A :-) 1.) Given - base = 9 cm
height ( alt ) = 12 cm
hypotenuse ( hypo ) = x
Solution -
By Pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 9 )^2 + ( 12 ) ^2
( x )^2 = 81 + 144
( x )^2 = 225
( x ) = _/225
( x ) = 15 cm
.:. The value of x ( hypotenuse ) = 15 cm
2.) Given - base = 10 cm
Height = 24 cm
Hypotenuse = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 10 )^2 + ( 24 )^2
( x )^2 = 100 + 576
( x )^2 = 676
( x ) = _/676
( x ) = 26
.:. The value of x ( hypotenuse ) = 26 cm
3.) Given - base = 3 cm
Height = 7 cm
Hypotenuse = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 3 )^2 + ( 7 )^2
( x )^2 = 9 + 49
( x )^2 = 58
( x ) = _/58
( x ) = 7.6
.:. The value of x ( hypotenuse ) = 7.6 cm
4.) Given - base = 10 cm
Height = 6 cm
Hypotenuse = x
Solution -
By pythagorus theorem
( Hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 10 )^2 + ( 6 )^2
( x )^2 = 100 + 36
( x )^2 = 136
( x ) = _/136
( x ) = 11.6
.:. The value of x ( hypotenuse ) = 11.6 cm
5.) Given - hypotenuse = 24 cm
height = 6 cm
Base = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( 24 )^2 = ( x )^2 + ( 6 )^2
( x )^2 = ( 6 )^2 - ( 24 )^2
( x )^2 = 36 - 576
( x )^2 = -540
( x ) = _/-540
( x ) = 23.2
.:. The value of x ( base ) = 23.2 cm
6.) Given - base = 1 cm
height = 1 cm
hypotenuse = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 1 )^2 + ( 1 )^2
( x )^2 = 1 + 1
( x )^2 = 2
( x ) = _/2
( x ) = 1.4
.:. The value of x ( hypotenuse ) = 1.4 cm
7.) Given - hypotenuse = 21 cm
height = 8 cm
Base = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( 21 )^2 = ( x )^2 + ( 8 )^2
441 = ( x )^2 + 64
( x )^2 = 64 - 441
( x )^2 = -377
( x ) = _/-377
( x ) = 19.4
.:. The value of x ( base ) = 19.4
8.) given - height = 24 cm
Hypotenuse = 30cm
Base = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( 30 )^2 = ( x )^2 + ( 24 )^2
900 = ( x )^2 + 576
( x )^2 = 576 - 900
( x )^2 = -324
( x ) = _/-324
( x ) = 18
.:. The value of x ( base ) = 18 cm
9.) ( i ) lets find ‘x’
Given - base = 9 cm
height = 5 cm
hypotenuse = x
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( x )^2 = ( 9 )^2 + ( 5 )^2
( x )^2 = 81 +25
( x )^2 = 106
( x ) = _/106
( x ) = 10.2
.:. The value of x ( hypotenuse )
= 10.2 cm
( ii ) lets find ‘y’
Given - base = 3 cm
height = 5 cm
Hypotenuse = y
Solution -
By pythagorus theorem
( hypo )^2 = ( base )^2 + ( alt )^2
( y )^2 = ( 3 )^2 + ( 5 )^2
( y )^2 = 9 + 25
( y )^2 = 34
( y ) = _/34
( y ) = 5.8
.:. The value of y ( hypotenuse )
= 5.8 cm
If there are n rows
And if each row has m seats.
Then the total number of seats shall be n × m.
Here
Number of rows = (c+8)
And number of seats in each row = (4c-1)
Using the concept
Total number of seats
= (c+8)(4c-1)
FOILing or Distributing we get
= c(4c) + c (-1) + 8(4c) +8 (-1)
= 4c² - c + 32 c -8
Combining like terms
=4c² +31c - 8
The expression for total number of seats = 4c² + 31c -8
Answer:
The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y=0 . Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don't want to consider for some reason.
Step-by-step explanation:
hope this helps
Answer:
D. y= x^2 - 5x + 2
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
5
2
,
−
33
4
)
Focus:
(
5
2
,
−
8
)
Axis of Symmetry:
x
=
5
2
Directrix:
y
=
−
17
2
x
y
0
−
2
1
−
6
5
2
−
33
4
3
−
8
4
−
6
_______________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
5
4
,
−
9
8
)
Focus:
(
5
4
,
−
1
)
Axis of Symmetry:
x
=
5
4
Directrix:
y
=
−
5
4
x
y
−
1
9
0
2
5
4
−
9
8
2
0
3
5
_____________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
1
,
0
)
Focus:
(
1
,
1
8
)
Axis of Symmetry:
x
=
1
Directrix:
y
=
−
1
8
x
y
−
1
8
0
2
1
0
2
2
3
8
____________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
5
2
,
−
17
4
)
Focus:
(
5
2
,
−
4
)
Axis of Symmetry:
x
=
5
2
Directrix:
y
=
−
9
2
x
y
0
2
1
−
2
5
2
−
17
4
3
−
4
4
−
2
