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3 years ago

Write as a single logarithm (show steps)

Mathematics

1 answer:

Effectus [21]3 years ago

7 0

1/3 log 125 can be rewritten as (1/3) log 5^3 = log 5

Similarly, 1/3 log 8 can be re-written as 1/3 log 2^3, same as (1/3)(3 log 2)= log 2

Thus, the fraction can be written in simpified form as log 5 / log 2.

The second term is the same as log m^5.

Thus, your final result is (log 5) / (log 2) + log m^5.

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Amy pays $2.70 for 3 apples and 2 bananas. One apple costs $0.40 more than one banana. Let a represent the price per apples.

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Answer:

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3 years ago

A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height it fell from. Let an repr

Scilla [17]

(A) The formula for nth bounce is $a_n = 20 (7/9)^{n}$ .

(B) 4.43 feet is the maximum height of the ball on the 6th bounce.

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An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

The height from where the ball is dropped = 20 feet.

Also, the ball bounces and returns to 7/9 to its original height.

(A)

The representation of the maximum height of the ball on the nth bounce can be given as

$a_n = 20 (7/9)^{n}$

(B)

The maximum height of the ball on the 6th bounce = 20 (7/9)⁶ = 4.43 feet

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1 year ago

Please I Really Need Help.The coordinate plane below represents a city. Points A through F are schools in the city.

almond37 [142]

Answer:

Part A) The system of inequalities is

$x\geq2$ and $y\geq2$

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

$x\geq2$ -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

$y\geq2$ -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)

Inequality A

$x\geq2$ -----> $2\geq2$ ----> is true

Inequality B

$y\geq2$ ------> $2\geq2$ ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)

Inequality A

$x\geq2$ -----> $3\geq2$ ----> is true

Inequality B

$y\geq2$ ------> $4\geq2$ ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

$y < -2x+2$