Answer:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Step-by-step explanation:
At first we translate mathematically each sentence:
(i) <em>Ali, Carrie and Bryan received a sum of money. </em>
- Ali's money.
- Bryan's money.
- Carrie's money.
(ii) <em>Bryan's money was </em>
<em> of Ali's money</em>.
(1)
(iii) <em>The ratio of Ali's money to Carrie's money was 4 : 1</em>.
(2)
(iv) <em>Ali had $ 160 more than Bryan</em>.
(3)
After some algebraic handling, we have the following system of linear equations:
(1b)
(2b)
(3b)
The solution of the system is: 
, 
, 
The sum of money is:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Answer: 16p^8q^4r^8 The yellow one
Step-by-step explanation:
Step 1: Use Multiplication Distributive Property: (xy)^a = x^a y^a. So 4^2p^2(q^3)(r^4)^2
Step 2: Simplify 4^2 to 16. So 16p^2(q^3)^2(r^4)^2
Step 3: Use Power Rule: (x^a)^b=x^ab. So 16p^2q^6(r^4)^2
Step 4: Use Power Rule: (x^a)^b=x^ab. So the answer is 16p^2q^6r^8. The yellow one
Answer:
7 units
Step-by-step explanation:
Answer:
8 1
/2
For this we need to determine what
2
/3 of 12 3/4 is, so we multiply the fractions together.
First, we draw our line.
|------------------------------------------------------------------------------------|
a e
Next, break up this line into segments using the information.
|----------------------|----------------------|--------------------|------------------|
a b c d e
The entire line is 29.
ab + bc + cd + de = ae
ab + bc + cd + de = 29
You also know that
bd = bc + cd
Due to midpoint theorem,
ab = bc
cd = de
Then,
2ab + 2cd = 29
The equations we will use are
bd = bc + cd eq1
2bc + 2cd = 29 eq2
Dividing both sides of the equation in eq2 yields
bc + cd = 14.5
bd = bc + cd
bd = 14.5
