Answer:
Step-by-step explanation:
<em>(17).</em> g(x) = x³ + 4x
f(x) = 4x + 1
( f × g )( x ) = ( x³ + 4x )( 4x + 1 ) = <em>4 </em>
<em> + x³ + 16x² + 4x</em>
<em>(19).</em> f(t) = 4t - 4
g(t) = t - 2
( 4f + 3g )( t ) = 4(4t - 4) + 3(t - 2) = 16t - 16 + 3t - 6 = <em>19t - 22</em>
<em>(21).</em> h(t) = t + 3
g(t) = 4t + 1
h(t - 2) + g(t - 2) = ( t - 2 ) + 3 + 4( t - 2 ) + 1 = t + 4t - 2 + 3 - 8 + 1 = <em>5t - 6</em>
By Pythagoras AB^2 = 12^2 - 6^2 = 108
AB = sqrt 108 = 10.39 to nearest hundredth
The perpendicular from M to DC will be parallel and equal to AB so it = 10.39.
Also AB^2 = CB * DB
108 = 6 * DB
DB = 108/6 = 18
so DC = 18-6 = 12
MD^2 = (1/2*12)^2 + 108 = 144
so MD = 12
Answer:
- h(x) = -2x^2 -x +3
- Reservoir A releases the same amount of water as Reservoir B over 1 week
Step-by-step explanation:
<u>Given</u>:
f(x) = x^2 -7x +5
g(x) = 3x^2 -6x +2
h(x) = f(x) -g(x)
<u>Find</u>:
h(x)
h(1)
<u>Solution</u>:
The expression for h(x) is found by evaluating its definition:
h(x) = (x^2 -7x +5) -(3x^2 -6x +2)
h(x) = x^2(1 -3) +x(-7 -(-6)) +(5 -2)
h(x) = -2x^2 -x +3
Then h(1) is found by substituting 1 for x:
h(1) = -2(1^2) -(1) +3 = -2 -1 +3
h(1) = 0 . . . . difference in release amounts after 1 week is 0
The true statements are ...
- h(x) = -2x^2 -x +3
- Reservoir A releases the same amount of water as Reservoir B over 1 week
Answer:
He would 36 miles all together.
Step-by-step explanation:
Consider the diagram showing the path Joel biked. Joel biked 9 miles east and then 12 miles north. If he biked back to his starting point using the most direct route, he would have ride 36 miles all together. Joel’s starting point is x.
In order to solve this, we must use the Pythagorean theorem.
The amount of miles would be found by adding the 3 sides together to find the sum or answer.
15 + 9 + 12 = 36 miles
Answer:
- π/3 radians, 3600 English minutes
- π/6 radians, 333,333 1/3 French seconds
Step-by-step explanation:
An English minute is (1/60)(π/180) radian = π/10800 radian.
A French second is (1/100)(1/100)(π/200) radian = π/2000000 radian.
So, the ratio of angle sizes in common units will be ...
27(π/10800) : 2500(π/2000000) = (2/800) : (1/800) = 2 : 1
Since the total of these ratio units is 2+1 = 3, we need to divide the right angle into 3 parts. The English part will be 2 of those; the French part will be 1 of them. A 1/3 part of a right angle is π/6 radians, so the right angle division will be ...
English : French = π/3 radians : π/6 radians
= 3600 English minutes : 333,333 1/3 French seconds
= 27 : 2500
