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3 years ago

How many solutions are in this equation?

Mathematics

2 answers:

Serjik [45]3 years ago

4 0

There are no solutions to this!

vfiekz [6]3 years ago

3 0

9(x-4)=9x-33

9x-36=9x-33

No solution so b =0

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There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r

zhannawk [14.2K]

Answer:

Step-by-step explanation:

The first cave has 7 times more bats than the last cave. So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves. So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats. Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end. If cave #45 has b bats, then caves #39-#44 have 77−b bats. And since caves #38-44 have 77 bats, then cave #38 has b bats. Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

x = 12

There are at most 12 bats in the 30th cave.

8 0

3 years ago

26. A single card is drawn from a deck. Find the probability that the card is either red or a face card.

Lana71 [14]

Answer:

8/13

Step-by-step explanation:

There are total 26 red cards in the deck of 52 cards.

There are also 12 face cards in the deck ( which is 6 of them are red, while 6 of them are black)

Since we only need either one of them, 26 + 6 = 32

The probability of drawn a card that either red or a face card is 32/52

The simplest form of this fraction is 8/13.

7 0

2 years ago

Here are the ingredients for making pineapple sorbet for 6 people. 800g 4 egg whites 1/2 lemon 100g cater sugar Ann makes pineap

zhuklara [117]

She would use 1200g of pineapple.

6 0

3 years ago

A candy company uses 8 gallons of corn syrup to make 1,776 pieces of candy. If they use 52 gallons of corn syrup per hour, how m

kondor19780726 [428]

Answer: 11,544 pieces of candy are made per hour.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

Gallons of corn syrup used: 8
Pieces of candy produced: 1,776
gallons of corn syrup per hour: 52

If we apply proportions:

8 /1,776 = 52/x

Where x is the pieces of candy made per hour.

Solving

x = 52x1, 776 /8

x = 11,544

11,544 pieces of candy are made per hour.

4 0

3 years ago

Complete the tables of values.

Vladimir [108]

Answer:

$a=1\\b=\frac{1}{16}\\\\c=\frac{1}{256}\\\\d=1\\e=\frac{4}{9}\\\\f=\frac{16}{81}$

Step-by-step explanation:

For the orange table:

Substitute the corresponding values of x into the function $f(x)=4^{-x}$ , then:

For a:

x=0

$f(0)=4^0=1$

For b:

x=2

$f(x)=4^{-2}=\frac{1}{16}$

For c:

x=4

$f(x)=4^{-4}=\frac{1}{256}$

For the blue table:

Substitute the corresponding values of x into the function $g(x)=(\frac{2}{3})^x$ , then:

For d:

x=0

$g(x)=(\frac{2}{3})^0=1$

For e:

x=2

$g(x)=(\frac{2}{3})^2=\frac{4}{9}$

For f:

x=4

$g(x)=(\frac{2}{3})^4=\frac{16}{81}$

3 0

2 years ago