Math Questions

[denttiger]

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Here are some questions... I think the answer key might be wrong on some of these because I usually don't miss these type of questions. Anyways.. can someone solve these for me! PS.. I'm horrible at math but getting better slowly, so I really need someone to explain the concept behind the trig question please!

1) Rich is one-sixth of his father's age. In 20 years he will be one-half of his father's age at that time. How old is his father?

2) What is the distance on a two-dimensional graph between (7,6) and (2,-6)?
I know how to do this one but keep getting an answer that is not a choice.

3) Two committees are formed with seven people on one committee and eight on the other. If three people are in both groups, how many people belong to only one group?

4) The value of sin(Pi/3) equals the value of:
a) sin (2pi/3)
b) sin (-pi/3)
c) sin (-5/6)
d) sin (5pi/6)
e) sin (-2pi/3)

5) What line would be perpendicular to y = 3x + 3 and contains the point (3,-1)?
Easy I know.. but their answer doesn't make sense. Please tell me what ya'll think and THANKS a ton!! Good luck to all studying, applying, or w/e else the pre-dent life requires!!

 

[DrAngie]

Here are some questions... I think the answer key might be wrong on some of these because I usually don't miss these type of questions. Anyways.. can someone solve these for me! PS.. I'm horrible at math but getting better slowly, so I really need someone to explain the concept behind the trig question please!

1) Rich is one-sixth of his father's age. In 20 years he will be one-half of his father's age at that time. How old is his father?

2) What is the distance on a two-dimensional graph between (7,6) and (2,-6)?
I know how to do this one but keep getting an answer that is not a choice.

3) Two committees are formed with seven people on one committee and eight on the other. If three people are in both groups, how many people belong to only one group?

4) The value of sin(Pi/3) equals the value of:
a) sin (2pi/3)
b) sin (-pi/3)
c) sin (-5/6)
d) sin (5pi/6)
e) sin (-2pi/3)

5) What line would be perpendicular to y = 3x + 3 and contains the point (3,-1)?
Easy I know.. but their answer doesn't make sense. Please tell me what ya'll think and THANKS a ton!! Good luck to all studying, applying, or w/e else the pre-dent life requires!!

Hey there,

I'll answer 1 and 3 for you and have to get back with you regarding the rest.

1) R = 1/6 F [Richard is one-sixth his father's age].
R+20 = 1/2 (F + 20) [in 20 years Richard will be half his father's age at that time

So, (remember, R = 1/6F)

1/6F + 20 = 1/2 (F + 20) set up the equation

1/6 F +20 = 1/2F + 1/2*20 multiply through the parenthses, rewrite the equation

1/6 F + 20 = 1/2F + 10 get like terms together

20-10 = 1/2 F - 1/6F get common denominator and simplify equation

10 = 3/6F -1/6F => 10 = 2/6F => 10 = 1/3F multiply each side by 3

30 = F (Richard's father is currently 30, Richard is 5, in 20 years he will be 25 and his father will be 50)

3) One group has 7 and the other has 8 and 3 people are in both groups. 7-3=4, 8-3=5; 4+5 =9. Therefore, there are 9 people that are only in one group. Or, to visualize it, what I would do is draw two conjoining circles and label one committee A and the other committee B. In the space where the circles overlap make three dots to represent the 3 people in both groups. In circle A make enough dots to equal 7 (when added to the 3) and in the other make enough dots to equal 8 (when added to the 3). You will have a total of 9 people that are only in one group (4 only in group A and 5 only in group B)--see attachment

 

[laundry]

1.
(x + 20)/2 = 1/6x + 20
x=30

2.
you need to come up with a right triangle. (7,6) and (2,-6) give you two legs 12 and 5 units of length. so the distance is 13. (5,12,13 right triangle.

3.
either i'm not reading straight at 12:30 AM, or the answer is 9...
8+7-3=9...i'm prolly wrong though

4.
again..must be tired...cause none of those are equal...

5.
y=-1/3x + b
plug in the coordinate to find b
-1 = (-1/3)3 +b
b=0
y=-1/3x

Cheers and nighty nighty 😴

 

[Lonely Sol]

4) The value of sin(Pi/3) equals the value of:
a) sin (2pi/3)
b) sin (-pi/3)
c) sin (-5/6)
d) sin (5pi/6)
e) sin (-2pi/3)

the pre-dent life requires!!

The answer should be A, since you know both Quad I and II have (+) signs and you know sin 2pi/3, which is 120 degress is exactly opposite of sin pi/3, which is 60 degrees. Therefore, there both have exact same sine values.

I agree with the all the answers by laundry

*Hope this helps, I suck at explaining!

 

[hoak]

4) The value of sin(Pi/3) equals the value of:
a) sin (2pi/3)
b) sin (-pi/3)
c) sin (-5/6)
d) sin (5pi/6)
e) sin (-2pi/3)

Yeah, I think the answer is A since sin (x) = sin (pi -x) => sin (pi/3) = sin(2pi/3). Correct me if I'm wrong

 

[denttiger]

Thanks a lot to all of you!!