽≤ 5}
R͓̽a͓̽n͓̽g͓̽e͓̽: {-1 ≥y͓̽≤ 4}
Answer:
Step-by-step explanation:
arithmetic sequence formula: 
where 
is the first term and 
is the common difference
Given:
⇒ 
⇒ 
Given:
⇒ 
⇒ 
Rearrange the first equation to make the subject:
a = 32 - 9d
Now substitute into the second equation and solve for
(32 - 9d) + 11d = 106
⇒ 32 + 2d = 106
⇒ 2d = 106 - 32 = 74
⇒ d = 74 ÷ 2 = 37
Substitute found value of into the first equation and solve for :
a + (9 x 37) = 32
a + 333 = 32
a = 32 - 333 = -301
Therefore, the equation is:
Answer:
y = 10
x = 64
Step-by-step explanation:
the equations containing y are adjacent angles in a parallelogram, meaning that they are supplementary, so we can create an equation:
5y + 2 + 12y + 8 = 180
solve this to get y = 10
the equation for x would be 2x + 5y + 8 = 180 because these angles are also supplementary
solve this to get x = 64
