Answer:
Step-by-step explanation:
Let's start with the original function.
We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4
respectively.
Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:
Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:
This function has vertical shift -2, phase shift -4/3 , amplitude 4, and period 4.
Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.
Answer:
which agrees with the first answer in the list of possible options.
Step-by-step explanation:
We can use the fact that the addition of all four internal angles of a quadrilateral must render 
. Then we can create the following equation and solve for the unknown "h":
Therefore the angles of this quadrilateral are:
Answer:
solve using long division.
75/4
what is the largest whole number smaller than 75 that 4 can go into?
72.
how many times can 4 go into 72?
18.
so then subtract 72 from 75 to get 3.
the new equation is
3/4
how many times can 3 go into 4?
0.75 times.
so add the 2 answers to get
18.75
4 can go into 75 18.75 times.
Answer:
The side c needs to be 12.85 for the triangle to have greatest perimeter
Step-by-step explanation:
We are given;
b = 13
a = 15
Angle at b: B = 55°
Let's find side c.
Using the law of cosines,we have;
b² = a² + c² - 2ac•cos(B)
13² = 15² + c² - 2•15•c•cos(55)
169 = 225 + c² - 30c•cos(55)
c² - 30c•cos(55) + 225 - 169 = 0
c² - 30c•cos(55) + 56 = 0
c² - 30c•(0.5736) + 56 = 0
c² - 30c•(0.5736) + 56 = 0
c² - 17.208c + 56 = 0
Using quadratic formula;
c = [-(-17.208) ± √((-17.208)² - (4•1•56)]/2(1)
c = [17.208 ± √(296.115 - 224)]/2
c = 8.604 ± 4.246
To have the greater perimeter, we need the larger value of c, thus we will use the positive sign and ignore the negative one ;
Thus,
c = 8.604 + 4.246 = 12.85
Take the area of the small photograph and divide it by four, assuming it's a square, each side would then be 6 inches. The large photograph has double the side length of the small one, so 6 multiplied by 2 is 12. To find the area of the large (square) photograph, multiply 12 by 12 as two of the sides, and the area of the large photo is 144 square inches
