log3 (x+1)+log3 2x= log3 (3x+1)​

To find the roots of the quadratic equation -10x^2 + 12x - 9 = 0, we can use the quadratic formula:
x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}
where
a is the coefficient of x^2, which is -10,
b is the coefficient of x, which is 12,
c is the constant term, which is -9.
First, let's identify the coefficients in our equation:
a = -10
b = 12
c = -9
Next, we will calculate the discriminant (Δ) using the formula:
Δ = b^2 - 4ac
Plug in the values of a, b, and c:
Δ = (12)^2 - 4*(-10)*(-9)
Δ = 144 - 4 * 10 * 9
Δ = 144 - 360
Δ = -216
Since the discriminant is negative, the quadratic equation has two complex roots. We will still use the quadratic formula to find them:
x = \frac{-b ± \sqrt{Δ}}{2a}
Substitute b, Δ, and a into the formula:
x = \frac{-12 ± \sqrt{-216}}{2 * (-10)}
Now, let's split the square root of the negative discriminant into real and imaginary parts:
√(-216) = √(216) * √(-1) = 14.697 * i
where i is the imaginary unit such that i^2 = -1. Substituting this into our quadratic formula gives:
x = \frac{-12 ± 14.697i}{-20}
Now, divide both the real and imaginary parts by -20:
x₁ = \frac{-12}{-20} + \frac{14.697i}{-20}
x₂ = \frac{-12}{-20} - \frac{14.697i}{-20}
Simplify those equations:
x₁ = \frac{12}{20} - \frac{14.697i}{20}
x₂ = \frac{12}{20} + \frac{14.697i}{20}
Further simplify by reducing the fractions:
x₁ = 0.6 - 0.73485i
x₂ = 0.6 + 0.73485i
Therefore, the roots of the quadratic equation -10x^2 + 12x - 9 = 0 are approximately x₁ = 0.6 - 0.73485i and x₂ = 0.6 + 0.73485i.

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

distance between the points given from the statement:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+( y_{2}-y_{1})^{2}} \\\\d=\sqrt{(-6-0)^{2}+(-3-4)^{2}}\\ \\d=\sqrt{36+49}\\\\d=\sqrt{85}[/tex]

Answer: Then you should pay her 4$ one hour

Step-by-step explanation:

Employees who earn increased commissions as their sales increase are paid a progressive commission. This method incentivizes employees to work harder to sell more, as their commission rate increases with sales volume.

Employees whose rate of commission increases as their sales increase are paid a progressive commission. With this method of remuneration, the more sales an employee makes, the higher their rate of commission becomes. This strategy is popular with both economists and the general public because it effectively incentivizes employees to work harder and achieve higher sales, leading to an increase in the overall performance of the business.

For example, a salesperson may earn a 10% commission on sales up to $10,000. However, any sales beyond that might attract a 15% commission rate, encouraging the employee to sell more. Such progressive commission schemes are common in sales-driven industries like real estate and retail.

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Answer: [tex]x=2[/tex]

Step-by-step explanation:

The equation for inverse variation is:

[tex]x=\frac{k}{y}[/tex]

Where "k" is the constant of variation.

If you solve for for the constant "k", you get the form:

[tex]k=xy[/tex]

So, if [tex]xy=2[/tex] then [tex]k=2[/tex]

Knowing the value of "k", you can find the value of "x" when [tex]y=1[/tex], by substituting these values into the equation [tex]x=\frac{k}{y}[/tex].

Therefore, you get that the value of "x" when [tex]y=1[/tex] is:

[tex]x=\frac{2}{1}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

Answer: x=5, y=15

Step-by-step explanation:

x= cost of a chair

y= cost of a table

The cost of each table and of each chair is x=5, y=15.

We have given that,

Five tables and eight chairs cost $115 three tables and five chairs cost $70.

Determine the cost of each table and of each chair.

A variable cost is a corporate expense that changes in proportion to how much a company produces or sells.

x= cost of a chair

y= cost of a table

Therefore, The cost of each table and of each chair is x=5, y=15.

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Answer:

C - 2 2/9

Step-by-step explanation:

7 1 /2 x + 3 2/ 3 = −13

Subtract 3 2/3 from each side

7 1 /2 x + 3 2/ 3 - 3 2/3 = −13 - 3 2/3

7 1/2x = -16 2/3

Change each mixed number to an improper fraction

7 1/2 = (2*7 +1)/2 = 15/2

16 2/3 = (3*16+2)/3 = 50/3

15/2 x = -50/3

Multiply each side by 2/15 to isolate x

2/15 * 15/2 x = -50/3 * 2/15

x = -100/45

Simplify

x = -20/9

Change back to a mixed number

9 goes into 20 2 times with 2 left over

x = -2 2/9

Answer:

$4440

Step-by-step explanation:

From the question, the annual cost of the plan is $14800

The employer pays 70% 0f the cost.

⇒70/100 ×14800 =$10360

Remaining amount to pay=

14800-10360=$4440

Answer: 48

Step-by-step explanation: All you are doing is substituting x and y with the numbers it gives u then u just solve. 2 to the 4th power is 16. 4 to the 3rd power is 64 and then times .5 gives u 32. then u add and get 16+32=48

Final answer:

Miryam Williams' total pay is $3,237.50.

Explanation:

To calculate Miryam Williams' total pay, we first need to calculate her commission.

Her commission is 3.5% of her total sales, which is $92,500.

Commission = 3.5% × $92,500 = $3,237.50.

Next, we need to determine if Miryam's commission exceeds $5,000.

Since her commission is $3,237.50, it does not exceed $5,000. Therefore, she does not receive the $500 bonus.

Finally, to calculate her total pay, we sum her commission and the bonus (which is $0 in this case).

Total Pay = Commission + Bonus = $3,237.50 + $0 = $3,237.50.

Answer: 15+X=27

Step-by-step explanation: 15+X=27 X Represents How Much More Is Added

Answer:

Average mean salary [tex]=$26327.83[/tex]

Step-by-step explanation:

We have been given year and respective salaries in each year.

1960 $4,995

1970 $8,626

1980 $15,970

1990 $31,367

2000 $41,807

2010 $55,202

Now we nee do to determine the average mean salary for the six decades, 1960 – 2010.

So we just need to add all those six salaries and divide that sum by 6 to find the average mean salary.

Average mean salary [tex]=\frac{(4995+8626+15970+31367+41807+55202)}{6}[/tex]

Average mean salary [tex]=\frac{(157967)}{6}[/tex]

Average mean salary [tex]=26327.83333333[/tex]

Hence final answer is approx:

Average mean salary [tex]=$26327.83[/tex]

The answer would be 26327.83

Add up all the salaries and you will get $157,967

Then divide 157,967 by how many salaries there are which there’s 6

You will then get the answer 26327.83

Answer:

The pizza price after discount is $10.20

Step-by-step explanation:

turn 15% to decimal

0.15

multiply by $12 to find how much 15% of 15 is

12 x 0.15 = 1.8

know subtract the discount [$1.8]

12 - 1.8 = 10.2

$10.20

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Answer:

You can subtract the discount percent from 100% and then multiply that by the original price.

Steps

1. Subtract the discount percent from 100%.

2. 100% – 15% = 85%

3. Multiply the original price by this percent.

4. The discounted price is $10.20.

Answer:

X= 20

Step-by-step explanation:

4x + 8 = 88

4x +8 - 8 = 88 - 8

4x = 80

4x/4 = 80/4

X = 20

For this case we must find the value of "x" of the following linear equation:

[tex]4x + 8 = 88[/tex]

We subtract 8 on both sides of the equation:

[tex]4x = 88-8\\4x = 80[/tex]

We divide between 4 on both sides of the equation:

[tex]\frac {4x} {4} = \frac {80} {4}\\x = 20[/tex]

So, the value of x is 20

Answer:

[tex]x = 20[/tex]

Answer:

-1

Step-by-step explanation:

The midline is the average of the maximum and minum.

0.5 = (y + 2) / 2

1 = y + 2

y = -1

The minimum is at y=-1.

For the given problem the value of ymin is -1.

Suppose maximum is denoted by ymax and minimum is denoted by ymin ymid represents the mid.

By mid point theorem y

mid   = (ymax + ymin)/2

Given ymid  = 0.5

         ymax  = 2

          ymin  = y

substituing values 0.5 = (2+ y)/21 = 2+yy = -1

yminimum  = -1

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Answer:

The Correct answer is: 1/3

Step-by-step explanation:

x = 2, y = 3

(4x + 1) / 3y²

(4*2 + 1) / 3*3²

(8 + 1) / (3*9)

9 / 27

= 1/3

Answer:

It would be Symmetric,

Uniform is when all of the lines are almost lined up perfectly with each other.

Symmetric is when the lines are in a mountain formation with both sides looking the same

Skewed it where one side will look very steep and the other side looks like a hill

Answer:

The answer is B. symmetric

Step-by-step explanation:

A symmetric distribution is one in which the two halves of the histogram appear as mirror-images of one another. So, this histogram is symmetric.

A "skewed left" or "skewed right" distribution is one in which the tail is on the left side or on the right side.

A uniform histogram has almost same height bars. This means that the data has approximately the same number of values in each group.

Answer:

85°

Step-by-step explanation:

Since you know that the overall angle measure for the whole shape is 540°, you can subtract the known angles measures to find the right one.

540-90

450-90

360-115

245-160

85

Answer:

1.  mean

2. mode

3. range

4. measures of central tendency

5. outliers

6. median

good luck

Step-by-step explanation:

Answer:

Mean

Mode

Range

Measures of Central Tendency

Outliers

Median

Step-by-step explanation:

Just did the USTP got a 100%

Hello,

You're asking: (3^5−3^4)(3^3+3^2)/24.

First, start with the three. (3^5)

(243−3^4)(3^3+3^2)/24

Do the 3 to the power of 4.

(243−81)(3^3+3^2)

Subtract 243-81 to 162.

162(3^3+3^2)/24

Do 3^3 to get 27.

162(27+32)/24

Then, do 3^2 to 9.

162(27+9)/24.

Add 27+9 to get 36 then set up multiplication.

(162)(36)/24

Multiply.

5832/24

Divide.

Therefore, you get 243 as your final answer.

Answer:

Since we can see that angle L and angle C are supplementary angles, we have the following equation:

∠C + ∠L = 180°

Therefore to find the measurement of angle C, we need to subjact the measurement of angle C from 180°:

∠L = 180° - ∠C

Answer:Angle L and angle C are supplementary angles. The sum of supplementary angles is 180°. So, I can find the measurement of angle L by subtracting the measurement of angle C from 180°.

Step-by-step explanation:

Final answer:

The conference rooms can accommodate approximately 34 attendees each, and the ballrooms can accommodate approximately 31 attendees each.

Explanation:

To find out how many attendees each room can accommodate, we need to divide the total number of attendees by the total number of rooms.

For the quarterly meeting, there are 2 conference rooms and 5 ballrooms, which can seat a total of 238 attendees. To find out how many attendees each room can accommodate, we divide 238 by 7 (2 + 5), which gives us approximately 34 attendees per room.

For the safety training event, there are 4 conference rooms and 5 ballrooms, which can seat a total of 286 attendees. Dividing 286 by 9 (4 + 5) gives us approximately 31 attendees per room.

Answer:

(D.) 6h + 26 > 80

Step-by-step explanation:

$6 an hour + the $26 > the $80 needed to buy the skis

The inequality represents the number of hours (h) Linda could babysit to earn at least enough money to buy the ski pass is 6h+26>80. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Linda has $26. She wants to buy a ski pass for $80.

Let the number of hours Linda worked in babysitting be h.

Now, the inequality is

6h+26>80

The inequality represents the number of hours (h) Linda could babysit to earn at least enough money to buy the ski pass is 6h+26>80. Therefore, option D is the correct answer.

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Answer:

4. 54- 8.5x>20

Step-by-step explanation:

Catherine only has $54, so she cannot spend more than that.

The canvas will cost at least $20, but we don't know how much exactly.

The tubes cost $8.50 each.

So, she starts with a total budget of $54, out of which she will buy paints (8.5x) and she wants to have at least $20 left for canvas.

So, we transpose those facts into the inequity:

54 - 8.5x > 20

Answer:

Opcion 4

[tex]54- 8.5x>20[/tex]

Step-by-step explanation:

We must identify the quantities.

Painting canvas

more than $ 20

Paint tubes (x):

$ 8.50 per tube = 8.50x

Available money:

$ 54

Then the expenses must not exceed $ 54, and the budget for the painting canvas must be greater than $ 20

The money after buying the paint tubes is:

[tex]54-8.50x[/tex]

We know that this amount must be greater than $ 20 because you need to buy the painting canvas. So  the inequality is:

[tex]54-8.50x> 20[/tex]

Using Pythagorean theorem, for the 8-feet wide picture window to pass through the 3-feet wide door, the door must be at least approximately 7.4 feet tall.

The picture window here is a rectangular sheet of glass. The longer side (8 feet) must fit through the door. The door is only 3 feet wide, which means that the 8-foot side of the window must be angled to pass through the door in vertical orientation.

To calculate the height of the door needed, consider the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of two sides (a2 + b2 = c2). Here 'a' is the width of the door (3 feet) and 'c' is the diagonal length of the window (8 feet). Solving for 'b' which represents the door's required height, we get:

b2 = c2 - a2

b2 = 82 - 32

b = sqrt(64 - 9) = sqrt(55)

Therefore, b is approximately 7.4 feet.

So the door must be at least 7.4 feet tall to pass the 8-feet picture window through it when angled vertically.

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The door needs to be approximately 21.3 feet tall for the glass to pass through.

To determine the height of the door, we need to consider that the glass is 8 feet wide. Since the door is only 3 feet wide, the glass needs to fit through a smaller opening. We can use similar triangles to find the height of the door. Let's set up a proportion:

8 / 3 = H / 8

Cross-multiplying, we get:

3H = 64

H = 64/3

Therefore, the door needs to be approximately 21.3 feet tall for the glass to pass through.

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Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

[tex]y = 4x + 1  (i)[/tex]

[tex]y = x^2 + 2x -2 (ii)[/tex]

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

[tex]4x+1=x^2 + 2x -2[/tex]

[tex]0=x^2 + 2x -2-4x-1[/tex]

[tex]0=x^2 + (2x -4x) +(-2-1)[/tex]

[tex]0=x^2 + (-2x) +(-3)[/tex]

[tex]0=x^2 -2x -3[/tex]

[tex]x^2 -2x -3 = 0 (iii)[/tex]

Now by factorization, equation iii can be written as

[tex]x^2 -3x +x -3 = 0[/tex]

[tex]x(x -3) + 1(x -3) = 0[/tex]

[tex](x -3)(x +1) = 0[/tex]

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Answer: 32 Quilts and you will have 11 squares left over

Step-by-step explanation:

Answer:

Here, the given expression is,

  ( By the cross multiplication ),

Since, an extraneous solution is a solution, which is emerged by solving the equation but it does not satisfying the equation,

But for x = -3, the equation  follows,

⇒ x = -3 is the non-extraneous,

⇒ The given equation has only one solution x = -3 which is non-extraneous.

Step-by-step explanation:

Answer:

x = -3 is not extraneous solution.

Step-by-step explanation:

[tex]\frac{6}{x-3} =\frac{3}{x}\\Cross\,\, Multiply\\6x =3(x-3)\\6x = 3x-9\\6x-3x=-9\\3x= -9\\x=-9/3\\x=-3[/tex]

An extraneous solution is the solution that is obtained by solving the question given but does not satisfy the original equation.

In our case x = -3

Putting value back to the original equation

[tex]\frac{6}{x-3} =\frac{3}{x}\\\frac{6}{-3-3} =\frac{3}{-3}\\\frac{6}{-6} =-1\\-1=-1[/tex]

Since our original equation is satisfied so,

x = -3 is not extraneous solution.

There will be a second image that will be showing the answer

Answer:

x = -1

Step-by-step explanation:

[tex] x^2 + 2x + 5 = 4 [/tex]

Subtract the constant term.

[tex] x^2 + 2x = -1 [/tex]

Add half of the coefficient of the x-term to complete the square.

[tex] x^2 + 2x + 1 = -1 + 1 [/tex]

[tex] (x + 1)^2 = 0 [/tex]

[tex] x + 1 = 0 [/tex]

[tex] x = -1 [/tex]

Answer:

30

Step-by-step explanation:

If we get 40% off, we still have to pay 100-40% = 60%

Take the original price * the percent we have to pay

50 * 60%

Change to decimal form

50 *.6

30

We have to pay $30

Answer:

f(x) = (x + 4)² - 3

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² + 8x + 13

To obtain f(x) in vertex form use the method of completing the square

add/ subtract (half the coefficient of the x- term)² to x² + 8x

f(x) = x² + 2(4)x + 16 - 16 + 13

f(x) = (x + 4)² - 3 ← in vertex form