Answer:
The perimeter of triangle ΔABC is approximately;
(A) 20.0
Step-by-step explanation:
In ΔABC, the coordinates of the vertices are given as follows;
A(-4, 1), B(-2, 3), C(3, -4)
The length, 'l', of the sides of the triangle with known 'x', am]nd 'y' coordinates are given as follows;
Therefore, we have;
The length of segment 
= √((3 - 1)² + (-2 - (-4))²) = 2·√2 ≈ 2.83
The length of segment 
= √(((-4) - 3)² + (3 - (-2))²) = √74 ≈ 8.6
The length of segment 
= √(((-4) - 1)² + (3 - (-4))²) = √74 ≈ 8.6
The perimeter of a geometric shape is equal to the sum of the length of sides of the figure
The perimeter of triangle ΔABC = (The length of segment ) + (The length of segment ) + (The length of segment )
∴ The perimeter of triangle ΔABC = 2·√2 + √74 + √74 ≈ 20.0.
Answer:
16%
Step-by-step explanation:
The indicated probability is actually the area under the standard normal curve to the left of the mean. I used the function normalcdf( on my TI-83 Plus calculator to find this quantity:
normalcdf(-1000,85,90,5) = 0.1587.
Note #1: This quantity (area / probability) is the area to the left of 85.
Note #2: by the Empirical Rule, 68% of data lies within 1 s. d. of the mean, so the area between the mean (90) and the score (85) is half of 68%, or 34%. Subtracting this from 50% (the area to the left of the mean), we get 16%, which is roughly equivalent to the 0.1587 we got earlier.
Answer:
$8.59
Step-by-step explanation:
The unit price is just asking for what one pair of gloves cost.
∴The unit price of the pairs of gloves is $8.59
Hope this helps!
Answer:
y=-4/3x-9
=
−
4
3
x
−
9
Step-by-step explanation:
First we need to get the slope of the perpendicular line
The slope of a perpendicular line is equal to the negative inverse of the slope of the given line
y
=
m
x
+
b
y
=
3
4
x
−
2
⇒
m
=
3
4
m
'
=
−
1
m
⇒
m
'
=
−
1
3
4
⇒
m
'
=
−
4
3
Now that we have the slope, we need to find the y-intercept.
To find the y-intercept, we need to plug-in values of
x
and
y
that the line passes through
y
'
=
m
'
x
'
+
b
⇒
y
'
=
−
4
3
x
'
+
b
⇒
7
=
−
4
3
(
−
12
)
+
b
⇒
7
=
16
+
b
⇒
b
=
−
9
Therefore, the equation of the line is
y
=
−
4
3
x
−
9
<span>Because G is the centroid of the triangle, therefore
AG = 2GF
That is,
5x + 4 = 2(3x - 1)
5x + 4 = 6x - 2
4 + 2 = 6x - 5x
6 = x
Therefore
AG = 5*6 + 4 = 34
GF = 3*6 - 1 = 17
A.F = AG + GF = 34 + 17 = 51
Answer: 51</span>
