Identify which is a hypothesis or a conclusion. A polygon is a rectangle. The polygon has four congruent angles

F(x)=x^2-3x+18 how many distinct real number zeros does f have?

vampirchik [111]

Answer:

None of the distinct real number zeros the function have.

Step-by-step explanation:

Considering the function

$f(x)=x^2-3x+18$

The zeroes of a function are those values that touches the x-axis. In order to find those values we must

Set $f(x) = 0$ in order to find those values

$0=x^2-3x+18$

$\mathrm{Switch\:sides}$

$x^2-3x+18=0$

$\mathrm{Solve\:with\:the\:quadratic\:formula}$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-3,\:c=18:\quad x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}$

$x=\frac{-\left(-3\right)+\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}$

$x=\frac{3+\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}$

As

$3+\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:18}=3+\sqrt{63}i$

so

$x=\frac{3+\sqrt{63}i}{2\cdot \:1}$

$x=\frac{3+3\sqrt{7}i}{2}$

$x=\frac{3}{2}+\frac{3\sqrt{7}}{2}i$

Similarly,

$x=\frac{-\left(-3\right)-\sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:18}}{2\cdot \:1}:\quad \frac{3}{2}-i\frac{3\sqrt{7}}{2}$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=\frac{3}{2}+i\frac{3\sqrt{7}}{2},\:x=\frac{3}{2}-i\frac{3\sqrt{7}}{2}$

BUT, NONE OF THEM ARE REAL NUMBER ZEROS.

Therefore, none of the distinct real number zeros the function have.

5 0

4 years ago

Is 27/250 a repeating or termating decimal

777dan777 [17]

27/250=0.108

so this decimal is non-repeating and terminating.

6 0

4 years ago

Should i use dy\dx (normal differentiation) or d²y\dx² (differentiation of the differentiation)?

11111nata11111 [884]

Use both!

You want to minimize P, so differentiate P with respect to x and set the derivative equal to 0 and solve for any critical points.

P = 8/x + 2x

dP/dx = -8/x² + 2 = 0

8/x² = 2

x² = 8/2 = 4

x = ± √4 = ± 2

You can then use the second derivative to determine the concavity of P, and its sign at a given critical point decides whether it is a minimum or a maximum.

We have

d²P/dx² = 16/x³

When x = -2, the second derivative is negative, which means there's a relative maximum here.

When x = 2, the second derivative is positive, which means there's a relative minimum here.

So, P has a relative maximum value of 8/(-2) + 2(-2) = -8 when x = -2.

7 0

3 years ago

Need to know asap!! thanks

PolarNik [594]

Answer:

628 9/16 m

Step-by-step explanation:

distance = (100)(2)(22/7) = 628.57 m or 628 9/16

6 0

3 years ago

A circle has a radius of 7.5 centimeters and a central angle AOB that measures 90°. What is the length of the intercepted arc AB

Kruka [31]

Let a be the arc length...

a/(2πr)=90/360

a/(2πr)=1/4

a=πr/2 and r=7.5 so

a=3.75π cm

a≈11.78 cm (to the nearest one hundredth of a cm)

7 0

3 years ago

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