# Practicing for SAT Math and had my first four part miserable failure sequence

• UltimateSomni
In summary, The first problem can be solved by comparing the two expressions x2+kx+7 and x2+(h+1)x+h and equating the coefficients of each power of x. This leads to the conclusion that k=8. For the second problem, the possible lengths of the sides of triangle ABC are 2,5,√29. In the third problem, plugging in the definition of f(x) into the equation (1/2)f(√t)=4 and solving for t gives the value of t. And for the fourth problem, to represent an even integer twice the value of an odd integer, simply double the odd integer.
UltimateSomni
For these four practice problems, I had little idea what the hell to do (plugging in seemed worthless), could anyone help? Sorry if this isn't what the board is suppose to be used for. Answers in spoiler tags.

If k and h are constants and x2+kx+7 is equivalent to (x+1)(x+h), what is the value of k?
8
-----------------------------------------------------------------

In the figure above, if the legs of the triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC?

2,5,sqrt 29
2,5,7
3,3,3 sqrt2
3,4,5
4,5, sqrt41

2,5 sqrt 29
-------------------------------------------------------

Let the function f be defines as f(x)=2x-1. If 1/2f(sqrt t)=4, what is the value of t?

3/sqrt 2
7/2
9/2
49/4
81/4

81/4
----------------------------------------------------------

If k is a positive integer, which of the following must represent an even integer twice the value of the odd integer?

2k
2k+3
2k+4
4k+1
4k+2

4k+2

It would be a great help if anyone could even point me into the right direction on these

1) Multiply out (x+1)(x+h) by FOILing and equate it to x2+kx+7. What's the first conclusion you must make? What's the second conclusion?

2) The most important thing here is the slope of that line. Take into account that the slope of the line is rise/run. What's a possibity for the value of rise? run? (looking at the answers) Once you have those two values, how do you find the hypotenuse?

3) Judging from the answer, it looks like you mean (1/2)f(sqrt t)= 4, not 1/[2f(sqrt t)]= 4. The use of parentheses here is very important. If f(x) = 2x - 1, what's f(sqrt(t))? Once you have this, plug it into (1/2)f(sqrt t)= 4 and solve for t.

4) Something is missing from this problem, but I think what you meant to say is define an odd integer (call it j) as j = 2k+1, where k is a positive integer. If this is the case, how do we represent twice the odd integer?

UltimateSomni said:
If k and h are constants and x2+kx+7 is equivalent to (x+1)(x+h), what is the value of k?
Multiply out (x+1)(x+h) and the answer is obvious.

In the figure above, if the legs of the triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC?
There are two conditions here. First, the ratio of the two legs has to equal 0.4, because the line goes through the origin and (4, 10). The second condition is the Pythagorean theorem.
-------------------------------------------------------

Let the function f be defines as f(x)=2x-1. If 1/2f(sqrt t)=4, what is the value of t?
This one CAN be solved just by plugging in: plug the definition of f into the equation, then solve for t.

If k is a positive integer, which of the following must represent an even integer twice the value of the odd integer?
For any integer k, 2k is even, and 2k+1 is odd. To be twice the value of an odd integer, just double that.

pmsrw3 said:
Multiply out (x+1)(x+h) and the answer is obvious.

There are two conditions here. First, the ratio of the two legs has to equal 0.4, because the line goes through the origin and (4, 10). The second condition is the Pythagorean theorem.
-------------------------------------------------------

This one CAN be solved just by plugging in: plug the definition of f into the equation, then solve for t.

For any integer k, 2k is even, and 2k+1 is odd. To be twice the value of an odd integer, just double that.

2. Got it, 2,5 sqrt 29 is the only one that fits the 4:10 ratio

3. Didn't realize it was that obvious

4. Okay the makes sense.

Still no idea what to do on the first one

UltimateSomni said:
Still no idea what to do on the first one
(x+1)(x+h)
x(x+h) + 1(x+h)
x^2 + xh + x + h
x^2 + x(h+1) + h

Does that help?

I still cannot figure it out.

UltimateSomni said:
I still cannot figure it out.
Sure you can. Compare these two expressions:

x2 + (h+1)x + h

x2 + kx + 7

What values of h and k make them the same?

I don't see why there is a limit to what h and k can equal.

UltimateSomni said:
I don't see why there is a limit to what h and k can equal.
You may be overthinking this a little. Just LOOK at the expressions

x2 + (h+1)x + h

x2 + kx + 7

Don't they look similar to you? What would it take to make them look identical? (And you know the answer, too -- try plugging that in and see what happens.)

okay I get it now

It might help if you know that for two polynomials (of equal degree), for the two polynomials to be equal for every x, each of the coefficients must be equal for every x. Your two polynomials are x2+kx+7 and x2+(h+1)x+h. Setting these two equal, with x2+kx+7=x2+(h+1)x+h, we can equate the coefficents of every power of x:

1=1 (the two coefficients of x2)
k=h+1 (the two coefficients of x)
7=h (the two coefficients of the constant term x0)

From there it's easy to conclude that k=8.

Char. Limit said:
It might help if you know that for two polynomials (of equal degree), for the two polynomials to be equal for every x, each of the coefficients must be equal for every x. Your two polynomials are x2+kx+7 and x2+(h+1)x+h. Setting these two equal, with x2+kx+7=x2+(h+1)x+h, we can equate the coefficents of every power of x:

1=1 (the two coefficients of x2)
k=h+1 (the two coefficients of x)
7=h (the two coefficients of the constant term x0)

From there it's easy to conclude that k=8.

O_O This is great. Thank you.

## What are some tips for practicing for SAT Math?

1. Start Early: Begin practicing for the SAT Math section at least a few months before the test date to give yourself enough time to improve your skills.

2. Familiarize Yourself with the Format: Familiarize yourself with the types of questions that will be asked on the SAT Math section and the format of the test. This will help you strategize and manage your time effectively.

3. Practice with Official SAT Practice Tests: Make sure to practice with official SAT practice tests to get a feel for the types of questions and level of difficulty.

4. Identify and Focus on Weak Areas: Take practice tests and identify your weak areas. Focus on improving those areas to increase your overall score.

5. Use Online Resources: Utilize online resources such as Khan Academy and other SAT prep websites to supplement your studying and practice.

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