A polynomial that has these factors could be
.
After solving for w using inverse operations, w would have to equal 5.74 to make this equation true.
Answer: (x3.19+y1.20 + z1.20) x 1.06
Step-by-step explanation:
Hi, to answer this question we have to write an expression.
Four-packs of permanent markers in assorted colors for $3.19 per pack.
3.19 x (x number of packs purchased)
spiral-bound notebooks, whether wide-ruled or college-ruled, sell for $1.20 each
1.20 y + 1.20 z (y wide-ruled notebooks, and z college-ruled notebooks)
The store charges a 6% sales tax on Cleo’s total bill, so we have to multiply the expression by 1+ 0.06 ( 1+ tax percentage in decimal form)
(x3.19+y1.20 + z1.20) x 1.06
9514 1404 393
Answer:
91°
Step-by-step explanation:
The similarity statement tells you that angles Q and H are congruent. The measure of angle H is shown as 91°, so that is the measure of angle Q.
m∠Q = 91°
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
