Answer:
16 feet
Step-by-step explanation:
Area of a Triangle: (Base*Height)/2.
Therefore, Base:(2A)/Height =(2*24)/2=16
Answer:
(a) 0.05 minutes per calorie burned
(b) Slope = 20
Step-by-step explanation:
(a) If 200 calories are burned in 10 minutes...then what about 1 calorie
; 1/200 × 10 = 0.05 minutes
(b) Slope of the graph...;just take any two points on the graph...which are (10;200) and (20;400)
Slope = (400 - 200) ÷ (20 - 10)
;Slope = 200 ÷ 10
;Slope = 20
You need to solve the equation for h.
<span>W= 50+2.3(h-60)
Distribute the 2.3.
W = 50 + 2.3h - 138
W = 2.3h - 88
Add 88 to both sides.
W + 88 = 2.3h
Switch sides.
2.3h = W + 88
Divide both sides by 2.3.
h = (W + 88)/2.3
</span>
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
<u>Ratio = Number of event 1 : Number of event 2</u> (in same unit, if necessary)
<u>10</u>
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
<u>11</u>
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
- <u>1 minute = 60 seconds</u>
- <u>1 week = 7 days</u>
- <u>1 hour = 60 minutes</u>
<u />
<u>12</u>
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
<u>13</u>
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
<u>14</u>
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
