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2 years ago

Why is b ≠ 1 a condition for f(x) = abx (x is a exponent i cant put it for some reason)?

Mathematics

1 answer:

timurjin [86]2 years ago

7 0

Answer:

1^x = 1

Step-by-step explanation:

If b = 1,

It will be a horizontal line:

y = a

Not an exponential curve

Because

y = a(1^x)

1 power anything is 1

y = a × 1

y = a

You might be interested in

a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group

enyata [817]

From the whole group half the club are boys.
fraction of boys from the whole class = 1/2
from this fraction, 4/9th of the boys have brown eyes
therefore fraction of boys who have brown eyes
= 4/9 of 1/2
the 'of' function is used to multiply
$\frac{4}{9} * \frac{1}{2}$
when multiplying fractions numerators are multiplied by numerators and denominators multiplied by denominators
$\frac{4*1}{9*2} = \frac{4}{18}$
4/18 can be simplified by dividing the whole number by a common number
4/18 divided by 2 = 2/9
the answer is 2/9
2/9 of the club are boys with brown eyes

3 0

3 years ago

Read 2 more answers

Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large

Debora [2.8K]

Answer:

x = 1,6 in ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in w = 8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x ) and ( w - 2*x ) and x is the height

( 12 - 2*x ) and ( w - 2*x )

V(ob) = (L - 2*x ) * ( - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0 12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in

b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max) = 67,58 in³

How do we Know that is the maximun value for V?

We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6

3 0

2 years ago

State the gradient of the line perpendicular to the line y=3x-2

kherson [118]

Answer:

-1/3

Step-by-step explanation:

3 is the gradient of the other line

m1×m2=-1 (equation for perpendicular lines)

m1×3= -1

m1= -1/3

Pls confirm if its correct

correct me if wrong

thanks! :)

7 0

2 years ago

HELP!!

WITCHER [35]

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle m∠K is 102° so option (B) is correct.

<h3>What is a triangle?</h3>

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

Triangle is a very common figure to deal with in our daily life.

It is known that the sum of all three angles inside a triangle will be 180°.

So, m∠A + m∠B + m∠C = 180°

m∠C = 180° - 58° - 44°

m∠C = 78°.

The exterior angle of C = 180- 78 = 102°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to m∠K is 102°".

For more about triangles,

brainly.com/question/2773823

#SPJ1

5 0

6 months ago

Read 2 more answers

How does the graph of f(x)=3lx+2l+4 relate to its parent function?

Sergeeva-Olga [200]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template above in mind, let's see this one

$\bf parent\implies f(x)=|x|
\\\\\\
\begin{array}{lllcclll}
f(x)=&3|&1x&+2|&+4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

A=3, B=1, shrunk by AB or 3 units, about 1/3
C=2, horizontal shift by C/B or 2/1 or just 2, to the left
D=4, vertical shift upwards of 4 units

check the picture below

7 0

2 years ago