Given the following functions, find (f•g)(x).
f(x) = 2x
g(x) = 3x - 2

The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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Answer:

Below

Step-by-step explanation:

● x^2 + 11x + 121/4 = 125/4

Substract 125/4 from both sides:

● x^2 + 11x + 121/4-125/4= 125/4 -125/4

● x^2 + 11x - (-4/4) = 0

● x^2 +11x -(-1) = 0

● x^2 + 11 x + 1 = 0

This is a quadratic equation so we will use the determinanant (b^2-4ac)

● a = 1

● b = 11

● c = 1

● b^2-4ac = 11^2-4*1*1 = 117

So this equation has two solutions:

● x = (-b -/+ √(b^2-4ac) ) / 2a

● x = (-11 -/+ √(117) ) / 2

● x = (-11 -/+ 3√(13))/ 2

● x = -0.91 or x = -10.9

Round to the nearest unit

● x = -1 or x = -11

The solutions are { -1,-11}

The solution of the equation x² + 11x + (121/4) = 125/4 will be 0.09 and negative 11.09.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation is given below.

x² + 11x + (121/4) = 125/4

Simplify the equation, then the equation will be

4x² + 44x + 121 = 125

4x² + 44x + 121 - 125 = 0

4x² + 44x - 4 = 0

x² + 11x - 1 = 0

We know that the formula, then we have

\(\rm x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}\)

The value of a = 1, b = 11, and c = -1. Then we have

\(\rm x = \dfrac{-11 \pm \sqrt {11^2 - 4 \times 1 \times (-1)}}{2 \times 1}\\\rm x = \dfrac{-11 \pm \sqrt {121 +4}}{2 }\\x = \dfrac{-11 \pm \sqrt {125}}{2 }\)

Simplify the equation, then we have

x = (- 11 ± 11.18) / 2

x = (-11 - 11.18) / 2, (-11 + 11.18) / 2

x = -11.09, 0.09

The solution of the equation will be 0.09 and negative 11.09.

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Answer:

f(x)=-5x+1x=−5x+1, find f(6)

f(6)= -5(6)+1(6)=-5(6)+1

F(6)=-24,-29

The height of the rectangular prism can be calculated using the following formula:

Volume (V) = Length (L) * Width (W) * Height (H)

Therefore, rearranging the formula, we can calculate the height of the prism:

Height (H) = Volume (V) / (Length (L) * Width (W))

For this problem, plugging in the known values, we get:

Height (H) = 490 cm³ / (10 cm * 7 cm)

Therefore,

Height (H) = 8.14 cm

Answer:

1:2

becuase it can be honestly

Answer:

0.4

Step-by-step explanation:

1.6 - 1.2 = 0.4

Taking into account the definition of a system of linear equations, the system of equations to be solved is

r= g+2

2g + 4.75r= 50

where "g" is the number of games Lauren played and "r" is the number of rides Lauren went on.

A system of linear equations is a set of two or more first degree equations, in which two or more unknowns are related and it is desired to find their value.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. Thit is, the values ​​of the unknowns must be find, and when the are replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

r= g+2

2g + 4.75r= 50

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This is 100% correct. Just got it right.

"g" is the number of games.

"r" is the number of rides.

System of equations

r =  g + 2

2g + 4.75r = 50

Answer:

1 hours = 60 min

60 x 9/10 = 54 min

3 divided by 54 = 1/18

so she walks 1/18 miles per hour.

Im not sure though. It might be 3 divided by 9/10 = 3 1/3. I’m not that confident in my answer. But it is definitely one of them, either 1/18 or 3 1/3.

Answer:

a

Step-by-step explanation:

The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem is important as it provides a way to prove the existence of solutions to polynomial equations and provides an analytical tool to find the exact location of the solutions.

This theorem is also known as the algebraic version of the Intermediate Value Theorem as it states that if a polynomial is continuous on a closed interval, then it must take on all values between its maximum and minimum.

The theorem can be easily proven by considering a single-variable polynomial of degree n and transforming it into a polynomial of degree n−1 with the same roots. By repeating this process, the polynomial can be reduced to a constant and hence, it must have at least one root.

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Let's begin by listing out the given information:

Answer:

A) How much material does he need to cover the one rectangular side of the tent with the rip? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.  

Answer: If David’s dad wanted to cover the rectangular side of the tent, he would need to multiply the sides together. Using the formula A = l x w, I can solve for 6 and 9. 9 x 6 = 54, so 54 = 6 x 9.  

B) If David’s dad wanted to re-cover the whole tent including the bottom, how much material would he need?  Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.

Answer: If he wanted to re-cover the whole tent, he would need the product of the rectangular side, the triangular side, and the bottom side. Using A = l x w, I can solve for each side of the tent, For the rectangular side you multiply six by nine, then multiply two by the product. 6 x 9 = 54 x 2 = 108. For the triangular side, I need to multiply six times seven, 6 x 7 = 42. For the bottom, I need to multiply seven times nine, 7 x 9 = 63. Finally, I need to add them all up. 108 + 42 + 63 = 213 ft².                    

C) What is the volume of the tent?  Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. (You need to find the area of one of the triangular bases, and then you can take that measurement and multiply it with the height of the entire prism.) V=Bh, where B = area of one of the triangular bases

Answer: I need to find the volume of the tent, so I need to find the formula which is V = B x h. The base is 63, because I needed to find the area of one of the triangular bases, so I multiplied 7 x 9 = 63. The height is 6, so I need to multiply 63 x 6. When I multiply 63 x 6, I get the product of 378, so the volume of the tent is 378 ft³.

Answer:

p = 61 degrees

Step-by-step explanation:

The sum of all angles that make up a striaght line is 180 degrees. To find p you just subtract the other angles from 180: 180 - 87 - 32 = 61.

The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

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True , Every matrix transformation is a linear transformation.

Is there a linear transformation for every matrix operation?

Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.      

                                    Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.

What alteration does matrix entail?

In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.

                                    Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.

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The 98% confidence interval for the average age of all students at the community college is 22.228 to 23.772 years.

To calculate the 98% confidence interval for the average age of all students at the community college, we can use the formula:

Confidence Interval = sample mean ± (Z * standard deviation / √sample size)

Given that the sample size is 36, the sample mean is 23 years, and the standard deviation is 1.9 years, we need to find the value of Z for a 98% confidence level.

The Z-value for a 98% confidence level corresponds to an area of 0.98 in the standard normal distribution. To find this value, we can look it up in a Z-table or use statistical software. The Z-value for a 98% confidence level is approximately 2.33.

Plugging in the values into the formula, we have:

Confidence Interval = 23 ± (2.33 * 1.9 / √36)

Calculating the expression:

Confidence Interval = 23 ± (2.33 * 1.9 / 6)

Confidence Interval = 23 ± (4.507 / 6)

Confidence Interval = 23 ± 0.751

Therefore, the 98% confidence interval for the average age of all students at the community college is:

22.249 to 23.751

The closest option among the given choices is c. 22.228 to 23.772.

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The length of each side of Kuljeet's square field is 25 meters. The length of each side of the field, we have to calculate the perimeter of the square field, as all the sides of a square are equal.

Let the length of each side of the square field be 'a'. Therefore, the perimeter of the square field = 4aAs we know, the cost of fencing per meter is Rs. 20,

the cost of fencing the entire square field = perimeter of the square field x cost of fencing per meter

4a x 20 = 80a

This cost is given as Rs. 2000

So, we can write the above equation as: 80a = 2000. Dividing both sides by 80, we get: a = 2000/80

a = 25

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Answer:

x≤7

Step-by-step explanation:

Answer:

2x-3

Step-by-step explanation:

Three less than is x-3, and twice a number is 2x, so the end result is 2x-3.

Answer:

2(x)-3

Step-by-step explanation:

or 2x-3

Answer: \(C(t) = 120(1-0.30)^t\)

Step-by-step explanation:

Exponential equation for decay:\(y= A(1-r)^t\), where A = initial value, r= decay rate , t= time.

As per given, A = 120ml , r= 0.30

\(C(t) = 120(1-0.30)^t\)

Hence, the required function that gives the medicine's concentration in milligrams per liter, C(t), t hours after the medicine was injected.

\(C(t) = 120(1-0.30)^t\)

Answer: Plain:  the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:

6√5 - 6i = 6(√5 - i) = 12 ∠ -30°

(√3 + √3i) = √3(1 + i) = 2 ∠ 45°

where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.

Now, we can multiply the two complex numbers in polar form:

(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°

= 24 ∠ 15°

Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.

The profit for the option writer is $3,900.

In this scenario, the option writer sold a put option on the Canadian dollar with an exercise price of USD 0.76/CAD. The premium received for the option was $0.039/CAD. The contract size is CAD 100,000, and the spot price at maturity is $0.76/CAD. However, since the spot price at maturity is equal to the exercise price of $0.76/CAD, the option is not exercised. As the option writer, the profit is determined by the premium received. In this case, the premium received per contract is $0.039/CAD. Multiplying this by the contract size of CAD 100,000, we get $3,900.

It's important to note that if the spot price at maturity had been lower than the exercise price, the option would have been exercised, resulting in a loss for the option writer equal to the difference between the exercise price and the spot price, multiplied by the contract size.

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Answer: We can prove that 5^(2n+1) + 2^(2n+1) is divisible by 7 for all n ∈ N (i.e., for all positive integers n) using mathematical induction.

Base case: When n = 1, we have:

5^(2n+1) + 2^(2n+1) = 5^(2(1)+1) + 2^(2(1)+1) = 5^3 + 2^3 = 125 + 8 = 133

133 is clearly divisible by 7, so the statement is true for n = 1.

Inductive step: Assume that the statement is true for some arbitrary positive integer k, i.e., assume that 5^(2k+1) + 2^(2k+1) is divisible by 7. We want to show that the statement is also true for k+1, i.e., that 5^(2(k+1)+1) + 2^(2(k+1)+1) is divisible by 7.

Using the laws of exponents, we can simplify 5^(2(k+1)+1) and 2^(2(k+1)+1):

5^(2(k+1)+1) + 2^(2(k+1)+1) = 5^(2k+3) + 2^(2k+3) = 5^3 * 5^(2k) + 2^3 * 2^(2k)

We can factor out 125 (which is divisible by 7) from the first term, and 8 (which is also divisible by 7) from the second term:

5^(2(k+1)+1) + 2^(2(k+1)+1) = 125 * 5^(2k) + 8 * 2^(2k)

We can rewrite 8 as 7+1:

5^(2(k+1)+1) + 2^(2(k+1)+1) = 125 * 5^(2k) + (7+1) * 2^(2k)

Distributing the 2^(2k) term and regrouping:

5^(2(k+1)+1) + 2^(2(k+1)+1) = 125 * 5^(2k) + 7 * 2^(2k) + 2^(2k)

Now we can use the inductive hypothesis that 5^(2k+1) + 2^(2k+1) is divisible by 7 to replace 5^(2k+1) + 2^(2k+1) with a multiple of 7:

5^(2(k+1)+1) + 2^(2(k+1)+1) = 125 * 5^(2k) + 7 * (5^(2k+1) + 2^(2k+1)) + 2^(2k)

By the inductive hypothesis, 5^(2k+1) + 2^(2k+1) is divisible by 7, so we can replace it with a multiple of 7:

5^(2(k+1)+1) + 2^(2(k+1)+1) = 125 * 5^(2k) + 7m + 2^(2k)

where m is some positive integer.

We can now see that 5^(2(k+1)+1) + 2^(2(k+1)+1) is divisible by 7, since it can be expressed as the sum of a multiple of 7 (i.e., 7m)

Answer:

Washing Machine 1 $480 × .5030 = $241.44

$480 - $241 = $238.56

So Wahsing Machine #1 was $480 and was marked down by .5030% which takes off $241.44 which brings us to the total to $238.56

Washington Machine #2

$480 × .30% = $144 × .20% = $28.80

So Washing Machine 2 was $480 and was marked down by .30% which took off $144 and was marked down by an additional .20% which took off an additional $28.80 which brings the Grand Total of $307.20.

Joanne should buy the first Washing Machine rather than the second Washing Machine because the first Washing Machine is $68.64 cheaper than the second Washing Machine.

Answer:

umm

Step-by-step explanation:

Answer:

sorry എനിക്ക് അറിയില്ല

Answer:

Step-by-step explanation:

8x -28 = 4(x - 28)

12x + 15 = 3(4x + 5)

Answer:

The answer is D. x=-1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Divide both sides by 10.

2. Add 4 to both sides.

3. Subtract 10x from both sides.

4. Divide both sides by -8.

The answer is D.

That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.

This is further explained below.

In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:

\(Va=100 \%X + 600 * 40 \%\)

\(Va= (600+X)60 \% (M_1V_1=M_1 V_2)\)

100X + 24000 = 36000 + 60x

X = 300.

In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.

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