If you have zero dollars you can’t buy anything
6x-y=3 this is the equation in standard form
The missing side of the triangles are 5, 16.92, 7 and 5 respectively.
Step-by-step explanation:
- Step 1: Use the Pythagoras Theorem to find the missing sides.
a² + b² = c²
In the first triangle, a = 3, b = 4.
c² = 3² + 4² = 9 + 16 = 25
⇒ c = 5
∴ Missing side is 5
In the second triangle, a = 15, b = 8
c² = 15² + 8² = 225 + 64 = 289
⇒ c = 16.92
Missing side is 16.92
In the third triangle, b = 24, c = 25
a² = c² - b²
a² = 25² - 24² = 625 - 576 = 49
⇒ a = 7
Missing side is 7
In the fourth triangle, a = 12, c = 13
b² = c² - a²
b² = 13² - 12² = 169 - 144 = 25
⇒ b = 5
Missing side is 5
Answer:
- $17,500 at 14%
- $16,000 at 12%
Step-by-step explanation:
Let x represent the amount loaned at 14%. Then the total interest earned is ...
0.14x +0.12(33,500 -x) = 4,370
0.02x = 350 . . . . . . . . . . subtract 4020 and simplify
x = 17500 . . . . . . . . . divide by 0.02
The amount loaned at 12% is $33,500 -17,500 = $16,000.
$17,500 was loaned at 14%
$16,000 was loaned at 12%
Answer:
Positive discriminant = 2 real solution
x= -5,-40
Step-by-step explanation:
The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.
The discriminant is the part of the quadratic formula inside the square root:

Every quadratic formula has the structure:

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

Our a=1, b=45 and c=200
Now we can substitute these values into the discriminant:

Solve:

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

(Same discriminant value)

Now to find the two solutions, we use both signs in the equation. Solution 1:


Our first solution is -5, now for the second:

The two solution to this equation are -5 and -40.
Hope this helped!