Answer:
740
Step-by-step explanation:
The n th term of an arithmetic series is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then
a₁ + 2d = 7 → (1)
a₁ + 6d = 23 → (2)
Subtract (1) from (2) term by term
4d = 16 ( divide both sides by 4 )
d = 4
Substitute d = 4 into (1)
a₁ + 2(4) = 7
a₁ + 8 = 7 ( subtract 8 from both sides )
a₁ = - 1
The sum to n terms of an arithmetic series is
= [ 2a₁ + (n - 1)d ] , thus
= [ (2 × - 1) + (19 × 4) ]
= 10(- 2 + 76) = 10 × 74 = 740
Answer:
Step-by-step explanation:
(vertical angles)
(Interior angles on the same side of transversal)
Answer:
- D. They are similar by the definition of similarity in terms of a dilation.
Step-by-step explanation:
<em>Refer to attached</em>
The points are plotted and connected to make triangles
As per the diagram, the triangles are similar, each side of ABC is reduced twice to make the corresponding sides of DEF, so the scale factor is 1/2.
<u>Correct choice is D</u>
- They are similar by the definition of similarity in terms of a dilation.
For slope m and point (x₁, y₁), the point-slope equation of the line can be written as
y -y₁ = m(x -x₁)
You have m = -4 and (x₁, y₁) = (4, -9), so the equation of your line is
D. y+9 = -4(x-4)