Which line shows the first error in the solution 6(x+2)=24

Answers

Answer 1

Answer: Line 4. 12 would be divided by 6, not multiplied.

Answer 2

Answer: the 4th line show the first error

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A cereal box is 19 centimeters long, 6 centimeters wide and 28 centimeters high. An artist is trying to create a design for the box. What is the surface area the artist needs to cover?

Answers

Surface area = Lateral area + Area of the base
Surface area = Perimeter of the base x high + 19 x 6
Surface area = (19+19+6+6) x 28 + 114
Surface area = 50 x 28 + 114
Surface area = 1544 centimeter square

If f(x) = -(x + 1)2 + 9, what is f(-2)?

Answers

Step-by-step explanation:

$f(x) = - (x + 12) \n plugging \: x = - 2 \n f( - 2) = - ( - 2 + 12) \n f( - 2) = - (10) \n \huge \red{ \boxed{ f( - 2) = - 10}} \n$

Carl Tinsley earns $1,970 per month. His family insurance plan costs $4,450 per year. His employer pays 66 percenof the cost. If this is his only deduction, how much is his
monthly paycheck after the medical insurance deduction
(rounded to the nearest dollar)? *

Answers

Answer:

$1,843.92

Step-by-step explanation:

4450/33%=1513

1513/12=126.083

1970-126.08=1843.92

Please help! Its for my big test tomorrow!

Answers

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m × b^n = b^(m + n) ⇒ in multiplication if they have same base

we add the power

2- b^m ÷ b^n = b^(m – n) ⇒ in division if they have same base we

subtract the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same

power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m) (for all nonzero real numbers b) ⇒ If we have

negative power we reciprocal the base to get positive power

6- If a^m = a^n , then m = n ⇒ equal bases get equal powers

7- If a^m = b^m , then a = b or m = 0

# Logarithmic rules:

1- $log_(a)b=n-----a^(n)=b$

2- $loga_(1)=0---log_(a)a=1---ln(e)=1$

3- $log_(a)q+log_(a)p=log_(a)qp$

4- $log_(a)q-log_(a)p=log_(a)(q)/(p)$

5- $log_(a)q^(n)=nlog_(a)q$

* Now lets solve the problems

# $3^(x+1)=9^(x+3)$

- Change the base 9 to 3²

∴ $9^(x+3)=3^(2(x+3))=3^(2x+6)$

∴ $3^(x+1)=3^(2x+6)$

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# $log_(6)(5x+4)=2$

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# $log_(2)x+log_(2)(x-3)=2$

- Use the rule 3 in the logarithmic equation

∴ $log_(2)x(x-3)=2$

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

of x in the given equation we will find $log_(2)(-1)$ and this

value is undefined, there is no logarithm for negative number

* The solution is x = 4

# $log_(4)11.2=x$

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# $2e^(8x)=9.2$ ⇒ divide the both sides by 2

∴ $e^(8x)=4.6$

- Insert ln for both sides

∴ $lne^(8x)=ln(4.6)$

- Use the rule $ln(e^(n))=nln(e)$ ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

QUESTION 1

${3}^(x + 1) = {9}^(x + 3)$

This is the same as:

${3}^(x + 1) = {3}^(2(x + 3))$

Equate the exponents.

x+1=2(x+3)

Expand:

x+1=2x+6

Group similar terms;

2x-x=1-6

x=-5

QUESTION 2

$log(9x - 2) = log(4x + 3)$

Equate the arguments.

9x-2=4x+3

Group similar terms;

9x-4x=3+2

5x=5

Divide through by 5

x=1

QUESTION 3

$log_(6)(5x + 4) = 2$

Take antilogarithm to obtain,

$5x + 4 = {6}^(2)$

This implies that,

5x+4=36

5x=36-4

5x=32

x=32/5

$x = 6 (2)/(5)$

QUESTION 4

$log_(2)(x) + log_(2)(x - 3) = 2$

Use the product rule of logarithms:

$log_(2)x(x - 3) = 2$

Take antilogarithm,

${x}^(2) - 3x = {2}^(2)$

${x}^(2) - 3x - 4 = 0$

Factor:

$(x + 1)(x - 4) = 0$

This implies that,

$x = - 1 \: or \: x = 4$

But the domain is x>0, therefore the solution is

x=4

QUESTION 5

$x=\log_(4)(11.2)$

$x=\log_(4)((56)/(5))$

$x=\log_(4)(56)-\log_(4)(5)$

x=1.7 to the nearest tenth.

QUESTION 6

$2e^(8x)=9.2$

Divide both sides by 2.

$e^(8x)=4.6$

Take natural log of both sides

${8x}=\ln(4.6)$

${x}=\ln(4.6)/ 8$

x=0.2 to the nearest tenth.

WILL MARK BRAINLIEST IF CORRECT!!! plz help I don’t understand at all & missed a week of school because I was sick. Find m

Answers

Answer:

23 degrees

Step-by-step explanation:

A straight line = 180 degrees, and there's a 90 degree angle on the left side, so (2x+14) + (x+7) = 90.

Then, just solve the equation.

3x + 21 = 90

3x = 69

x = 23

Therefore, m = 23 degrees

Answer:

23 degrees

Step-by-step explanation:

A straight line = 180 degrees, and there's a 90 degree angle on the left side, so (2x+14) + (x+7) = 90.

Then, just solve the equation.

3x + 21 = 90

3x = 69

x = 23

Therefore, m = 23 degrees

Al runs 8 miles per hour. Bob runs 1 mile in 8 minutes. Carl runs 2 miles in 15 minutes. Dan runs 1/2 of a mile in 3.5 minutes. Who runs the fastest?

Answers

Answer:Dan

Step-by-step explanation:

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