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3 years ago

Which number line represents the solution to 2.5 – 1.2x < 6.5 – 3.2x?

Mathematics

2 answers:

serg [7]3 years ago

4 0

we have

$2.5-1.2x < 6.5-3.2x$

Group terms that contain the same variable, and move the constants to the opposite side of the inequality

$3.2x-1.2x < 6.5-2.5$

Combine like terms

$2x < 4$

$x < 2$

The solution is the interval-------> (-∞,2)

All real number less than $2$

The answer in the attached figure

tensa zangetsu [6.8K]3 years ago

3 0

2.5 – 1.2x < 6.5 – 3.2x

-1.2x + 3.2x < 6.5 - 2.5

3.2x - 1.2x < 4

2x < 4

x < 4/2

x < 2

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Then, the equation will be:

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Applying distributive property:

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Adding similar terms:

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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.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$ .

Thus Kendra dives out of the water surface at 6 feet from the board.

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3 years ago