Answer:
Step-by-step explanation:
From the figure attached,
Point B has been dilated to form point B'.
B(3, 1) → B'(6, 2)
→ B'[(2 × 3), (2 × 1)]
Since rule for the dilation of a point (x, y) by a factor of k is,
B(x, y) → B'(kx, ky)
By comparing the coordinates k = 2 is the scale factor by which the point B has been dilated about the origin.
Therefore, other vertices of the quadrilateral will be,
A(-2, 3) → A'(-4, 6)
C(1, -1) → C'(2, -2)
D(-3, -2) → D'(-6, -4)
D. since angle pqr is 52 and angle stu is 50. you know that su has to be shorter than pr
hope this helps!
The term "closed" in math means that if you take two items from a set, do some operation, then you'll always get another value in the same set (sometimes you may get the same value as used before). For example, adding two whole numbers leads to another whole number. We therefore say "the set of whole numbers is closed under addition". This applies to integers as well because integers are positive and negative whole numbers. So we can say that integers are closed under addition.
Integers are not closed under division. Take two integers like 2 an 5 and divide: 2/5 = 0.4 which is not an integer. Integers don't have decimal parts.
The set of whole numbers is {0,1,2,3,...} and we can subtract the two values 1 and 2 to get 1-2 = -1. The order matters here. Subtracting a larger value from a smaller leads to a negative. The value -1 is not in the set of whole numbers. So we can say that whole numbers is not closed under subtraction
Finally, the set of irrational numbers is closed under addition. Adding any two irrational numbers leads to another irrational number. For instance, pi+sqrt(2) = 3.142 + 1.414 = 4.556; I'm using rounded decimals as approximate values. An irrational number is one where we cannot write it as a fraction of integers. Contrast that with a rational number in which we can write it as a fraction of integers. Example: 10 = 10/1 is a rational number.
Answer:
b =± 5 sqrt(3)
Step-by-step explanation:
f(b) = b^2 – 75
To find the roots set the equation equal to zero
b^2 -75 =0
Add 75 to each side
b^2 – 75+75 = 0+57
b^2 = 75
Take the square root of each side
sqrt(b^2) = ±sqrt(75)
b = ±sqrt(3*25)
We know that sqrt(ac) = sqrt(a) sqrt(c)
b = ±sqrt(3)*sqrt(25)
b =± 5 sqrt(3)
Answer:
You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance. ( D )
Step-by-step explanation:
let : P = 0.6
x = 135 , n = 200
<em>p </em>= 135 / 200 = 0.675
H0 : P = 0.6
Ha : P ≠ 0.6
performing the test statistic = ( 0.675 - 0.6 ) / 
= 0.075 / 0.0346 ≈ 2.17
p-value = 2 * P ( Z > - 2.17 ) ( using excel function ; NORMSDIST )
= 2 * 0.015 = 0.03
