Differentiate with respect to y
\(5y = {y} ln( {x}^{2} ) \)
​

Answer:

7,300

Step-by-step explanation:

6900x2 years=13,800 total tuition.

13800-2500-4000 (2000x2)=7,300

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

A

Step-by-step explanation:

The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:

B. 1 real root and 2 complex roots.

The function in this problem is defined as follows:

F(x) = x³ + 2x² + 4x + 8.

The function is of the third degree, hence the total number of zeros of the function is of 3.

From the graph, the function has only one x-intercept, which is given as follows:

x = -2.

Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.

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Answer:

2 9/20

Step-by-step explanation:

\(9\frac{3}{4}-7\frac{3}{10}\\\frac{39}{4} -\frac{73}{10}\\\frac{39x5}{4x5}-\frac{73x2}{10x2}\\\frac{195}{20}-\frac{146}{20}\\\frac{49}{20}\\2\frac{9}{20}\)

*I used an x for the multiplication symbol...there's no variable involved in this.  

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Answer:

$0.95

Step-by-step explanation:

Since it cost $2.85 for 3 pounds of apples, dividing 2.85 by 3 will give us one pound of apples.

2.85/3 = $0.95

Hope this helps! Please comment if it does or not. :)

Answer:

87 is the answer

Hope it helps!!!

Step-by-step explanation:

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

132cm^2

Step-by-step explanation:

to solve for the area of this we can split it into smaller shapes and sum the areas afterward-

the top rectangle has an area equal to Length x Width

4x7 = 28cm^2

the centre rectangle is done similarly-

7x8 = 56cm^2

lastly the two triangles which are solved with base x height divided by two

now since we know that the centre piece is 7cm across, and that the two side triangles are equal in size, that means that we know the base to be 19-7 divided by 2 which gives 6 each-

\(\frac{(6)(8)}{2}\) (2) = (6)(8) = 48cm

now summing them we have 28 + 56 + 48 = 132cm^2

380 songs

a function is the rule that defines the relation between 2 variables,

given the function

the input value is m ( the number of months)

and the output value (N) is the number of songs,

so

Step 1

to know how many songs he will have after 1 year, we need to input the time, but remember the input must be in number of months,hence

evaluate the function for m=12

therefore, he will own 380 songs

I hope this helps you

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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Answer:

Step-by-step explanation:

Answer:

We can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.

Substituting the given values, we have:

PV = $31.48 x [(1 - (1 + 0.152/12)^(-18)) / (0.152/12)]

PV = $31.48 x [(1 - 0.5159) / 0.0127]

PV = $1,007.97

Therefore, the equivalent cash price of the iPod is $1,007.97.

Answer:

I think its 32, I don't know how to put it into a linear equation I hope it helps enough though.

Answer:

\(\boxed {x = -1}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(15 + 3x = 3(2 - 2x)\)

-Use Distributive Property:

\(15 + 3x = 3(2 - 2x)\)

\(15 + 3x = 6 - 6x\)

-Take \(6x\) and add it to \(3x\):

\(15 + 3x + 6x = 6 + 6x - 6x\)

\(15 + 9x = 6\)

-Subtract both sides by \(15\):

\(15 - 15 + 9x = 6 - 15\)

\(9x = -9\)

-Divide both sides by \(9\):

\(\frac{9x}{9} = \frac{-9}{9}\)

\(\boxed {x = -1}\)

Therefore, the value of \(x\) is \(-1\).

Answer: There can be multiple combos.

Answer:

9

Step-by-step explanation:

We are dealing with two angles that make up a right angle, otherwise known as complementary angles. With this in mind, we can set up an equation to solve for w.

90 = 4w-7 + 7w-2

99 = 11w

w = 9

Answer:

The center of the circle is at the point (2, -3), and its radius is 4 units

Step-by-step explanation:

The equation of the circle in standard form can be obtained by completing the square for both x and y terms as follows:

7x^2 - 28x + 7y^2 + 42y - 35 = 0

7(x^2 - 4x) + 7(y^2 + 6y) = 35

7(x^2 - 4x + 4 - 4) + 7(y^2 + 6y + 9 - 9) = 35

7[(x - 2)^2 - 4] + 7[(y + 3)^2 - 9] = 35

7(x - 2)^2 + 7(y + 3)^2 - 112 = 0

7(x - 2)^2 + 7(y + 3)^2 = 112

Dividing by 112 on both sides, we get:

(x - 2)^2 + (y + 3)^2 / 16 = 1

Therefore, the equation of the circle in standard form is (x - 2)^2 + (y + 3)^2 / 16 = 1.

The center of the circle is at the point (2, -3), and its radius is 4 units.

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

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Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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Answer:

Step-by-step explanation:

Area of rectangle+area of triangle

hope the picture helps

The general form representation of the polynomial which is as described in the task content is; f(x) = 4x³ + 38x² + 24x - 360.

It follows from the task content that the Polynomial in discuss has;

Therefore, the factored form of a polynomial can be written as follows;

P(x) = a (x - p) (x - q) (x - r) where p, q and r are the roots of the polynomial and a is the leading coefficient.

Since the factors of the polynomial f(x) are; (x + 6), (x + 6) and (x - 5/2).

Hence, the polynomial f(x) in discuss can be written as follows;

f(x) = 4 (x + 6) (x + 6) (x - 5/2)

f(x) = (x + 6) (x + 6) (4x - 10)

f(x) = 4x³ + 38x² + 24x - 360

Therefore, the required polynomial in standard form is; f(x) = 4x³ + 38x² + 24x - 360.

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Answer:

C. 3(x+1)(x-1)-4x

Step-by-step explanation:

3(x+1)(x-1)-4x

(x+1)(x-1)=x^2-1

3(x^2-1)-4x

3x^2-4x-3

Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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