Write (9,-4) and (1,6) in slope intercept form,

12x+7<−11 OR 5x−8>40<br> solve for x

kipiarov [429]

Answer:

x < -1.5 U x > 9.6

Step-by-step explanation:

12x + 7 < -11

x < -1.5

5x - 8 > 40

5x > 48

x > 9.6

6 0

2 years ago

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What is the value of x in the equation 3X minus 4Y equals 65, when Y equals four

Vika [28.1K]

Answer:

Step-by-step explanation:

3x-4y=65

3x=65+4y

x=(65+4y)/3, when y=4

x=(65+4*4)/3

x=(65+16)/3

x=81/3

x=27

8 0

2 years ago

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Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.