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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.

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Find the slope of a line if the points (2,-1) and (5,3) are on the line

Romashka [77]

Answer:

$\huge{ \boxed{ \sf{ \frac{4}{3} }}}$

Step-by-step explanation:

$\star{ \sf{ \: Let \: the \: points \: be \: A \: and \: B}}$

$\star{ \sf{ \: Let \: a(2,-1) \: be \: (x1 \:, y1) \: and \: b (5,3) \: be \: (x2 \:, y2)}}$

$\underline{ \sf{Finding \: the \: slope \: of \: the \: line}}$

$\boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1} }}$

$\mapsto{ \sf{Slope = \frac{3 - ( - 1)}{5 - 2} }}$

$\mapsto{ \sf{Slope = \frac{3 + 1}{5 - 2}}}$

$\mapsto{ \sf{Slope = \frac{4}{3} }}$

Hope I helped!

Best regards! :D

~ $\text{TheAnimeGirl}$

4 0

3 years ago

Solve 7(x + 2) = -49

nata0808 [166]

Answer:

x= -9

Step-by-step explanation:

7(x+2)=-49

divide both sides by 7

(x+2)=-7

subtract 2 from both dies

x= -9

3 0

3 years ago

Read 2 more answers

How to write an equation for the line perpendiculer and trhough the given ppoint?

valentinak56 [21]

A method that always works is to find the slope of the given line, then find the negative reciprocal of that. Your result will be the slope of the perpendicular line. Using this slope and the given point, fill in the parameters of the point-slope form of the equation of a line.

For m = slope of given line and (h, k) = given point, the perpendicular line will be
y = (-1/m)(x -h) +k

Often, this equation can be simplified to another appropriate form, such as slope-intercept form (y = mx+b) or standard form (ax+by=c).

_____
The slope of a given line can be found by solving its equation for y. The slope is the coefficient of x in that solution. If the given line is characterized by two points, (x1, y1) and (x2, y2), then its slope is m = (y2-y1)/(x2-x1).

In the unusual case where the given line is vertical (x=<some constant>), the slope of the perpendicular line is zero, and the line you want becomes y=k.

5 0

3 years ago

ALGEBRA 1, SEMESTER 2

SIZIF [17.4K]

So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):

$f(0)=\frac{2*0+3}{3*0-3}\\ f(0)=\frac{0+3}{0-3}\\ f(0)=\frac{3}{-3}\\ f(0)=-1\\ \\ f(8)=\frac{2*8+3}{3*8-3}\\ f(8)=\frac{16+3}{24-3}\\ f(8)=\frac{19}{21}$

Now that we have their y's, we can use the slope, aka average rate of change, formula, which is $\frac{y_2-y_1}{x_2-x_1}$ . Using what we have, we can solve it as such:

$\frac{\frac{19}{21}-(-1)}{8-0}=\frac{\frac{40}{21}}{8}=\frac{40}{21*8}=\frac{40}{168}=\frac{5}{21}$

In short, the average rate of change from x = 0 to x = 8 is 5/21.

8 0

3 years ago

The regular price rounded to the nearest cent

Daniel [21]

Answer:

$189.43

Step-by-step explanation:

To find the original price, write a proportion. In your proportion, write one ration that has sale price over original price. The other ratio should be written with the corresponding percent values. Since the sale price is 65% off then you paid 35% of the regular the price. The proportion should be:

$\frac{66.30}{x}= \frac{35}{100}$

To solve cross multiply numerator and denominator of each fraction.

66.30(100) = x(35)

6630 = 35x

189.43 = x

This means the regular price is $189.43.

3 0

3 years ago