There are 10 history books in a bookcase. When
the number of books increases by x percent, the
new number of history books is 24. What is the
value of x?
A) 58
B) 70
C) 120
D) 140​

The rectangle with dimensions 21 m by 21 m has the largest area among rectangles with a perimeter of 84 m.

To find the dimensions of a rectangle with a perimeter of 84 m that maximizes the area, we need to use the properties of rectangles.

Let's assume the length of the rectangle is l and the width is w.

The perimeter of a rectangle is given by the formula: 2l + 2w = P, where P is the perimeter.

In this case, the perimeter is given as 84 m, so we can write the equation as: 2l + 2w = 84.

To maximize the area, we need to find the dimensions that satisfy this equation and give the largest possible value for the area. The area of a rectangle is given by the formula: A = lw.

Now we can solve the perimeter equation for l: 2l = 84 - 2w, which simplifies to l = 42 - w.

Substituting this expression for l into the area equation, we get: A = (42 - w)w.

To maximize the area, we can find the critical points by taking the derivative of the area equation with respect to w and setting it equal to zero:

dA/dw = 42 - 2w = 0.

Solving this equation, we find w = 21.

Substituting this value of w back into the equation l = 42 - w, we get l = 42 - 21 = 21.

Therefore, the dimensions of the rectangle that maximize the area are l = 21 m and w = 21 m.

In summary, the dimensions of the rectangle are 21 m by 21 m, so the answer is A. 21, 21.

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Answer:

j=2

Step-by-step explanation:

11j - 3j = 16

Combine like terms

8j = 16

Divide each side by 8

8j/8 = 16/8

j = 2

Answer:

2

Step-by-step explanation:

11j-3j=16

subtract 11 from 3 to get 8

8j=16

divide 16 by 8 to get 2

j=2

The price elasticity of demand for x is -1.25.

Price elasticity of demand (PED) is a measure of how responsive quantity demanded is to changes in price. It is calculated as follows:

```

PED = (% change in quantity demanded)/(% change in price)

```

In this case, the price of x increases by 12% and the quantity demanded decreases by 15%. Therefore, the PED is -1.25.

A PED of -1.25 means that the quantity demanded is relatively inelastic. This means that a change in price will have a relatively small effect on quantity demanded.

The demand for x is a normal good. This means that as the price of x increases, the quantity of value demanded of x will decrease.

The demand for x is relatively inelastic. This is because the PED is -1.25, which is less than -1. A PED of -1 or less indicates that the demand is inelastic.

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Answer:

Total cost of dinner = P + 0.15p = 23

Step-by-step explanation:

Consider the information provided.

The cost of dinner at a restaurant is $P.

The tip offered for the service was, $0.15p.

The total of the cost of dinner and the tip offered for the service is:

T = P + 0.15p = 23

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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\({\huge{\boxed{\mathfrak{Question}}}\)

\(4x + 5y = 6\\5x + 4y = 5\)

The lines are

A. perpendicular.

B. parallel

C. neither

__________________________

C. Would be our answer because parallel lines never intersect

perpendicular lines form 90 degrees of all sides.

Answer:

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

Step-by-step explanation:

We want to find the equation of the line that passes through the points (0, 3) and (5, -3). The linear equation is y = (-6/5)*x + 3

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be written as:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

In this case, we know that the line passes through (0, 3) and (5, -3) then the slope is:

\(a = \frac{-3 - 3}{5 - 0} = \frac{-6}{5}\)

Then the line is:

y = (-6/5)*x + b

To get the value of b, we use the fact that the line passes through (0, 3), so we have:

3 = (-6/5)*0 + b

3 = b

Then the linear equation is just:

y = (-6/5)*x + 3

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Answer:

17.2x + 16.4

Step-by-step explanation:

→ Perimeter = All sides added together

8.6x + 3 + 8.6x + 3 + 5.2 + 5.2

→ Simplify

17.2x + 6 + 10.4

→ Simplify further

17.2x + 16.4

Answer:

50,000 Square Miles.

Step-by-step explanation:

30% = 1/3

30,000/1 * 1/3 = 10,000

10,000 * 5 = 50,000

If this question helped pls give me brainliest :) have fun

As a supervisor, if some freshmen cadets in your squad are struggling with a particular skill like the "about face,"

A supervisor is a person who oversees the work of others and ensures that tasks are completed efficiently and effectively. They are typically responsible for managing a team of employees and providing guidance and direction to help them achieve their goals.

Supervisors are essential in most industries, including manufacturing, retail, healthcare, education, and many others. They are often responsible for hiring and training new employees, setting performance expectations, and monitoring progress to ensure that goals are met. They may also be responsible for developing work schedules, coordinating team meetings, and handling employee conflicts.

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a) Based on the least amount that Austin has been charged in a month as $80.25, the possible numbers of minutes he has used his phone in a month are 102 and 103 minutes.

b) Using m for the number of minutes Austin has used his phone in a month, and solving the inequality for m, m ≥ 102.5.

Inequality is a mathematical statement that two or more algebraic expressions are unequal.

Inequalities can be represented by:

The monthly fee that Austin pays for his phone service = $29

The charge per minute of use (variable cost) = $0.5

The least amount charged Austin per month = $80.25

Let the number of minutes = m

29 + 0.5m ≥ 80.25

Solving the inequality:

29 + 0.5m ≥ 80.25

0.5m ≥ 80.25 - 29

0.5m ≥ 51.25

m ≥ 102.5

m = 102, 103

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Answer:

m∠3 = 105°

Step-by-step explanation:

Line 'l' is parallel to line 'm' and a transversal is intersecting these parallel lines at two distinct points.

m∠3 + m∠6 = 180° [Consecutive interior angles]

Since, ∠6 = 75° [Given]

m∠3 + 75° = 180°

m∠3 = 180 - 75

        = 105°

Therefore, measure of ∠3 is 105°.

In the given diagram, the measure of ∠3 is 105°

From the question,

We are to determine the measure of ∠3

In the diagram, ∠3 and ∠6 are consecutive interior angles

NOTE:

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary

That is,

∠3 + ∠6 = 180°

From the given information,

∠6 = 75°

Then, we can write that

∠3 + 75° = 180°

∠3 = 180° - 75°

∠3 = 105°

Hence, the measure of ∠3 is 105°

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Answer:

Step-by-step explanation:

Answer:

Hey bro, how u doin today? 4kt anybody safe

When the shape in the diagram rotates about the dashed line, shape 3, which is a cone with a cylindrical neck, forms a vertical section of a funnel. The correct answer is (C) Shape 3.

If the shape in the diagram rotates about the dashed line, the solid of the revolution formed will be a vertical section of a funnel, which corresponds to shape 3.

Shape 1 is a flat-top cone, which means it has a pointed top and a flat circular base. Rotating it about the dashed line would result in a solid with a pointed top and a flat circular base, resembling a cone. This does not match the description of a funnel, so shape 1 is not the correct answer.

Shape 2 is described as a 3D hexagon with a cylindrical hexagon on its top. Rotating it about the dashed line would not create a funnel shape but a more complex structure, which does not match the given description.

Shape 3 is a cone-shaped body with a cylindrical neck. When this shape is rotated about the dashed line, it will create a solid with a funnel-like shape, with a pointed top and a wider base. This matches the description provided, making shape 3 the correct answer.

Shape 4 is described as a 3D circle with a cylinder on top. Rotating it about the dashed line would not create a funnel shape, but rather a cylindrical shape with a circular base. In conclusion, the correct answer is C. Shape 3.

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Answer:

47% and 45%

Step-by-step explanation:

please mark brainiest

Based on the calculations, the volume of this pyramid is equal to 1440 cm³.

Given the following data:

Length of right triangular base = 9 centimeters and 15 centimeters.

Height of right triangular base = 32 centimeters.

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

h is the height of a pyramid.

b is the base area of a pyramid.

Substituting the parameters into the formula, we have:

Volume = 1/3 × 9 × 15 × 32

Volume = 3 × 15 × 32

Volume of pyramid = 1440 cm³.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

The result of the operation (13/2x) - (13/3x) is 13/6x.

To perform the indicated operation of (13/2x) - (13/3x), we need to find a common denominator for the two fractions.

The denominators are 2x and 3x. The least common multiple (LCM) of 2x and 3x is 6x.

Now, we need to convert the fractions so they have a common denominator of 6x.

For the first fraction, (13/2x), we need to multiply the numerator and denominator by 3 to get a denominator of 6x:
(13/2x) * (3/3) = 39/6x

For the second fraction, (13/3x), we need to multiply the numerator and denominator by 2 to get a denominator of 6x:
(13/3x) * (2/2) = 26/6x

Now that both fractions have a common denominator of 6x, we can subtract them:
(39/6x) - (26/6x) = (39 - 26)/6x = 13/6x

Therefore, the result of the operation (13/2x) - (13/3x) is 13/6x.

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Answer:

see explanation

Step-by-step explanation:

? and 110° are alternate exterior angles and are congruent , that is

? = 110°

84° and ? are alternate interior angles and are congruent , so

? = 84°

? and 100° are consecutive interior angles and sum to 180° , then

? + 100° = 180° ( subtract 100° from both sides )

? = 80°

Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = \(2^{4}\), where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

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Answer:

{ x: x€R | x≤7, x }

Step-by-step explanation:

I think they are asking set builder form for the expression

For any other explaination or enquiry pleas ask me down in comments...

Answer:

” THE TIMES they are A -changin

Step-by-step explanation:

The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The table is given below.

Then the equation of the line will be

(y – 8) = [(8 – 6) / (0 – 20)](x – 0)

       y = -0.1x + 8

If the drain is at the minimum point.

Then the distance from the wall defined by the y-axis will be 8 feet.

Then the correct option is B.

The complete question is given below.

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Answer: $576.99 in 3 years

Step-by-step explanation:

Answer:

546.36

Step-by-step explanation:

Interest rate calculator

The difference between the length and the breadth of the rectangular paper, having a perimeter of 100 cm, and an area of 600 square cm, is 10 cm.

In the question, we are given that the perimeter of rectangular paper is 100 cm and the area is 600 square cm.

We are asked to find the difference of length and breadth of the paper.

We assume the length and the breadth of the paper to be l cm and b cm respectively.

By the formula of the perimeter, the perimeter of the rectangular paper is 2(l + b) cm.

But, the value for the perimeter of the paper is given to be 100 cm.

Thus, we get an equation, 2(l + b) = 100, or, l + b = 50.

Also, its area = lb square cm.

The value for the area is given to be 600 square cm.

Thus, the equation we get is, lb = 600.

We are asked to find the difference between the length and the breadth of the paper, that is, l - b, assuming l >b.

Now, we know that, (x - y)² = (x + y)² - 4xy.

Putting l as x, and b as y, we get:

(l - b)² = (l + b)² - 4lb.

Substituting the values of l + b = 50, and lb = 600, we get:

(l - b)² = (50)² - 4(600),

or, (l - b)² = 2500 - 2400,

or, (l - b)² = 100,

or, l - b = √100,

or, l - b = 10.

Thus, the difference between the length and the breadth of the rectangular paper, having a perimeter of 100 cm, and an area of 600 square cm, is 10 cm.

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Step 1

Given;

Required; To find the side length.

Step 2

State the area(A) of an equilateral triangle.

Step 3

Find the side length

But, the side length cannot be negative, therefore, the side length of the equilateral triangle = 12 units

To find cos(2θ), we can use the identity cos(2θ) = 1 - 2sin²θ or cos²θ - sin²θ.

Since csc θ = -5/2 and we know that sin θ = 1/csc θ, we can find that sin θ = -2/5.

We also know that tan θ > 0, which means that the angle θ is in either the first or third quadrant. In the first quadrant, both sin θ and cos θ are positive, while in the third quadrant, both sin θ and cos θ are negative. However, since we know that csc θ is negative, θ must be in the second quadrant. Therefore, cos θ is negative.

We can use the Pythagorean identity sin²θ + cos²θ = 1 to find that cos θ = -√(21)/5.

Now, we can use the identity cos(2θ) = cos²θ - sin²θ to find:

cos(2θ) = (-√(21)/5)² - (-2/5)²
         = 21/25 - 4/25
         = 17/25

Therefore, the exact value of cos(2θ) is 17/25.

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Answer:

-0.8 is the correct answer of this question

Answer:

-16/45

Step-by-step explanation:

When you mulitply these two fractions together it's best to muliteply them by the number across so therefore 8x-2= -16 and 15x3= 45 which you end up with -16/45

Answer:

sqrt(25/36) = 5/6 or sqrt(25)/36 = 5/36. Based on what your question states.

Step-by-step explanation:

Answer:

Hrm

Step-by-step explanation:

\(\sqrt{25} =5\)

\(\frac{5}{36}\)