The point (1,−1) satisfies the inequality 40x−22y≤50.

I need help please quick!!!!

11111nata11111 [884]

Answer:

C

Step-by-step explanation:

6 0

3 years ago

How to find the x-intercepts of a parabola from the vertex, (-1,-108) and the y intercept (0,-105)?

Ulleksa [173]

Answer:

* The x-intercepts are -7 and 5

Step-by-step explanation:

* At first lets revise the standard and general forms of the

quadratic function which represented graphically by the parabola

- f(x) = a(x - h)² + k ⇒ standard form

- Where point (h , k) is the vertex of the parabola

- f(x) = ax² + bx + c ⇒ general form

- Where a, b, c are constant

- c is the y-intercept ⇒ means x = 0

- h = -b/2a

- k = f(h)

* Lets solve the problem

- We will find the equation of the parabola

∵ The vertex is (-1 , -108)

∴ h = -1 and k = -108

∵ y-intercept = -105

- Equate the two forms

∵ ax² + bx + c = a(x - h)² + k ⇒ solve the ( )²

∴ ax² + bx + c = a(x² - 2hx + h²) + k ⇒ open the bracket

∴ ax² + bx + c = ax² - 2ahx + ah² + k ⇒ by comparing the two sides

∴ c = ah² + k

- Substitute the value of c , h , k in it

∴ -105 = a(-1)² + -108

∴ -105 = a - 108 ⇒ add 108 to the both sides

∴ 3 = a

- Lets write the equation in the standard form

∴ y = 3(x - -1)² + -108

∴ y = 3(x + 1)² - 108

* To find the x-intercepts means the parabola intersects the x-axis,

then put y = 0

∴ 3(x + 1)² - 108 = 0 ⇒ Add 108 to the both sides

∴ 3(x + 1)² = 108 ⇒ divide the both sides by 3

∴ (x + 1)² = 36 ⇒ take square root for both sides

∴ (x + 1) = ± 6

# x + 1 = 6 OR x + 1 = -6

∵ x + 1 = 6 ⇒ subtract 1 from both sides

∴ x = 5

∵ x + 1 = -6 ⇒ subtract 1 from both sides

∴ x = -7

* The x-intercepts are -7 and 5

∴

3 0

2 years ago

Fission tracks are trails found in uranium-bearing minerals, left by fragments released during fission events. An article report

Harlamova29_29 [7]

Answer:

Mean track length for this rock specimen is between 10.463 and 13.537

Step-by-step explanation:

99% confidence interval for the mean track length for rock specimen can be calculated using the formula:

M± $\frac{t*s}{\sqrt{N}}$ where

M is the average track length (12 μm) in the report
t is the two tailed t-score in 99% confidence interval (2.977)
s is the standard deviation of track lengths in the report (2 μm)
N is the total number of tracks (15)

putting these numbers in the formula, we get confidence interval in 99% confidence as:

12± $\frac{2.977*2}{\sqrt{15}}$ =12±1.537

Therefore, mean track length for this rock specimen is between 10.463 and 13.537

4 0

2 years ago

If the tip of the arrow moves to (0,2), what is the center of rotation?

LiRa [457]

The answer is A. (2,2)....

8 0

3 years ago

This is review, please help it’s due tomorrow!

Svet_ta [14]

I dont see anything

3 0

2 years ago