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3 years ago

Is it possible for an exponential equation to have no solutions? If so, give an example. If not, explain why.

1 answer:

4 0

A function f(x) has solutions if we can find a value to plug in that leads to 0. In other words, there are solutions to f(x) = 0. Another term for "solution" is "root" or "x intercept"

An exponential function may cross the x axis at one point only. Though there are plenty of cases when there are no solutions at all. For instance, in the case of f(x) = (2^x) + 10

The right hand side will never be equal to zero no matter what you plug in for x. The graph will never cross the axis.

To answer your question, yes it is possible to have an exponential equation to have no solutions.

You might be interested in

h(x)= \dfrac{1}{8} x^3 - x^2h(x)= 8 1 x 3 −x 2 h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided b

Nesterboy [21]

Answer:

$\dfrac{1}{2}$

Step-by-step explanation:

Given the function $h(x)=\dfrac{1}{8}x^3-x^2$

The average rate of change of the function h(x) over the interval $a\le x\le b$ can be calculated using formula

$\dfrac{h(b)-h(a)}{b-a}$

In your case,

$a=-2,\\ \\b=2,$

so the average rate of change is

$\dfrac{h(2)-h(-2)}{2-(-2)}\\ \\=\dfrac{(\frac{1}{8}\cdot 2^3-2^2)-(\frac{1}{8}\cdot (-2)^3-(-2)^2)}{4}\\ \\=\dfrac{(1-4)-(-1-4)}{4}\\ \\=\dfrac{-3+5}{4}\\ \\=\dfrac{2}{4}\\ \\=\dfrac{1}{2}$

6 0

3 years ago

Which pair shows equivalent expressions?

Dmitry_Shevchenko [17]

Which pair shows equivalent expressions?

A.2(2/5x + 2)=2 2/5x + 1

B.2(2/5x + 2)=4/5x + 4

C.2(2/5x + 4)=4/5x + 2

D.2(2/5x + 4)=2 2/5x + 8

Solution:

$2(\frac{2}{5}x + 2)$

Let us distribute 2 inside the parenthesis.

That is, we use distributive property:

a(b+c)=ab+ac

$2(\frac{2}{5}x + 2) =\frac{2*2}{5}x+2*2$

So, $2(\frac{2}{5}x + 2) =\frac{4}{5}x+4$

Answer:Option (b)

$2(\frac{2}{5}x+4)$

Applying distributive property, a(b+c)=ab+ac

$2(\frac{2}{5}x+4) =2*\frac{2}{5} x+2*4$

$2(\frac{2}{5}x+4) =\frac{2*2}{5} x+2*4$

$2(\frac{2}{5}x+4) =\frac{4}{5} x+8$

So, Option (B) is correct.

8 0

3 years ago

Read 2 more answers

14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.

Bess [88]

Hello :
the <span>coordinates </span> circumcenter for ∆DEF :
x = (1+7+1)/3
y = (1+1+5//3
x=3
y= 7/3

6 0

3 years ago

What is the solution to the equation?

Zielflug [23.3K]

Answer:

Exact form - $\frac{25}{2}$

Decimal form - 12.5

Mixed number form - 12 $\frac{1}{2}$

Have a nice day.

4 0

2 years ago

The length of the base of a right triangle is twice the height. If the height is ten meters, find the area of the right triangle

Ber [7]

Answer:

the answer is C... 100 m2

Step-by-step explanatii just took the test and it was right. the base would be 20 and the height would be 10. from there you just you the formula for area of a right triangle.

4 0

3 years ago