The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 3 hours for a

Mathematics

1 answer:

Blababa [14]3 years ago

3 0

Answer:

180

Step-by-step explanation:

hours = constant / temperature hours varies inversely as the temperature

3 = c / 60

c (constant) = 3 * 60 = 180

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Answer:

539

Step-by-step explanation:

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3 years ago

Match each number with its place in order from smallest (1st) to largest (6th).

zheka24 [161]

90 would be the largest then 59,48, -56, -80, and leaving -84 to be the smallest

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3 years ago

If f(x)=3x-1 and g(x)=x+5, find (f o g)(x) and (g o f)(x)<br><br> (f o g)(x)=<br><br> (g o f)(x)

Nuetrik [128]

Answer:

(f o g)(x)= 3x + 14

(g o f)(x) = 3x + 4

Step-by-step explanation:

(f o g)(x) = f(g(x)) = f(x + 5) = 3(x + 5) - 1 = 3x + 15 - 1 = 3x + 14

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3 years ago

Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.

blagie [28]

A.
$5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0$

B.
$3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}$

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
$3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 12 to both sides} \\
x=11$

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3 years ago

Select the simplification that accurately explains the following statement.

lutik1710 [3]

Answer:

Option (b) is correct.

$(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2$