Answer:
D)4x + 6/(x + 1)(x - 1)
Step-by-step explanation:
A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle
where
is the perimeter
is the length
is the width
We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so 
and 
.
Replacing values:
Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula 
where 
is the first term and 
is the second term. We can infer that 
and 
. So, 
. Replacing that:
We can see that the common denominator of our fractions is 
. Now we can simplify our fraction using the common denominator:
We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).
Given t = time and h = height
From the equation.
h is the axis od symmetry
(h, k) is the vertex.
In the equation, h is 1 and k is 16.
So the maximum value is 16 at t = 1.
The ball reaches maximum at 16 and it takes t = 1 to reach the maximum point.
Answer:
2.7 in²
Step-by-step explanation:
similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.
so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.
in other words
EF = BC × 2/3
2 = 3 × 2/3
correct
how do we calculate the area of a triangle ?
Area = baseline × height / 2
from BAC we know
Area = 6
baseline = 3
height = ?
6 = 3 × height / 2
12 = 3 × height
height = 4
aha !
now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3
so, for EDF we know
Area = ?
baseline = 2
height = 4 × 2/3 = 8/3
therefore, the area is
Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7
the shirt answer would be :
we know from the 2 baselines that the scaling factor for each distance is 2/3.
for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.
2/3 × 2/3 = 4/9
=>
Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7
x+142 =3x+64
subtract x from each side
142 = 2x+64
subtract 64 from each side
142-64 = 2x
78=2x
divide by 2
78/2 = x
x=39
The number is 39
Answer:
xº=71º
Step-by-step explanation:
Take the triangle BDH
Once the sum of interior angles of a triangle is 180º:
40º+31º+yº=180º
71º+yº=180º
yº=109º
Once yº and xº are supplementary angles (add up to 180º):
yº+xº=180º
109º+xº=180º
xº=71º
