Find a direct relationship between x and y.
-$$\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }$$
A) $y = x ^ { 2 } + 9 x + 20$
B) $y = x ^ { 2 } + x + 20$
C) $y = x ^ { 2 } - 7 x + 12$
D) $y = x ^ { 2 } + x + 12$

Question

Quizplus · Accepted Answer

To find a direct relationship between $x$ and $y$, we first express $t$ in terms of $x$ from the first equation: $t = x + 4$. Then, we substitute this expression for $t$ into the second equation for $y$:$$y = (x + 4)^2 + (x + 4)$$$$y = x^2 + 8x + 16 + x + 4$$$$y = x^2 + 9x + 20$$Therefore, the correct relationship is $y = x^2 + 9x + 20$.

Find a Direct Relationship Between X and Y x=t−4 and y=t2+t\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }x=t−4 and y=t2+t

Find a Direct Relationship Between X and Y $\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }$