A student is solving the problem |2−9x|=29. They know that one answer can be found by solving the equation 2−9x = 29. They subtract 2 to get −9x=27 and then divide by -9 to get x=−3. They think that this is one answer, and then take the absolute value of this to get their other answer of x=3. Did this student solve this problem correctly? If so, how can you show that they got it correct. If not, what mistake did they make and what should they have done instead?

The total surface area of the television is 21,584 square centimeters.

To find the total surface area of the television, we need to calculate the area of all six sides and add them up.

The front and back sides have the same dimensions and area, so we can find the area of one and multiply it by two. The same goes for the left and right sides.

The area of the front/back sides is:

120 cm x 68 cm = 8160 sq cm

Multiplying by 2 gives us the total area of both front/back sides:

2 x 8160 sq cm = 16,320 sq cm

The area of the left/right sides is:

68 cm x 14 cm = 952 sq cm

Multiplying by 2 gives us the total area of both left/right sides:

2 x 952 sq cm = 1904 sq cm

The area of the top and bottom sides is:

120 cm x 14 cm = 1680 sq cm

Multiplying by 2 gives us the total area of both top/bottom sides:

2 x 1680 sq cm = 3360 sq cm

Adding up all six sides, we get:

16,320 sq cm + 1904 sq cm + 3360 sq cm = 21,584 sq cm

Therefore, the total surface area of the television is 21,584 square centimeters.

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To find f'(-2), we need to first find the derivative of f(x) using the chain rule.

f'(x) = (1/(5x² + 20x + 1)) * (10x + 20)

Then, we can plug in x = -2 to get f'(-2):

f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)

f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)

f'(-2) = 0

Therefore, f'(-2) is equal to 0.

To find f'(-2) for f(x) = ln(5x² + 20x + 1), we first need to find the derivative of f(x) using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

1. Let u = 5x² + 20x + 1. Then, f(x) = ln(u).
2. Find the derivative of f(x) with respect to u: f'(x) = d[ln(u)]/du = 1/u.
3. Find the derivative of u with respect to x: du/dx = d(5x² + 20x + 1)/dx = 10x + 20.
4. Apply the chain rule: f'(x) = (1/u) * (du/dx) = (1/(5x² + 20x + 1)) * (10x + 20).

Now, to find f'(-2), simply substitute -2 for x in the derivative:

f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = (1/(-19)) * 0

Since any number multiplied by 0 is 0, we have:

f'(-2) = 0.000

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Answer:

A = 28 units²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = FG = 8 and h = FE = 7 , then

A = [tex]\frac{1}{2}[/tex] × 8 × 7 = 4 × 7 = 28 units²

To calculate the net sales, we need to subtract the discounts, sales returns and allowances, and freight in from the gross sales.

Therefore, we have:

Net sales = Gross sales - Discounts - Sales returns and allowances - Freight in

Substituting the given values, we get:

Net sales = $50,000 - $1,800 - $4,380 - $2,750 = $41,070

Therefore, the net sales of the company are $41,070. Answer: (d).

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The expression for the length of one side of the square is: 5x + 8.

To see why, note that the area of a square is given by side squared, so we can set up an equation:

[tex]side^2 = 25x^2 + 80x + 64[/tex]

Taking the square root of both sides, we get:

[tex]side =[/tex] √ [tex](25x^2 + 80x + 64)[/tex]

Simplifying the square root, we get:

side = √[(5x + 8)(5x + 8)]

And finally, we can take the square root of the perfect square to get:

side = 5x + 8.

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The total amount the customer still owe is $38.25. Customer: "I prepaid 70% of the total cost of $127.50 last week."
Employee: "Okay. The total you still owe is $38.25."

Here the customer prepaid 70% of total cost of $127.50 last week and the employee need to replay how much amount the customer still owe is. To find out the total amount the customer still owes after prepaying 70% of the total cost of $127.50,

So the total amount the customer still owe is $38.25.

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The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.

Area = (1/2) * (Base1 + Base2) * Height

In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.

Plugging in the known values into the formula:

337.5 = (1/2) * (25 + 20) * Height

Simplifying the expression:

337.5 = (1/2) * (45) * Height

Multiplying both sides of the equation by 2 to get rid of the fraction:

675 = 45 * Height

Dividing both sides by 45 to solve for the height:

Height = 675 / 45

Height = 15 ft

Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.

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a. The equation is Total Cost = 0.75x + $600

b. Total cost is $60,600 and net profit is $19,400.

c. The breakeven level of sales volume is $2,400.

a. The equation relating total cost and sales volume can be expressed as:

Total Cost = Cost of Goods Sold + Selling Expenses + Fixed Expenses

where Cost of Goods Sold = 60% (100% - 40%) of the sales volume

           Selling Expenses = 15% of the sales volume

           Fixed Expenses = $600.

Therefore, the equation can be written as:

Total Cost = 0.6x + 0.15x + $600
                 = 0.75x + $600

b. For sales of $80,000, we can substitute x = $80,000 into the equation:

Total Cost = 0.75x + $600
                 = 0.75($80,000) + $600
                 = $60,000 + $600
                 = $60,600

To calculate net profit before taxes, we need to subtract the total cost from the sales volume:

Net Profit before Taxes = Sales - Total Cost
                                       = $80,000 - $60,600
                                       = $19,400

c. To find the breakeven level of sales volume, we need to set the net profit before taxes to zero and solve for x:

Net Profit before Taxes = Sales - Total Cost
               0                      = x - (0.6x + 0.15x + $600)
               0                      = 0.25x - $600
            0.25x                  = $600
               x                       = $2,400

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Paul and Marlena should deposit approximately $2,431.23 into an account now to have enough for their cruise in ten years.

So, the correct answer is B. $2,431.23.

To calculate the amount Paul and Marlena should deposit into an account now in order to have enough for their cruise in ten years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{ (nt)}[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times that interest is compounded per year

t = the number of years

In this case, the principal amount (P) is what we need to find.

The future value (A) is given as $5,800.

The interest rate (r) is 5.3% or 0.053 as a decimal.

The interest is compounded daily, so n = 365 (number of days in a year).

Using the formula, we can rearrange it to solve for P:

[tex]P = A / (1 + r/n)^{(nt)[/tex]

Substituting the given values:

[tex]P = 5800 / (1 + 0.053/365)^{(365\times 10)[/tex]

Calculating this expression:

P ≈ 2,431.23

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The slope of the line is 5,520 and it means the price of the diamond increases at a rate of 5,520 per diamond's weight.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this situation, it can be modeled by this linear equation:

y = mx + c

y = 5,520x - 1,091

By comparison, we have the following:

Slope, m = 5,520.

y-intercept, c = -1,091.

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Complete Question:

The function described by the equation y =5,520x - 1,091 is a model of the relationship between a diamond's weight and its price. What does the slope of the line mean in the context of this problem?

According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.

Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.

Cost of teddy bear × number + cost of dolls × number = total expenditure

14x + 3y = 158 : equation 1

8x + 12y = 296 : equation 2

Divide the equation by 4

2x + 3y = 74 : equation 3

Subtraction equation 3 from equation 1

14x + 3y = 158

- 2x + 3y = 74

12x = 84

x = 84/12

x = $7

So, the cost of teddy bear = $7

keep the value of x in equation 3 to find the cost of y

2×7 + 3y = 74

14 + 3y = 74

3y = 74 - 14

3y = 60

y = 60/3

y = $20

Thus, the cost of teddy bear and dolls are $7 and $20.

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The statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number

From the question, we have the following parameters that can be used in our computation:

13 + √50

When the above expression is evaluated we have

13 + √50 = 20.0710678119

The above result (20.0710678119) is an irrational number

This is because the number 20.0710678119 cannot be expressed as a ratio of two integers

Hence, the statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number

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Answer:

BCA

Step-by-step explanation:

The interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

Let's label the stages A, B, and C. To find the interior angles at each stage, we can use the Law of Cosines:

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (c^2 + a^2 - b^2) / 2ca

cos(C) = (a^2 + b^2 - c^2) / 2ab

where a, b, and c are the distances between the centers of the stages.

Using the given distances, we have:

a = 100, b = 135, c = 210

cos(A) = (135^2 + 210^2 - 100^2) / (2*135*210) ≈ 0.309

cos(B) = (210^2 + 100^2 - 135^2) / (2*210*100) ≈ -0.692

cos(C) = (100^2 + 135^2 - 210^2) / (2*100*135) ≈ -0.905

To find the interior angles, we can take the inverse cosine (also known as arccosine) of each value:

A ≈ 71.7 degrees

B ≈ 133.4 degrees

C ≈ 175.0 degrees

So the interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

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Luna and her friend Maka decided to make sandwiches using 1/3 of a baguette. To ensure fairness, they agreed to divide the baguette equally between them. They carefully measured the baguette and cut it into two equal parts, ensuring each of them received an equal portion.

Luna and Maka then began assembling their sandwiches. They spread their preferred fillings on their respective portions of the baguette, adding layers of vegetables, meats, and condiments to create delicious sandwiches.

After completing their sandwich preparation, Luna and Maka sat down together to enjoy their culinary creations. They appreciated the taste and quality of their sandwiches, delighted by the shared experience and the equal distribution of the baguette.

As they savored each bite, Luna and Maka cherished their friendship and the simple joy of sharing a meal together. They found contentment in the realization that even the smallest things, like a shared baguette, could strengthen their bond and create lasting memories.

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Answer: I think you can easily do this yourself :)
Look up the definition of all the answers, and it'll lead you straight to the answer :D
I remember doing algebra, and it seemed really hard, but once it's all over you'll be like "oooh it makes so much sense looking back on it"

Step-by-step explanation:

The correct point which is solution of equation of line is,

⇒ (1, 2)

We have to given that;

Equation of line is,

⇒ 3x - y = 1

Take a point 2,

⇒ (1, 2) = (x, y)

Plug into above equation of line is,

⇒ 3x - y = 1

⇒ 3 x 1 - 2 = 1

⇒ 3 - 2 = 1

⇒ 1 = 1

Thus, The correct point which is solution of equation of line is,

⇒ (1, 2)

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The correct statement regarding the solution to the system of equations is given as follows:

4) (2, 1) is the solution to both lines A and B.

The system of equations in the context of this problem is defined as follows:

Replacing the second equation into the first, the value of x is obtained as follows:

-3x + 7 = x - 1

4x = 8

x = 2.

Hence the value of y is given as follows:

y = 2 - 1

y = 1.

Meaning that point (2,1) is a solution to both lines.

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After 50 minutes, you will have placed 675 pieces

Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.

We can start by finding the number of pieces you place in 50 minutes.

Every minute, you place 10 more pieces, so in 50 minutes, you will place:

10 x 50 = 500 pieces

Adding the pieces you have already placed, we get:

175 + 500 = 675 pieces

Therefore, after 50 minutes, you will have placed 675 pieces

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The difference in overall gain is $280.10. OPtion C

We have to first find the gains for Stock A and Stock B at high and low prices:

Stock A:

High price gain: 115 * ($105.19 - $90) = $1,747.85

Low price gain: 115 * ($103.25 - $90) = $1,523.75

Stock B:

High price gain: 30 * ($145.18 - $145) = $5.40

Low price gain: 30 * ($143.28 - $145) = -$51.60

Calculate total gains:

High price total gain: $1,747.85 + $5.40 = $1,753.25

Low price total gain: $1,523.75 + (-$51.60) = $1,472.15

Difference in overall gain: $1,753.25 - $1,472.15 = $280.10

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The Midpoint of AB  ((x1 + x2)/2, (y1 + y2)/2) lies on the perpendicular bisector of AB.

Assuming that chord AB is a straight line segment, the point that lies on the perpendicular bisector of AB is the midpoint of AB. This is because the perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it.

Therefore, to find the point that lies on the perpendicular bisector of chord AB, we need to find the midpoint of AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B, respectively.

Let (x1, y1) and (x2, y2) be the coordinates of points A and B, respectively. Then the midpoint of AB is:

((x1 + x2)/2, (y1 + y2)/2)

This point lies on the perpendicular bisector of AB.

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The child can make 120 different bracelets using one of each charm. To solve this problem, we need to use a combinatorial approach.

The number of different bracelets that the child can make depends on the number of charms that can be used for each bracelet & the order in which they are arranged. Since each charm can be used only once, we have to choose five charms out of the total of five available charms, which can be done in 5C5 ways.

We can think of this problem as a permutation problem. There are five distinct charms, and we need to choose five of them to make a bracelet. The order in which we choose the charms matters, as each order gives us a different bracelet. Therefore, we need to use the formula for permutations.

The formula for permutations is given by:

nPr = n! / (n-r)!

where n is the total number of objects, and r is the number of objects we want to choose.

For this problem, n = 5 (since there are five distinct charms), and r = 5 (since we want to choose all five charms).

Plugging these values into the formula, we get:

5P5 = 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 / 1 = 120

Therefore, the child can make 120 different bracelets.

Alternatively, we can also think of this problem as a multiplication principle problem. There are five distinct charms, & we need to choose one charm out of five for the first position, one charm out of four for the second position, one charm out of three for the third position, one charm out of two for the fourth position, & one charm out of one for the fifth position.

Using the multiplication principle, we can multiply these numbers together to get the total number of different bracelets:

5 x 4 x 3 x 2 x 1 = 120

Therefore, the child can make 120 different bracelets using one of each charm.

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Answer:

(4,6) on the coordinate plane is the 1st quadrant. You start at the origin, go 4 to the right and 6 up.

Hope this helped !!

The cylindrical storage container can hold 549.5 cubic inches of cat litter.

To find the volume of the cylindrical storage container, we need to use the formula:

V = πr²h

Where:

π is a constant approximately equal to 3.14

r is the radius of the container

h is the height of the container

Substituting the given values, we get:

V = 3.14 x 5² x 7

V = 549.5 cubic inches

Since we know that the  vessel can hold549.5 boxy  elevation of cat  waste, we can use this value to determine how  important cat  waste can fit in the  vessel in other units.   For  illustration, if we want to know how  numerous liters of cat  waste can fit in the  vessel, we can convert boxy  elevation to liters using the conversion factor 1 liter = 61.02 boxy  elevation.   boxy  elevation61.02 boxy  elevation per liter = 8.998 liters   thus, the spherical  storehouse  vessel can hold  roughly 9 liters of cat  waste.

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The length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm

Rhombus is a special type of parallelogram in which all four sides are congruent. The opposite angles of a rhombus are also congruent, and the diagonals bisect each other at right angles.

Now, let's consider the given rhombus abcd, where ad = 8cm and m∠ade=20°. We need to determine the length of diagonals ac and bd.

First, let's use the law of cosines to find the length of side ae. We know that ad = 8cm, and m∠ade=20°, so we can use the formula:

ae² = ad² + de² - 2ad(de)cos(m∠ade)

Substituting the values, we get:

ae² = 8² + de² - 2(8)(de)cos(20°)

Next, we can use the fact that a rhombus has all sides congruent to find the length of side de. Since abcd is a rhombus, we know that ac and bd are also congruent diagonals that bisect each other at right angles. Therefore, we can draw diagonal ac and use the Pythagorean theorem to find the length of ac:

ac² = (ae/2)² + (de/2)²

Substituting ae² from the previous equation, we get:

ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²

Simplifying the equation and using the fact that ac and bd are congruent, we get:

bd² = ac² = (8² + de² - 2(8)(de)cos(20°))/2

Finally, we can use the Pythagorean theorem to find the length of diagonal bd:

bd² = ab² + ad²

Substituting ab = ac/2 and ad = 8cm, we get:

bd² = (ac/2)² + 8²

Substituting ac² from the previous equation, we get:

bd² = ((8² + de² - 2(8)(de)cos(20°))/8)² + 8²

Simplifying the equation, we get:

bd ≈ 12.22 cm

Similarly, we can solve for ac using the equation we derived earlier:

ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²

Substituting de ≈ 9.84cm (which we can solve for from the equation ae² = 8² + de² - 2ad(de)cos(m∠ade)), we get:

ac ≈ 15.58 cm

Therefore, the length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm

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Answer:

---------------------------

The given point (0, 5) represents the y-intercept and we have a slope of -1.

It translates as:

By substituting we get equation:

This is option C.

(a) The expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3).

(b) The least possible integer value of x for the rectangular solid to exist is 4.

a. To express the length, width, and height of the right rectangular prism in terms of x, we can factor the volume expression, 6x³ - 3x² - 45x.

Factoring out the greatest common factor, 3x:

3x(2x² - x - 15)

Now, factor the quadratic expression:

3x(2x² - x - 15)

To factor the quadratic expression further, find two numbers whose product equals the constant term (-15) and whose sum equals the coefficient of the linear term (-1). These two numbers are -5 and 3.

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

Thus, the expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3)

b. For the rectangular solid to exist, all dimensions (length, width, and height) must be positive. Let's examine the constraints on x for each dimension:

1. 3x > 0
2. 2x + 5 > 0 → x > -5/2
3. x - 3 > 0 → x > 3

Since x must satisfy all three inequalities, the least possible integer value of x for the rectangular solid to exist is x = 4.

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The price of the advertisement that originally costs $110 after a 15% markdown is $ 83.5.

Original price = $110

Markdown percent = 15%

Reduce in price = 15% of 110

To calculate this, we divide the percent by 100 and multiply it by the number given. Like in the above case, we divide 15 by 100 to get 0.15 and multiply it by 110.

= 0.15 * 110 = 16.5

Price after markdown = original price - reduction in price

= 110 - 16.5

= $ 83.5

Thus, the price for a quarter-page ad of the school yearbook which used to be $110 has come down to $83.5 after a 15 % markdown to attract more sponsors.

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