The exponential function which represented by the values in the table is 
⇒ 3rd answer
Step-by-step explanation:
The form of the exponential function is 
, where
- a is the initial value (when x = 0)
- b is the growth/decay factor
- If k > 1, then it is a growth factor
- If 0 < k < 1, then it is a decay factor
The table:
→ x : f(x)
→ -2 : 16
→ -1 : 8
→ 0 : 4
→ 1 : 2
→ 2 : 1
∵
- To find the exponential function substitute the value of x and f(x)
by some values from the table to find a and b, at first use the
point (0 , 4) to find the value of a
∵ x = 0 and f(x) = 4
∴ 
- Remember that any number to the power of zero equal 1
except the zero
∵ 
∴ 4 = a(1)
∴ a = 4
Substitute the value of a in the equation
∴ 
- Chose any other point fro the table to find b, lets take (1 , 2)
∵ x = 1 and f(x) = 2
∴ 
∴ 2 = 4 b
- Divide both sides by 4
∴ 
- Substitute the value of b in the equation
∴
The exponential function which represented by the values in the table is
Learn more:
You can learn more about the logarithmic functions in brainly.com/question/11921476
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Answer:
A
Step-by-step explanation: i am in math 8
lol
Answer:
the answer would be 6:30 pm
Step-by-step explanation:
if you left work at 5:15 and it took 1 1/4 min to get home
you would
find 1/4 witch would be 15 min because 60/4= 15
then add 1:15 to 5:15
1:15 + 5:15 = 6:30 pm
you arrived home at 6:30 pm
Simplify:
5(a + 5) + -3 = 3(2 + -1a)
Reorder the terms:
5(5 + a) + -3 = 3(2 + -1a)
(5 * 5 + a * 5) + -3 = 3(2 + -1a)
(25 + 5a) + -3 = 3(2 + -1a)
Reorder the terms again:
25 + -3 + 5a = 3(2 + -1a)
Combine like terms:
]25 + -3 = 22
22 + 5a = 3(2 + -1a)
22 + 5a = (2 * 3 + -1a * 3)
22 + 5a = (6 + -3a)
Solve:
22 + 5a = 6 + -3a
To solve for variable 'a':
You have to move all terms containing A to the left, all other terms to the right.
Then add '3a' to each side of the equation:
22 + 5a + 3a = 6 + -3a + 3a
Combine like terms:
5a + 3a = 8a
22 + 8a = 6 + -3a + 3a
Combine like terms again:
-3a + 3a = 0
22 + 8a = 6 + 0
22 + 8a = 6
Add '-22' to each side of the equation.:
22 + -22 + 8a = 6 + -22
Combine like terms:
22 + -22 = 0
0 + 8a = 6 + -22
8a = 6 + -22
Combine like terms once more:
6 + -22 = -16
8a = -16
Divide each side by '8'.
a = -2
Simplify:
a = -2
Answer: a=-2
Hope I could help! :)
Diagram of two triangles
The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).
The diagram on the left is missing its hypotenuse - the variable <em>c</em><em>.</em><em> </em>The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.
Note: The hypotenuse is the <em>longest</em><em> </em>side of a right triangle.
Word Problen
The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.
Standard form of Pythagorean theorem.
Equation with the legs substituted and the missing hypotenuse value - <em> </em><em>c</em><em>.</em>
Square the legs and add.
Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.
Thus the diagonal distance is 29 blocks.
Check by substituting.
