Find an equation for the nth term of the arithmetic sequence.

a16 = 21, a17 = -1

an = 351 + 22(n + 1)
an = 351 - 22(n + 1)
an = 351 + 22(n - 1)
an = 351 - 22(n - 1)

The unknown number(n) is equal to - 2 satisfying asked statement.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the unknown number be 'n'.

Given, If 3 is added to twice a number,

and this sum is multiplied by 2​,

the result is the same as if the number is multiplied by 3

and 4 is added to the product.

∴ (2n + 3)×2 = n×3 + 4.

4n + 6 = 3n + 4.

4n - 3n = 4 - 6.

n = - 2.

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Two complementary angles are given as 4x - 16 and 2x + 10. Solving for x we find x = 16. Substituting x into the expressions for the angles, we find the angles to be 48 and 42 degrees.

The task here is to find the value of two angles that are complementary. Given the expressions for the angles are 4x - 16 and 2x + 10. As complementary angles, they sum up to 90 degrees. Hence, mathematically, we can express this as (4x - 16) + (2x + 10) = 90.

Solving the equation, combine like terms to get 6x - 6 = 90. Then, add 6 to both sides to get 6x = 96. Divide each side by 6 to find x, hence x = 16.

Substitute x = 16 into 4x - 16, therefore the first angle is 4×16 - 16 = 48 degrees. Similarly, substitute x = 16 into 2x + 10, hence the second angle is 2×16 + 10 = 42 degrees. The angles are thus 48 and 42 degrees, which adds up to 90).

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Answer:

No solution hope this helps:)

Step-by-step explanation:

the length of the rectangle is either -11 inches or 40 inches.

Given the following data;

Translating the word problem into an algebraic equation, we have;

[tex]L = W + 29[/tex]

To find the length of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

[tex]Area = L * W[/tex]

Substituting the values into the formula, we have;

[tex]440 = (W + 29) * W\\\\440 = W^{2} + 29W[/tex]

Rearranging the equation, we have;

[tex]W^{2} + 29W - 440 = 0[/tex]

W e would solve the quadratic equation by factorization;

[tex]W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)[/tex]

Width, W = -40 0r 11 inches.

Next, we would find the length of the rectangle;

When Width, W = -40;

[tex]L = W + 29[/tex]

[tex]L = -40 + 29[/tex]

Length, L = -11 inches

When Width, W = 11;

[tex]L = W + 29[/tex]

[tex]L = 11 + 29[/tex]

Length, L = 40 inches

Therefore, the length of the rectangle is either -11 inches or 40 inches.

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y - y1 = m (x - x1)

where m is the slope and (x1 , y1) is the point given

We are given:

m= -1

the point is (2, 4)

Then:

Answer:

A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.

Step-by-step explanation:

The following best defines the two quantities that are measured to find the call rate of a phone company:

A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.

In this way we can determine that how much money will it cost in dollars for each minute of phone call.

3x-6 = 2x+11

3x = 2x+17

x = 17

3(17)-6 = 45

2(17)+11 = 45

45+45 = 90

answer is C 90 degrees:right

Answer:

Your answer would be A 10cm

Answer:

3 1/100

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Answer:  The required value of c that makes the given statement true is 5.

Step-by-step explanation:  We are given to find the value of c that makes the following statement TRUE :

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we need to equate the coefficients of the same powers of the unknown variable x.

From equation (i), we have

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5\\\\\Rightarrow -2cx^{3+3}-2x^{3+2}=-10x^6-2x^5\\\\\Rightarrow -2cx^6-2x^5=-10x^6-2x^5.[/tex]

Equating the coefficients of [tex]x^6[/tex] on both sides of the above equation, we get

[tex]-2c=-10\\\\\Rightarrow c=\dfrac{-10}{-2}\\\\\Rightarrow c=5.[/tex]

Thus, the required value of c that makes the given statement true is 5.

Answer:D

Step-by-step explanation:

1 yard = 3 ft

10/3 = 3 1/3 yards

3 1/3 x 4 = 13 1/3 square yards

Final answer:

To represent the relationship between Matt and Andy's ages mathematically, let x be Andy's age, and express Matt's age as 2x + 5. The inequality x + (2x + 5) < 35 simplifies to x < 10, indicating Andy's age must be less than 10.

Explanation:

The question involves creating an inequality to represent the relationship between Matt and Andy's ages, where Matt is five years older than twice Andy's age, and the sum of their ages is less than 35.

Let x represent Andy's age. The formula for Matt's age would be 2x + 5. To find the range of possible values for Andy's age, you would write the inequality  x + (2x + 5) < 35.

Solving this inequality involves combining like terms and isolating the variable x.

Step 1: Combine like terms.

x + 2x + 5 < 35

Step 2: Simplify the inequality.

3x + 5 < 35

Step 3: Subtract 5 from both sides to isolate the term with x.

3x < 30

Step 4: Divide both sides by 3 to solve for x.

x < 10

This tells us that Andy's age must be less than 10 for the conditions to be met.

The simplified form of the expression (y^8)(y^2) is y^10, found by applying the laws of exponents that dictate adding the exponents when multiplying with the same base.

The simplified form of the expression (y8)(y2) can be found using the laws of exponents which state that when multiplying two powers with the same base, you add the exponents. Here, since the base is y, and we have exponents 8 and 2, we add them together:

y8 × y2 = y8+2

This simplifies to y10, which is the compressed form of the given expression.

Final answer:

To simplify the expression (y⁸)(y²), use the rule of exponents which says that you add the exponents when multiplying powers with the same base, resulting in y¹⁰.

Explanation:

The question requires simplifying an algebraic expression with exponents. The given expression is (y⁸)(y²). To simplify this, we use the rule of exponents which states that when multiplying two powers with the same base, you add the exponents. Therefore, y⁸ × y² = y⁸₊²} = y¹⁰