Consider the exponential function f(x) = b^x, where b ≠ 1. Explain WHY the base has such a restriction.

Answer:

[tex]3x^{3} -25x^{2} -44x+10[/tex]

Step-by-step explanation:

Hello!

To solve this we distribute what in one parenthesis into the other

                 3x                  

3x * x^2 = 3x^3

3x * -10x = -30x^2

3x * 2 = 6x

                 5                  

5 * x^2 = 5x^2

5 * -10x = -50x

5 * 2 = 10

Now we put like terms together and simplify

3x^3 + 0 = 3x^3

-30x^2 + 5x^2 = 25x^2

6x - 50x = -44x

0 + 10 = 10

Put it all together

3x^3 + 25x^2 - 44x + 10

Hope this helps!

Answer:

3x^3 + 25x^2 - 44x +10

Step-by-step explanation:

To answer this use FOIL

First Outer Inner Last

In this problem start by distributing the 3x

3x^3-30x^2+6x

Next distribute the 5 in the second parenthesis

5x^2 - 50x + 10

Lastly, add like terms (terms that have the same variable and powers)

3x^3 - 25x^2 +6x +10

Answer:

p=2

Step-by-step explanation:

17-2p=2p+5+2p

17-2p=4p+5

17=6p+5

12=6p

2=p

Answer:

The answer is

Step-by-step explanation:

Divide both sides of the equation by ln 2

That's

We have

Covert the logarithm into exponential form using the property

\: \: is \: \: \: the \: \: \: same \: \: \: as \: \: \: \:

Are all the same

So

is the same as

Divide both sides by 4

We have the final answer as

Hope this helps you

Answer:

[tex]\large \boxed{{m= \frac{3}{4} }}[/tex]

Step-by-step explanation:

Parralel lines have the same slope.

The slope will be [tex]\frac{3}{4}[/tex]

The line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4

The slope is the measure of the steepness of a line. It is also known as the gradient of a line.

Two parallel lines are known to have equal slopes. For example;

Therefore for the line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4

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Answer:

x=-1, x=2, x=3

Step-by-step explanation:

Factor the left side of the equation.

(x+1)(x^2+x-6)

(x+1)(x-2)(x-3)

Now set everything equal to 0

x+1=0

x-2=0

x-3=0

Now solve for x

therefore, the answer is x=-1, x=2, x=3

Step-by-step explanation:

Hey, there!!

Let me simply clear you.

The given points are (6,2) and (-6,-8).

Remember if you are finding the equation of the line passing through point, you will get equation in slope intercept form.

As in your question there are two points we must use double point formula,

[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

[tex]( y - 2) = \frac{ - 8 - 2}{ - 6 - 6} (x - 6)[/tex]

Simplifying them we get,

6(y-2)= 5(x-6)

6y - 12 = 5x -30

Therefore, 5x - 6y - 18 = 0 is the required equation.

Hope it helps.....

Since

[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^3}{(x+1)^2}[/tex]

we can perform synthetic division twice, first for

[tex]\dfrac{x^3}{x+1}[/tex]

then dividing the result by [tex]x+1[/tex] again.

...  ||  1     0    0    0

-1  ||        -1     1    -1

================

...  ||  1     -1    1     -1

This translates to

[tex]\dfrac{x^3}{x+1}=x^2-x+1-\dfrac1{x+1}[/tex]

Now divide [tex]x^2-x+1[/tex] by [tex]x+1[/tex]. (Dividing the remainder term by [tex]x+1[/tex] can wait until the end.)

...  ||  1    -1      1

-1  ||        -1     2

=============

...  ||  1    -2     3

or equivalently,

[tex]\dfrac{x^2-x+1}{x+1}=x-2+\dfrac3{x+1}[/tex]

Taking everything together, we have

[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^2-x+1}{x+1}-\dfrac1{(x+1)^2}[/tex]

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac3{x+1}-\dfrac1{(x+1)^2}[/tex]

Combine the last two fractions:

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3(x+1)-1}{(x+1)^2}[/tex]

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3x+2}{(x+1)^2}[/tex]

which agrees with the solution we found in your other question.

(There's a variant of synthetic division that works with directly dividing a polynomial by another one of any degree, but it's basically just a condensed version of applying the algorithm for dividing a polynomial twice by a linear one, like we've done here.)

Answer:

width= 3.17

Step-by-step explanation:

Divide 38 (the area) by 12 (the width)

Answer:

Step-by-step explanation:

-5 - (-7) = -5 + 7 = (-5) + (7) = (7) + (-5) = 7 - 5 = 2

Answer:

Exact: 0.1414

Rounded: 0.1

Step-by-step explanation:

Answer:

14/18 =0.7778

Step-by-step explanation:

14/18 =0.7777.........=0.7778 rounded to the nearest thousandth

Answer:

B=45

The sum of the interior angle of a triangle is equal to 180

Therefore equate angle A, B and C to 180

then add them to get 135 + c=180

group like terms,135 crosse the equal sign to be negative

which is c=18p-135

c=45

Answer:

happy prince was born and one day he died

The true statements are: 3, 4 and 5

Step-by-step explanation:

search it up

Answer:

2,3,and 4

Step-by-step explanation:

Answer:

by the way and the answer is c for yhe reasin because the of tje by theand i thaith

Answer:

C = 100

Step-by-step explanation:

PEMDAS

multiplication and division first from left to right so

125/25 = 5

5x5 = 25

25 + 75 = 100

Answer:

C. 100

Step-by-step explanation:

To complete this question you must use systems of equations.

First you must complete multiplication or division depending on which comes first in the left to right sequence. In this case it is 125/25 which equals 5. This now makes the equation 75+5 x 5

Next, you complete any other division or multiplication Which in this case is, 5x5. The answer to this is 25, making the new equation, 75+25 which when added together equals 100!

And that is how you use systems of equations. Hope it helps ;)

Answer:

19/8

Step-by-step explanation:

To find the mixed number

Take the denominator times the whole number

8*2 = 16

Add the numerator

16+3 = 19

Put this over the denominator

19/8

Answer:

10.8 km/hr

Step-by-step explanation:

Given that

radius of the diameter is 4 cm

Converting 4 cm to km, we have

4/100000 = 0.00004 km or 4*10^-5 km

Angular speed is given as

v = 2πr/T

Where T is, 1/n,and n is the number of revolutions

v = (2 * 3.142 * 0.00004) / (1/7000)

v = 0.00126 / 0.007

v = 0.18 km/min

This is in km/min, now we convert to km/hr as requested.

0.18 * 60 = 10.8 km/hr

Answer:

Step-by-step explanation:

[tex]\frac{8}{30}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4}{15}[/tex]

Answer:

[tex]\frac{4}{1}[/tex]

Step-by-step explanation:

Given:

2/20 : 1/40

A). First re-write the ratio as follows;

(i) Change the ratio sign to division (÷). i.e

2/20 ÷ 1/40

(ii) Solve the expression by changing the division to multiplication(×). This also means you will need to swap the numerator and the denominator of the second term. i.e (1 / 40) becomes (40 / 1)

(2/20) × (40 / 1) = [tex]\frac{2}{20}[/tex] × [tex]\frac{40}{1}[/tex] = [tex]\frac{4}{1}[/tex]

B). Now convert the result from above to unit rate. A unit rate is a rate in which the denominator has a value of 1.

So to convert   [tex]\frac{4}{1}[/tex]  to unit rate, we keep simplifying until the denominator becomes 1.

And since the denominator is already 1, there is no need for further simplification.

Therefore, 2/20 : 1/40 to unit rate is  [tex]\frac{4}{1}[/tex]

Answer:4/1

Step-by-step explanation:

I say this because you are supposed to divided it and the answer is 4 then you find the answer choice with a 1 as the denominator and it should say 4/1 and that is the correct answer.

a) 16 month

b) $12 000

$8000 + 250m = $10000 + 125m

250m - 125m = $10000 - $8000

125m = $2000

m = $2000 : 125

m = 16 months

16 months

$8000 + $250×16 =

= $8000 + $4000

= $12000

$10000 + $125×16 =

= $10000 + $2000

= $12000

Answer:

I think that, please check it y=3x

Answer:

[tex] \boxed{\sf x = 14} [/tex]

Step-by-step explanation:

Solve for x:

[tex] \sf \implies 11 = \frac{1}{2} (x + 8)[/tex]

[tex] \sf 11 = \frac{1}{2} (x + 8) \: is \: equivalent \: to \: \frac{1}{2} (x + 8) = 11 : [/tex]

[tex] \sf \implies \frac{1}{2} (x + 8) = 11[/tex]

[tex] \sf Multiply \: both \: sides \: of \: \frac{1}{2} (x + 8) = 11 \: by \: 2 : [/tex]

[tex] \sf \implies \frac{1}{ \cancel{2}} (x + 8) \times \cancel{2 }= 11 \times 2[/tex]

[tex] \sf \implies 1(x + 8) = 11 \times 2[/tex]

11 × 2 = 22:

[tex] \sf \implies x + 8 = 22[/tex]

Subtract 8 from both sides:

[tex] \sf \implies x + (8 - 8) = 22 - 8[/tex]

8 - 8 = 0:

[tex] \sf \implies x = 22 - 8[/tex]

22 - 8 = 14:

[tex] \sf \implies x = 14[/tex]

The value of x is 4, for the equation 11 = 1/2 (x + 8).

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

11 = 1/2 (x + 8)

Simplify the equation by multiplying 2 in both the sides,

11 × 2 =2 × 1/2 × (x + 8)

22 = x + 8

Subtract 8 from both the sides,

22 - 8 = x + 8 - 8

14 = x

or x = 14

The required value of x for the given equation is 14.

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Answer:

Step-by-step explanation:

1. 3(x - 5)

2. 0.5x + 6.

Answer:

1) 3(x-5)

2) 1/2x+6

Step-by-step explanation:

Three times the difference between x and five.

Three times=3* or 3(

difference between x and five= x-5

Together it will be

3(x-5)

One half times a number increased by six

One half times a number= 1/2x

increased by six= +6

Together it will be

1/2x+6

Hope this helps ;) ❤❤❤

The value of each digit in a number is known as the place value. The time rounded to the nearest tenth is 13.2 seconds.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

Given the time to run is 13.245, now tenth means the value that is after the decimal. Since the value after the tenth is 4, therefore, the tenth value will remain the same but the numbers after that will be erased.

Hence, the time rounded to the nearest tenth is 13.2 seconds.

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Answer:

You must first divide 3 from both sides.

Step-by-step explanation:

Whenever you solve an equation such as this you are always trying to isolate the variable that is given. In this case we are arriving at the value of d alone.

3d = -81

d = -27

Hope this helps!

Answer:

i believe that 3 needs to be eliminated

Step-by-step explanation:

3d÷3=-81÷3

d=27

hope i helped :D

Answer:

D. 264°

Step-by-step explanation:

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,

60° = 1/2[(18x - 6)° - (5x +17)°]

60° * 2 = (18x - 6 - 5x - 17)°

120° = (13x - 23)°

120 = 13x - 23

120 + 23 = 13x

143 = 13x

143/13 = x

11 = x

x = 11

(18x - 6)° = (18*11-6)°= (198 - 6)° = 192°

(5x +17)° = (5*11 +17)° =(55+17)° = 72°

m (arc KNL) = (18x - 6)° + (5x +17)° = 192° + 72°

m (arc KNL) = 264°

Answer:

241/90 or 2 61/90

Step-by-step explanation:

Let's call the given number 2.67(7) = x

Then use below steps:

241/90

2  61/90

2.67(7) =

= (2677 - 267)/900

= 2410⁽¹⁰/900

= 241/90

= 2  61/90

Answer:

This is the product of three nines (three factors of 9). 9 × 9 × 9 × 9 = 6561 --> This is the product of four nines (four factors of 9). It's a common mistake among educators to state that 81 is what we get by "multiplying nine by itself twice".

Answer:

I believe the answer is 2x² - 88 - 24, since it is the only one with a number in front of the x²

Step-by-step explanation:

y = x² - 2x - 24

y = 2x² - 88 - 24

y = x² + 5x - 25

y = x² + 3x - 10x - 24