Length (2, 6) to (-4, 6) is sqrt((x2 - x1))^2 + (y2 - y1)^2) = sqrt((-4 -2)^2 + (6 - 6)^2) = sqrt((-6)^2 + 0) = 6
Length (2, 6) to (-4, 4) is sqrt((-4 - 2)^2 + (4 - 6)^2) = sqrt((-6)^2 + (-2)^2) = sqrt(36 + 4) = sqrt(40) = 2sqrt(10) units
Length (-4, 6) to (-4, 4) is sqrt((-4 - (-4))^2 + (4 - 6)^2) = sqrt(0^2 + (-2)^2) = 2
So the length of the longest side is 2sqrt(10) units
Answer:
m<GFA = 110
Step-by-step explanation:
1. ABCD - parallelogram Definition of a parallelogram
(AB ll CD) (AD ll BC)
2. m<B + m<C = 180 Consectuive angles in a
110 + m<C = 180 parallelogram are supplementary
m<C = 70
3. m<GCB = 1/2 m<C Definition of angles bisector
m<GCB = 70
4. m<B = m<D = 110 Opposite angles in a
parrallelogram are congruent
5. m<CDG = 1/2 m<D Defintion of an angle bisector
m<CDG = 55
6. m<GCB+m<CDG+m<CGD=180 Sum of anlges in a triangle (ΔCDG)
70 + 55 + m<CGD = 180
125 + m<CGD = 180
m<CGD = 55
7. m<CGD + m<DGF = 180 Linear pair, supplmentary angles
55 + m<DGF = 180
m<DGF = 125
8. m<C = m<A = 70 Opposite angles in a paralellogram
are congruent
9. m<ADG = 1/2m<D Definiton of an angle bisector
m<ADG = 55
10.m<ADG+m<DFG+m<GFA+m<A=360 Sum of angles in quadrilateral
55 + 125 + m<GFA + 70 = 360 DGFA
m<GFA + 250 = 360
m<GFA = 110
Answer:
f(4) =11
Step-by-step explanation:
f(x)=3x-1
Let x = 4
f(4)=3*4-1
= 12-1
= 11
Answer:
Step-by-step explanation:
In the exponential growth/decay function
, in our situation,
y is the number of ants remaining in the colony after the growth or decay,
a is the initial number of ants in the colony, and
b is the growth/decay rate. Rule: if b is greater than 1, the function is growth; if b is greater than 0 but less than 1, the function is decay.
Our equation looks like this (it's given):
a = 50, which is the initial number of ants in the colony.
b = .8 (which actually means that then number of ants is declining by 20% each week). Since .8 is a fraction of 1, this is decay.
So far, we know that 1 and 4 are true. Let's look at 5. We have to do some solving to find out if it's true or not. If the number of ants after x = 2 weeks is 32, then we plug in 2 for x and see if the y we get as the answer is 32:
and
y = 50(.64) so
y = 32
5 is true as well. Let's test 6 by replacing x with 8 and seeing if y = 10:
and
y = 50(.16777216) so
y = 8.388
6 is not true.
1, 4, 5 are true
It would cost $26 because 3x8=24. 3/1/3=1. so 1/3=$1.
