Answer: 266
Step-by-step explanation: This is a ratio problem. If there are 14 chocolates with nuts out of every 32 chocolates, you can use this as a ratio and set it up as a proportion.
(1) 14 chocolates w/ nuts / 32 chocolates = n chocolates / 608 chocolates
(2) Solve for n: 8,512 = 32n; n = 266
Answer: Okay, the answer is x^2/68+(y+3)^2/17=1.
Step-by-step explanation: Step. 1 Complete the square for 4y^2+24y: 4(y+3)^2−36.
Step 2. You’ll need to substitute 4(y+3)^2−36 for 4y^2+24y in the equation x^2+4y^2+24y=32: x^2+4(y+3)^2–36=32.
Step 3. So you’ll need to move –36 to the right side of the equation by adding 36 to the both sides: x^2+4(y+3)^2=32+36.
Step 4 You add 32 and 36: x^2+4(y+3)^2=68.
Step 5. You divide each term by 68 to make the right side equal to one: x^2/68+4(y+3)^2/68=68/68.
And step 6. You’ll need to simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation be 1: x^2/68+(y+3)^2/17=1. I hope you download Math-way app to calculate this ellipse in standard form to be extremely helpful, please mark me as brainliest, and have a great weekend! :D
Answer:
k = 16 , (4, 0 )
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
• b² - 4ac = 0 , then 2 real and equal roots
Here
y = x² - 8x + k
with a = 1, b = - 8, c = k , then
b² - 4ac
= (- 8)² - (4 × 1 × k)
= 64 - 4k , and equating to zero
64 - 4k = 0 ( subtract 64 from both sides )
- 4k = - 64 ( divide both sides by - 4 )
k = 16
Then
y = x² - 8x + 16
Equate to zero to find the root
x² - 8x + 16 = 0 ← left side is a perfect square
(x - 4)² = 0
x - 4 = 0 ( add 4 to both sides )
x = 4
The point on the x- axis is (4, 0 )
No, in order for this to be correct, you'd have to move BOTH decimals in the same direction the same amount of places.<span />
That’s an acute triangle since all angles seem less then 90 degrees
