2.06 Quadratic inequalities
Interactive practice questions
The product of two consecutive numbers is smaller than the sum of those two numbers.
If the smaller number is $m$m, which of the following inequalities represents this situation?
$m\left(m+1\right)<2m+1$m(m+1)<2m+1
$m\left(m-1\right)\le2m$m(m−1)≤2m
$m\left(m+1\right)>m+m+1$m(m+1)>m+m+1
$m\left(m+1\right)>m+1$m(m+1)>m+1
Sean is buying a circular coffee table for his living room. To fit, the area of the table can be at most $35$35 square feet.
If the radius of the table is $r$r ft, which of the following equations represents this situation?
An ball is thrown from a height of $50$50 feet with an initial velocity of $103$103 feet per second, and after $t$t seconds its height (in feet) is given by $h=-16t^2+103t+50$h=−16t2+103t+50.
Write an inequality to represent the range of times $t$t for which the ball is more than $30$30 feet above ground level.
Do not solve for $t$t.
A farmer has two square plots of land, one with sides twice as long as the other, which have a combined area of $4805$4805 square yards. She wants to use at least $\frac{2}{5}$25 of this land to grow wheat.
If the side length of the smaller plot of land is $x$x yards, write an inequality to represent the situation.
Do not solve for $x$x.