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3 years ago

How many x-intercepts does the graph of each quadratic equation have? Show your work.

Mathematics

1 answer:

Alex73 [517]3 years ago

4 0

Answer:

Step-by-step explanation:

In each case we find the discriminant b^2 - 4ac.

If the discriminant is negative, we have two unequal, complex roots.

If the discriminant is zero. we have two equal, real roots.

If the discriminant is positive, we have two unequal real roots.

#51: 8v^2 - 12v + 9: the discriminant is (-12)^2 - 4(8)(9) = -144. we have two unequal, complex roots

#52: (-11)^2 - 4(4)(-14) = 121 + 224 = 345. we have two unequal real roots.

#53: (-5)^2 - 4(7)(6) = 25 - 168 (negative). we have two unequal, complex roots.

#54: (4)^2 - 16 = 0. We have two equal, real roots.

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The equation y = 3.5x represents the rate, in miles

avanturin [10]

Answer:

Piyush walks faster than Laura

Step-by-step explanation:

we know that

The rate or speed is equal to the slope of the linear equation

<em>Laura</em>

y=3.5x

The slope is $3.5\ \frac{mi}{h}$

<em>Piyush</em>

Determine the slope of the line

we have the points

(0,0) and (4,18)

The line represent a direct variation (because passes through the origin)

$m=\frac{y}{x}$

For x=4 h, y=18 mi

substitute

$m=\frac{18}{4}=4.5\ \frac{mi}{h}$

Compare the slopes

$4.5\ \frac{mi}{h} > 3.5\ \frac{mi}{h}$

therefore

Piyush walks faster than Laura

5 0

3 years ago

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How can I solve this polynomial (x^4+4x^3-x-4)/(x^3-1)

Lerok [7]

Distributive property?

4 0

3 years ago

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the

Norma-Jean [14]

The graphs of f(x) and g(x) are transformed function from the function y = x^2

The set of inequalities do not have a solution

<h3>How to modify the graphs</h3>

From the graph, we have:

$f(x) = x^2 -3$ and $g(x) = -x^2 +2$

To derive y < x^2 - 3, we simply change the equality sign in the function f(x) to less than.

To derive y > x^2 + 2, we perform the following transformation on the function g(x)

Shift the function g(x) down by 2 units
Reflect across the x-axis
Shift the function g(x) down by 3 units
Change the equality sign in the function g(x) to greater than

<h3>How to identify the solution set</h3>

The inequalities of the graphs become

y < x^2 - 3 and y > x^2 + 2

From the graph of the above inequalities (see attachment), we can see that the curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution