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Evgen [1.6K]
3 years ago
15

HELPP I NEED TO TURN THIS IN 5 Mins!!!!!

Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

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Help Me! Please!!!!!!!!!!!!!!!!!!!
natulia [17]
A)
Let c be the number of right guesses.
the probability of c answers =.25 and probability of the wrong answer is 1-.25=.75
c distribution is in the parameter of (20, .25).
b) mean = 20 * .25== 5
c) p of c guess =.25 ^20 =9.095* 10 ^-13
d) p of 10 c guess =.014 or 1.4% it is not possible for him to have 10 right guess.


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2 years ago
1/2 divided by 3/5 equals what
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3 0
3 years ago
The diameter of a circle has endpoints P(-6,-11 ) and Q(4, 7). Write an equation for the circle. Be sure to show and explain all
MrMuchimi

Answer:

(x + 1)^2 + (y + 2)^2 = 106

Step-by-step explanation:

The formula for a circle is

(x - h)^2 + (y - k)^2 = r^2

Where (h, k) is the center of the circle and r is the raadius

--------------------------------------

The center is the midpoint of the diameter end points

(h, k) = ( (-6 + 4)/2 , (-11 + 7)/2 )

(h, k) = (-1, -2)

The radius is the distance from the center to an endpoint

Using (h, k) and Q

r^2 = (4 - -1)^2 + (7 - -2)^2

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r^2 = 106

-------------------------------

Plug into the circle formula

(x + 1)^2 + (y + 2)^2 = 106

7 0
2 years ago
A farmer sells almonds according to the chart below. The more pounds of almonds that are sold, lower cost the cost per pound is
Naddik [55]

Answer:

horizontal line with a open circle at (20,10) and an closed circle at (30,10)

$ 207.50

Step-by-step explanation:

20.75 is between 20  and 30

From the given table , we can see that

for more than 20, up to 30 pounds, the cost per pound is $10

This means, the pounds greater than 20  and less than 30  cost per pound is $10

More than 20 means pounds not equal to 20. its close to 20

So there is a open circle at 20

Cost per pound remains the same from 20  to 30

So horizontal line with a open circle at (20,10) and an closed circle at (30,10)

Total cost of 20.75 pounds of almonds = 20.75 * 10 = 207.50

4 0
3 years ago
Read 2 more answers
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