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3 years ago

Step by step explanation

Mathematics

1 answer:

vodka [1.7K]3 years ago

4 0

Answer: x = 4 and y = -3

Step-by-step explanation:

2x + 4y = -4

2x = -4 - 4y

x = -2 - 2y

Now that we have solved the first equation for x, we plug (-2 - 2y) into the other equation in place of x and then solve for y.

3(-2 -2y) + 5y = -3

-6 - 6y + 5y = -3

-y = 3

y = -3

Now that we know y, we plug it into the original equation and solve for x.

2x + 4(-3) = -4

2x + -12 = -4

2x = 8

x = 4

You can check the answer by plugging both x and y into either of the original equations.

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What is the sum of the first eight terms of the geometric series 2 + 6 + 18 + 54 + … ?

UkoKoshka [18]

2+6+18+54+162+486+1458+4375=6561

you multiply the previous number by three to find the next value

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3 years ago

What is the binomial expansion of (2x – 3)^5?

Tanya [424]

Answer:

Step-by-step explanation:

(2x + 3)^5 = C(5,0)2x^5*3^0 +

C(5,1)2x^4*3^1 + C(5,2)2x^3*3^2 + C(5,3)2x^2*3^3 + C(5,4)2x^1*3^4 + C(5,5)2x^0*3^5

Recall that

C(n,r) = n! / (n-r)! r!

C(5,0) = 1

C(5,1) = 5

C(5,2) = 10

C(5,3) = 10

C(5,4) = 5

C(5,5) = 1

= 1(2x^5)1 + 5(2x^4)3 + 10(2x^3)3^2 + 10(2x^2)3^3 + 5(2x^1)3^4 + 1(2x^0)3^5

= 2x^5 + 15(2x^4) + 90(2x^3) + 270(2x^2) + 405(2x) +243

= 32x^5 + 15(16x^4) + 90(8x^3) + 270(4x^2) + 810x + 243

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7 0

3 years ago

Read 2 more answers

‼️GEOMETRY‼️

ella [17]

Answer:

A.) 1018 square inches

Step-by-step explanation:

The largest sphere will have a diameter equaling the length of the cube (see picture).

If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

$SA=4\pi r^2$

For this formula, we need the radius of the sphere. Divide the diameter by 2:

$\frac{18}{2}=9$

The radius is 9 inches. Plug this into the equation:

$SA=4\pi *9^2$

Simplify the equation:

$SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87$

Round the result to the nearest whole number:

$1017.87$ → $1018$

The surface area is 1,018 inches².

:Done

Picture:

In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.

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3 years ago

Which of the following is 38/6 converted to a mixed number

Monica [59]

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3 years ago

I need help with this question plz

pashok25 [27]

First you need to distribute the exponent into the terms for the first parenthesis.

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Then you multiply -27x⁶y⁹ by x²y.

You just need to add the exponents of x and y:

-27x⁶⁺²y⁹⁺¹

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3 years ago