<h2>Answer-Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:</h2><h2 /><h2>A(x) = \frac{f(b)-f(a)}{b-a}A(x)= </h2><h2>b−a</h2><h2>f(b)−f(a)</h2><h2> </h2><h2> </h2><h2 /><h2>Given the function:</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^xf(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>x</h2><h2> </h2><h2 /><h2>We have to find the average rate of change from x = 1 to x= 2</h2><h2 /><h2>At x = 1</h2><h2 /><h2>then;</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^1 = 5f(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>1</h2><h2> =5</h2><h2 /><h2>At x = 2</h2><h2 /><h2>then;</h2><h2 /><h2>f(x) = 20 \cdot(\frac{1}{4})^2=20 \cdot \frac{1}{16} = 1.25f(x)=20⋅( </h2><h2>4</h2><h2>1</h2><h2> </h2><h2> ) </h2><h2>2</h2><h2> =20⋅ </h2><h2>16</h2><h2>1</h2><h2> </h2><h2> =1.25</h2><h2 /><h2>Substitute these in above formula we have;</h2><h2 /><h2>A(x) = \frac{f(2)-f(1)}{2-1}A(x)= </h2><h2>2−1</h2><h2>f(2)−f(1)</h2><h2> </h2><h2> </h2><h2 /><h2>⇒A(x) = \frac{1.25-5}{1}=-3.75A(x)= </h2><h2>1</h2><h2>1.25−5</h2><h2> </h2><h2> =−3.75</h2><h2 /><h2>therefore, average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75</h2>
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The answer is 1/40.First you have to do 1/4 times 10 which you put over 1 so 1/4 times 10/1,than you flip one of the #'s so 1/4 times 1/10 which equals 1/40
Answer:
Q7. 11.3 inches (3 s.f.)
Q8. 96.2 ft
Q9. 36.4cm
Step-by-step explanation:
Q7. Please see attached picture for full solution.
Q8. Let the length of a side of the square be x ft.
Applying Pythagoras' Theorem,
Thus, the perimeter of the square is
Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.
Since the perimeter of the equilateral triangle is 126cm,
length of each side= 126÷3 = 42 cm
The green line drawn in picture 3 is the altitude of the triangle.
Let the altitude of the triangle be x cm.
sin 60°= 
(to 3 s.f.)
Therefore, the length of the altitude of the triangle is 36.4cm.
For box of 100 gloves, each glove = 44.95/100 =
$0.4495
For box of 50 gloves, each glove = 23.50/50 = $0.47
<span>
Thus the box of 100
gloves is good to buy than the box of 50 gloves.</span>
Answer:
BD = 3 units
Step-by-step explanation:
Since, AD is an angle bisector of ∠BAC,
m∠BAD = m∠CAD = 20°
CD = 3 units
In ΔACD and ΔABD,
m∠BAD = m∠CAD = 20° (Given)
AD ≅ AD [Reflexive property]
Therefore, by H-A property of congruence both the triangles will be congruent.
And by CPCTC,
CD ≅ BD = 3 units
