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3 years ago

Use the definition of logarithm to simplify each expression.

1 answer:

7 0

$1)\ \ \ log 10 ^{10}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10}\ \ \ \Leftrightarrow\ \ \ \ \ \ x=10\\\\2) \ \ \ log 10 ^{100}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{100}\ \ \ \Leftrightarrow\ \ \ x=100\\ \\ 3)\ \ \ log 10 ^ {10-4}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10-4}\ \ \ \Leftrightarrow\ \ \ x=6$

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7a +42 +8< -10 + 9a -64a

Mamont248 [21]

Answer:

a < -30/31

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

7a + 42 + 8 < -10 + 9a - 64a

Step 2: Solve for a

Combine like terms (a): 7a + 42 + 8 < -10 - 55a
Combine like terms: 7a + 50 < -10 - 55a
[Addition Property of Equality] Add 55a on both sides: 62a + 50 < -10
[Subtraction Property of Equality] Subtract 50 on both sides: 62a < -60
[Division Property of Equality] Divide 62 on both sides: a < -30/31

Here we see any number a less than -30/31 would work as a solution to the inequality.

3 0

2 years ago

7,7.5,8,8.5,9 common difference

raketka [301]

Answer:

$0.5$

Step-by-step explanation:

$9-8.5$

$=0.5$

3 0

3 years ago

Read 2 more answers

Solve the problem:

stepan [7]

volume of the box is 675 cubic inches

A machine produces open boxes using square sheets of plastic.

It is a square sheet so length and width are same

Lets assume length as x so width is also x

The machine cuts equal-sized squares measuring 3 inches on a side from each corner of the sheet.

After turning up the sides the height of the box becomes 3 inches

We know the volume of a box formula

Volume = Length * width * height

We know length is x , width is x and height = 3

So V = x * x * 3

Given volume = 675 cubic inches

$675 = x * x * 3$

$675 = x^2* 3$

Divide by 3 on both sides

$225 = x^2$

Now we take square root on both sides

x = 15

the length of one side of the open box is 15 inches.

5 0

3 years ago

in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?

lora16 [44]

Answer:sin =perpendicular/hypotenuse

Step-by-step explanation:

Sin angle is given use tan theta or cos theta to find the RS

5 0

3 years ago

A runner passes the 12-mi point after 2 hours and reaches the 15-mi point 30 minutes later. Assuming a constant rate, find th

Arturiano [62]

Answer:

6 mph

Step-by-step explanation:

Difference in distance

= 15 - 12

= 3 mi

time taken

= 30 mins

= 1/2 hour

Speed

= 3 ÷ 1/2

= 6 mph

8 0

3 years ago