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CaHeK987 [17]
3 years ago
13

Consider three consecutive odd integers. The ratio of the smallest number to one less than twice the smallest

Mathematics
1 answer:
uranmaximum [27]3 years ago
8 0

Let <em>x</em> be the smallest of the three integers. Then the next two are <em>x</em> + 2 and <em>x</em> + 4.

• "The ratio of the smallest number to 1 less than twice the smallest number..."

This translates to

<em>x</em> / (2<em>x</em> - 1)

• "... the ratio of 3 more than the middle number to twice the largest number."

This translates to

((<em>x</em> + 2) + 3) / (2 (<em>x</em> + 4))

or, simplifying a bit,

(<em>x</em> + 5) / (2<em>x</em> + 8)

The ratioes are said to be equivalent, so

<em>x</em> / (2<em>x</em> - 1) = (<em>x</em> + 5) / (2<em>x</em> + 8)

Solve for <em>x</em> :

<em>x</em> (2<em>x</em> + 8) = (<em>x</em> + 5) (2<em>x</em> - 1)

2<em>x</em>² + 8<em>x</em> = 2<em>x</em>² + 9<em>x</em> - 5

8<em>x</em> = 9<em>x</em> - 5

-<em>x</em> = -5

<em>x</em> = 5

So the three integers are 5, 7, and 9.

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2 years ago
Solve for u. u+1/4=-4/5
DedPeter [7]

Answer:

u = (-21)/20

Step-by-step explanation:

Solve for u:

u + 1/4 = (-4)/5

Put each term in u + 1/4 over the common denominator 4: u + 1/4 = (4 u)/4 + 1/4:

(4 u)/4 + 1/4 = -4/5

(4 u)/4 + 1/4 = (4 u + 1)/4:

1/4 (4 u + 1) = -4/5

Multiply both sides of (4 u + 1)/4 = (-4)/5 by 4:

(4 (4 u + 1))/4 = (-4)/5×4

4×(-4)/5 = (4 (-4))/5:

(4 (4 u + 1))/4 = (-4×4)/5

(4 (4 u + 1))/4 = 4/4×(4 u + 1) = 4 u + 1:

4 u + 1 = (-4×4)/5

4 (-4) = -16:

4 u + 1 = (-16)/5

Subtract 1 from both sides:

4 u + (1 - 1) = (-16)/5 - 1

1 - 1 = 0:

4 u = (-16)/5 - 1

Put (-16)/5 - 1 over the common denominator 5. (-16)/5 - 1 = (-16)/5 - 5/5:

4 u = (-16)/5 - 5/5

-16/5 - 5/5 = (-16 - 5)/5:

4 u = (-16 - 5)/5

-16 - 5 = -21:

4 u = (-21)/5

Divide both sides by 4:

u = ((-21)/4)/5

5×4 = 20:

Answer:  u = (-21)/20

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3 years ago
HELP PLEASE ASAP 55 POINTS I BEG YOU!!!!!!
Alja [10]

Answer:1 b+1T+1 U=5617b+1 T =9062b+7T+5U = 1758

Step-by-step explanation:

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3 years ago
You are playing in a fantasy football league and Lamar Jackson scored 45 fantasy points. If he keeps his average of 28 fantasy p
jekas [21]

Answer:

213 points

The y-intercept is how many points Jackson already scored, and the slope is how many points he is scoring every game.

Step-by-step explanation:

Jackson earns 28 points per game, so after 6 games, he earns 168 points (just multiply 6 by 28). He already scored 45 points, so if you add them together, he scored a total of 213 points.

The y-intercept is 45, what he already scored, and the slope is 28, how many points he scores per game.

Hope I helped!!!

4 0
3 years ago
Gym A charges a $25 membership fee and a $25 monthly fee. Gym B charges a $55 membership fee and a $10 monthly fee. After how ma
bearhunter [10]

Answer: 75

solve:

For gym A

total cost= membership fee+monthly fee

membership fee=25

monthly fee=25

cost of x month=25x

total cost=25+25x

for gym B

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now total cost are same

25+25x=55+10x

15x=30

x=30/15

x=2.

2 months

and amount =25+25*2=75

4 0
3 years ago
Read 2 more answers
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