16.03.2021

Find the value of x in 4^x=1/16

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09.07.2023, solved by verified expert
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Find the value of x in 4^x=1/16, №18010643, 16.03.2021 17:44

Step-by-step explanation:

Find the value of x in 4^x=1/16, №18010643, 16.03.2021 17:44

Then you CROSS MULTIPLY.

WHICH IS.

4x × 16 = 1

64x = 1

Then you divide both sides by coefficient of x which is 64.

Find the value of x in 4^x=1/16, №18010643, 16.03.2021 17:44

x = 1/64

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Mathematics
Step-by-step answer
P Answered by Master

x = \frac{1}{64}

Step-by-step explanation:

\frac{4x}{1} =  \frac{1}{16}

Then you CROSS MULTIPLY.

WHICH IS.

4x × 16 = 1

64x = 1

Then you divide both sides by coefficient of x which is 64.

\frac{64x}{64}  =  \frac{1}{64}

x = 1/64

Mathematics
Step-by-step answer
P Answered by PhD

x=7

Step-by-step explanation:

(4+7+x+1+x+3+x+4+14+16)/7=x+3

(11+x+1+x+3+x+4+14+16)/7=x+3

(49+3x)/7=x+3

49+3x/7=x+3

49+3x=7x+21

49=4x+21

28=4x

x=7

Mathematics
Step-by-step answer
P Answered by PhD

x=7

Step-by-step explanation:

(4+7+x+1+x+3+x+4+14+16)/7=x+3

(11+x+1+x+3+x+4+14+16)/7=x+3

(49+3x)/7=x+3

49+3x/7=x+3

49+3x=7x+21

49=4x+21

28=4x

x=7

Mathematics
Step-by-step answer
P Answered by PhD

Part 1) Option A x=-13/8

Part 2) Option B x=1

Part 3) Option C x=1/2

Part 4) Option C x=4

Part 5) Option D x=15

Part 6) Option B x=2\frac{1}{4}

Part 10)  Option B x=2

Part 11) Option A x=-14/9  

Part 13) Option A r=-3

Part 14) Option D

Part 15) Option D

Part 16) Option C 4n-5=2n+3; n = 4

Part 17) Option D y=-5

Part 18) Option D x=-1

Part 19) Option D distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

Part 20) Option B  p=-1

Step-by-step explanation:

Part 1) we have

3(-2x-1)=2(x+5)

solve for x

-6x-3=2x+10

2x+6x=-3-10  

8x=-13

x=-13/8

Part 2) we have

3(2x-1)=\frac{1}{2}(4x-2)+2

solve for x

6x-3=2x-1+2

6x-2x=-1+2+3

4x=4

x=1

Part 3) we have

-4(3-2x)+2x=2x-8

solve for x

-12+8x+2x=2x-8

8x=-8+12

8x=4

x=1/2

Part 4) we have

10(x+2)=5(x+8)

solve for x

10x+20=5x+40

10x-5x=40-20

5x=20

x=4

Part 5) we have

-25(x-4)=-55(x-10)

solve for x

-25x+100=-55x+550

-25x+55x=550-100

30x=450

x=450/30

x=15

Part 6) we have

-9(x-5)=x+22\frac{1}{2}  

solve for x

remember that

22\frac{1}{2}=\frac{45}{2}

-9x+45=x+\frac{45}{2}

x+9x=45-\frac{45}{2}

10x=\frac{45}{2}  

x=\frac{45}{20}

convert to mixed number

x= \frac{45}{20}=\frac{9}{4}=2\frac{1}{4}

Part 7) The model is not included

Part 8) The model is not included

Part 9) The model is not included

Part 10) we have

5-x=(1/2)(x+4)

solve for x

5-x=(1/2)x+2

(1/2)x+x=5-2

(3/2)x=3

x=2

Part 11) we have

x-2x(12-(1/2))=2(4-2x)+20

solve for x

x-24x+x=8-4x+20

x-24x+x+4x=8+20

-18x=28

x=-14/9        

Part 12) The model is not included

Part 13) we have

5(r-1)=2(r-4)-6

solve for r

5r-5=2r-8-6

5r-2r=-8-6+5

3r=-9

r=-3

Part 14) and  Part 15)

the answer is the option D

Look for parenthesis and apply the distributive property; combine like terms; move your variable terms to one side and constants to the other side of the equal sign; go in reverse PEMorDAorS to isolate the variable using inverse operations

Part 16)

Let

n------> the number

we know that

4n-5=2n+3 -----> algebraic expression that represent the situation

solve for n

4n-2n=3+5

2n=8

n=4

Part 17) we have

-2(y+2)+5y=6y+11

solve for y

-2y-4+5y=6y+11

6y-5y+2y=-4-11

3y=-15

y=-5

Part 18) we have

4(3x-1)=3+8x-11

solve for x

12x-4=8x-8

12x-8x=-8+4

4x=-4

x=-1

Part 19) we have

14 - 2(3p + 1) = 6(4 + p)

 14 - 6p-2 = 24+6p ------> distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

Part 20) we have

14 - 2(3p + 1) = 6(4 + p)

step 1

distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

14 - 6p-2 = 24+6p

step 2

Group terms that contain the same variable and move the constant to the other side

6p+6p=14-2-24

step 3

Combine like terms

12p=-12

step 4

Divide by 12 both sides

p=-1

Mathematics
Step-by-step answer
P Answered by Master
Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456 ☆
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018 ☆
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55 ☆
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25☆
Mathematics
Step-by-step answer
P Answered by PhD

Part 1) Option A x=-13/8

Part 2) Option B x=1

Part 3) Option C x=1/2

Part 4) Option C x=4

Part 5) Option D x=15

Part 6) Option B x=2\frac{1}{4}

Part 10)  Option B x=2

Part 11) Option A x=-14/9  

Part 13) Option A r=-3

Part 14) Option D

Part 15) Option D

Part 16) Option C 4n-5=2n+3; n = 4

Part 17) Option D y=-5

Part 18) Option D x=-1

Part 19) Option D distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

Part 20) Option B  p=-1

Step-by-step explanation:

Part 1) we have

3(-2x-1)=2(x+5)

solve for x

-6x-3=2x+10

2x+6x=-3-10  

8x=-13

x=-13/8

Part 2) we have

3(2x-1)=\frac{1}{2}(4x-2)+2

solve for x

6x-3=2x-1+2

6x-2x=-1+2+3

4x=4

x=1

Part 3) we have

-4(3-2x)+2x=2x-8

solve for x

-12+8x+2x=2x-8

8x=-8+12

8x=4

x=1/2

Part 4) we have

10(x+2)=5(x+8)

solve for x

10x+20=5x+40

10x-5x=40-20

5x=20

x=4

Part 5) we have

-25(x-4)=-55(x-10)

solve for x

-25x+100=-55x+550

-25x+55x=550-100

30x=450

x=450/30

x=15

Part 6) we have

-9(x-5)=x+22\frac{1}{2}  

solve for x

remember that

22\frac{1}{2}=\frac{45}{2}

-9x+45=x+\frac{45}{2}

x+9x=45-\frac{45}{2}

10x=\frac{45}{2}  

x=\frac{45}{20}

convert to mixed number

x= \frac{45}{20}=\frac{9}{4}=2\frac{1}{4}

Part 7) The model is not included

Part 8) The model is not included

Part 9) The model is not included

Part 10) we have

5-x=(1/2)(x+4)

solve for x

5-x=(1/2)x+2

(1/2)x+x=5-2

(3/2)x=3

x=2

Part 11) we have

x-2x(12-(1/2))=2(4-2x)+20

solve for x

x-24x+x=8-4x+20

x-24x+x+4x=8+20

-18x=28

x=-14/9        

Part 12) The model is not included

Part 13) we have

5(r-1)=2(r-4)-6

solve for r

5r-5=2r-8-6

5r-2r=-8-6+5

3r=-9

r=-3

Part 14) and  Part 15)

the answer is the option D

Look for parenthesis and apply the distributive property; combine like terms; move your variable terms to one side and constants to the other side of the equal sign; go in reverse PEMorDAorS to isolate the variable using inverse operations

Part 16)

Let

n------> the number

we know that

4n-5=2n+3 -----> algebraic expression that represent the situation

solve for n

4n-2n=3+5

2n=8

n=4

Part 17) we have

-2(y+2)+5y=6y+11

solve for y

-2y-4+5y=6y+11

6y-5y+2y=-4-11

3y=-15

y=-5

Part 18) we have

4(3x-1)=3+8x-11

solve for x

12x-4=8x-8

12x-8x=-8+4

4x=-4

x=-1

Part 19) we have

14 - 2(3p + 1) = 6(4 + p)

 14 - 6p-2 = 24+6p ------> distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

Part 20) we have

14 - 2(3p + 1) = 6(4 + p)

step 1

distribute the -2 to the 3p and 1; distribute the 6 to the 4 and p

14 - 6p-2 = 24+6p

step 2

Group terms that contain the same variable and move the constant to the other side

6p+6p=14-2-24

step 3

Combine like terms

12p=-12

step 4

Divide by 12 both sides

p=-1

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