If f ( x ) f(x) is an exponential function where f ( − 3.5 ) = 25 f(−3.5)=25 and f ( 6 ) = 33 f(6)=33, then find the value of f ( 6.5 ) f(6.5), to the nearest hundredth.
Answers
Given:
f(x) is an exponential function.
To find:
The value of f(6.5).
Solution:
Let the exponential function is
...(i)
Where, a is the initial value and b is the growth factor.
We have, . So, put x=-3.5 and f(x)=25 in (i).
...(ii)
We have, . So, put x=6 and f(x)=33 in (i).
...(iii)
On dividing (iii) by (ii), we get
Putting b=1.03 in (iii), we get
Putting a=27.63 and b=1.03 in (i), we get
Therefore, the required exponential function is .
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One day a store sold 30 sweatshirts. White ones cost $11.95 and yellow ones cost$11.50. In all, $349.95 worth of sweatshirts were sold. How many of each color were sold?
An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. If the diameter of the cone is 2 inches and the height is 6 inches, what is the volume of vanilla ice cream in the cone? (round to nearest tenth)
Answers
twice of 12=24 so the heighs are 12 and 24
V=LWH
V1=5*5*12=300
V2=5*5*24=600
total volume=300+600=900 in^3
Please help fast thankyou
Answers
Answer:
x = 2
Step-by-step explanation:
5x + 3= x + 11
5x - x = 11 - 3
4x = 8
x = 2
b 3(6 +3x)
c 6 ( 3 + x)
d (3 + 2x)
Answers
Answer:
c:) 6(3 + 2x)
Step-by-step explanation:
The given expression is 18 + 12x. To simplify this expression, we can first look for any common factors that can be factored out. In this case, we can factor out 6, which gives:
18 + 12x = 6(3 + 2x)
So, the simplified expression 18 + 12x is 6(3 + 2x).
B) The lines remain parallel only if rotated 360°.
C) Rotated parallel lines always remain parallel lines.
D) Rotating parallel lines result in perpendicular lines.
Answers
Answer:
C) Rotated parallel lines always remain parallel lines.
Step-by-step explanation:Rotated parallel lines remain parallel lines.
Rotation is a rigid transformation, so the lines remain parallel.
Answer:
c
Step-by-step explanation:
rotated parallel lines remain parallel lines
-5, 0, 3
0, -1 ± √24
0, -1 ± √6
0, 1 ± √6
Answers
First, take common factor:
x(x^2 - 2x - 5 )= 0
Now use the quadratic formula to find the roots of the trinomial
x = [- b +/- √(b^2 - 4(a)(c)] / 2a
x = [2 +/-2√6 ]/2
x = 1 + √6 and x = 1 -√6
Then the solutions are:
x =0; x = 1 + √6; x = 1 - √6
That is the las option shown.
Answers
Answer:
Convert these mixed numbers into improper fractions.
-45/8 + 7/2
Find the common denominator which is 8 in this case.
-45/8 + 7(4) / 2(4)
-45/8 + 28/8
Which equals -17/8
or -2 1/8