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3 years ago

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john made two candles in the shape of rectangular prisms. The first candle is 12cm high, 4 cm long, and 6 cm wide. The second ca

ndle is 4 cm higher, but has the same length and width. How much additional wax was needed to make the taller candle?

1 answer:

anzhelika [568]3 years ago

6 0

Answer:

96 $cm^3$

Step-by-step explanation:

To determine how much additional wax was needed to make the taller candle, we determine the volume of each of the candles and find the difference in their volumes

<u>First Candle</u>

Height=12cm
Length=4 cm
Width= 6 cm

Volume=Height X Length X Width

=12 X 4 X 6

=288 $cm^3$

<u>Second Candle</u>

The second candle is 4cm higher

Height=12+4=16cm
Length=4 cm
Width= 6 cm

Volume=Height X Length X Width

=16 X 4 X 6

=384 $cm^3$

Difference in Volume = 384-288 =96 $cm^3$

Therefore, 96 $cm^3$ of additional wax was used to make the second candle.

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Lelechka [254]

Answer:

AN = 16 units

Step-by-step explanation:

So we can use the fact that $\frac{AN}{FN} =\frac{OR}{FR}$

Since this is an isosceles triangle, segments FO and FR are both equal to 7

Manipulating the equation above to solve for AN we have $AN = \frac{(FN)(OR)}{FR}$

Substituting in the known values we have $AN=\frac{(10)(11.2)}{7} =16$

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3 years ago

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The admission fee at a zoo is $2 for children and $4 for adults. If 1800 people enter the zoo and $6000 is collected, how many a

ipn [44]

Answer:

The number of adults is $1,200$

Step-by-step explanation:

Let

x------> the number of children

y------> the number of adults

we know that

$x+y=1800$ -------> equation A

$2x+4y=6000$ -------> equation B

Multiply equation A by $-2$

$-2(x+y)=-2*1800$ --------> $-2x-2y=-3600$ ------> equation C

Adds equation B and equation C

$2x+4y=6000\\-2x-2y=-3600\\---------\\4y-2y=6000-3600\\2y=2400\\y=2400/2\\y=1200$

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3 years ago

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Emory ran 3 miles in 30 minute. At this pace, how long will it take Emory to run 9 miles? Explain your method AND your reasoning

kvasek [131]

Answer:

It will take him 1 hour and 30 minutes. (90 minutes)

Step-by-step explanation:

If he is running 1 mile in 10 minutes and he needs to run 9 miles the just multiply 9 by 10 to get 90 then simplify if you need to to get 1 hour and 30 minutes.

Hope this helped and have a great rest of your day.

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3 years ago

Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate

kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality $x^{2}-5x+4\leq 0$ . To do that, factorize, then we have that $(x-4)(x-1)\leq 0$ . This implies that

$x-1\leq 0\, \text{and}\, x-4\geq 0$

or

$x-1 \geq 0\, \text{and}\, x-4\leq 0$

In the first case the solution is the empty set $\emptyset$ . In the second case the solution is the interval $1\leq x \leq 4$ . Now we have that

$A=[1,4]$

$B=(3,5)$

$C=(3,4]$ .

To show that $A\cap B\subseteq C$ consider $x\in A\cap B$ . Then $1\leq x \leq 4\, \text{and}\, 1$ , this implies that $3$ , then $x\in C$ . Now, to show that $C\subseteq A\cap B$ consider $x\in C$ , then $3$ , then $1\leq x \leq 4\, \text{and}\, 3$ , then $x\in [1,4] \, \text{and}\, x\in (3,5)$ , this implies that $x\in A\cap B$ .

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3 years ago

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Ilya [14]

Answer:

The answer would be -1,-3.

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