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Volgvan
3 years ago
5

Two numbers are in the ratio 3: 7. If 1 is added to the smaller number and 7 is added to the larger, they will be in the ratio 1

: 3. Find the numbers.
Mathematics
1 answer:
pashok25 [27]3 years ago
7 0

Answer:

6 and 14

Step-by-step explanation:

The numbers are in the ratio 3 : 7 = 3x : 7x (x is a multiplier )

adding 1 to smaller number is 3x + 1 and 7 to the larger is 7x + 7, then

3x + 1 : 7x + 7 = 1 : 3

Expressing the ratio in fractional form

\frac{3x+1}{7x+7} = \frac{1}{3} ( cross- multiply )

3(3x + 1) = 7x + 7

9x + 3 = 7x + 7 ( subtract 7x from both sides )

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Thus the numbers are

3x = 3(2) = 6

7x = 7(2) = 14

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Answer:

The situation represents the arithmetic sequence

Step-by-step explanation:

∵ The cost of the first night is $240

∵ The cost of each night after the first is $210

∵ The number of nights is x

∵ The total cost of staying at the hotel x nights is y

∴ y = 240 + 210(x - 1)

Put x = 1 , 2 , 3, 4 and then check the type of the sequence

∴ y = 240 + 210(1 - 1) = 240

∴ y = 240 + 210(2 - 1) = 450

∴ y = 240 + 210(3 - 1) = 660

∴ y = 240 + 210(4 - 1) = 870

∵ The difference between each two consecutive terms are constant

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∴ The sequence is arithmetic sequence

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3 years ago
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mina [271]

Answer:

A = 3/2

B = 3

C = 6

D = 12

Step-by-step explanation:

Simply plug it in. When you have a negative exponent, you basically switch the sign of the exponent and put a one over the number itself.

  • So we have 2^-1. This is the same as 3(\frac{1}{2^1}) =3( \frac{1}{2}) = \frac{3}{2} = a
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6 0
3 years ago
Given f(x) = -6x - 1 and g(x) = x3, choose<br> the expression for fºg)(x).
Gelneren [198K]

Answer:

- 6x³ - 1

Step-by-step explanation:

Substitute x = g(x) into f(x), that is

(f ○ g)(x)

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3 years ago
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polet [3.4K]

Answer:

Area =55.4ft^2

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

\tan(60) = \frac{4\sqrt 3}{x}

Solve for x

x = \frac{4\sqrt 3}{\tan(60)}

\tan(60) = \sqrt 3

So:

x = \frac{4\sqrt 3}{\sqrt 3}

x = 4

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

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So, the area of the rhombus is 4 times the area of 1 triangle

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3 years ago
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lbvjy [14]

Answer:

3n−32=7n+28

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Step-by-step explanation:

Let's solve your equation step-by-step.

3n−32=7n+28

Step 1: Subtract 7n from both sides.

3n−32−7n=7n+28−7n

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Step 2: Add 32 to both sides.

−4n−32+32=28+32

−4n=60

Step 3: Divide both sides by -4.

−4n/−4=60/−4

n=−15

3 0
3 years ago
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