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3 years ago

18 less than three times a number is twice the number. Define a variable write an equation and solve to find the number.

Mathematics

1 answer:

ycow [4]3 years ago

4 0

Answer:

n = 18

Step-by-step explanation:

N = variable

Equation: 3n - 18 = 2n

Solve:

3n - 18 = 2n

3n = 2n + 18 Add 18 to both sides

3n - 2n = 18 Subtract 2n from both sides

n = 18

Hope this helps,

♥<em>A.W.E.</em><u><em>S.W.A.N.♥</em></u>

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6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a² + b² + ab) – (a + b) (a² + b²– ab) iii) (b² – 49) (b + 7) + 3

Shkiper50 [21]

Step-by-step explanation:

(a + b)(5a – 3b) + (a – 3b)(a – b)

Expand each of the terms separately

That's

(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²

= 5a² + 2ab - 3b²

(a – 3b)(a – b) = a² - ab - 3ab + 3b²

= a² - 4ab + 3b²

<u>Add the terms</u>

That's

5a² + 2ab - 3b² + a² - 4ab + 3b²

<u>Group like terms</u>

5a² + a² + 2ab - 4ab - 3b² + 3b²

We have the answer as

(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)

Expand the terms separately

<u>For (a – b) (a² + b² + ab)</u>

Using the rule

x³ - y³ = (x - y)( x² + xy + y²) expand the expression

So we have

(a – b) (a² + b² + ab) = a³ - b³

<u>For (a + b) (a² + b²– ab)</u>

Using the rule

x³ + y³ = (x + y)( x² - xy + y²) expand the expression

We have

(a + b) (a² + b²– ab) = a³ + b³

Subtract the terms

That's

a³ - b³ - (a³ + b³)

Remove the parenthesis

a³ - b³ - a³ - b³

Group like terms

a³ - a³ - b³ - b³

We have the final answer as

(b² – 49) (b + 7) + 343

Expand the terms

That's

b³ + 7b² - 49b - 343 + 343

We have the final answer as

Hope this helps you

6 0

3 years ago

Round 22,810 to the nearest thousand

Anettt [7]

Answer:

It would be 23,000.

4 0

2 years ago

Read 2 more answers

Which loan has the lowest total repayment?

Maru [420]

Answer:

O B

Step-by-step explanation:

i think

5 0

2 years ago

Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

PLZ ANSWER QUICK-MATH TRIG

IRISSAK [1]

Answer:

FG = 9.7ft

Step-by-step explanation:

Find the diagram in the attachment.

The diagram is a right angled triangle since one of its angle is 90°

Using SOH CAH TOA to calculate the length FG which is the hypotenuse.

According to SOH

Sin∠G = Opposite/Hypotenuse

To get the ∠G,

∠F+∠H+∠G = 180°

18°+90°+∠G = 180°

∠G = 180°-108°

∠G = 72°

Sin72° = 9.2/FG

FG = 9.2/sin72°

FG = 9.67feet

FG = 9.7ft (to the nearest tenth of a foot)

7 0

3 years ago