Algebra › Algebra 1
If an object is hung on a spring, the elongation of the spring varies directly as the mass of the object. A 20 kg object increases the length of a spring by exactly 7.2 cm. To the nearest tenth of a centimeter, by how much does a 32 kg object increase the length of the same spring?
Let be the mass of the weight and the elongation of the spring. Then for some constant of variation
,
We can find by setting
from the first situation:
so
In the second situation, we set and solve for
:
which rounds to 11.5 centimeters.
Give the coefficient of in the product
.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two terms and one constant are multiplied; find the three products and add them, as follows:
Add: .
The correct response is .
Solve for , given the equation below.
No solutions
Begin by cross-multiplying.
Distribute the on the left side and expand the polynomial on the right.
Combine like terms and rearrange to set the equation equal to zero.
Now we can isolate and solve for by adding
to both sides.
Solve for .
,
,
,
,
The two fractions on the left side of the equation need a common denominator. We can easily do find one by multiplying both the top and bottom of each fraction by the denominator of the other.
becomes
.
becomes
.
Now add the two fractions:
To solve, multiply both sides of the equation by , yielding
.
Multiply both sides by 3:
Move all terms to the same side:
This looks like a complicated equation to factor, but luckily, the only factors of 37 are 37 and 1, so we are left with
.
Our solutions are therefore
and
.
If , then solve
We know . When solving a function, we substitute the value of x into the function. In other words, anywhere we see an x, we will replace it with -4.
Give the coefficient of in the binomial expansion of
.
If the expression is expanded, then by the binomial theorem, the
term is
or, equivalently, the coefficient of is
Therefore, the coefficient can be determined by setting
:
Find a line parallel to the line that has the equation:
Lines can be written using the slope-intercept equation format:
Lines that are parallel have the same slope.
The given line has a slope of:
Only one of the choices also has the same slope and is the correct answer:
The retail price of gold is . Suppose Billy bought twenty gold coins at wholesale price for
each. How many gold coins can Billy buy at retail price from his profit if he chose to sell all twenty coins at
each?
Determine how much Billy has spent on all twenty gold coins. Since he bought 20 gold coins at wholesale price, multiply 20 by the price of gold at $100.
Billy has spent on
gold coins at wholesale price.
Determine his profit after he sells all gold coins at
each.
This amount is his revenue after selling all his 20 coins.
Profit is the total revenue minus the cost Billy has spent.
After subtracting the initial cost, Billy has $600 profit from selling all his 20 gold coins at $130 each.
Divide the profit with the retail cost of the gold coins to determine how many gold coins he can buy at retail price with his profit.
Billy can only buy gold coins at retail price as a result of his profit.
The answer is:
Convert the percent into a fraction:
In order to change a percent into a fraction, the first step is to take the percent and place it over 100:
Then simplify as needed:
For this question the final answer will be 21/50
Which of the following pairs of lines are parallel?
Lines can be written in the slope-intercept form:
In this form, equals the slope and
represents where the line intersects the y-axis.
Parallel lines have the same slope: .
Only one choice contains tow lines with the same slope.
The slope for both lines in this pair is .