A sunflower is 15 inches tall and grows 2 inches a week. How many weeks will it take for the

A quadratic function is defined by

ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

5 0

3 years ago

Find the total number of diagonals in a regular nonagon.

anastassius [24]

Answer:

7

Step-by-step explanation:

number of diagonals in a regular polygon = number of sides - 2.

A nonagon is a polygon having 9 sides.

Total number of diagonals in a regular nonagon

= 9 - 2

= 7

3 0

2 years ago

Write an inequality for the given graph.

Gekata [30.6K]

Answer:

$y$

Step-by-step explanation:

Find the equation of the dashed line

The line pass through the points

$A(0,-3)$ -----> is the y-intercept of the line

$B(6,0)$

Find the slope of the line m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0+3}{6-0}=0.5$

Remember that

The equation of the line into slope intercept form is equal to

$y=mx+b$

we have

$m=0.5$

$b=-3$

substitute

$y=0.5x-3$

Find the inequality

we know that

The solution of the inequality is the shaded area below the dashed line

so

$y$

4 0

2 years ago

30 POINTS The question is the picture above Help PLEASE Giving 30 points

Papessa [141]

.73 x .05= .0365

.733333333 x .0000000555555555= .036555555555

i think this is correct hope this helps

5 0

2 years ago

Read 2 more answers

Shishir bought 4000 orange at 70 paisa each. But 400 of them were rotten. He sold 2000 oranges at 90 paisa each.If he plans to m

Ipatiy [6.2K]

Answer:

He needs to sell the rest of the oranges at 75 paisa each.

Step-by-step explanation:

Consider the given information that, Shishir bought 4000 orange at 70 paisa each.

Note: 1 rupees = 100 paisa

Thus, 70 paisa = 70/100 rupees = 0.70 rupees

Therefore, the cost price of 4000 oranges is:

4000×0.70 rupees = 2800 rupees

The selling price of 2000 oranges is:

2000×0.90 rupees = 1800 rupees

The number of oranges now Shishir have:

4000 - 2000 - 400 = 1600

He wants to make a profit of RS 200. Thus the selling price of 4000 oranges should be:

2800 rupees + 200 rupees = 3000 rupees

He earned 1800 rupees by selling 2000 oranges at 90 paisa. So, the remaining amount that he needs to make with 1600 oranges is:

3000 rupees - 1800 rupees = 1200 rupees

Therefore, the cost of one orange is:

1600 oranges = 1200 rupees

1 orange = 1200/1600 rupees

1 orange = 0.75 rupees

Hence, he needs to sell the rest of the oranges at 75 paisa each.

4 0

3 years ago