Answer:

Step-by-step explanation:
<u>Composite Function</u>
Given f(x) and g(x) as real functions, the composite function
is defined as:

It can be found by substituting g into f.
We are given the functions:
f(x) = -x + 3
g(x) = -x -1
Find

Removing parentheses:

Simplifying:

Answer:
Part 1) The length of the diagonal of the outside square is 9.9 units
Part 2) The length of the diagonal of the inside square is 7.1 units
Step-by-step explanation:
step 1
Find the length of the outside square
Let
x -----> the length of the outside square
c ----> the length of the inside square
we know that

step 2
Find the length of the inside square
Applying the Pythagoras Theorem

substitute



step 3
Find the length of the diagonal of the outside square
To find the diagonal Apply the Pythagoras Theorem
Let
D -----> the length of the diagonal of the outside square




step 4
Find the length of the diagonal of the inside square
To find the diagonal Apply the Pythagoras Theorem
Let
d -----> the length of the diagonal of the inside square




Answer:
a = 5
Remainder when p(x) is divided by x+2 = 62
Step-by-step explanation:
Given:
P(x) = x⁴-2x³+3x²-ax+3a-7
When x+1 divides the polynomial p(x) the ramainder is 19.
Applying remainder theorem,
x = -1
p(-1) = 19
Substitute the x = -1 into the polynomial expression
p(-1) = (-1)⁴-2(-1)³+3(-1)²-a(-1)+3a-7 = 19
1+2+3+a+3a-7 = 19
6-7+4a = 19
4a-1 = 19
4a = 19+1
4a = 20
a = 20/4
a = 5.
Hence, a = 5
p(x) = x⁴-2x³+3x²-5x+8
If p(x) is divided by x+2,
Then the remainder is p(-2)
p(-2) = (-2)⁴-2(-2)³+3(-2)²-5(-2)+8
p(-2) = 16+16+12+10+8
p(-2) = 62
Hence the remaider when p(x) is divided by x+2 is 62
For problem 1, the number classification problem,
Natural: 1
Whole: 0
Integer: -3
Rational: 6
Irrational: pi
When plotting pi, put it just in front of the number 3
Answer:
28 pizzas
Step-by-step explanation:
one pizza is enough food for four campers
there are 112 campers so divide 112 by 4
to check this 28 multiplied by 4 is what
112 so the answer is correct