- Both numbers are less than 10. The distance between the two numbers on the number line is 14.

The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x +2 y = 5x + 2

Sveta_85 [38]

Answer:

I think your functions are $y=2^{x}$ , $y=2*5^{x}$ and $y=2+5^{x}$

If yes then then the third function which is $y=2+5^{x}$ .

Step-by-step explanation:

The function $c^{x}$ where c is a constant has

Domain : $c\geq 0$

Range : ( 0 , ∞ )

The above range is irrespective of the value of c.

I have attached the graph of each of the function, you can look at it for visualization.

$y=2^{x}$ ⇒ This function is same as $c^{x}$ so its range is ( 0 , ∞ ).

$y=2*5^{x}$ ⇒ If we double each value of the function $y=5^{x}$ , which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as ( 0 , ∞ ).

$y=2+5^{x}$ ⇒ If we add 2 to each value of the function $y=5^{x}$ , which has range ( 0 , ∞ ), the lower limit will change as 0+2=2 but the upper limit will be same as ∞. Therefore the range will become as ( 2 , ∞ ).

3 0

2 years ago

Read 2 more answers

Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule says that any number raised to zero is 1. For example, $3^{0} = 1$ .


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
1) x = 0
Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$

2) x = 2
Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$

3) x = 4
Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
1) x = 0
Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$

2) x = 2
Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$

3) x = 4
Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$

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Answers:
a = 1
b = $\frac{1}{16}$ 
c = $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

5 0

2 years ago

Alejandro bought $3.50 worth of pencils and erasers at the school store. Pencils cost $0.50 apiece, and erasers cost $0.75 apiec

Natalka [10]

The correct answer is B

6 0

2 years ago

Read 2 more answers

Sam and Bruno were computing how many kilometers they rode in the 3 bike trips they took last month. In order, they rode 45.7, 4

TiliK225 [7]

Answer:

Correct solution:

45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 divided by 0.621 = 200.64

Step-by-step explanation:

they rode 45.7, 40.9, and 38 miles

= (45.7 + 40.9 + 38) miles

= 124.6 miles

Convert 124 .6 miles to kilometers

1 kilometer = 0.621 miles

124.60 miles = 124.60 / 0.621

= 200.64 kilometers

This is the correct solution because he divided 124.60 miles by 0.621

45.7 + 40.9 + 38.0 = 124.6 miles. 124.6 divided by 0.621 = 200.64

4 0

2 years ago

Read 2 more answers

JL has coordinates J(-6, 1) and L(-4,3). Find the coordinates of the midpoint.

ikadub [295]

Answer:

The coordinates of the mid-point of JL are (-5 , 2)

Step-by-step explanation:

If point (x , y) is the mid-point of a segment whose end-points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , then $x=\frac{x_{1}+x_{2}}{2}$ and $y=\frac{y_{1}+y_{2}}{2}$