-10 + a = 6a - 7a

Rearrange the left hand side

a - 10 = 6a - 7a

Simplify 6a - 7a

a - 10 = -a

Add a on both sides

2a - 10 = 0

Add 10 on both sides

2a = 10

Divide by 2 on both sides

a = 5

4 0

3 years ago

Work out the value of z, given that x+y=42 and x/13=y/8=z/9.

Andru [333]

Answer:

z = 18

x = 26 and y = 16

Step-by-step explanation:

Given:

$x + y = 42$

$\dfrac{x}{13}=\dfrac{y}{8}=\dfrac{z}{9}$

Rewrite $x + y = 42$ to make $y$ the subject:

$\implies y=42-x$

Substitute this into $\dfrac{x}{13}=\dfrac{y}{8}$ :

$\implies \dfrac{x}{13}=\dfrac{42-x}{8}$

Cross multiply:

$\implies 8x=13(42-x)$

$\implies 8x=546-13x$

$\implies 21x=546$

$\implies x=26$

Substitute found value of x into $x + y = 42$ and solve for y:

$\implies 26 + y = 42$

$\implies y=16$

Substitute found value of y into $\dfrac{y}{8}=\dfrac{z}{9}$ and solve for z:

$\implies \dfrac{16}{8}=\dfrac{z}{9}\\\\\implies 2=\dfrac{z}{9}\\\\\implies 18=z$

4 0

3 years ago

A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather f

Alchen [17]

Answer:

The grower should spend the $5,000, thereby reducing the profit to $95,000.

But, this is based on a 20% probability of freezing temperature during the next week.

Step-by-step explanation:

A) If freezing weather happens with a 20% chance, the profit will be reduced to $60,000.

With this probability, the probable loss will be 20% X $40,000 = $8,000.

B) If the grower can protect the fruit against freezing weather at a cost of $5,000, then she should go ahead. Doing this, the profit will be reduced to $95,000 because of the cost.

However, it is worthy to note that freezing weather happens at 20% chance. This implies that the freezing weather might not happen, 80% chance. But, prudence still demands that necessary precautions are taken, and this includes protecting the crop at a cost of $5,000.

4 0

4 years ago