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Sindrei [870]
3 years ago
9

Which statement best describes why there is no real solution to the quadratic equation y = x2 - 6x + 13?

Mathematics
1 answer:
Ahat [919]3 years ago
6 0
This is the quadratic equation
x = -b +/- (sq root)(b^2 - 4(a)(c) all over 2a
If inside the square root the value is <0. You can't get an answer.
Now figure the rest out
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On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an
ExtremeBDS [4]

Answer:

y\geq x-2

x+2y

Step-by-step explanation:

step 1

<em>Find the equation of the first inequality</em>

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{0+2}{2-0}

m=\frac{2}{2}

m=1

The equation in slope intercept form is equal to

y=mx+b

we have

m=1

b=-2 ---> the y-intercept is given

substitute

y=x-2

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

y\geq x-2

step 2

<em>Find the equation of the second inequality</em>

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{0-2}{4-0}

m=\frac{-2}{4}

m=-\frac{1}{2}

The equation in slope intercept form is equal to

y=mx+b

we have

m=-\frac{1}{2}

b=2 ---> the y-intercept is given

substitute

y=-\frac{1}{2}x+2

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

y

Rewrite

Multiply by 2 both sides

2y

x+2y

therefore

The system of inequalities is

y\geq x-2

x+2y

see the attached figure to better understand the problem

5 0
3 years ago
Read 2 more answers
What is the length of the resulting arrow when you add two arrow in the negative direction?
klio [65]
Bavsgshshhahahahhaa bsbsbsb
7 0
2 years ago
What is the length of segment RS?
Evgesh-ka [11]

Answer:

3

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
Im the diagram shown JKL~ MNP. Find MP and PN.
Vilka [71]

Answer: MP=10, PN=6

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

\\\\frac{MP}{5}=\frac{8}{4}\\\\MP=10\\\\\frac{PN}{3}=\frac{8}{4}\\\\PN=6

7 0
2 years ago
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