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Mumz [18]
3 years ago
6

Determine the exact value of k so that the quadratic function f(x) = x2 - kx + 5 has only one zero.

Mathematics
2 answers:
galben [10]3 years ago
6 0
I like this question. When we factorise this question the brackets have to be identical.
5 has to be square rooted to become √5. From, FOIL we know that the last digit is times by the other last digit to find the 5, as our brackets are identical this number is the same. The square root of 5.
This number is doubled in identical brackets to find the middle number. so it is 2√5. As there is a minus number there the brackets are: (x-√5)(x-√5). Multiplying this out gives us: x²-2√5 x+5. k=2√5 (or -2√5, depending on if the minus is counted or not)
JulsSmile [24]3 years ago
3 0
f(x)=ax^2+bx+c\\\\\Delta=b^2-4ac\\\\if\ \Delta < 0-no\ zeros\\if\ \Delta=0-one\ zero\\if\ \Delta > 0-two\ zeros


f(x)=x^2-kx+5=0\\\\a=1;\ b=-k;\ c=5\\\\\Delta=(-k)^2-4\cdot1\cdot5=k^2-20\\\\one\ zero\ if\ \Delta=0\\\\therefore\\k^2-20=0\ \ \ \ |add\ 20\ to\ both\ sides\\\\k^2=20\\\\k=\pm\sqrt{20}\\\\k=\pm\sqrt{4\cdot5}\\\\\boxed{k=-2\sqrt5\ or\ k=2\sqrt5}
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A tree is leaning at a 5° angle from vertical, making an 85° angle with the ground. When the sun is at a 65° angle of elevation,
Vinvika [58]
D = 25 ft is the length of a shadow. L -  the length of a tree.
Two angles are 85° and 65° and the third is 180° - ( 65° + 85° ) =
= 180° - 150° = 30°.
We will use the Sine Law:
25 / sin 30° = L / sin 65°
25 / 0.5 = L / 0.9063
25 * 0.9063 = 0.5 L
22.6577 = 0.5 L
L = 22.6577 : 0.5
L = 45.3 ft.
Answer: the approximate length of the tree is 45.3 ft.


3 0
3 years ago
Drag numbers to the table so it shows a proportional relationship between x and y.
dezoksy [38]

Answer:

7.5         30

45         180

Step-by-step explanation:

The given line has x = 1.25 and y = 5.

y/x = 5/1.25 = 4

x is multiplied by 4 to get y since 1.25 * 4 = 5.

That means the equation is

y = 4x

For a proportional function, every value of x must be multiplied by 4 to get y.

x = 7.5

y = 4x = 4(7.5) = 30

7.5          30

We need to find the values for the last line.

11 * 4 = 44

There is no 44

13.75 * 4 = 55

There is no 55.

17.5 * 4 = 70

There is no 70

30 * 4 = 120

There is no 120.

45 * 4 = 180

There is a 180.

45         180

Answer:

7.5         30

45         180

8 0
2 years ago
a coin is tossed, then a letter in the word accomplishment is chosen at random. find the probability of heads, then a vowel
emmasim [6.3K]

Answer:

\frac{5}{52}

Step-by-step explanation:

Coin toss:

Total\ outcome=\{H,T\}\\\\Favourable\ outcome=\{H\}\\\\P(Head)=\frac{Favourable\ outcome}{Number\ of\ total\ outcome}\\\\P(Head)=\frac{1}{2}

Letter Selection:

Number\ of\ total\ outcomes=26\ \ \ \ \ \ \ as\ total\ letters\ are\ 26\\\\Favourable\ outcomes=5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ as\ there\ are\ 5\ vowels\\\\P(vowel)=\frac{Favourable\ outcomes}{Number\ of\ total\ outcomes}\\\\P(vowel)=\frac{5}{26}

These\ two\ events\ are\ independent.\\\\Hence\ probability\ of\ head\ and\ then\ vowel=\frac{1}{2}\times \frac{5}{26}=\frac{5}{52}

4 0
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hope this helps ^-^
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Jaime needs to buy a new refrigerator for his apartment. He found what he needed for
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