The second a first object do follow geometric demetions
Answer:
Given,
Diagonals are equal
AC=BD .......(1)
and the diagonals bisect each other at right angles
OA=OC;OB=OD ...... (2)
∠AOB= ∠BOC= ∠COD= ∠AOD= 90
0
..........(3)
Proof:
Consider △AOB and △COB
OA=OC ....[from (2)]
∠AOB= ∠COB
OB is the common side
Therefore,
△AOB≅ △COB
From SAS criteria, AB=CB
Similarly, we prove
△AOB≅ △DOA, so AB=AD
△BOC≅ △COD, so CB=DC
So, AB=AD=CB=DC ....(4)
So, in quadrilateral ABCD, both pairs of opposite sides are equal, hence ABCD is parallelogram
In △ABC and △DCB
AC=BD ...(from (1))
AB=DC ...(from $$(4)$$)
BC is the common side
△ABC≅ △DCB
So, from SSS criteria, ∠ABC= ∠DCB
Now,
AB∥CD,BC is the tansversal
∠B+∠C= 180
0
∠B+∠B= 180
0
∠B= 90
0
Hence, ABCD is a parallelogram with all sides equal and one angle is 90
0
So, ABCD is a square.
Hence proved.
Step-by-step explanation:
Please use " ^ " to indicate exponentiation: F(x) = 5 + 3x − x^2. One way to determine the range of a quadratic function, such as this function is, is to find the vertex. The y-value of the vertex is the max or the min of the function.
In this case, we have f(x) = -x^2 + 3x + 5, and the associated coefficients are a = -1, b = 3 and c = 5. The axis of symmetry is x = -b/[2a].
Here, the equation of the axis of symmetry is x = -3/[2*-1), or x = 3/2.
Find the corresponding y value by subbing 3/2 for x in f(x) = -x^2 + 3x + 5:
f(3/2) = -(3/2)^2 + 3(3/2) + 5 = -9/4 + 9/2 + 20/4, or 9./4.
Thus, the vertex, representing a maximum, is (3/2, 29/4).
The range is (-infinity, 29/4].
Answer:
a
The sale was for a 43% decrease.
Step-by-step explanation:
The computation of the percent off of the coat during the sale is shown below:
Regular price is $35.25
And, in the sale the price is $19.99
So, the percent off would be
= ($35.25 - $19.99) ÷ ($19.99)
= 43% decrease
hence, the percent off of the coat during the sale is 43% decrease
Therefore the correct option is a.
And, all the other options are incorrect
Answer:
Step-by-step explanation:
x + y = 25 ...........................(1)
{4x + 2y =64} / 2 divide the equation by 2
2x + y = 32 ........................(3)
Step Two
subtract (1) from (3)
2x + y = 32
x + y = 25
x = 7
Therefore from equation 1 we get x + y = 25
but x = 7
7 + y = 25 Subtract 7 from both sides.
y = 25 - 7
y = 18
Check
4*x + 2*y = 64
4*7 + 2*18 =? 64
28 + 36 = ? 64
64 = 64
The checks out to be the right answer.
