Hard Math Problems- Need some help

Test Preparation SAT Preparation
1

<p>I know the answers but I don't know you can get that answer. If anyone can help me out with 1 or more problems, I would appreciate it.</p>

<p>These problems are from the blue book:</p>

<p>Pg 522, #17
1) In the xy-plane, line L passes through the origin and in perpendicular to the line 4x+y=k, where k is a constant. If the 2 llines intersect at the point
(t, t+1), what is the value of t?
a) -4/3
b) -4/5
c) 3/4
d) 5/4
e) 4/3</p>

<h1>20</h1>

<p>2)When 15 is divided by the positive integer k, the remander is 3. For how many different vaules of k is this ture?
a)1
b)2
c)3
d)4
e)5</p>

<p>pg 534. #13
3) Let the function f be defined by f(x) = x+1. If 2f(p)=20, what is the value of f(3p)?</p>

<h1>15</h1>

<p>4) A meauring cup contains 1/5 of a cup of orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is oranje juice?</p>

<p>Picture problems
pg 551, #16
pg 532, #8</p>

<p>Again, any help will be appreciated.</p>

<p>If anyone wants to know the answers I will post them.</p>

2

<p>1) slope of line L = 1/4 so equation of line L is y=x/4. plug (t, t+1) into y=x/4 and solve for t.</p>

<p>2) find values where the remainder equals 3, there are patterns to this. when 15 is divided by 12, the remainder is 3 so you find factors of 12 that cannot be divided into a number between 12 and 15. k=12, 4, 6 so C? </p>

<p>3) f(p)=10 so p= 9. f(3p)=28</p>

<p>4) 3/4 is filled w/ O, G, and P juice. so 1/4 is filled with each. there is already 1/5 so 1/4+1/5=9/20</p>

<p>I don't have the book so i can't do the rest. i'm not sure if these are the right answers, but that's how i would approach the problems.</p>

3

<p>what are the answers, may be i can explain</p>

4

<p>Thanks x3rose.
Here are the answers:
1) a) -4/3 , sorry but can you be more detailed when you say plug t, t+1 in
2) c) 3
3) 28
4) actually it's 7/15 or .466 (difficultly is medium)
9/20 = .45, I think this would be wrong </p>

<p>I'll post some pics of the other 2 problems tommorrow.</p>

<p>Thanks a lot.</p>

5

<p>I think he means plug the answer choices in for number one.</p>

6

<p>Ok for number forget k</p>

<p>You get 2 equations
y = 4x
y = 1/4x
now plug in the points
T + 1 = 1/4T
-3/4T = 1
T = -4/3</p>

<p>For number 4. i see what she did wrong.</p>

<p>The first fraction is 1/5</p>

<p>There is 4/5 left and that is further split into 3 equal parts because there are 3 different juices. So you get 4/15 of each juice</p>

<p>So you get 1/5 + 4/15 = 7/15</p>

<p>Changed :D</p>

7

<p>oh yes gyros is right. sorry i can't subtract. yeah, i can do calculus but can't do basic math.. quite sad.</p>

<p>btw, i'm a girl.</p>

8

<p>Thanks gyros321 and everyong for helping me. For #4, I misread the problem. </p>

<p>I'll be posting a couple of more problem up. I've been doing intense studying over the SAT. It hasn't let me slept in a month. It's so strange. How one test can decide everything. Oh well, there's always a retest. </p>

<p>I've been scoring around 690 on practice test on math. I have 5 more days till I take the SAT.</p>

9

<p>551 #16</p>

<p>Since it asks for a rectangular region of 12L by 10L units wide, we know that the area will be 120L^2. We are given FIVE rectangles of dimensions L by W. </p>

<p>Since we're looking for an L^2 term, we seek for a way to find W in terms of L.</p>

<p>Remember that opposite sides of a rectangle are equal, so in the picture 2L = 3W. Solving for w gives us w=2L/3.</p>

<p>Be careful here, we need to find the number of rectangles of dimension L x W to cover an area of 120L^2. Read carefully to make sure you aren't solving for five rectangles instead of individual ones.</p>

<p>So we have w. L x W = L x 2L/3 = (2L^2)/3. Dividing the total area by the number of individual rectangles, we get the number needed. So the answer is E) 180</p>

<p>For #8, you could find the exact function, but notice that the outputs of function f are equal. Thus, f(2)=f(0), f(1) is of course = f(1), and f(3) = f(-1).
Remember outputs are y values and inputs are x values when dealing with coordinate geometry. Answer is C</p>

10

<p>You've gotten some good answers; this</a> thread has a list of previously discussed questions that you might find useful.</p>

11

<p>For 532 #8</p>

<p>-The graph shows a parabola
-The only information you need here is in the last sentence(If f(b) = f(3), which of the following could be the value of b?)
-So basically, you're trying to find 2 values for x that when plugged into the function f(x) will equal the same y value.
-so when x = 3, y = 5(you can do this visually by tracing along the parabola)
-now all you have to do is find the other point in the graph that has the same y value and this point has an x value of -1(ans-c). The coordinates would be (-1, 5)</p>

12

<p>Thanks for all the help. </p>

<p>I'll check that thread out tanman, before posting questions.</p>

13

<p>I've check out the thread and I didn't find these problems.
I've been missing 6-7 total on math-which gives me a range of 660-720.</p>

<p>anyways, here are the problems:</p>

<p>Picture problems
pg 586, # 18</p>

<p>pg 599 #17
This was the answer from someone else:
"here's the thing. you'll have 11 line segments because besides V there are other 11 vertices, but V is conected with 3 vertices directly(meaning through edges). so your answer is 11-3=8.
hope you understand"</p>

<p>I don't get what the question is asking. I know that V is connected with 3 vertices directly but what does that have to do with, "How many of these segments will not lie on an edge of the figure."</p>

14

<p>586, #18:</p>

<p>We are told AB=BC and DE = EF=DF. That means the big triangle ABC is isosceles and the smaller triangle DEF is equilatreral. The angle measures of an equilateral triangle are all 60 degrees, so label them 60.</p>

<p>We are given ABC is 30 degrees, so label that, and label angles BAC and BCA 75 degrees. You know this because the triangle is isosceles, and 180-30 = 150/2 = 75 degrees.</p>

<p>We are also given angle BDE is 50 degrees, so label that.</p>

<p>The only other thing we need to know in order to calculate the measure of angle DFA is angle ADF - you know this because it is a supplementary angle (adds up to 180 degrees) with BDE (50 degrees) and FDE (60 degrees). If you don't see why this is, notice that they are on a straight line.</p>

<p>Therefore, angle ADF is 70 degrees (because 50+60+70=180), and angle DFA is 35 degrees because it is the third angle of the triangle with a 70 degree and 75 degree angle in it. </p>

<p>So the answer is B, 35 degrees.</p>

<p>599 #17:</p>

<p>In geometry, an "edge" is where two sides meet. For example, the four solid slanted vertical lines that connect the top base to the bottom base are all edges - as are the sides of the hexagonal top base. </p>

<p>Now that you know what an edge is, you can understand the question: it asks, how many segments can be drawn connecting point V to the other verticles in the figure, which do not lie on the edges of the figure?</p>

<p>Looking at the figure, you can see that there are only 3 straight line segments which would lie (completely) on edges of the figure. That would be, the line from V to the vertice directly under it, and from V to the two vertices directly left and right of it. All other lines connecting V to the other vertices (and you can try drawing these lines if it helps you visualize it) must travel over a side of the figure, or through empty space, in order to connect.
Notice the distinction between "side" and "edge."</p>

<p>Since there are 3 that lie on edges, and 11 different lines being drawn (one for each vertice) the answer is 11-3 = 8.</p>

<p>Hope that makes more sense.</p>

15

<p>Thanks obsessedAndre for breaking it down. It makes the problem a lot easier to understand.</p>

16

<h1>17</h1>

<p>1) In the xy-plane, line L passes through the origin and in perpendicular to the line 4x+y=k, where k is a constant. If the 2 llines intersect at the point
(t, t+1), what is the value of t?
a) -4/3
b) -4/5
c) 3/4
d) 5/4
e) 4/3</p>

<p>4x + y = k
y = k -4x
slope : -4
Slope of line L must be 1/4, and the y-intercept of L must be 0.</p>

<p>L: y = x/4</p>

<p>Now substitute t and (t+1) for x and y respectively</p>

<p>t+1 = t/4
4t+4 = t
4 = -3t
t = -4/3</p>

<h1>20</h1>

<p>2)When 15 is divided by the positive integer k, the remander is 3. For how many different vaules of k is this ture?
a)1
b)2
c)3
d)4
e)5</p>

<p>If the remainder is 3, k must be a factor of 12 but not a factor of 15. </p>

<p>Factors of 12 = 1,2,3,4,6,12
Factors of 15 = 1,2,3,5,15</p>

<p>Values of k: 4,6,12</p>

<p>Answer: C</p>

17

<p>pg 534. #13
3) Let the function f be defined by f(x) = x+1. If 2f(p)=20, what is the value of f(3p)?</p>

<p>2f(p) = 20 = 2(p+1)
p=9.</p>

<p>f(3p) = f(27) = 27+1 = 28</p>

<h1>15</h1>

<p>4) A meauring cup contains 1/5 of a cup of orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is oranje juice?</p>

<p>1/5 + (1/3)(4/5) = 1/5 + 4/15 = 3/15 + 4/15 = 7/15</p>

18

<p>Came across another problem. 657, #16.</p>

<p>It's a picture problem but basicall it's a small circle inside of a large circle. The large circle is shaded.</p>

<p>The figure above consists of two circles that have the same center. If the shaded is 64(pie) square inches and the smaller circle has a radius of 6 inches, what is the radius, in inches, of the larger circle.</p>

19

<p>pg 657 #16</p>

<p>area of the big cirl=64pi+area of small circle
area of small cirlce=36pi
area of large circle=100pi
100pi=(r of large circle)^2*pi
r=10</p>

<p>hope that made sense</p>

20

<p>It did, I don't know what I was thinking. I have more problems. </p>

<p>picture problems:
1)Quit embarassing but pg 670#4 (easy difficulty)</p>

<p>2) 683, #14 (medium)</p>

<p>Maybe, I'm think too much or too less.</p>