Hardcover books cost $8 and paperbacks cost $3. John buys 15 books for $70. How many of each book type did he buy?

Let [tex]\( x \)[/tex] be the number of CDs. The equation representing the statement "1 more than twice as many CDs is 17" is [tex]\( 2x + 1 = 17 \).[/tex]

Let's break down the statement into a mathematical expression. "Twice as many CDs" is represented by [tex]\( 2x \)[/tex]. Adding "1 more than" to this gives [tex]\( 2x + 1 \)[/tex]. Finally, the statement "is 17" translates to [tex]\( 2x + 1 = 17 \),[/tex] creating the equation that represents the given information.

The complete question is: Explain the statement "1 more than twice as many CDs is 17"

Answer:

The area of ABCD = 12² = 12 * 12 = 144 m²

Step-by-step explanation:

Given that ABCD in the model, is a square.

All the edges of the pyramid in the model have length 12m.

So, the length of one side of the square = 12 m

The area of the square = (side length)²

∴ the area of ABCD = 12² = 12 * 12 = 144 m²

Answer:

Its 144m^2

Step-by-step explanation:

Answer: $115

Step-by-step explanation:

The overhead cost for the insurance company to insure a driver, given a 4.2% accident probability and an average accident cost of $29,500, with the premium of $1,354, is $115.

The subject matter is on determining the overhead cost for an insurance company. The probability of a driver having an accident is 4.2% or 0.042 in decimal. The cost of an accident is $29,500. Therefore, the expected cost of a claim is 0.042 * $29,500 = $1,239. The insurance premium paid by the driver is $1,354. The overhead cost for the company is the premium minus the expected cost of claim. So, the overhead cost is $1,354 - $1,239 = $115. Therefore, the answer is C. $115

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Answer:

It'd be easier to explain if you gave an example, but when it asks what equivalent fractions are being represented in the shaded area , it's asking how much is shaded. So if you have a pizza half cheese, and half pepperoni and it's asking what part is pepperoni the answer would be 1/2. I hope you understood this. If you don't send the full question.

Step-by-step explanation:

Answer:

steps in attached picture

Step-by-step explanation:

Answer:

A. x+3y =4

A. 3x-y=5

B. x+2y-z =8

B. X-Y+22 =0

B. 2X-3Y+Z =1

Step-by-step explanation:

To determine which linear systems have unique solutions, calculate the determinant of the coefficient matrix for each system.

In order to determine which of the given linear systems have unique solutions, we need to use the determinant of the coefficient matrix.

To do this, we need to calculate the determinant of the 3x3 coefficient matrix for each system:

System 1:
0x + 3y = 4
3x - y = 5
x + 2y - z = 8

Determinant = (0) (-1) (-2) + (3)(1)(1) + (1)(3)(1) - (3)(-1)(1) - (1)(3)(-2) - (0)(2)(1) = 18

Since the determinant is non-zero (18), System 1 has a unique solution.

Similarly, we can calculate the determinants for the other systems to determine their solutions.

System 2: determinant = -88

System 3: determinant = -48

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The question is worded a bit strangely (in my opinion anyway), but I think your teacher wants you to describe how exponents work.

Let's say we had the expression [tex]5^3[/tex]

The base is 5 as its the bottom most value (think of something like the base of a tree or building). The exponent is 3.

The exponent of 3 tells the reader to multiply the base 5 by itself 3 times like so

[tex]5^3 = 5*5*5 = 125[/tex]

With larger exponents, it becomes more tedious to write out all the repeated multiplications, which is why many calculators have an exponent button to save time.

An exponent signifies how many times a base is multiplied by itself. The expression "5 squared" (5²) means 5 x 5 = 25. Similarly, "5 cubed" (5³) means 5 x 5 x 5 = 125. This concept of exponentiation is essential in mathematics for representing repeated multiplication of a number.

An exponent indicates the number of times a base is multiplied by itself. For example, the exponent "2" in the expression "5²" means that the base "5" is multiplied by itself, resulting in 5 x 5 = 25. This is also known as squaring a number. Similarly, an exponent of "3" denotes cubing, which means the base is multiplied by itself three times. For instance, 5³ equals 5 x 5 x 5, which equals 125.

It's also important to understand that when we talk about exponents, we are often referring to powers. If the base is "b" and the exponent is "n", then the expression can be written as bn, indicating a chain of multiplications of "b", "n" times. For instance, witnessing an expression like (10²)³, we multiply the exponents to get a new exponent (2 x 3 = 6), resulting in 10⁶.

The concept of exponents is a foundational element in various mathematical operations and is crucial for understanding more complex mathematical concepts.

Answer:

Step-by-step explanation:

3x = 39.....so instead of just subbing in all ur answer choices....just solve for x

3x = 39...divide both sides by 3, cancelling out the 3 on the left side

x = 39/3

x = 13 <=====

Answer: 5

On god bro, Trust me

Answer: For every 5 quarts of blue, you should have 3 quarts of yellow. Since you have 25 quarts of blue in the mix (5*5), there should be 3*5 or 15 quarts of yellow. As there are only 9, you need to add 6 quarts of yellow to get the proper ratio of blue to yellow.

Step-by-step explanation:

Final answer:

To create the specific shade of green glaze, one must adjust the existing mix of 25 quarts blue and 9 quarts yellow to reach a 5:3 blue to yellow ratio. The calculation shows that an additional 6 quarts of yellow glaze are needed to achieve the desired shade.

Explanation:

To achieve the specific shade of green glaze, which is made of 5 parts blue to 3 parts yellow, we must adjust the current mixture of 25 quarts blue glaze and 9 quarts yellow glaze. We first determine the ratio of blue to yellow glaze in the current mixture:

25 quarts blue / 9 quarts yellow = approximately 2.78 parts blue to 1 part yellow.

To achieve the desired 5:3 ratio, the blue glaze needs to be reduced or the yellow glaze needs to be increased. Since removing material can be difficult, we focus on adding yellow glaze. Using the proportion method:

5 parts blue / 3 parts yellow = 25 parts blue / x parts yellow

We cross-multiply and solve for x, the amount of yellow glaze needed:

5x = 75 → x = 15

Therefore, we would need 15 parts of yellow glaze to match 25 parts of blue glaze. Since we already have 9 parts (quarts) of yellow glaze, we need to add:

15 - 9 = 6 quarts of yellow glaze.

Finally, add 6 more quarts of yellow glaze to achieve the specific shade of green glaze.

Answer:

Step-by-step explanation:

What's the question?

Answer:

I don't know how to explain the math, but I know the answer is 115 women for every 100 men.

Answer:

  about 115 women

Step-by-step explanation:

You need to raise the value on the left side of the ratio by a factor of 100/87. Multiply both numbers by that factor, and you get ...

  (100/87)(87) : (100/87)(100)

  = 100 : (10,000/87) = 100 : 114.9425...

  ≈ 100 : 115

There are about 115 women for each 100 men.

Answer:

50

Step-by-step explanation:

36 + I-14I

36 + 14

= 50

brainly plz

Answer:

50 :)

Step-by-step explanation:

Here are the solutions to the inequalities:

[tex]1. \(x < \frac{1}{4}\)[/tex]

[tex]2. \(x > 1\)[/tex]

[tex]3. \(x < \frac{1}{2}\)[/tex]

[tex]4. \(x < \frac{-1}{7}\)[/tex]

[tex]5. \(x > 15\)[/tex]

[tex]6. \(x < \frac{3}{8}\)[/tex]

[tex]7. \(s < -2\)[/tex]

[tex]8. \(s > 1\)[/tex]

[tex]9. \(t < 2\)[/tex]

[tex]10. \(x < 11\)[/tex]

[tex]11. \(x > 12\)[/tex]

[tex]12. \(x < 16\)[/tex]

[tex]13. \(r < 4\)[/tex]

[tex]14. \(s > 36\)[/tex]

[tex]15. \(x < 7\)[/tex]

Of course, I'd be happy to help you solve these inequalities! Let's go through each one step by step:

[tex]1. \(-8x + 2 > 0\)[/tex]

  First, let's isolate x:

[tex]\(-8x > -2\)[/tex]

  Divide both sides by -8, and remember to reverse the inequality sign:

[tex]\(x < \frac{-2}{-8}\) \\\(x < \frac{1}{4}\)[/tex]

[tex]2. \(+5x > x + 4\)[/tex]

  Subtract x from both sides:

[tex]\(+4x > 4\)[/tex]

  Divide both sides by 4, and remember to reverse the inequality sign:

[tex]\(x > \frac{4}{4}\) \\ \(x > 1\)[/tex]

[tex]3. \(12x + 4 < 10\)[/tex]

  Subtract 4 from both sides:

[tex]\(12x < 6\)[/tex]

  Divide both sides by 12:

[tex]\(x < \frac{6}{12}\)\\ \(x < \frac{1}{2}\)[/tex]

[tex]4. \(-10x + 5 - 4 > 4x + 3\)[/tex]

  Combine like terms:

[tex]\(-10x + 1 > 4x + 3\)[/tex]

  Subtract 1 from both sides:

[tex]\(-10x > 4x + 2\)[/tex]

  Add 10x to both sides:

[tex]\(0 > 14x + 2\)[/tex]

  Subtract 2 from both sides:

[tex]\(-2 > 14x\)[/tex]

  Divide both sides by 14, and remember to reverse the inequality sign:

[tex]\(x < \frac{-2}{14}\) \\\(x < \frac{-1}{7}\)[/tex]

[tex]5. \(6x + 5 < 7x - 10\)[/tex]

  Subtract 6x from both sides:

 [tex]\(5 < x - 10\)[/tex]

  Add 10 to both sides:

  [tex]\(15 < x\)[/tex]

6.[tex]\(24x - 4 < 8x + 2\)[/tex]

  Subtract 8x from both sides:

  [tex]\(16x - 4 < 2\)[/tex]

  Add 4 to both sides:

  [tex]\(16x < 6\)[/tex]

  Divide both sides by 16:

 [tex]\(x < \frac{6}{16}\) \\\(x < \frac{3}{8}\)[/tex]

7. [tex]\(-3s + 3 > 9\)[/tex]

  Subtract 3 from both sides:

  -3s > 6

  Divide both sides by -3, and remember to reverse the inequality sign:

  [tex]\(s < \frac{6}{-3}\) \\ \(s < -2\)[/tex]

8. [tex]\(4s + 2s > 6\)[/tex]

  Combine like terms:

  6s > 6

  Divide both sides by 6:

 [tex]\(s > \frac{6}{6}\) \\ \(s > 1\)[/tex]

9. [tex]\(6t < 12\)[/tex]

  Divide both sides by 6:

 [tex]\(t < \frac{12}{6}\)\\ \(t < 2\)[/tex]

10. 11x < 121

   Divide both sides by 11:

   [tex]\(x < \frac{121}{11}\)\\ \(x < 11\)[/tex]

11. 3x > 36

   Divide both sides by 3:

  [tex]\(x > \frac{36}{3}\) \\ \(x > 12\)[/tex]

12. 25x < 400

   Divide both sides by 25:

   [tex]\(x < \frac{400}{25}\) \\\(x < 16\)[/tex]

13. [tex]\(16r < 8(8)\)[/tex]

   Simplify the right side:

   16r < 64

   Divide both sides by 16:

   [tex]\(r < \frac{64}{16}\) \\ \(r < 4\)[/tex]

14. 6s > 216

   Divide both sides by 6:

  [tex]\(s > \frac{216}{6}\) \\ \(s > 36\)[/tex]

15. 9x < 63

   Divide both sides by 9:

  [tex]\(x < \frac{63}{9}\) \\ \(x < 7\)[/tex]

Answer:

6.601

Step-by-step explanation:

16.1(0.41)

Answer:

800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.

Step-by-step explanation:

Given:

A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat.

If the mixture is to be made from milk containing 5% butterfat, and cream

containing 20% butterfat.

Now, to find the pints of each is needed.

Let the pints of 5% butterfat be [tex]x.[/tex]

And the pints of 20% butterfat be [tex]y.[/tex]

So, the total pints of milk:

[tex]x+y=1000[/tex]

[tex]x=1000-y[/tex]  ......(1)

As, given:

1,000 pints of milk that contains 8% butterfat.

The mixture of milk containing 5% butterfat, and cream containing 20% butterfat.

According to question:

[tex]5(x)+20(y)=8(1000)[/tex]

[tex]5x+20y=8000[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex]5(1000-y)+20y=8000[/tex]

[tex]5000-5y+20y=8000[/tex]

[tex]5000+15y=8000[/tex]

Subtracting both sides by 5000 we get:

[tex]15y=3000[/tex]

Dividing both sides by 15 we get:

[tex]y=200.[/tex]

The pints of 20% butterfat = 200 pints.

Now, to get the pints of 5% butterfat we put the value of [tex]y[/tex] in equation (1):

[tex]x=1000-y[/tex]

[tex]x=1000-200[/tex]

[tex]x=800.[/tex]

The pints of 5% butterfat = 800 pints.

Therefore, 800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.

Answer:

Part A) [tex]0.12x+2,700\geq 5,400[/tex]

Part B) see the explanation

Step-by-step explanation:

Part A) Write an inequality that will represent the amount of sales Ollie will need in order to cover his monthly expenses

Let

x ----> the amount of sales monthly

Remember that

[tex]12\%=12/100=0.12[/tex]

we know that

The fixed amount of $2,700 plus the commission of 12% on all of his sales for the month must be greater than or equal to $5,400

so

The inequality that represent this problem is

[tex]0.12x+2,700\geq 5,400[/tex]

Part B) Find the solution and describe what the graph would look like on a number line

we have

[tex]0.12x+2,700\geq 5,400[/tex]

Solve for x

subtract 2,700 both sides

[tex]0.12x \geq 5,400-2,700\\0.12x \geq 2,700[/tex]

Divide by 0.12 both sides

[tex]x\geq \$22,500[/tex]

The minimum amount of sales needed to cover his monthly expenses is $22,500

In a number line the solution is the shaded area at right of x=22,500 (closed circle)

see the attached figure to better understand the problem

Answer:

2x^2 + 3x + 4

Step-by-step explanation:

generally, using long division,

(2x^3-3x^2-5x-12)/(x-3) = 2x^2 + 3x + 4

Answer:

2x^2 + 3x + 4

Step-by-step explanation:

generally, using long division,

(2x^3-3x^2-5x-12)/(x-3) = 2x^2 + 3x + 4

The diameter of a circle with a circumference of 15 meters, using 3 for pi, is 5 meters.

To determine the diameter of a circle when given its circumference and using 3 as the approximation for pi, you can use the formula for the circumference of a circle, which is C = πd, where C is the circumference and d is the diameter. Since we're using 3 for pi (π), when C = 15 meters, the formula becomes 15 = 3d. To find the diameter, divide both sides of the equation by 3, giving us d = 15 / 3, which equals 5 meters.

It sounds like D) technology is the best fit here.

Technology is used to help provide people with the things they need, for example clean water.

Answer:

First you have to find out how many he paints in 1 week.

Divide 91/7

You should then have 13 as your answer.

Then do 13 times 4 which would equal 52.

4 weeks = 52 portraits

If you want to see if it is right you can add 13 from 52 and once your at 7 you'll have 91.

Hope this helps! :)

Answer: 100 - 24x

Step-by-step explanation:

The formula for calculating the perimeter of a square is given by :

P = 4l , where l is the length of the side.

Perimeter of square A will be

P = 4 ( 2x - 7 )

P = 8x - 28

Perimeter of square B will be ;

P = 4 ( -4x + 18 )

P = - 16x + 72

Perimeter of square B - Perimeter of square A implies

-16x + 72 - ( 8x - 28 )

-16x + 72 - 8x + 28

collecting the like terms

-16x - 8x + 72 + 28

-24x + 100

⇒ 100 - 24x

Answer: one solution

Step-by-step explanation: Given :

2x + 3y = -3 ........................... equation 1

3x + 5y = -9 ........................... equation 2

Solving the system of linear equation by elimination method. We will multiply equation 1 by 3 and equation 2 by 2, then we have

6x + 9y = -9 ........................ equation 3

6x + 10y = -18 .................... equation 4

Subtract equation 3 from equation 4 , ten we have

y = -9

substitute y = -9 into equation 1 to find the value of x , that is

2x + 3y = -3

2x + 3 ( -9 ) = -3

2x - 27 = -3

2x = -3 + 27

2x = 24

x = 12

Therefore , x = 12 and y = -9 . This means that the system has one solution since there is only one value for x and one value for y

Answer:

72.64°

Step-by-step explanation:

Tan θ 16/5

θ= tan-1 (16/5)

=72.64°

The the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have given that a dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree

We have to find the angle of elevation

We can see in a figure.

What is the angle of elevation?

The angle between the horizontal line of sight and the object.

Use inverse trig because we are finding a missing angle.

use tan because we have given height of tree (one side) and a distance between dog and tree(second side)

TanΘ = opposite/adjacent

Apply inverse of tan both sides,

Θ = [tex]tan^{-1}[/tex](16/5)

Θ = 7.26

Therefore,

The the angle of elevation = 72.6 degrees

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Answer: exactly 100

Step-by-step explanation:

Answer:

500 CDs

Step-by-step explanation:

We have the ratio of [tex]15:6[/tex] for each worker. If you have a 40 hour work week, we can assume that they work 5 days a week. This means they have a 5*40=200 hours to work. If we multiply the ratio to get [tex]x:200[/tex]while it still equals our first one, we multiply and get 500 CDs.

Answer:168 minutes

Step-by-step explanation:

14 / 5=2.8 x60=168

s(t(-5)) First find t(-5), since you know x = -5, substitute/plug in -5 for x in t(x) = 5x - 4

t(x) = 5x - 4

t(-5) = 5(-5) - 4

t(-5) = -25 - 4

t(-5) = -29

s(t(-5)) plug in -29 for t(-5)

s(-29) = -3(-29) - 2 (- times a - equals a positive)

s(-29) = 87 - 2

s(-29) = 85

Your answer is 85

x = 6, you can substitute/plug in 6 for x in the expression since x equals 6

4x + 6         Plug in 6 for x

4(6) + 6

24 + 6

30

Answer:

-120

Step-by-step explanation:

-60/1/2 = -60/1 x 2

= -120/1

= -120

Answer: 27.69⁰

Step-by-step explanation:

Formula for finding the internal angle of a regular polygon is

( 2n - 4 )right angle triangle or

( 2n - 4 )90°, it can also be broken down by factorizing the expression since 2 is common,

( n - 2 )180 or supplementary

Now to find the value of n which correspond to the number of sides the polygon has, we equate the formula to the angle sum of the polygon.

( n - 2 ) × 180° = 1980°

open the bracket

180n° - 360° = 1980°

180n°            = 1980° + 360°

                    = 2340

To find n, divide by 180 which is the coefficient of n

               n   = ²³⁴⁰/₁₈₀

                    = 13

The polygon has 13, sides

To find the measure of each angle,

Recall, the sum total of external angle  = 360⁰

Therefore, to find the value of each of the angles, we divide 360 by n which is 13

                 ³⁶⁰/n

                = ³⁶⁰/₁₃

                = 27.69⁰

Answer:

Sides: 13 sides

Measure of each angle: 152.3

Step-by-step explanation:

Since we know the sum of the measures of the interior angles of a convex polygon to be 1,980, we can use the angle-sum theorem formula:

(n-2)180=?

to get our answer.

Equation:

(13-2)180 = 1,980

From here we continue using the angle sum theorem but instead with the intent of finding the measure of each individual interior angle (They will all be equal to the same degree)

Use formula

(n-2)180

     n

Equation:

(13-2)180

     13

This will give you the answer 152.3.

Sorry if this doesn't explain everything correctly or enough, but I hope I helped. :D

(Btw, if you want more of an explanation as how to properly use formulas to get the number of sides, you can go and check out the answer before mine! It really helps, this answer was mainly to just explain the second answer the way I did it that gave me the correct answer!)