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leva [86]
3 years ago
12

Use the identity x^3+y^3+z^3−3xyz=(x+y+z)(x^2+y^2+z^2−xy−yz−zx) to determine the value of the sum of three integers given:

Mathematics
1 answer:
RoseWind [281]3 years ago
4 0

Inserting all the given information into the identity, we have

684-3(210)=(x+y+z)(110-107)\implies x+y+z=18

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Consider the function: f(x) = 2x^2 - 1.5x - 5 and its graph.
Dominik [7]

Answer:

f(x) = -4x² + 19x - 18

Step-by-step explanation:

f(x) = 2x^2 - 1.5x - 5

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

y=f(x-2) = 2(x-2)^2 - 1.5(x-2) - 5\\y = 2(x^2-4x+4) - 1.5x+3 - 5\\y=2x^2-8x+8-1.5x+3-5\\y=2x^2-9.5x+6

f(x) = 2x² - 9.5x + 6

If it is then translated 3 units in the positive y, we add 3 to the input function to get:

y=f(x)+3=2x^2-9.5x+6+3\\y = 2x^2-9.5x+9

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

y =2( 2x^2-9.5x+9) = 4x^2-19x+18\\y= 4x^2-19x+18

iii) reflected across the x-axis

we multiply the parent function by –1, to get a reflection about the x-axis.

y= -1(4x^2-19x+18)=-4x^2+19x-18\\y=f(x)=-4x^2+19x-18

5 0
3 years ago
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