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2 years ago

You are given that 4a-2b = 10 (a) Write down the value of 2a - b

Mathematics

1 answer:

Simora [160]2 years ago

6 0

Answer:

2a - b = 5

Step-by-step explanation:

4a - 2b = 10

take out the highest common factor of the left side

2(2a - b) = 10

divide both sides by two

2a - b = 10/2

2a - b = 5

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2 years ago

Write as logarithm with base 4: 4 -5 2 -4

NeX [460]

Answer:

log_4(256)=4

log_4(1/1024)=-5

log_4(16)=2

log_4(1/256)=-4

Step-by-step explanation:

We want to write a number, x, such that

Log_4(y)=x.

In exponential form that is 4^x=y.

So first number is x=4.

4^4=256 which means log_4(256) is 4 as a logarithm with base 4.

The second number is x=-5.

4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.

The third number is x=2.

4^2=16 so log_4(16) is 2 as a logarithm with base 4.

The fourth number is x=-4.

Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).

8 0

2 years ago

Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actual

NISA [10]

Answer:

Randy is 48 years old

Sandy is 12 years old

Todd is 27 years old

Step-by-step explanation:

Given

Represent their ages with the first letters of their names:

$R + S + T = 87$

$R = 4 * S$

$T = 15 + S$

Required

Determine their individual ages

We'll solve the above equations using substitution method of simultaneous equations

Substitute 15 + S for T and 4 * S for R in $R + S + T = 87$

This gives:

$4 * S + S + 15 + S = 87$

$4 S + S + 15 + S = 87$

Collect Like Terms

$4 S + S + S = 87 - 15$

$6S = 72$

Divide through by 6

$S = 72/6$

$S = 12$

This implies that Sandy is 12 years old

Substitute 12 for S in $R = 4 * S$ and $T = 15 + S$

$R = 4 * 12$

$R = 48$

$T = 15 + 12$

$T = 27$

This implies that Randy is 48 years old and Todd is 27

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2 years ago