Answer
x=-2 and y=-3
Step-by-step explanation:
Step: Solvey=5x+7for y:
Step: Substitute5x+7 for y in 3x+y=−9:
3x+y=−9
3x+5x+7=−9
8x+7=−9(Simplify both sides of the equation)
8x+7+−7=−9+−7(Add -7 to both sides)
8x=−16
8x/8=−16/8
(Divide both sides by 8)
x=−2
Step: Substitute−2 for x in y=5x+7:
y=5x+7
y=(5)(−2)+7
y=−3(Simplify both sides of the equation)
Answer:
x = pi/2..only
Step-by-step explanation:
The equation states that...,
tan^2x.sin x = tan^2x
;we simplify the equation by dividing both sides by tan^2x...which then leaves our equation as,
; sin x = 1
; x = sin^-1 (1)
; Hence x = pi/2
9514 1404 393
Answer:
66 m
Step-by-step explanation:
The perimeter is the sum of the measures of <em>all</em> of the sides. There are two side measures that are missing from the diagram.
The missing horizontal measure is ...
17 m - 8 m = 9 m
The missing vertical measure is ...
16m -7 m = 9 m.
If you add these to the sum you already calculated, you will get the correct answer:
48 m + 9 m + 9 m = 66 m . . . perimeter of the figure
_____
If you're paying attention, you see that the sum of the measures of the two shorter horizontal segments is the same as the measure of the longer horizontal segment. Likewise, the sum of the measurements of the two shorter vertical segments is the same as that of the longer vertical segment.
In other words, the perimeter of this (and any) L-shaped figure is the same as the perimeter of a rectangle having the same horizontal and vertical dimensions as the long sides of the figure.
P = 2(17 m +16 m) = 2(33 m) = 66 m
Answer:
The value of x would be 
Step-by-step explanation:
Given,
The dimension of the cardboard = 10 ft by 10 ft,
∵ After removing four equal squares of size x ( in ft ) from the corners,
The dimension of the resultant box would be,
Length = ( 10 - 2x ) ft,
Width = ( 10 - 2x ) ft,
Height = x ft,
The volume of box,
Differentiating with respect to x,
Again differentiating with respect to x,
For maxima or minima,
By quadratic formula,
For x = 5/3, V'' = negative,
While for x = 5, V'' = Positive,
Hence, the value of x would be 5/3 ft for maximising the volume.
