$\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\$

$\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276$

$\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}$

8 0

3 years ago

Which two statements are missing in steps 3 and 4?

Snezhnost [94]

Answer:

∠B ≅ ∠Y △ABC ~ △ZYX by the SAS similarity theorem.

Step-by-step explanation:

1. $AB=6$ units

$YZ=3$ units

$BC=8$ units

$XY=4$ units, then

$\dfrac{AB}{ZY}=\dfrac{BC}{YX}=2$

2. $\angle B$ and $\angle Y$ are right angles - given

3. $\angle B\cong \angle Y$ two right angles are always congruent.

4. $\triangle ABC\sim \triangle ZYX$ by SAS similarity theorem.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

4 0

3 years ago

Read 2 more answers

Jim's monthly salary is $1,079.40. His monthly job hours are 140. What is his hourly rate of pay?

alex41 [277]

I'm guessing 7.71

Step-by-step explanation:

1,079.40/140

3 0

3 years ago