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marshall27 [118]
3 years ago
10

(2x - 4) – 2 = 1 - 2(x – 3) I need help with this one may someone help me??

Mathematics
1 answer:
AnnyKZ [126]3 years ago
8 0

Answer:

\boxed {x = \frac{13}{4}}

Step-by-step explanation:

Solve for the value of x:

(2x - 4) - 2 = 1 - 2(x - 3)

-Subtract 2 from 4:

(2x - 4) - 2 = 1 - 2(x - 3)

2x - 6 = 1 - 2(x - 3)

-Use <u>Distributive Property</u>:

2x - 6 = 1 - 2(x - 3)

2x - 6 = 1 - 2x - 6

-Add 2x to both sides:

2x - 6 + 2x = 1 - 2x + 2x - 6

4x - 6 = 7

-Add both sides by 6:

4x - 6 + 6 = 7 + 6

4x = 13

-Divide both sides by 4:

\frac{4x}{4} = \frac{13}{4}

\boxed {x = \frac{13}{4}}

Therefore, the value of x is \frac{13}{4}.

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4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.
olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 4, the last two terms vanish and we're left with

x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

x\equiv72\equiv2\pmod7

which is what we want, so no adjustments needed here.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

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3 0
3 years ago
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many h
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Let

x-----> the number of hours that Candice spent doing her homework

y-----> the number of hours that Ronald spent doing his homework

we know that

x=5\frac{1}{4}\ hours

convert mixed number to an improper fraction

5\frac{1}{4}\ hours=\frac{5*4+1}{4}= \frac{21}{4}\ hours

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x=\frac{21}{4}\ hours -------> equation A

y=\frac{1}{2}x ------> equation B

Substitute equation A in equation B

y=\frac{1}{2}*\frac{21}{4}=\frac{21}{8}\ hours

convert an improper fraction to a mixed number

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Answer:

The entire floor can contain approximately 4178 fans

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The first step is to calculate the area of the basketball floor.

we can do this by multiplying the length by the breadth as such 94 X 50 = 4700 square feet.

The second step is to calculate the area occupied by 8 of the fans. We can do this by multiplying 3 ft by 3ft = 9 square feet.

From this, it will be easier to estimate the area occupied by only one fan. This can be got by dividing 9 square feet by 8.  

This is = 1.125 square feet.

To get the number of students it can occupy, we divide the total area of the court by the area occupied by one student.

4700/ 1.125 =4177.8 \approx 4178 fans

4 0
3 years ago
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