Algebra Word Problem Solutions

Cindy separated her fruit flies into equal groups. She estimates that there are 2¹⁰ fruit flies in each of 2² jars. How many fruit flies does Cindy have in all?

${\displaystyle \frac{\frac{5}{7}}{\frac{5}{6}}}$

${\displaystyle 100={10}^x}$

Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?

A biologist has found that the number of branches on a certain rare tree can be modeled by the polynomial $b(y)=4y^2+y$ where y is the number of years after the tree reaches a height of 6 feet. The number of leaves on each branch can be modeled by the polynomial $l(y)=2y^3+3y^2+y$. Write a polynomial describing the total number of leaves on the tree.

${\displaystyle {\log 10}^x=2a\text{and}{\log 10}^y=\frac{b}{2}}$ write ${\displaystyle {10}^a}$ in terms of x

A coffee merchant sells three blends of coffee. A bag of houseblend contains 300 grams of Colombian beans, 50 grams of Kenyanbeans, and 150 grams of French roast beans. A bag of specialblend contains 200 grams of Colombian beans, 200 grams of Kenyanbeans, and 100 grams of French roast beans. A bag of Gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyanbeans and 50 grams of French roast beans. Merchant has on hand 30kg of Colombian beans, 15 kg of Kenyan beans and 15 kg of French roast beans. One bag of the house blend produces profit of $0.50 , onebag of the Special blend produces a profit of $1.50, and one bag ofthe gourmet blend produces a profit of $2.00. How many bags of eachtype should the merchant prepare if he wants to use up all of thebeans and maximize his profit? What is the maximum profit?

${\displaystyle \frac{3}{2x+3}-1(2x-3)=\frac{4}{4x^2-9}}$

Find ${\displaystyle \frac{3}{7}of28}$

To simplify: The expression and eliminate coefficients if any:
a) ${\displaystyle \sqrt{4}\left\{b^3\right\}\sqrt{b}}$
b) ${\displaystyle \left(2\sqrt{a}\right)\left(\sqrt{3}\left\{a^2\right\}\right)}$

Find the value of x that satisfies the inequality.
${\displaystyle \left|\frac{x-1}{2}\right|\le 1}$

Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3

1. Evaluate the following exponentials with explanations. You may need to use a calculator with a Y x key.
EXAMPLE: X $-1/4$. If X = 4, this gives _0.7071__. Compute to two decimal places or more.
a. X $-1/5$ , When X = 2, this gives ____.
b. X 1 , When X = 4, this gives ____.
c. X $1/2$, When X = 64, this gives ____.
d. X $3/4$ , When X = 2, this gives ____.
My last question was rejected with the explanation that their is no formulas that go with a-d. This is the exact question the instructor asked us to work on.

Which expression below is equivalent to $(9x-4)+13(3x-2)$?

(A) $9x+26$

(B) $48x-30$

(C) $39x-26$

(D) $48x+30$

How can the division algorithm be used to check the result of the polynomial division.

Write a quadratic equation with the given solutions. -1 and -6

Show that the inverse of any linear function $f(x)=mx+b$, where $m\ne 0$, is also a linear function. Give the slope and y-intercept of the graph of f-1 in terms ofm and b.

Linear equations of first order.
Solve the initial-value problem on the specified interval $y^{\prime }+y\tan x=\sin 2xon(-\frac{1}{2}\pi ,\frac{1}{2}\pi )\text{with}y=2\text{when}x=0$.

Write a definition of Piecewise-Defined functions