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2 years ago

Which graph represents the solution set to this system of inequalities?

Mathematics

1 answer:

Serggg [28]2 years ago

6 0

Answer:

Step-by-step explanation:

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Solve for x : log(3x) + log(x + 4) = log(15). Please explain it to me.

zlopas [31]

Answer:

x = 1

Explanation:

$\sf \rightarrow log(3x) + log(x + 4) = log(15)$

Rule: log(a) + log(b) = log(ab)

$\sf \rightarrow log(3x(x + 4)) = log(15)$

cancel out log on both sides

$\sf \rightarrow 3x(x + 4) = 15$

relocate constant variable

$\sf \rightarrow 3x^2 + 12x -15 = 0$

take 3 as a common factor

$\sf \rightarrow 3(x^2 + 4x -5) = 0$

divide both sides by 3

$\sf \rightarrow x^2 + 4x -5 = 0$

middle term split

$\sf \rightarrow x^2 + 5x -x-5 = 0$

factor common terms

$\sf \rightarrow x(x + 5) -1(x+5)= 0$

collect into groups

$\sf \rightarrow (x-1)(x+5)= 0$

set to zero

$\sf \rightarrow x-1 = 0 , \ x+5= 0$

relocate variables

$\sf \rightarrow x = 1, \ x = -5$

There must be a positive solution for log, so the solution is only x = 1

3 0

2 years ago

Read 2 more answers

Write the expressions "Four times the difference of a number and 7 is 32", "One third of a number is 12 less than the number its

Anna71 [15]

Part 1) "Four times the difference of a number and $7$ is $32$ "

Let

x--------> the number

we know that

the expressions is equal to

$4(x-7)=32$

therefore

the answer part 1) is

$4(x-7)=32$

Part 2) "One third of a number is $12$ less than the number itself"

Let

x--------> the number

we know that

the expressions is equal to

$\frac{1}{3} x=(x-12 )$

therefore

the answer part 2) is

$\frac{1}{3} x=(x-12 )$

Part 3) "Ten increased by the quotient of a number and $2$ is $-15$ "

Let

x---------> the number

we know that

the expressions is equal to

$10+ (\frac{x}{2} )= -15$

therefore

the answer Part 3) is

$10+ (\frac{x}{2} )= -15$

Part 4) "One less than the product of a number and $3$ is $5$ more than the number itself"

Let

x---------> the number

we know that

the expressions is equal to

$(3x)-1=5+x$

therefore

the answer Part 4) is

$(3x)-1=5+x$

3 0

3 years ago

Read 2 more answers

A trapezoid has interior angle measures of 90,90 ,75 and X degrees. Find the measure of angle x in the trapezoid. Enter only the

alexgriva [62]

The angles inside a trapezoid add up to equal 360 degrees

X = 360-90-90-75 = 105 degrees.

7 0

3 years ago

HURRY PLEASE I NEED IT ASAP 15 POINTSS!!!!

expeople1 [14]

D shows equivalent expressions

3 0

2 years ago

Read 2 more answers

What is the 50th term of the linear sequence below? 27 , 25 , 23 , 21 , 19

lesya [120]

Answer:

-73 sorry if im wrong

Step-by-step explanation:

find nth term but replace n with 50 equation is -2n+27

4 0

3 years ago