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If $p=3x+4$ and $v=x+5$, which of the following is equivalent to $p\nu-2p+\nu$ ?
$3x^{2}+12x+7$
$3x^{2}+14x+17$
$3x^{2}+19x+20$
$3x^{2}+26x+33$
$x^{2}-x-1=0$
What values satisfy the equation above?
$x=1$ and $x=2$
$x=-\frac{1}{2}$ and $x=\frac{3}{2}$
$x=\frac{1+\sqrt{5}}{2}$ and $=\frac{1-\sqrt{5}}{2}$
$x=\frac{-1+\sqrt{5}}{2}$ and $x=\frac{-1-\sqrt{5}}{2}$
$(x+5)+(2x-3)$
Which of the following is equivalent to the given expression?
$3x-2$
$3x+2$
$3x-8$
$3x+8$
Which expression is equivalent to $\frac{8x(x-7)-3(x-7)}{2x-14}$, where $x>7$?
$\frac{x-7}{5}$
$\frac{8x-3}{2}$
$\frac{8x^{2}-3x-14}{2x-14}$
$\frac{8x^{2}-3x-77}{2x-14}$
$x=49$
$y=\sqrt{x}+9$
The graphs of the given equations intersect at the point $(x,y)$ in the $xy$-plane. What is the value of $y$?
16
40
81
130
$h(x)=2(x-4)^{2}-32$
The quadratic function $h$ is defined as shown. In the $xy$-plane, the graph of $y=h(x)$ intersects the $x$-axis at the points $(0,0)$ and $(t,0)$, where $t$ is a constant. What is the value of $t$?
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8
The function $\bm{f}$ is defined by $\bm{f}(\bm{x})=(-8)(2)^{x}+22$. What is the $y$-intercept of the graph of $\bm{y}=\bm{f}(\bm{x})$ in the xy-plane?
$(0,14)$
$(0,2)$
$(0,22)$
$(0,-8)$
$x^{2}-2x-9=0$
One solution to the given equation can be written as $1+\sqrt{k}$, where $k$ is a constant. What is the value of $k$?
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40
$\bm{f}(\bm{x})=9,000(0.66)^{x}$
The given function $f$ models the number of advertisements a company sent to its clients each year, where $\bm{x}$ represents the number of years since 1997, and $0\leq\bm{x}\leq 5$. If $y=\bm{f}(\bm{x})$ is graphed in the $xy$-plane, which of the following is the best interpretation of the $y$-intercept of the graph in this context?
The minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708.
The minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000.
The estimated number of advertisements the company sent to its clients in 1997 was 1,708.
The estimated number of advertisements the company sent to its clients in 1997 was 9,000.
The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?
$w=4(9^{n})$
$w=4(9^{n-1})$
$w=9(4^{n})$
$w=9(4^{n-1})$
$x-y=1$
$x+y=x^{2}-3$
Which ordered pair is a solution to the system of equations above?
$(1+\sqrt{3},\sqrt{3})$
$(\sqrt{3},-\sqrt{3})$
$(1+\sqrt{5},\sqrt{5})$
$(\sqrt{5},-1+\sqrt{5})$
Which of the following is equivalent to the expression $x^{4}-x^{2}-6$?
$(x^{2}+1)(x^{2}-6)$
$(x^{2}+2)(x^{2}-3)$
$(x^{2}+3)(x^{2}-2)$
$(x^{2}+6)(x^{2}-1)$
$(2x+5)^{2}-(x-2)+2(x+3)$
Which of the following is equivalent to the expression above?
$4x^{2}+21x+33$
$4x^{2}+21x+29$
$4x^{2}+x+29$
$4x^{2}+x+33$
| Time (years) | Total amount (dollars) |
|---|---|
| 0 | 604.00 |
| 1 | 606.42 |
| 2 | 608.84 |
Lisa opened a savings account at a bank. The table shows the exponential relationship between the time $t$, in years, since Lisa opened the account and the total amount $n$, in dollars, in the account. If Lisa made no additional deposits or withdrawals, which of the following equations best represents the relationship between $t$ and $n$?
$n=(1+604)^{t}$
$n=(1+0.004)^{t}$
$n=604(1+0.004)^{t}$
$n=0.004(1+604)^{t}$
$(ax+3)(5x^{2}-bx+4)=20x^{3}-9x^{2}-2x+12$
The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $ab$?
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40