b) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)

Find g'(x) =

The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 43/4h if the area of trapezoid is 14 square units.

Given that area is equal to 1-2(\(b_{1} -b_{2}\))h and area is 14 square units.

We know that area of trapezoid is equal to (a+b)h/2.

We have to put the given equation equal to 14 to get our first equation.

14=1-2(\(b_{1} -b_{2}\))h

14=1-2\(b_{1}\)h+2\(b_{2}\)h

2\(b_{1}\)h-2\(b_{2}\)h=-13------------1

Now put the value of area in the formula of area of trapezoid.

14=\((b_{1} +b_{2})h/2\)

\(b_{1}\)h+\(b_{2}h\)=28-----------------2

Multiply equation 2 by 2 and then subtract 2 from 1

\(2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h\)=-13-56

-4\(b_{2}h\)=-43

\(b_{2}\)=43/4h

Put the value of \(b_{2}\) in 2 to get the value of \(b_{1}\).

\(b_{1} h+43/4h*h=28\)

\(b_{1}\)=69/4h

Hence The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 51/4h if the area of trapezoid is 14 square units.

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Answer:

15 J

Step-by-step explanation:

There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.

1. Set up the equation

80 + x + 5 = 100

2. Simplify

x + 85 = 100

3. Solve for x by subtracting 85 from both sides

x = 15

Answer:

The correct answer is 15J which is B.

Answer:

Length= 30 in

Width= 10 in

Step-by-step explanation:

Let the width of the rectangle be x in.

Length of rectangle

= 3 (width)

= 3x

Perimeter of rectangle= 2(length) +2(width)

80= 2(3x) +2(x)

80= 6x +2x

8x= 80 (simplify)

x= 80 ÷8 (÷8 on both sides)

x= 10

Thus width of rectangle= 10 in

Length of rectangle

= 3(10)

= 30 in

Point A is a solution to the system of inequalities for the given coordinate grid.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The given coordinate grid shows points A through K.

The system of inequalities is given, as follows:

y ≤ -2x + 10

y > (1/2)x - 2

The solution to the system of inequalities is the region that is above the line for the second inequality and below the line for the first inequality. This region is the shaded region that lies between the two lines, which represents the set of points that satisfies both inequalities.

Thus, point A is a solution to the system of inequalities

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Check the picture below.

Answer:

mid

Step-by-step explanation: you

Step-by-step explanation:

1 ton = 2000 pounds

2000+2500 = 45000 pounds

The total weight would be 4,500 pounds .

Ton, unit of weight in the avoirdupois system equal to 2,000 pounds (907.18 kg) in the United States .

According to the question

You added 2,500 pounds and 1 ton

As we know  

1 ton  = 2,000 pounds

So,

Adding 1 ton and 2,500 pounds  

= 2,000 pounds + 2,500 pounds  

= 4,500 pounds

Hence, the total weight would be 4,500 pounds .

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Answer:

H: (2, 14)

O: (4,15)

U: (6,14)

S: (2,10)

E: (6,10)

Step-by-step explanation:

the image on the grid is after doin x- 1 and y-7

to get the preimage do the inverse , x + 1 , y + 7

note- a coordinate is written as (x,y)

so, add 1 to all the x's and 7 to all the y's on the coordinates on the grid!

and sorry for asking but, if this is right could i please get a thanks & brainliest recently a moderator deleted ALL my answers (over 400 answers) causing me to lose over 3k points so id appreciate it alot thanks xoxo

F(x) = 2x³ - x² + 5x − 3 is the polynomial that is in standard form. Thus, option D is correct.

Algebraic expressions called polynomials can include exponents that are multiplied, divided, or added. Different types of polynomials exist. specifically, monomial, binomial, and trinomial. A polynomial with only one term is referred to as a monomial. A polynomial with two unlike terms is referred to as a binomial. An algebraic expression with three terms is known as a trinomial.

Monomials - The term "monomial" refers to algebraic expressions with a single term. In other words, it is an expression that includes any number of similar terms. Hence the name "Bi"nomial," binomials are algebraic expressions with two unlike terms. Trinomials - Trinomials are algebraic expressions with three dissimilar terms, hence the name "Tri"nomial.

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Answer:

BC = 4

Step-by-step explanation:

The diagram shows a circle with radius AE and chord BD.

Assuming that the radius bisects the chord, then AE is perpendicular to BD. So the measure of angle ACB is 90°.

This means that triangle ACB is a right triangle, with legs AC and BC, and hypotenuse AB.

The length of the radius is:

\(AE = 3 + 2 = 5\)

As AB is also the radius, AB = 5.

To find the length of BC, use Pythagoras Theorem:

\(AC^2+BC^2=AB^2\)

    \(3^2+BC^2=5^2\)

      \(9+BC^2=25\)

\(9+BC^2-9=25-9\)

           \(BC^2=16\)

        \(\sqrt{BC^2}=\sqrt{16}\)

            \(BC=4\)

Therefore, the length of line segment BC is 4.

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

Step-by-step explanation:

1. j

2. k

3. L

4. Lj

5. kL

6. jk

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:

  (x, y, z) = (1, -3, 1)

Step-by-step explanation:

Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:

  (x, y, z) = (1, -3, 1)

__

Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.

Using the first equation to write an expression for z, we have ...

  z = 4x +3y +6

Substituting that into the second and third equations gives ...

  6x -y +3(4x +3y +6) = 12   ⇒   18x +8y = -6

  8x +2y +4(4x +3y +6) = 6   ⇒  24x +14y = -18

Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:

  3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)

  10y = -30

  y = -3

Substituting into the first equation (of the equations in x and y), we have ...

  18x +8(-3) = -6

  18x = 18

  x = 1

Finally, substituting into the equation for z gives ...

  z = 4(1) +3(-3) +6 = 1

The solution is (x, y, z) = (1, -3, 1).

___

The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.

Answer: 726.

Step-by-step explanation:

we have:

a, b and c non-negative numbers.

we know that:

a + b + c = 36.

(i also assume that the numbers are whole numbers)

and "one of the numbers is twice one of the others"

Then we can write:

a = 2*b

replacing that in the above equation, we get:

2*b + b + c = 36

3*b + c = 36.

Then the product between the 3 numbers will be:

P = a*b*c = (2*b)*b*c = 2*b^2*c.

Because we have b squared in the product, we want to find the maximum possible value of b, such that:

3*b + c = 36.

3*b = 36 - c

We know that 36 is a multiple of 3, and also is 3*b.

Then 36 - c must also be a multiple of 3, this means that c must be a multiple of 3 (and the smallest possible), which is 3.

Then if we have:

3*b = 36 - 3 = 33

3*b = 33

b = 33/3 = 11.

The prodct will be:

P = 2*(11^2)*3 = 726.

The maximum value of the product of the three given numbers is;

P_max  = 726

Let the three non-negative numbers be x, y and z

We are told that they sum up to 36.

Thus;

x + y + z = 36.

Now, one of the numbers is twice one of the other numbers.

Thus;

x = 2y

Then, we now have;

2y + y + z = 36

⇒ 3y + z = 36.

We want to find the maximum value of the  product between the 3 numbers. Let's say their product is P, then we have;

P = xyz

P = 2y²z

Since y is squared here, then let's make 3y the subject in 3y + z = 36.

3y + z = 36.

3y = 36 - z

since 3 is multiplied by y, it means that  36 - z be a multiple of 3 and we can infer that z must also be a multiple of 3. If we take z = 3, we have;

Then if we have:

3y = 36 - 3

3y = 33

y = 33/3

y = 11.

Since Product is P = 2y²z, then we have;

P = 2 × 11² × 3

P_max  = 726

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The scientific notation to write the number -20,000 with a power of 10.

Given that

To find

So, according to the question

We have

For finding the scientific notation form of given number, first we have to know about scientific notation with a power of 10.

Scientific notation with a power of 10

So, now we can convert that number in a form of Scientific notation.

n = -20,000

Now multiply \(\frac{10^4}{10^{4}}\), we will get

n = -20,000 × \(\frac{10^4}{10^{4}}\)

n = \(\frac{-20,000\times 10^4}{10000}\)

n = - 2× 10⁴

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Answer:

-8

Step-by-step explanation:

any number divided by a nega is going to be neg if it is multiplied by two nega's its positive.

Answer:

Step-by-step explanation:

Which statement about 4(x-3) is true?

O A. 4(x - 3) has three terms.

B. 4(x-3) has two variables.

C. 4(x - 3) is a product.

ОО

D. 4(x-3) is a sum.

C IS CORRECT

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

(-31)/72

Step-by-step explanation:

Simplify the following:

4/9 - 7/8

Put 4/9 - 7/8 over the common denominator 72. 4/9 - 7/8 = (8×4)/72 + (9 (-7))/72:

(8×4)/72 + (9 (-7))/72

8×4 = 32:

32/72 + (9 (-7))/72

9 (-7) = -63:

32/72 + (-63)/72

32/72 - 63/72 = (32 - 63)/72:

(32 - 63)/72

32 - 63 = -(63 - 32):

(-(63 - 32))/72

| 6 | 3

- | 3 | 2

| 3 | 1:

Answer: (-31)/72

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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\((\stackrel{x}{-2}~~,~~\stackrel{y}{27}) ~~ \textit{lies on }\textit{\LARGE f}\qquad \textit{so then}\qquad f(\stackrel{x}{-2})~~ = ~~\stackrel{y}{27}\)

Answer:

Step-by-step explanation:

We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:

x3 = 512

To solve for x, we need to take the cube root of both sides of the equation:

x = ∛512

Using a calculator or simplifying by prime factorization, we can find that:

512 = 2^9

So,

∛512 = ∛2^9 = 2^3 = 8

Therefore, there were 8 fish in the aquarium in 2016.

Answer:

Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):

x3 = 512

To solve for x, we can isolate x by dividing both sides of the equation by 3:

x = 512/3

x = 170.67 (rounded to two decimal places)

Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:

x ≈ 171

So there were 171 fish in the aquarium in 2016.

Step-by-step explanation:

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork