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2 years ago

Find the value of x and y (please explain)

Mathematics

1 answer:

katovenus [111]2 years ago

7 0

Answer:

x=55,y=20

Step-by-step explanation:

180-75=105

2x-5=105

2x=110

x=55

4x+25=105

4y=80

y=20

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2 years ago

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Sati [7]

Answer:

a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence: $\boxed{\bold{a_n=7n-12}}$

Step-by-step explanation:

a₁ + a₂ + a₃ = 6

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2 ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7 ⇒ a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

$a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}$

6 0

2 years ago

Solve square root of x + square root of x+2 = 2

andrew-mc [135]

The value of x is $\frac{1}{4}$

Step-by-step explanation:

Given:

$\sqrt{x} + \sqrt{x + 2} = 2$

Rearranging the radical on left side,

$\sqrt{x + 2} = 2 - \sqrt{x}$

Power on both sides,

$(\sqrt{x + 2})^{2} = (2 - \sqrt{x})^{2}$

Simplifying the left,

$x + 2 = (2 - \sqrt{x} )^{2}$

For the RHS equation, use the property of (a-b)² = (a²-2ab+b²),

$= > x + 2 = {2}^{2} - (2 \times 2 \sqrt{x}) + ( \sqrt{x})^{2}$

Now calculating its powers,

$= > x + 2 = 4 - 4\sqrt{x} + x$

Now sending -4√x to the LHS (left side), its sign becomes plus (+),

$= > 4 \sqrt{x} = 4 + x - x - 2$

Now the +x and -x will be cancelled,

$= > 4 \sqrt{x} = 4 - 2$

$= > 4 \sqrt{x} = 2$

Bringing 4 to the right side, it becomes the denominator,

$= > \sqrt{x} = \frac{2}{4}$

$= > \sqrt{x} = \frac{1}{4}$

Now powering both sides,

$= > ( \sqrt{x})^{2} = ( \frac{1}{2})^{2}$

$= > x = \frac{1}{4}$

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2 years ago

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