Answer:
the slope is 3/2
the x intercept is (-1/3,0)
the y intercept is (0, 1/2)
X=2h, y=3k
Substitute these values into equations.
y+2x = 4 ------> 3k+2*2h=4 -----> 3k +4h =4
2/y - 3/2x = 1-----> 2/3k -3/(2*2h) = 1 ------> 2/3k - 3/4h =1
We have a system of equations now.
3k +4h =4 ------> 3k = 4-4h ( Substitute 3k in the 2nd equation.)
2/3k - 3/4h =1
2/(4-4h) -3/4h = 1
2/(2(2-2h)) - 3/4h = 1
1/(2-2h) -3/4h - 1=0
4h/4h(2-2h) -3(2-2h)/4h(2-2h) - 4h(2-2h)/4h(2-2h) =0
(4h- 3(2-2h) - 4h(2-2h))/4h(2-2h) = 0
Numerator should be = 0
4h- 3(2-2h) - 4h(2-2h)=0
Denominator cannot be = 0
4h(2-2h)≠0
Solve equation for numerator=0
4h- 3(2-2h) - 4h(2-2h)=0
4h - 6+6h-8h+8h² =0
8h² +2h -6=0
4h² + h-3 =0
(4h-3)(h+1)=0
4h-3=0, h+1=0
h=3/4 or h=-1
Check which
4h(2-2h)≠0
1) h= 3/4 , 4*3/4(2-2*3/4)=3*(2-6)= -12 ≠0, so we can use h= 3/4
2)h=-1, 4(-1)(2-2*(-1)) =-4*4=-16 ≠0, so we can use h= -1, also.
h=3/4, then 3k = 4-4*3/4 =4 - 3=1 , 3k =1, k=1/3
h=-1, then 3k = 4-4*(-1) =8 , 3k=8, k=8/3
So,
if h=3/4, then k=1/3,
and if h=-1, then k=8/3 .
Answer:
D. 
Step-by-step explanation:
We have been given a table that represents the the number of electoral votes California was assigned each decade of the past century. We are asked to find the 3rd quartile of our given data.
The number of votes are: 9, 13, 13, 22, 25, 32, 40, 45, 47, 54, 55.
We will use upper quartile formula to solve our given problem.
, where, n represents the number of elements in the data set.
We can see that our data set has 11 data points, so upon substituting n=11 in above formula we will get,
Now let us count 9th term of our data set. Upon counting our data set from left to right we can see that 9th term of our data set is 47, therefore, 3rd quartile of our given data is 47 and option D is the correct choice.
Answer:
- 1
Step-by-step explanation:
Using the order of operations PEMDAS ( parenthesis, exponents, multiplication, division, addition, subtraction )
Given
17 - 6 × 10 ÷ 2 + 12 ← perform multiplication
= 17 - 60 ÷ 2 + 12 ← perform division
= 17 - 30 + 12 ← perform addition/ subtraction from left to right
= - 13 + 12
= - 1
