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2 years ago

If 3^x=243^4, then what is x?

Mathematics

1 answer:

natita [175]2 years ago

7 0

Answer:

x=20

Step-by-step explanation:

3^x=243^4

3^x=(3^5)^4

3^x =3^20

x=20

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A sports stadium has 10000 seats, divided into box seats, lower-deck seats, and upper-devk seats. Box seats sell for 10 dollars,

lesantik [10]

Answer:

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

Step-by-step explanation:

Let number of box seats = $x$

Let number of lower deck seats = $y$

Let number of upper deck seats = $z$

As per question statement:

$x+y+z=10000$ ...... (1)

Cost for box seat = $10

Cost for $x$ box seats = 10 $x$

Cost for lower deck seat = $8

Cost for $y$ lower deck seats = 8 $y$

Cost for lower deck seat = $5

Cost for $z$ lower deck seats = 5 $z$

As per question statement:

$10x+8y+5z=70000$ ..... (2)

$z = 4x$ ..... (3)

Putting value of $y$ in (1) and (2):

$x+y+4x=10000\\\Rightarrow 5x+y=10000$ ....... (4)

$10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)$

8 $\times$ (4) - (5):

$10x =$ 10000

$\Rightarrow x = 1000$

By (3):

$z = 4000$

Now, by equation (1):

$y$ = 5000

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

6 0

2 years ago

Postulate: If two lines intersect, then they intersect in exactly one point. true or false

ololo11 [35]

Answer:

Step-by-step explanation:

The given postulate If two lines intersect, then they intersect in exactly one point is true because whenever the two lines intersect they intersect at one point only and we know that a postulate is a statement that we accept without proof.

The given theorem If two distinct planes intersect, then they intersect in exactly one line is true as theorem is a statement that has been proved and it has been proved that if two distinct planes intersect, then they intersect in exactly one line.

The figures are drawn to prove them.

7 0

3 years ago

Find the markup and the cost of the following item. Round answers to the nearest cent.

marysya [2.9K]

Answer:

1st question: M=22.62 while C=75.38

2nd question: M=.22 while C=1.97

Step-by-step explanation:

If a mirror costing x dollars is marked up 30%, then we have to find x such that 30%x+x is 98 dollars.

We are solving:

.3x+x=98

Combine like terms:

1.3x=98

Divide both sides by 1.3:

x=75.38

M=98-75.38=22.62

C=75.38

So M=22.62 while C=75.38.

If ream of paper cost x and is marked up 11%, then we have to find x such that 11%x+x is 2.19.

We are solving:

.11x+x=2.19

1.11x=2.19

x=1 97

M=2.19-1.97=.22

So M=.22 while C=1.97

5 0

3 years ago

Divide 40x/64y by 5x/8y.

Lemur [1.5K]

<u>Answer:</u>

The correct answer option is C. 1.

<u>Step-by-step explanation:</u>

We are to divide $\frac { 4 0 x } { 6 4 y }$ by $\frac { 5 x } { 8 y }$ .

Rewriting them as a fraction in whole:

$\frac { \frac { 4 0 x } { 6 4 y } } {\frac { 5 x } { 8 y } }$

Changing the division into multiplication by taking the reciprocal of the fraction in the denominator to get:

$\frac { 4 0 x } { 6 4 y }$ × $\frac{8y}{5x}$

Cancelling out the like terms to get:

6 0

2 years ago

Thanks, brainliest, and 5 stars!!

frez [133]

I hope this helps its step 2 gl

4 0

2 years ago

If 3^x=243^4, then what is x?​

If 3^x=243^4, then what is x?