Answer:
Sample Response: Yes, Billy is correct. The fractions are placed on the correct tick marks. The smaller fraction is located to the left of the larger fraction.
Step-by-step explanation:
<span>Simplifying
49x^2 + -9 = 0
Reorder the terms:
-9 + 49x^2 = 0
Solving
-9 + 49x^2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 49x^2 = 0 + 9
Combine like terms: -9 + 9 = 0
0 + 49x^2 = 0 + 9
49x^2 = 0 + 9
Combine like terms: 0 + 9 = 9
49x^2 = 9
Divide each side by '49'.
x^2 = 0.1836734694
Simplifying
x^2 = 0.1836734694
Take the square root of each side:
x = {-0.428571429, 0.428571429}
hope this helps!!</span>
Answer:
x = 5√2
y = 5√6
z = 5√3
ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
ΔABC, ΔBDC, and ΔADB are all similar triangles to each other.
By definition of similar triangles, the corresponding sides have the same ratios.
CD from ΔBDC corresponds to BD from ΔADB, and BD from ΔBDC corresponds to AD from ΔADB. So:
CD / BD = BD / AD
10 / x = x / 5
x² = 50
x = 5√2
Since ΔBDC is right, we can use the Pythagorean Theorem to solve for y:
CD² + BD² = BC²
10² + (5√2)² = y²
y² = 100 + 50 = 150
y = 5√6
Again, since ΔΔABD is right, we can use the Pythagorean Theorem to solve for z:
AD² + BD² = AB²
5² + (5√2)² = z²
z² = 25 + 50 = 75
z = 5√3
Answer:
Triangle 1: x = 80 degrees, acute
Triangle 2: x = 10 degrees, right
Step-by-step explanation:
Triangle 1:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:
Solve for x:
So, x = 80 degrees
Because all the angles are less than 90 degrees, this is an acute triangle.
Triangle 2:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation (with the right angle given):
Solve for x:
So, x = 10 degrees
Because there is an angle measuring 90 degrees, this is a right triangle.
Profit = revenue - expenses
expenses : 125,000 + 6.50x
revenue : 9x
so to make a profit, ur revenue (income) has to be higher then ur expenses
revenue > expenses
A. ) 9x > 125,000 + 6.50x
9x - 6.50x > 125,000
2.5x > 125,000
x > 125,000 / 2.5
x > 50,000......so they would have to sell at least 50,001 devices to make a profit <==
B.) the cost of making 1 device is 10% more then the company predicted....10% more then 6.50.....6.50(1.10) = 7.15.....this is the new cost of making 1 device <==
9x > 125,000 + 7.15x ....this is the inequality with the 10% more added
9x - 7.15x > 125,000
1.85x > 125,000
x > 125,000 / 1.85
x > 67,567.5......so to make a profit, they would have to sell at least 67,568 devices to make a profit <==
