Answer:
72 degrees.
Step-by-step explanation:
If the angle is x degrees its complement is 90-x degrees and it's supplement is 180-x degrees.
4(90-x) = 2/3(180 - x)
360 - 4x = 120 - 2/3 x
360 - 120 = -2/3 x + 4x
240 = -2/3 + 12/3 x
240 = 10/3 x
x = 240 * 3/10
x = 72 degrees.
X+y+5=0
y=-x-5
If a solution exists y=y so we can say
x^2-9x+10=-x-5 add x+5 to both sides
x^2-8x+15=0 now factor
x^2-3x-5x+15=0
x(x-3)-5(x-3)
(x-5)(x-3) so x=3 and 5, using y=-x-5
y(3)=-8 and y(5)=-10
So the two solutions are:
(3,-8) and (5,-10)
B. Line K has a slope of -3
Answer:
the standard form equation is 1/2x^2-x-3/2=0
the vertex form equation is 1/2(x-1)^2-2=0
Step-by-step explanation:
Unfortunately, this can't be written in slope intercept form but I can write it in standard form(ax^2+bx+c) or vertex form (a(x-h)+k)
The vertex is (1,-2)
I estimate a=1/2 because the graph was widened and that can only be done by a fraction.
So, 1/2(x-1)^2-2=0
To find it in standard form
foil (x-1)(x-1)= x^2-2x+1
Then multiply by 1/2(x^2-2x+1)= 1/2x^2-x+1/2-2
To add 1/2-2. You mulitply -2 by 2/2 which equals 1/2-4/2 which equals -3/2
So the standard form equation is 1/2x^2-x-3/2=0
An arithmetic sequence is a sequence in which the difference between each consecutive term remains same (constant).
The explicit formula for an arithmetic sequence is 
, where a is first term of sequence, d is the common difference between consecutive terms.
A) We can see from Julio's swimming distance that it is in arithmetic sequence as after every successive training session Julio's swimming distance increased by 0.30 miles.
Therefore, we can see that Julio's training schedule is an arithmetic sequence.
B) Let us find Julio will take how many days to swim 2.95 miles by using explicit formula.
Let us substitute our given information in above formula.
We are told that Julio swims every two days, this implies that he would swim on alternate days. So he will swim 2.95 miles on 10*2 =20th day.
Let us find 20th day will be which day. As Julio started his training schedule on Tuesday, 20th day will be a Sunday. Therefore, Julio will swim for 2.95 miles on a Sunday.
