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57 problems match “linear equations”. Clear

Three numbers from pairwise sums ●○○○○ 10 ptsLet the three numbers be $x$ , $y$ and $z$ with $x+y=10$ , $y+z=19$ and $x+z=21$ . Find $x$ , $y$ and $z$ .
Point on the quadrant bisector ●○○○○ 10 ptsPoint $P(a+3,\ 7+a)$ lies on the bisector of the second and fourth quadrants. Find $a$ .
Continuity constant for a piecewise function ●○○○○ 10 ptsLet $f(x)=\begin{cases} kx^{2} & \text{if } x\le 2 \\ x+k & \text{if } x>2\end{cases}$ . Find the value of the constant $k$ that makes $f$ continuous. Round to two decimal places.
Dimensions of a rectangular patio ●○○○○ 10 ptsThe perimeter of a rectangular outdoor patio is $60$ ft. The length is $4$ ft greater than the width. Find the width and the length of the patio, in feet.
Coordinates of a vector in R^4 ●○○○○ 10 ptsLet $a_1 = [1, 1, 0, 0]$ , $a_2 = [0, 1, 1, 0]$ and $a_3 = [0, 0, 1, 1]$ . Find the coefficients $\alpha_1, \alpha_2, \alpha_3$ such that $v = [1, 3, 5, 3] = \alpha_1 a_1 + \alpha_2 a_2 + \alpha_3 a_3$ , that is, find the coordinate representation $[\alpha_1, \alpha_2, \alpha_3]$ of $v$ .
Length of a rectangular driveway ●○○○○ 10 ptsA rectangular concrete driveway has a perimeter of 108 ft and a width of 12 ft. Find its length in feet.
Average speed from milestones ●●○○○ 20 ptsA car travels at a uniform speed. The driver sees a milestone showing a two-digit number $XY$ . One hour later the driver sees a milestone showing the same digits in reverse order, $YX$ . One hour after that the driver sees a milestone showing a three-digit number $X0Y$ , with a 0 between the same two digits. What is the speed of the car, in km/h?
Return speed on a round trip ●●○○○ 20 ptsA car travels the 120 miles from $A$ to $B$ at 60 miles per hour, and then returns to $A$ on the same road. If the average rate of the round trip is 45 miles per hour, what is the rate, in miles per hour, of the car traveling back from $B$ to $A$ ?
Largest of four integers from triple averages ●●○○○ 20 ptsDewa writes down a list of four integers. He calculates the average of each group of three of the four integers. These averages are $32, 39, 40, 44$ . What is the largest of the four integers?
Fixed point of a functional definition ●●○○○ 20 ptsLet $h(4x-1) = 2x + 7$ for all real $x$ . For what value of $x$ is $h(x) = x$ ?