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Anestetic [448]
2 years ago
9

A+c=r+d solve for a, answer please :(

Mathematics
2 answers:
RoseWind [281]2 years ago
7 0

Answer:

a = r + d - c

Step-by-step explanation:

All we do is transpose c to the other side to isolate a.

Elanso [62]2 years ago
5 0

Answer:

a = r + d - c

Step-by-step explanation:

a + c = r + d

You want a alone on the left side. c is being added to a.

To get rid of the c, you must subtract c from the left side, but the rule of equations is that you must do the same operation to both sides of the equation. We subtract c from both sides of the equation.

a + c - c = r + d - c

c - c = 0, so the c is eliminated from the left side.

We now have

a + 0 = r + d - c

a = r + d - c

You might be interested in
why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a
zheka24 [161]

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

5 0
3 years ago
Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth.
katrin [286]

x=5.38 . Correct option C)5.38

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

Here we have , Find the value of x. O is the center of the circle. Round your answer to the nearest hundredth.  picture is attached  . Let's find out:

In the given figure , Let's draw a line from center to the point where cord of length 8 unit is touching the circle or intersecting or , where this chord finishes . This line is radius of circle and is denoted by x , So now we have a right angle triangle with dimensions as :

Perpendicular =3.6\\Base=\frac{8}{2}=4\\Hypotenuse=x

By Pythagoras Theorem ,

Hypotenuse^2=Perpendicular^2+base^2

⇒ x^2=(3.6)^2+(4)^2

⇒ x=\sqrt{(3.6)^2+(4)^2}

⇒ x=\sqrt{12.96+16}

⇒ x=\sqrt{28.96}

⇒ x=5.38

Therefore , x=5.38 . Correct option C)5.38

6 0
3 years ago
Gerry plans to place a 29 foot ladder against the side of his house to clean his gutters. The bottom of the ladder will be 3 fee
tensa zangetsu [6.8K]

Answer:

8\sqrt{13}

Step-by-step explanation:

Using the pythagorean theorem (Assuming the house's walls are perpindicular to the ground):

a^2+b^2=c^2

we can find that 3=a and 29=c

3^2+b^2=29^2

9+b^2=841

b^2=832

b=\sqrt{832}

b=\sqrt{64*13}

b=8\sqrt{13}

That is the height that the ladder will reach

5 0
2 years ago
Write an equation then solve
frutty [35]
$21.50 - $4 = $17.50 If you start with $21.50, subtract the $4 entrance fee, you have $17.50 left to spend on rides. To figure out how many rides you can go on, divide $17.50 by $2.50. You can go on 7 rides. Here's the equation:

(21.5-4)/2.5=amount of rides

(21.5-4)/2.5= 7 rides


7 0
3 years ago
Read 2 more answers
Need this answered quick
melisa1 [442]

95.7942857 pie form hope this is right got it off the internet so yeah



7 0
3 years ago
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