Answer:
D. 6 + 6 + 30 + 40 + 50 = 132
Surface area of triangular prism:
(perimeter of base) × length + base × height
(s₁ + s₂ + s₃)(l) + bh
Here, provided with:
So, the surface area:

Only option D gives 132 as an answer which is equivalent to the area.
Answer:
40 mL of vinegar,
280 mL of dressing
Step-by-step explanation:
Let v = the milliliters ( mL ) of 100% vinegar,
Then it should be that 320 - v = mL of dressing.
v + .12( 320 - v ) = .23( 320 ) - So in this case the mL of vinegar is associated with the percent of vinegar composed. 100 percent is, in other words, 1, and is multiplied by " v " the mL of 100% vinegar. 1
v is also v, and so is written as such in our equation. 0.12 is the decimal form of the 12% vinegar, associated with the mL of dressing - as the italian dressing is composed of 12% vinegar. 23% is 0.23 in decimal form, multiplied by the mL of of vinegar in the mixture, 320 mL.
Let's solve for the mL of 100% vinegar, subtracting from 320 to receive the mL of dressing,
v + .12( 320 - v ) = .23( 320 ) - Distribute " .12 "
v + 38.4 - 0.12v = .23( 320 ) - Multiply " 0.32 " by " 320 "
v + 38.4 - 0.12v = 73.6 - Combine like terms and add / subtract
0.88v = 35.2 - Divide 0.88 on either side
v = 40 mL of vinegar,
320 - v = 320 - 40 = 280 mL of dressing
Answer: x = 40
Step-by-step explanation:
these two angles are vertical angles, they will equal each other
therefore, move numbers and variables to the opposite sides of the = sign to isolate the X
3x-10 = 2x + 30
+10 +10 move the -10 by doing opposite
_____________
3x = 2x + 40
-2x -2x move -2x by doing opposite
____________
x = 40
you can check your work by substituting 40 in place of x
3(40) - 10 = 2(40) +30
120-10 = 80 + 30
110 = 110
answer is correct
Answer:
a. 29
Step-by-step explanation:
Example:

This suggests two solutions,

and

.
However, upon plugging these solutions back into the equation, you get

which checks out, but

does not because

is defined only for

(assuming you're looking for real solutions only). So, we call

an extraneous solution, and the complete solution set (over the real numbers) is

.