Answer:
16008
Step-by-step explanation:
Sum of an arithmetic sequence is:
S = (n/2) (2a₁ + (n−1) d)
or
S = (n/2) (a₁ + a)
To use either equation, we need to find the number of terms n. We know the common difference d is 1 − (-9) = 10. Using the definition of the nth term of an arithmetic sequence:
a = a₁ + (n−1) d
561 = -9 + (n−1) (10)
570 = 10n − 10
580 = 10n
n = 58
Using the first equation to find the sum:
S = (n/2) (2a₁ + (n−1) d)
S = (58/2) (2(-9) + (58−1) 10)
S = 29 (-18 + 570)
S = 16008
Using the second equation to find the sum:
S = (n/2) (a₁ + a)
S = (58/2) (-9 + 561)
S = 16008
Answer:
Given: Consider a triangle ABC in which AD is median drawn from vertex A.
To prove: AB + AC > AD
Proof: In Δ A B D
AB + B D> AD ⇒[In a triangle sum of lengths of two sides is greater than the third side] .................(1)
In Δ A CD
AC + DC > AD [In a triangle sum of lengths of two sides is greater than the third side] .................(2)
Adding (1) and (2)
AB + AC+ B D + D C > B D + DC
A B+ A C+ B C > 2 B D .................(3)
Also , Considering Δ AB C
AB + B C > B C ⇒[In a triangle sum of lengths of two sides is greater than the third side]
⇒ AB + B C - B C >0 ........................(4)
Adding (3) and (4)
A B+ B C+B C+ AB +A C- B C > 2 A D
⇒2 AB + 2 A C> 2 A D
Dividing both side of inequality by 2, we get
A B+ A C> A D
Hence proved.
9ft²=1student
xft²=66students
9ft² xft²
_______=_________
1student 66students
Cross multiply
1x=594
divide both sides by 1
x=594ft²
Answer=594ft²
Answer:
y = x² + 2x + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here the vertex = (- 1, 4), thus
y = a(x + 1)² + 4
To find a substitute (0, 5) a point on the graph into the equation
5 = a(0 + 1)² + 4
5 = a + 4 ( subtract 4 from both sides )
a = 1, thus
y = (x + 1)² + 4 ← expand and simplify
= x² + 2x + 1 + 4
= x² + 2x + 5
Answer:
The correct answer is D) 4/5 and 40/50
Step-by-step explanation:
In order to find this, do the division and find the decimal answer. When they match, they are equivalent.
4/5 = .8
40/50 = .8
