y=(-2/5)x + 6
Step-by-step explanation:
y-6= (-2/5)x or y=(-2/5)x + 6
11 by 16
Explanation:
Set up two equations
2
x
+
2
y
=
54
x
×
y
=
176
Solving the first equation for x
2
x
+
2
y
−
2
y
=
54
−
2
y
this gives
2
x
=
54
−
2
y
Divide both sides by 2
(
2
x
2
)
=
54
−
2
y
2
This gives.
x
=
27
−
y
putting this value into the second equation gives.
(
27
−
y
)
×
y
=
176
multiplying across the parenthesis gives
27
y
−
y
2
=
176
subtracting 176 from both sides gives
is
27
y
−
y
2
−
176
=
0
multiplying by negative one gives
−
27
y
+
y
2
+
176
=
0
factoring this into y gives
(
y
−
11
)
×
(
y
−
16
)
=
0
Solving for both y's gives
y
=
11
,
y
=
16
Answer:
width = length = 3 inches
height = 7 inches
Step-by-step explanation:
If x is the width and length of the base, and y is the height, then:
y = x + 4
The volume of the box is:
63 = x²y
The surface area of the box is:
93 = x² + 4xy
Substitute the first equation into the third.
93 = x² + 4x (x + 4)
93 = x² + 4x² + 16x
0 = 5x² + 16x − 93
0 = (x − 3) (5x + 31)
x = 3
y = 7
Use the second equation to check your answer.
63 = (3)²(7)
63 = 63
Answer:
x = 10
Step-by-step explanation:
OA = OD ( both radii of the circle )
OD = OB + BD = x + 16
OB is at right angles to OB ( line from centre to midpoint of chord is right )
Using Pythagoras' identity in right triangle ABO
OA² = OB² + AB² , that is
(x + 16)² = x² + 24²
x² + 32x + 256 = x² + 576 ( subtract x² from both sides )
32x + 256 = 576 ( subtract 256 from both sides )
32x = 320 ( divide both sides by 32 )
x = 10
