The given equation is:
ax2 + bx + c = 0
We have the resolvent is:
x = (- b +/- root (b2 - 4ac)) / (2a)
The discriminant is:
b2 - 4ac = 0
The solution will be:
x = (- b) / (2a)
Thus, the equation has a real solution.
Answer:
option B
(3,52)(7,108)
slope = (108 - 52) / (7 - 3) = 56/4 = 14
y = mx + b
slope(m) = 14
(3,52)...x = 3 and y = 52
sub and find b, the y int (the original amount of cards)
52 = 3(14) + b
52 = 42 + b
52 - 42 = b
10 = b
so ur equation is y = 14x + 10....with x being the number of years and y being the total cards. <== ur equation is y = 14x + 10
He started with 10 cards....and has been adding 14 cards every year.
so after 10 years...
y = 14(10) + 10
y = 140 + 10
y = 150 <== after 10 years, he will have 150 cards
Let, the length be l and breadth be b.
So, 2(l + b) = 26
Or, l + b = 13
Or, l = 13 - b
So, we may write like this,
Area = l * b
Or, l * b > 30
Or, l (13 - l) > 30
Or, 13l - l^2 > 30
Or, l^2 - 13l + 30 > 0
Or, l^2 - 3l - 10l + 30 > 0
Or, l(l - 3) - 10(l - 3) > 0
Or, (l - 3)(l - 7) > 0
Or, l - 7 > 0
Or, l > 7.
Now, putting the value of l,
We get, l * b > 30
Or, 7 * b > 30
Or, b > 30/7
➡️ Therefore, we get,
Length > 7
Breadth > 30/7
That's it..
The semi-annual net cash flow the company must achieve in order for the purchase to be made is $2500.
<h3>How to calculate the cash flow?</h3>
Number of period = 6 × 2 = 12
Rate = 4% / 2 = 2%
Annual cash flow × PVIFA × (2% × 12) + $7500 × PVIF(2%,12) - $32348 = 0
Annual cash flow × 10.5753 = $32348 - $7500 × 0.7885
Annual cash flow × 10.5753 = $32348 - $5914
Annual cash flow × 10.5753 = $26434
Annual cash flow = 26434/10.5753
Annual cash flow = $2500
Learn more about cash flow on:
brainly.com/question/735261
The statement must be true is AC = DF ⇒ A
Step-by-step explanation:
When two triangles are congruent, then
- Their corresponding sides are equal in lengths
- Their corresponding angles are equal in measures
- Their perimeters and areas are equal
∵ ΔABC ≅ DEF
- Their corresponding sides and angles are equal
∴ AB = DE ⇒ AB is the corresponding side of DE
∴ BC = EF ⇒ BC is the corresponding side of EF
∴ AC = DF ⇒ AC is the corresponding side of DF
∴ ∠A ≅ ∠D ⇒ ∠A is the corresponding angle of ∠D
∴ ∠ABC ≅ ∠DEF ⇒ ∠ABC is the corresponding angle of ∠DEF
∴ ∠C ≅ ∠F ⇒ ∠C is the corresponding angle of ∠F
- Look to the answer to find the correct statement
∴ AC = DF
The statement must be true is AC = DF
Learn more:
You can learn more about the congruent of triangles in brainly.com/question/6108628
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