Question 1

Simplify.

Accepted Answer

The answer of Simplify. ...

Question 2

Simplify. Write your answer in exponent form.

Accepted Answer

The answer of Simplify. Write your answer in exponent form....

Question 3

Write the number in scientific notation.

Accepted Answer

The answer of Write the number in scientific notation. ...

Question 4

Find the simple interest and the total amount including interest. $$\begin{array} { c | c | c | c | c } 
\text { Principal } & \text { Annual Interest Rate } & \text { Time in Years } & \text { Interest } & \text { Total Amount } \
\hline \$ 5000 & 5.2 \% & 5 & &
\end{array}$$

Accepted Answer

The answer of Find the simple interest and the total...

Question 5

Multiply the conjugates.

Accepted Answer

The answer of Multiply the conjugates. ...

Question 6

Factor the binomial completely. $$
25 x ^ { 2 } - 81 y ^ { 2 }
$$

Accepted Answer

This is a difference of squares, factored as $(a+b)(a-b)$ where $a = 5x$ and $b = 9y$.

Question 7

Factor the polynomial completely.
$x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$

Accepted Answer

The given polynomial can be rearranged and factored by grouping: $x^2y^2 - 16y^2 - 9x^2 + 144$. This can be rewritten as $(x^2y^2 - 16y^2) - (9x^2 - 144)$, which simplifies to $y^2(x^2 - 16) - 9(x^2 - 16)$. Factoring out the common term $(x^2 - 16)$, we get $(x^2 - 16)(y^2 - 9)$. Further factoring each quadratic gives $(x - 4)(x + 4)(y - 3)(y + 3)$.

Question 8

Factor the binomial completely. $$5 n ^ { 2 } - 80$$

Accepted Answer

The answer of Factor the binomial completely. \[5 n ^...

Question 9

Find the vertex of the parabola.

Accepted Answer

The answer of Find the vertex of the parabola. ...

Question 10

Perform the indicated operations. $$
\left( 19 t ^ { 4 } - 2 t ^ { 2 } + 4 t \right) + \left( 2 t ^ { 4 } - 4 t + 27 \right) - \left( 4 t ^ { 4 } + t ^ { 2 } + 19 \right)
$$

Accepted Answer

Combine like terms: $ (19t^4 + 2t^4 - 4t^4) + (-2t^2 - t^2) + (4t - 4t) + (27 - 19) = 17t^4 - 3t^2 + 8 $.

Question 11

Simplify.

Accepted Answer

The answer of Simplify. ...

Question 12

Factor completely.
$t ^ { 4 } x ^ { 2 } - 6 t ^ { 3 } x ^ { 3 } + 9 t ^ { 2 } x ^ { 4 }$

Accepted Answer

Each term in the expression shares a common factor of $t^2x^2$, and the remaining terms form a perfect square trinomial $(t-3x)^2$.

Question 13

Clear parentheses and combine like terms.

Accepted Answer

The answer of Clear parentheses and combine like terms. ...

Question 14

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5,730 years. If a sample of wood from an ancient artifact had 15 grams of carbon- 14 initially, the amount remaining, in grams, is given by

where  t  is the number of years since the tree died. How many grams would be present after 5,730 years?

Accepted Answer

The answer of Scientists often use a process called carbon...

Question 15

The amount of $6,000 is invested at 5% for 3 years.
a. Compute the ending balance if the bank calculates simple interest.
b. Compute the ending balance if the bank calculates interest compounded annually.
c. How much more interest is earned in the account with compound interest?

Accepted Answer

The answer of The amount of $6,000 is invested at...

Question 16

If a bank compounds interest quarterly for 10 years, how many total compound periods are there?

Accepted Answer

Since the interest is compounded quarterly, there are 4 compound periods per year. For 10 years, the total compound periods are 4 * 10 = 40.

Question 17

Simplify the expression. Write the answer in exponent form. $$7 ^ { 5 } \cdot 7 ^ { 7 }$$

Accepted Answer

The answer of Simplify the expression. Write the answer in...

Question 18

If a bank compounds interest semiannually for 8 years, how many total
compound periods are there?

Accepted Answer

The answer of If a bank compounds interest semiannually for...

Question 19

Add the polynomials.

Accepted Answer

The answer of Add the polynomials. ...

Question 20

Multiply the polynomials. $$
( 3.4 a + 7 ) ( 0.5 a - 9 )
$$

Accepted Answer

To multiply the polynomials, distribute each term in the first polynomial across each term in the second polynomial: $3.4a \times 0.5a = 1.7a^2$, $3.4a \times -9 = -30.6a$, $7 \times 0.5a = 3.5a$, and $7 \times -9 = -63$. Combining like terms, $1.7a^2 - 30.6a + 3.5a - 63 = 1.7a^2 - 27.1a - 63$.

Quiz 4: Living in a Nonlinear World

Simplify.

Simplify. Write your answer in exponent form.

Write the number in scientific notation.

Find the simple interest and the total amount including interest. $\begin{array} { c | c | c | c | c } \text { Principal } & \text { Annual Interest Rate } & \text { Time in Years } & \text { Interest } & \text { Total Amount } \\\hline \$ 5000 & 5.2 \% & 5 & &\end{array}$

Multiply the conjugates.

Factor the binomial completely. $25 x ^ { 2 } - 81 y ^ { 2 }$

Factor the polynomial completely. $x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$

Factor the binomial completely. $5 n ^ { 2 } - 80$

Find the vertex of the parabola.

Perform the indicated operations. $\left( 19 t ^ { 4 } - 2 t ^ { 2 } + 4 t \right) + \left( 2 t ^ { 4 } - 4 t + 27 \right) - \left( 4 t ^ { 4 } + t ^ { 2 } + 19 \right)$

Simplify.

Factor completely. $t ^ { 4 } x ^ { 2 } - 6 t ^ { 3 } x ^ { 3 } + 9 t ^ { 2 } x ^ { 4 }$

Clear parentheses and combine like terms.

The amount of $6,000 is invested at 5% for 3 years. a. Compute the ending balance if the bank calculates simple interest. b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest?

If a bank compounds interest quarterly for 10 years, how many total compound periods are there?

Simplify the expression. Write the answer in exponent form. $7 ^ { 5 } \cdot 7 ^ { 7 }$

If a bank compounds interest semiannually for 8 years, how many total compound periods are there?

Add the polynomials.

Multiply the polynomials. $( 3.4 a + 7 ) ( 0.5 a - 9 )$

Quiz 4: Living in a Nonlinear World

Simplify.

Simplify. Write your answer in exponent form.

Write the number in scientific notation.

Multiply the conjugates.

Factor the binomial completely. 25x2−81y225 x ^ { 2 } - 81 y ^ { 2 }25x2−81y2

Factor the polynomial completely. x2y2−9x2−16y2+144x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144x2y2−9x2−16y2+144

Factor the binomial completely. 5n2−805 n ^ { 2 } - 805n2−80

Find the vertex of the parabola.

Perform the indicated operations. (19t4−2t2+4t) +(2t4−4t+27) −(4t4+t2+19) \left( 19 t ^ { 4 } - 2 t ^ { 2 } + 4 t \right) + \left( 2 t ^ { 4 } - 4 t + 27 \right) - \left( 4 t ^ { 4 } + t ^ { 2 } + 19 \right) (19t4−2t2+4t) +(2t4−4t+27) −(4t4+t2+19)

Simplify.

Factor completely. t4x2−6t3x3+9t2x4t ^ { 4 } x ^ { 2 } - 6 t ^ { 3 } x ^ { 3 } + 9 t ^ { 2 } x ^ { 4 }t4x2−6t3x3+9t2x4

Clear parentheses and combine like terms.

The amount of $6,000 is invested at 5% for 3 years. a. Compute the ending balance if the bank calculates simple interest. b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest?

If a bank compounds interest quarterly for 10 years, how many total compound periods are there?

Simplify the expression. Write the answer in exponent form. 75⋅777 ^ { 5 } \cdot 7 ^ { 7 }75⋅77

If a bank compounds interest semiannually for 8 years, how many total compound periods are there?

Add the polynomials.

Multiply the polynomials. (3.4a+7) (0.5a−9) ( 3.4 a + 7 ) ( 0.5 a - 9 ) (3.4a+7) (0.5a−9)

Factor the binomial completely. $25 x ^ { 2 } - 81 y ^ { 2 }$

Factor the polynomial completely. $x ^ { 2 } y ^ { 2 } - 9 x ^ { 2 } - 16 y ^ { 2 } + 144$

Factor the binomial completely. $5 n ^ { 2 } - 80$

Perform the indicated operations. $\left( 19 t ^ { 4 } - 2 t ^ { 2 } + 4 t \right) + \left( 2 t ^ { 4 } - 4 t + 27 \right) - \left( 4 t ^ { 4 } + t ^ { 2 } + 19 \right)$

Factor completely. $t ^ { 4 } x ^ { 2 } - 6 t ^ { 3 } x ^ { 3 } + 9 t ^ { 2 } x ^ { 4 }$

Simplify the expression. Write the answer in exponent form. $7 ^ { 5 } \cdot 7 ^ { 7 }$

Multiply the polynomials. $( 3.4 a + 7 ) ( 0.5 a - 9 )$