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soldi70 [24.7K]
3 years ago
9

|x+6| =8 A) x=-2 and x= -14 B) x= -2 and x= 14 C) x=2 and x= -14 D) x=2 and x= -2

Mathematics
1 answer:
erica [24]3 years ago
5 0

Answer:

C) x=2 and x= -14

Step-by-step explanation:

|x + 6| = 8

means

x + 6 = 8 or x + 6 = -8

x + 6 = 8

x = 2

x + 6 = -8

x = -14

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How many batches of ravioli can I make , from 1 gallon at $1.80 that requires 24 ounces
Olin [163]

Answer:

5

Step-by-step explanation:

You can make 5 batches because theres 128 ounces in one gallon so youd divide 128 by 4 and get 5.333 etc. Then youd round to the nearest whole number.

6 0
3 years ago
Find the solution to the system of equations. <br> x+y+z=23 <br> y+z=14 <br> z=9
Ne4ueva [31]
<span>A) x+y+z=23
B) y+z=14
C) z=9
Since z = 9 then
A) x + y = 14
B) y = 5
A) </span><span><span>x + y+ z=23</span>
A) x + 5  + 9 = 23
A) x = 9
 
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3 0
3 years ago
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
A right cone has radius 5 ft and slant height 9 ft. The radius and slant height are both multiplied by 1/2. Which of the followi
grin007 [14]
The surface area would be subtracted by 1/2
4 0
3 years ago
@mehek14
gayaneshka [121]
X=cost per hamburgurs
y=cost per hot dog

200x+150y=1450
200x+250y=1750

we can multiply first equation by -1 and add to 2nd

-200x-150y=-1450
<u>200x+250y=1750 +</u>
0x+100y=300

100y=300
divide both sides by 100
y=3

sub back

200x+150y=1450
200x+150(3)=1450
200x+450=1450
minus 450 both sides
200x=1000
divide both sides by 200
x=5


the cost of a hamburgur is $5
the cost of a hot dog is $3
8 0
3 years ago
Read 2 more answers
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