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ioda
3 years ago
7

FILL IN THE BLANKS 1) 257x_____=(-257) 2)(-30)x_____=(-270) 3)_____x(-21)=_____ 4)918x_____=0 5)(-56)x[(-9)+(-1)]=_____

Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

Answer:

(a)\ 257 * [-1] =-257

(b)\ (-30) * [9] =-270

(c) The additive inverse of -21 is 21

(d)\ 918 *[0]=0

(e)\ (-56) * [(-9)+(-1)] = 560

Step-by-step explanation:

Required

Fill in the blanks

<em>Represent all blanks with x</em>

(a)\ 257 * x =-257

Divide both sides by 257

x =\frac{-257}{257}

x = -1

So:

(a)\ 257 * [-1] =-257

(b)\ (-30) * x =-270

Divide both sides by -30

x =\frac{-270}{-30}

x = 9

So:

(b)\ (-30) * [9] =-270

(c)The complete question here is to determine the additive inverse of (-21)

The additive inverse of a number x is -x

So:

(-21) \to -(-21)

(-21) \to 21

(d)\ 918 *x=0

Divide both sides by 918

x=\frac{0}{918}

x = 0

So:

(d)\ 918 *[0]=0

(e)\ (-56) * [(-9)+(-1)] = x

Solve the inner brackets

(-56) * [-9-1] = x

(-56) * [-10] = x

Multiply

560 = x

So:

(e)\ (-56) * [(-9)+(-1)] = 560

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For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)


By knowing this things, we can solve our problem as follows:


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g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2


  • Then translating<em> 5 units down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5


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SECOND.

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g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2


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g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1


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<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

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