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asambeis [7]
2 years ago
7

Julia is allowed to watch no more than 5 hours of television a week. so far this week, she has watched 1.5 hours. write and solv

e an inequality to show how many hours of television julia can all watch this week.
Mathematics
1 answer:
gulaghasi [49]2 years ago
5 0
<span>X + 1.5 ≤ 5 X ≤ 3.5 "Julia is allows to watch no more than 5 hours of television" X ≤ 5 "She has watched 1.5 hours" X + 1.5 ≤ 5 So the inequality to solve is: X + 1.5 ≤ 5 Now to solve it, just subtract 1.5 from both sides: X + 1.5 ≤ 5 X + 1.5 - 1.5 ≤ 5 - 1.5 X ≤ 3.5 So Julia can watch up to 3.5 more hours of TV this week.</span>
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andrew-mc [135]

across

1) 10

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4 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
3 years ago
On a coordinate plane, triangle J K L has points (negative 2, 1), (0, 3), and (2, negative 1). Reflect the figure over the line
svetlana [45]

Answer:

J'(2, 1)

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Step-by-step explanation:

On a coordinate plane, coordinates of the points J, K and L are (-2, 1), (0, 3) and (2, -1) respectively.

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Only sign of x coordinates get changed while y coordinates remain the same.

Following this rule coordinates of the images of J' and K' will be

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6 0
2 years ago
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Mumz [18]

Answer:

No

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