Maths problem sat study guide

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1

Hi,
I dont know how to find the answer of the 8p374 in the sat official study guide version 2.

" the figure above shows line l in the xy-coordinate plane.Line m( not showm) is obtained by horizontally translating each point on line l 2 units to the left. If the equation of m is y=4/5x+k, what is the value of k ? "

In the figure, we can see 2 points of l : (-5,0) and (0,4)
Thanks :))

2

I forgot i have some other problem …
The 3 p 367 :

For which of the following graphs of f does f(x)=f(-x) for all values of x shown ?
5 figures are proposed but i dont know how to find the answer …

The 5 p368

Which of the following is an equation of the line that has a y-intercept of 2 and an x-intercep of 3 ?
A: -2x+3y= 4
B : -2x+3y=6
C: 2x +3y= 4
D : 2x+3y = 6
E : 3x +2y = 6

The 7 p368

On the staircase shown above, both the depth and the height of each step are s and each step forma a right angle. What is the value of t in terms of s ?

We see 7 steps ans t represent all the step

A : 10s
B : 14s
C : 7s(square root) 2
D : 7s (squre root) 3
E : 2s(square)

The 8 p369

The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x betwen 0 and 12 ?

We see a figure with 4 values of x=0 between 0 and 5

A : 8
B : 9
C : 10
D : 11
E : 12

The 12 p 371

In the figure above, the four circles have the same center and their radii are 1,2,3 and 4 respectively. What is the ratio of the area of the small shadded ring ( radii 2 i think ) to the area og the large shadded rinf ( 4 i think ) ?

A : 1:2
B : 1:4
C : 3:5
D : 3:7
E : 5:7

Thanks thanks thanks thanks

3
  1. Equation of line l: y = (4/5)x + 4. To obtain line m, translate l 2 units to the left. Then (-7,0) is on line m, for example. We can easily find k by just plugging in (-7,0) in the equation for line m:

0 = (4/5)(-7) + k
–> k = 28/5

2.Not sure what the answer is (I don’t have the book), but any function that is symmetric about the y-axis works (f is called an “even” function in this case).

  1. (0,2) and (3,0) are on the line. You can either plug into the answer choices, or find that the slope of the line connecting (0,2) and (3,0) is -2/3, so the equation is y = (-2/3)x + 2. This is equivalent to y + (2/3)x = 2 <--> 3y + 2x = 6, or D.
  2. Is t the distance from the foot of the bottom step to the end of the top step? If so, assuming I visualized correctly, the diagram will look like seven 45-45-90 triangles, each of side length s (the depth/height of each step). It follows that t should equal 7s sqrt(2), C.
  3. I will need the diagram for this one. If the four roots of f(x) are in the interval (0,5) (open interval), then there are also four roots along open interval (5,10). But we need the number of roots of f(x) along (0,2) to figure out (10,12).

If 0 is a root of f(x), then 5 and 10 are also roots.

  1. Assuming you are referring to the rings of thickness 1 whose outer radii are 2 and 4:

The area of the smaller ring is pi(2^2 - 1^2) = 3pi (just subtract the area of the smallest circle from the area of the circle of radius 2). The area of the largest ring with inner radius 3, outer radius 4 is pi(4^2 - 3^2) = 7pi. Their ratio is 3pi: 7pi = 3:7, D.

4

For this question, forget the design of the stairs. Simply build a right triangle with t as the hypotenuse. The sides are easy to define as 7s. From there it is a basic Pythagorean equation.

5

^Yeah, that works too.

6

Thanks thanks thanks thanks thanks thanks thanks thanks :))))