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Example Questions
Example Question #231 : New Sat
How many times does the equation below cross the x-axis?
You can solve this problem two ways.
3. You can solve for where the graph crosses the x-axis by setting the equation equal to zero, factoring, and solving.
2. You can quickly sketch the graph by choosing some x values and solving for y.
We see that the graph passes the x-axis twice.
Example Question #232 : New Sat
Simplify the expression by rationalizing the denominator, and write the result in standard form:
Multiply both numerator and denominator by the complex conjugate of the denominator, which is :
Example Question #233 : New Sat
Find the solutions for
The first step is to set it equal to zero.
Now we will use the quadratic formula.
In this case , ,
Example Question #234 : New Sat
and are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?
The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.
Perimeter A = 45” and perimeter B = 135”
The proportion of Perimeter A to Perimeter B is .
This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.
15” x 3 = 45”
10” x 3 = 30“
Example Question #235 : New Sat
If and , what is the length of ?
AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.
Since we have a triangle, the opposites sides of those angles will be in the ratio .
Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to .
which also means
Example Question #54 : New Sat Math No Calculator
Find the solutions to
First step is to set it equal to zero
Now factor out an
Set up the equations, and solve for .
Example Question #236 : New Sat
Find the value of .
Subtracting the second equation from the first, we acquire .
Adding this equation to the third equation, we get .
Therefore, .
Example Question #1 : Direct And Inverse Variation
The temperature at the surface of the ocean is . At meters below the surface, the ocean temperature is . By how much does the temperature decrease for every meters below the ocean's surface?
This may seem confusing, but is pretty straightforward.
Thus, for every 125 meters below the surface, the temperature decreases by one degree.
To find how much it decreases with every 100 meters, we need to do the following:
Thus, the temperature decreases by every 100 meters.
Example Question #56 : New Sat Math No Calculator
Let be a number. Increasing by twenty percent yields that same result as decreasing the product of four and by five. Calculate the value of .
None of these
The problem tells us that increasing by twenty percent gives us the same thing that we would get if we decreased the product of four and by five. We need to find expressions for these two situations, and then we can set them equal and solve for .
Let's find an expression for increasing by twenty percent. We could represent this as the following:
Let's find an expression for decreasing the product of four and by five. First, we must find the product of four and , which can be written as . Then we must decrease this by five, so we must subtract five from , which could be written as the following:
Now we must set the two expressions equal to one another.
Subtract from both sides. We can rewrite as so that it has a common denominator with
Now we can add five to both sides.
Now we can multiply both sides by , which is the reciprocal of
The answer is:
Example Question #57 : New Sat Math No Calculator
Solve the following system of equations:
What is the sum of and ?
This problem can be solved by using substitution. Write the first equation in terms of and substitute it into the second equation.
So and thus and solving for and then .
So the sum of and is 7.