Simplify the polynomial (−8x) x (−2x)

1 answer:

4 0

Negative multiplied by a negative is positive
8 multiplied by 2 is 16
x mutiplied by x is equal to x square
combine them all up and you get ......
$16 x^{2}$ is the answer :-)

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Lupe and her friends spend $20 on hot dogs and popcorn at a

vodomira [7]

Answer:

They buy 6 hotdogs and 5 popcorn

Step-by-step explanation:

Assume that they buy x hotdogs and y popcorn

∵ They buy a total of 11 hotdogs and popcorn

∵ The number of hotdogs is x and the number of popcorn is y

∴ x + y = 11 ⇒ (1)

∵ Hot dogs cost $2.50 each

∵ Popcorn costs $1.00 each

∵ They spend $20 on hot dogs and popcorn

→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20

∴ 2.5(x) + 1(y) = 20

∴ 2.5x + y = 20 ⇒ (2)

Now we have a system of equations to solve it

→ Subtract equation (1) from equation (2)

∵ (2.5x - x) + (y - y) = (20 - 11)

∴ 1.5x + 0 = 9

∴ 1.5x = 9

→ Divide both sides by 1.5 to find x

∴ x = 6

→ Substitute the value of x in equation (1) to find y

∵ 6 + y = 11

→ Subtract 6 from both sides

∴ 6 - 6 + y = 11 - 6

∴ y = 5

∴ They buy 6 hotdogs and 5 popcorn

8 0

2 years ago

Hip hop music makes up 75% of Landon's music library. If he has downloaded 120 hip hop songs, how many songs does Landon have in

Otrada [13]

Answer: 160 songs.

Step-by-step explanation:

75% hip hop music - 120 songs

100% all music - x songs

Let's write the proportion:

$\dfrac{120}{75} =\dfrac{x}{100} \\\\75x=120 \cdot 100\\75x=12000\\75x : 75 = 12000 : 75\\x = 160$

Thus, Landon have 160 songs in his music library.

4 0

2 years ago

Point C ∈ AB , AB = 30m. Point C is 1.5 times farther from point A than from point B. Find AC and CB.

Shtirlitz [24]

let's say that C is "x" units farther from B, that means that CB = x, and therefore AC = 1.5x.

$\bf \underset{\leftarrow ~~30~~\to}{\boxed{A}\stackrel{1.5x}{\rule[0.35em]{18em}{0.25pt}}C\stackrel{x}{\rule[0.35em]{10em}{0.25pt}}\boxed{B}}
\\\\\\
AB=AC+CB\implies \stackrel{AB}{30}=\stackrel{AC}{1.5x}+\stackrel{CB}{x}\implies 30=2.5x
\\\\\\
\cfrac{30}{2.5}=x\implies 12=x
\\\\[-0.35em]
~\dotfill\\\\
AC=1.5(12)\implies AC=18~\hspace{8em} CB=x\implies CB=12$