Consider the following.
3^5x − 1 = 7
(a) Find the exact solution of the exponential equation in terms of logarithms.

(b) Use a calculator to find an approximation to the solution rounded to six decimal places.

Answer:

b^2

Step-by-step explanation:

You're going to add the exponents from b x b, both carry a 1 in their powers (or exponents)

so b^1 + b^1 = b^2

Answer:

b^2

Step-by-step explanation:

b*b = b^2

Answer:

13 units

Step-by-step explanation:

(x₁,y₁) = (-5 , 3)   & (x₂ , y₂) = (7 ,8)

[tex]Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\[/tex]

              [tex]= \sqrt{(7-[-5])^{2}+(8-3)^{2}} \\\\= \sqrt{(7+5)^{2}+(8-3)^{2}} \\\\= \sqrt{(12)^{2}+(5)^{2}}\\\\=\sqrt{144+25}\\\\=\sqrt{169}\\\\= 13[/tex]

Step-by-step explanation:

[tex]a {}^{3} + b {}^{3} [/tex]

Notice how that for both a and b are raised to an odd power. This means we can factor this by a binomial raised to an odd power.

Let divide this by

[tex]a + b[/tex]

Since that is also a odd power.

[tex]( {a}^{3} + {b}^{3} ) \div (a + b)[/tex]

We get

a quotient of

[tex]( {a}^{2} - ab + {b}^{2} )[/tex]

So our factors are

[tex](a + b)( {a}^{2} - ab + {b}^{2} )[/tex]

Answer:

[tex](a+b)(a^{2} -ab+b^{2} )[/tex]

Step-by-step explanation:

[tex]\textbf{We need to factor this expression}[/tex] [tex]\textbf{by applying the sum of two cubes rule:}[/tex]

[tex]\Longrightarrow[/tex] [tex]A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )[/tex]

Here,  

A= a

B= b

So, [tex](a+b)(a^{2} -ab+b^{2} )[/tex]

[tex]\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto[/tex]

[tex]\textsl{OAmalOHopeO}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Put the numbers in place of the corresponding variables and do the arithmetic.

  √(2a) -b = √(2·8) -(-5) = 4 +5 = 9

  -3ac +2b = -3(8)(1/4) +2(-5) = -6 -10 = -16

  b² -8c = (-5)² -8(1/4) = 25 -2 = 23

what you're trying to do is form an equation for y

6x + 5y = 10    

5y = -6x + 10         we need y to be singular so divide by numeral before y

y = - 6x/5 + 10/5

y = - 6x/5 + 2

Step-by-step explanation:

what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?

if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.

so, all possible outcomes are 4²⁰.

that means the probability to guess all 20 right is

1/4²⁰

a tiny, tiny number.

and the probabilty to have all wrong ?

she has 4 choices to pick 1 of 3 wrong answers.

so, the probability is 3/4 to answer the first question wrong.

for that she has again then the same chance to get the second question wrong too.

so, it is 3/4 × 3/4 = 9/16

and so on.

the probability to guess all 20 wrong is then

(3/4)²⁰ ≈ 0.0032

that is still a small number but much, much larger than the probability to get everything right.

still, even the goal to truly get everything wrong is highly unlikely.

Answer:

n = 12

Step-by-step explanation:

n + 5 = 2n - 7

7+5=2n-n

12=n

12+5=2(12)-7

9514 1404 393

Answer:

  3/11 were left

Step-by-step explanation:

A packet of oranges is 11/11. Subtracting 4/11 +4/11 = 8/11 from that leaves ...

  11/11 -8/11 = (11 -8)/11 = 3/11

3 elevenths were left.

Answer:

-4

Step-by-step explanation:

(f(a+h)-f(a))/h=(2-4(a+h)-2+4a))/h=-4h/h=-4

This question is solved using proportions, as the table gives us the number of words per page given the dimensions, and the number of pages, which lets us calculate the number of words.

Doing this, we get that the story will be composed of 792,800 words.

-------------------------------------------

Thus, considering that there will be 991 pages, each with 800 words, the total number of words in the story will be of:

[tex]991 \times 800 = 792,800[/tex]

The story will be composed of 792,800 words.

A similar question is given at https://brainly.com/question/19905617

Answer:

A, B, E, F

Step-by-step explanation:

24>12, 24>15, 24>13, 24>18, 24<42, 24<41

Answer:

0.152

Step-by-step explanation:

0.4 × 0.38

→ Multiply 0.4 by 10

0.4 × 10 = 4

→ Multiply 0.38 by 100

38

→ Multiply the 2 answers together

4 × 38 = 152

→ Divide by the answer by 1000

152 ÷ 1000 = 0.152

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  sin(tan^-1(x)) = x/√(x² +1)

Step-by-step explanation:

We know that for an angle in a right triangle...

  Tan = Opposite/Adjacent

and

  Sin = Opposite/Hypotenuse

so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...

  Hypotenuse² = Opposite² + Adjacent² = x² +1

Then the sine of the angle is ...

  sin(tan^-1(x)) = x/√(x² +1)

Answer:

300 miles

Step-by-step explanation:

Let us consider the miles they travelled is 'm'

Mileage for Primo= 21 + (m × 0.20) = 21+0.2m

Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m

Question says The mileage is equal when Ultimo's charge is 4× Primo

Thus,

4 × (21+0.2m) = 24+ m

84 + 0.8m = 24 + m

60 = 0.2m

m = 300

Answer:x2.2

Step-by-step explanation:

Answer:

1.94 oz

Step-by-step explanation:

x/97 = 200/10000

97*200 = 10,000x

19400 = 10,000x

1.94 oz

You can also do it this way:

200/10000 = 0.02

0.02 * 97 = 1.94

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...

  0.55(130 -x) +0.80(x) = 0.70(130)

  0.25x +71.5 = 91 . . . simplify

  0.25x = 19.5 . . . . . . subtract 71.5

  x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%

  130-78 = 52 . . . . amount of 55%

52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.

Answer:

No

97/1000 is the same as 97 divided by 1000

the decimal would be .097, not .97

64°

Step-by-step explanation:

The 36-ft distance can be regarded as the opposite side of the triangle formed by the leaning ladder while its length of 40 ft is the hypotenuse. So using the definition of a sine of an angle, we know that

[tex]\sin \theta = \dfrac{opposite}{hypotenuse} = \dfrac{36\:\text{ft}}{40\:\text{ft}}[/tex]

or

[tex]\theta = \sin^{-1}\left(\dfrac{36}{40}\right) = \sin^{-1}(0.9)[/tex]

[tex]\:\:\:\:=64°[/tex]

Answer:

x+19

Step-by-step explanation:

3x+12 - 2x+7 = x+19

Answer:

x-19

Step-by-step explanation:

expand the brackets

3x+12-2x-7

3x-2x-12-7

x-19

Answer:

8

Step-by-step explanation:

-3x+143=119

-3x=119-143

-3x=-24

x=-24/-3

x=8

Answer:

40%

Step-by-step explanation:

Total amount of marbles are 25

the chances of getting green marbles out of all the marbles are 10/25 or 0.4

and since we are looking for percentages we have to multiply 0.4 by 100

0.4 x 100 = 40

From eq(1)

[tex]\\ \sf\longmapsto x=3-3y\dots(3)[/tex]

Putting the value in eq(2)

[tex]\\ \sf\longmapsto 3y-2(3-3y)=12[/tex]

[tex]\\ \sf\longmapsto 3y-6-6y=12[/tex]

[tex]\\ \sf\longmapsto -3y-6=12[/tex]

[tex]\\ \sf\longmapsto -3y=12+6[/tex]

[tex]\\ \sf\longmapsto -3y=18[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{18}{-3}[/tex]

[tex]\\ \sf\longmapsto y=-6[/tex]

Putting value in eq(3)

[tex]\\ \sf\longmapsto x=3-3(-6)[/tex]

[tex]\\ \sf\longmapsto x=3+18[/tex]

[tex]\\ \sf\longmapsto x=21[/tex]

Answer:

x=-3 & y=2

Step-by-step explanation:

x+3y=3----(i)

3y-2x=12----(ii)

Solving eqn--(i)

x+3y=3

or, x=3-3y---(iii)

Substituting the value of x from eqn --(iii) in eqn (ii) ,we get

3y-2x=12

or, 3y-2(3-3y)=12

or, 3y-6+6y=12

or,9y=18

y=18/9=2

Substituting the value of x in eqn--(iii),

x=3-3y=3-3*2=3-6=-3

Answer:

$30.00 -( $8.00 +  $21.00) =

$1 left  

$1.00  

Step-by-step explanation:

FOOD non-Food

 $2.50   $6.00  

 $1.50   $3.00  

 $4.00   $11.00  

SUM  $8.00   $20.00  

Tax   $1.00  

The boy have only $1 .

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

According to the given question.

The amount of money the boy initially had = $30.00

The amount of money he spent on tickets = $6

Amount of money spent of drink = $2.50

Amount of money spent on cotton candy =$1.50

Amount of money spent on burger = $4

Amount of money spent on souvenir  = $3.00

Amount of money spent on shirt = $11.0

Now,

The total money spent on non-food items

= $6 +$3 + $11

= $20

So, the amount paid as a tax for non food items = 5% of $20 = [tex]\frac{5}{100} (20)[/tex]=$1

And,

The total amount spent including tax

= $1 + $20 + $2.50 + $1.50 + $4.00

= $29

Therefore,

The amount of money is left = $30 - $29 = 1

Hence, the boy have only $1.

Find out more information about percentage here:

https://brainly.com/question/14699403

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