Answer:
Step-by-step explanation:
From the attachment, we have:
Rotation: 180 degrees clockwise
Required
Find J', K' and L'
When a point (x, y)is rotated 180 degree clockwise, the resulting point is: (-x, -y)
So, we have:
Answer:
f(2) = -40
Step-by-step explanation:
Just substitute x=2 into the function:
f(x) = 2x³ - 3x² - 18x - 8
f(2) = 2(2)³ - 3(2)² - 18(2) - 8
f(2) = 2(8) - 3(4) - 36 - 8
f(2) = 16 - 12 - 44
f(2) = 4 - 44
f(2) = -40
42789 times 54678
is 2,339,616,942
Show Work:
<span>Calculate 9 x 8, which is 72.
Since 72 is two-digit, we carry the first digit 7 to the next column.
</span>
3 <span>Calculate 8 x 8, which is 64. Now add the carry digit of 7, which is 71.
Since 71 is two-digit, we carry the first digit 7 to the next column.
</span>
4 <span>Calculate 7 x 8, which is 56. Now add the carry digit of 7, which is 63.
Since 63 is two-digit, we carry the first digit 6 to the next column.
</span>
5 <span>Calculate 2 x 8, which is 16. Now add the carry digit of 6, which is 22.
Since 22 is two-digit, we carry the first digit 2 to the next column.
</span>
6 <span>Calculate 4 x 8, which is 32. Now add the carry digit of 2, which is 34.
Since 34 is two-digit, we carry the first digit 3 to the next column.
</span>
7 <span>Bring down the carry digit of 3.
</span>
8 <span>Calculate 9 x 7, which is 63.
Since 63 is two-digit, we carry the first digit 6 to the next column.
</span>
9 <span>Calculate 8 x 7, which is 56. Now add the carry digit of 6, which is 62.
Since 62 is two-digit, we carry the first digit 6 to the next column.
</span>
10 <span>Calculate 7 x 7, which is 49. Now add the carry digit of 6, which is 55.
Since 55 is two-digit, we carry the first digit 5 to the next column.
</span>
11 <span>Calculate 2 x 7, which is 14. Now add the carry digit of 5, which is 19.
Since 19 is two-digit, we carry the first digit 1 to the next column.
</span>
12 <span>Calculate 4 x 7, which is 28. Now add the carry digit of 1, which is 29.
Since 29 is two-digit, we carry the first digit 2 to the next column.
</span>
13 <span>Bring down the carry digit of 2.
</span>
14 <span>Calculate 9 x 6, which is 54.
Since 54 is two-digit, we carry the first digit 5 to the next column.
</span>
15 <span>Calculate 8 x 6, which is 48. Now add the carry digit of 5, which is 53.
Since 53 is two-digit, we carry the first digit 5 to the next column.
</span>
16 <span>Calculate 7 x 6, which is 42. Now add the carry digit of 5, which is 47.
Since 47 is two-digit, we carry the first digit 4 to the next column.
</span>
17 <span>Calculate 2 x 6, which is 12. Now add the carry digit of 4, which is 16.
Since 16 is two-digit, we carry the first digit 1 to the next column.
</span>
18 <span>Calculate 4 x 6, which is 24. Now add the carry digit of 1, which is 25.
Since 25 is two-digit, we carry the first digit 2 to the next column.
</span>
19 <span>Bring down the carry digit of 2.
</span>
20 <span>Calculate 9 x 4, which is 36.
Since 36 is two-digit, we carry the first digit 3 to the next column.
</span>
21 <span>Calculate 8 x 4, which is 32. Now add the carry digit of 3, which is 35.
Since 35 is two-digit, we carry the first digit 3 to the next column.
</span>
22 <span>Calculate 7 x 4, which is 28. Now add the carry digit of 3, which is 31.
Since 31 is two-digit, we carry the first digit 3 to the next column.
</span>
23 <span>Calculate 2 x 4, which is 8. Now add the carry digit of 3, which is 11.
Since 11 is two-digit, we carry the first digit 1 to the next column.
</span>
24 <span>Calculate 4 x 4, which is 16. Now add the carry digit of 1, which is 17.
Since 17 is two-digit, we carry the first digit 1 to the next column.
</span>
25 <span>Bring down the carry digit of 1.
</span>
26 <span>Calculate 9 x 5, which is 45.
Since 45 is two-digit, we carry the first digit 4 to the next column.
</span>
27 <span>Calculate 8 x 5, which is 40. Now add the carry digit of 4, which is 44.
Since 44 is two-digit, we carry the first digit 4 to the next column.
</span>
28 <span>Calculate 7 x 5, which is 35. Now add the carry digit of 4, which is 39.
Since 39 is two-digit, we carry the first digit 3 to the next column.
</span>
29 <span>Calculate 2 x 5, which is 10. Now add the carry digit of 3, which is 13.
Since 13 is two-digit, we carry the first digit 1 to the next column.
</span>
30 <span>Calculate 4 x 5, which is 20. Now add the carry digit of 1, which is 21.
Since 21 is two-digit, we carry the first digit 2 to the next column.
</span>
31 <span>Bring down the carry digit of 2.
</span>
32 <span>Calculate 342312 + 2995230 + 25673400 + 171156000 + 2139450000, which is 2339616942</span>
<span> </span>
<h2>
The first one:</h2>
<u>solve for x.</u>
Step 1: Add -y to both sides.
x+y+z+−y=2+−y
x+z=−y+2
Step 2: Add -z to both sides.
x+z+−z=−y+2+−z
<u>x=−y−z+2</u>
<u>solve for y.</u>
Step 1: Add -x to both sides.
x+y+z+−x=2+−x
y+z=−x+2
Step 2: Add -z to both sides.
y+z+−z=−x+2+−z
<u>y=−x−z+2</u>
<u>solve for z.</u>
Step 1: Add -x to both sides.
x+y+z+−x=2+−x
y+z=−x+2
Step 2: Add -y to both sides.
y+z+−y=−x+2+−y
<u>z=−x−y+2</u>
<u />
<h2>
The second one:</h2>
<u>solve for x.
</u>
Step 1: Add y to both sides.
x−y−z+y=2+y
x−z=y+2
Step 2: Add z to both sides.
x−z+z=y+2+z
<u>x=y+z+2</u>
<u>solve for y.</u>
Step 1: Add -x to both sides.
x−y−z+−x=2+−x
−y−z=−x+2
Step 2: Add z to both sides.
−y−z+z=−x+2+z
−y=−x+z+2
Step 3: Divide both sides by -1.
−y
/−1 = −x+z+2
/−1
<u>y=x−z−2</u>
<u>solve for z.</u>
Step 1: Add -x to both sides.
x−y−z+−x=2+−x
−y−z=−x+2
Step 2: Add y to both sides.
−y−z+y=−x+2+y
−z=−x+y+2
Step 3: Divide both sides by -1.
−z
/−1 = −x+y+2
/−1
<u>z=x−y−2</u>
<u />
<h2>
The third one:</h2>
<u>solve for x.
</u>
Step 1: Add y to both sides.
x−y+z+y=−6+y
x+z=y−6
Step 2: Add -z to both sides.
x+z+−z=y−6+−z
<u>x=y−z−6</u>
<u>solve for y.</u>
Step 1: Add -x to both sides.
x−y+z+−x=−6+−x
−y+z=−x−6
Step 2: Add -z to both sides.
−y+z+−z=−x−6+−z
−y=−x−z−6
Step 3: Divide both sides by -1.
−y
/−1 = −x−z−6
/−1
<u>y=x+z+6</u>
<u>solve for z.</u>
Step 1: Add -x to both sides.
x−y+z+−x=−6+−x
−y+z=−x−6
Step 2: Add y to both sides.
−y+z+y=−x−6+y
z=−x+y−6
I hope this was helpful <3
Answer:
price of each bags of popcorn = $9.75
price of each drinks = $5
Step-by-step explanation:
Let
price of each bags of popcorn = a
price of each drinks = b
Caleb total cost
7a + 2b = 78.25.......(i)
Jeremiah total cost
a + 10b = 59.75.......(ii)
7a + 2b = 78.25
a + 10b = 59.75
a = 59.75 - 10b
insert the value of a in equation (i)
7a + 2b = 78.25
7( 59.75 - 10b) + 2b = 78.25
418.25 - 70b + 2b = 78.25
418.25 - 68b = 78.25
418.25 - 78.25 = 68b
340 = 68b
b = 340/68
b = 5
Insert the value of b in equation (ii)
a + 10b = 59.75.......(ii)
a + 10 × 5 = 59.75
a = 59.75 - 50
a = 9.75
price of each bags of popcorn = $9.75
price of each drinks = $5