Answer:
The value of x is 5 units.
C is correct.
Step-by-step explanation:
We need to solve for x from the given figure.
In ΔADB and ΔCDB
∠ABD=∠BCD (Corresponding angle of two right triangle)
∠ADB=∠CDB (Each 90°)
∴ ΔADB ≈ ΔCDB By AA similarity
If two triangles are similar then ratio of their corresponding height are same.
Substitute the value of side into the expression
Cross multiply and solve for x
x can't be negative because side of triangle is positive.
Hence, The value of x is 5 units.
Answer:
No solutions
Step-by-step explanation:
Solve for x the system of two inequalities:
First, solve each inequality separately:
1.
2.
Now, we get
and
There are no common values for x, for which both inequalities hold, so the system of two inequalities has no solutions.
Answer:
Profit function: P(x) = -0.5x^2 + 40x - 300
profit of $50: x = 10 and x = 70
NOT possible to make a profit of $2,500, because maximum profit is $500
Step-by-step explanation:
(Assuming the correct revenue function is 90x−0.5x^2)
The cost function is given by:
And the revenue function is given by:
The profit function is given by the revenue minus the cost, so we have:
To find the points where the profit is $50, we use P(x) = 50 and then find the values of x:
Using Bhaskara's formula, we have:
So the values of x that give a profit of $50 are x = 10 and x = 70
To find if it's possible to make a profit of $2,500, we need to find the maximum profit, that is, the maximum of the function P(x).
The maximum value of P(x) is in the vertex. The x-coordinate of the vertex is given by:
Using this value of x, we can find the maximum profit:
The maximum profit is $500, so it is NOT possible to make a profit of $2,500.