What is the justification for each step in the solution of the equation?

23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12 Distributive Property
2x=6x+13
−4x=13 Addition or Subtraction Property of Equality
x=−134

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Answer:

[tex]x=+-2i\sqrt{6}[/tex]

Step-by-step explanation:

[tex]x^2+24=0[/tex]

To solve for x we need to get x alone

Subtract 24 from both sides

[tex]x^2+24=0[/tex]

[tex]x^2=-24[/tex]

Now take square root on both sides to remove the square

[tex]x^2=-24[/tex]

[tex]\sqrt{x^2} =\sqrt{-24}[/tex]

[tex]x=+-2\sqrt{-6}[/tex]

square root of -1 is 'i'

[tex]x=+-2i\sqrt{6}[/tex]

Answer:

Step-by-step explanation:

2i√6 and -2i√6 :))

Answer:

Admission to the fair = $ 18

[tex]y = 2.50x +18[/tex].

Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.

Step-by-step explanation:

The total money Henry spent was $ 55.50

If Henry only spent the money on the tickets for the rides and at the entrance to the fair, then we know that:

Bought 15 tickets at 2.5 $

Therefore the price of the admission to the fair is the total expense ($ 55.50) minus the expense in the tickets for the rides ($ 2.50 * 15)

55.50 - 15 * 2.50 = 18

So:

Admission to the fair = $ 18

Ticket for the rides = $ 2.50

So if we call y at the total cost and x the number of tickets for the rides:

[tex]y = 2.50x +18[/tex].

This is a linear equation that represents the total cost.  

Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.

To find the cost of admission to the fair, set up a linear equation using the given information: 2.5x + y = 55.50. The coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.

To find the cost of admission to the fair, we can set up a linear equation based on the given information. Let's denote the cost of the admission as y and the number of ride tickets as x. We are given that the county fair charges $2.50 per ticket, so the cost of the ride tickets would be 2.5x. Additionally, we know that Henry bought 15 ride tickets and spent a total of $55.50, so we have the equation 2.5x + y = 55.50.

The linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission is 2.5x + y = 55.50.

In this equation, the coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.

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To prime factorization would be A: 2 X 3 X 5 X 7

Because if your do 2 X 3 it would be 6

Then you do 5 X 7 it would be 35

And 6 X 35 would be 210

AND THAT IS FACTORING THE PROBLEM

[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]

[tex]\frac{(new) - (original)}{original} = \frac{\frac{3}{8}- \frac{5}{4} }{\frac{5}{4} }[/tex]

[tex]\frac{3}{8} - \frac{5}{4} (\frac{2}{2}) = \frac{3}{8} - \frac{10}{8} = \frac{-7}{8}[/tex]

 [tex]\frac{-7}{8}[/tex] ÷ [tex]\frac{5}{4}[/tex]

=  [tex]\frac{-7}{8}[/tex] * [tex]\frac{4}{5}[/tex]

= [tex]\frac{-7(4)}{8(5)}[/tex]

= [tex]\frac{-7}{2(5)}[/tex]

=  [tex]\frac{-7}{10}[/tex]

= -0.70

multiply by 100 to get the percent: - 70% (the negative represents decrease)

Answer: 70% decrease

Use the formula (n - 2) * 180 to find the sum of the interior measures of a polygon.

n stands for the number of sides that the polygon has, so substitute 10 for n since a decagon has 10 sides.

(10 - 2) * 180, start by solving inside the parentheses and subtracting 10 and 2.

(8) * 180, multiply.

B. 1,440 is your answer.

Rays are always named with two points rays

the time returning=x h,

the time going=(x-1) h,

s=t*v

s=(x-1)*50,

s=x*40,

(x-1)*50=x*40

x=5h,

s=t*v=5*50=250 miles

[tex]-18-5y\geq52\qquad|\text{add 18 to both sides}\\\\-5y\geq70\qquad|\text{change the signs}\\\\5y\leq-70\qquad|\text{divide both sides by 5}\\\\y\leq-14\\\\Answer:\ \boxed{d.\ y\leq-14}[/tex]

Explanation of how to find the remainder using long division with a polynomial expression.

Long Division Example:

We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.

Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.

Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.

Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.

Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.

The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.

To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.

We will first isolate x² by subtracting 24 from both sides of the equation:

x² = -24

Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:

x = ±√(-24)

This simplifies to:

x = ±√(24) × ±i

Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:

x = ±2√(6)i

Answer:

y = -8/7x - 3

Step-by-step explanation:

A line represents a linear relationship between x and y with constant slope and defined for all values of x and y.

Any line equation in slope intercept form would be of the form

y =mx+c where

m = slope of line

and c = y intercept

In our quesion we are given that slope of line = -8/7

and intercept = negative 3 = -3

Hence equation is

y =-8x/7-3

x > 4 is your answer

Final answer:

The trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.

Explanation:

The trinomial factorization you are asking about is -1(x - 6)(x + 8). To find out the trinomial it factors from, you need to multiply the two binomials together and then multiply by -1. Let's do this step by step:

Multiply the binomials using the FOIL method, which stands for First, Outer, Inner, Last. This gives us the following intermediate step: (x - 6)(x + 8) = x(x) + x(8) - 6(x) - 6(8)

Simplify the intermediate step: x² + 8x - 6x - 48

Combine like terms: x² + 2x - 48

Finally, multiply the entire expression by -1 to give the final trinomial: -x² - 2x + 48.

Thus, the trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.

Answer:

Step-by-step explanation:

(2005, 12,000)        (2005, 12,000)

   x1          y1                x2           y2

m= (12,250-1200) /  (2010-2005) = 250/5 = 50/1 = or 50

3 * 4 + 3 = 12 + 3 = 15

Answer: He had 15 apples.

f(x) = x2 ÷ 3 + x

f(6)

Replace X with 6 then follow order of operations.

6^2 / 3 + 6

6^2 = 36:

36 / 3 + 6

36 /3 = 12:

Add:

12 + 6 = 18

The answer is 18

Answer:

The value [fog](3) is 29.

Step-by-step explanation:

The given functions are

[tex]f(x)=2x+7[/tex]

[tex]g(x)=x^2+2[/tex]

We have to find [fog](3).

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(3)=f(g(3))[/tex]

[tex](f\circ g)(3)=f(3^2+2)[/tex]              [tex][\because g(x)=x^2+2][/tex]

[tex](f\circ g)(3)=f(11)[/tex]

[tex](f\circ g)(3)=2(11)+7[/tex]              [tex][\because f(x)=2x+7][/tex]

[tex](f\circ g)(3)=22+7[/tex]

[tex](f\circ g)(3)=29[/tex]

Therefore the value [fog](3) is 29.

An integer is close to zero if it is "small".

By small, we mean that it is small in absolute value. In fact, for any given distance [tex] d [/tex], there are two integers that are [tex] d [/tex] units away from zero: [tex]d [/tex] and [tex] -d [/tex].

So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.

So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.

All except generals

Union supported African Americans as soldiers

They worked as slaves so obviously cooks

Answer:

Step-by-step explanation:

The emancipation proclamation allowed the  African American men to serve in the Union army.

They worked as cooks. Enslaved blacks were sometimes used for camp labor also.

But they did not served as generals in the army.

Hence, the answer is :

Answer:

No

Step-by-step explanation:

11-10 = 1

He spent 1 hour more this week

Which is:

1/10 × 100 = 10% more

Marcus spent 10% more time doing homework this week. His calculation is wrong.

Time used last week by marcus = 10 hours

Time used this week by marcus = 11 hours

Difference in hours  = 11  - 10  = 1 hour

This means that Marcus used 1 more hour this week than last week

% increase = 1/10 * 100

% increase  = 10%

This shows that he spent 10% more time doing homework this week.

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2 - 3(2x + 1) < 6x(2 - 4)

2 - 6x - 3 < 12x - 24x

-1 - 6x < -12x

-1 < -6x

Dividing by -6 both sides gives you;

1/6 < x or;

Final answer is x > 1/6

Answer:

A) x ≥ 1 6

: )