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2 years ago

Simplify using the distributive property

Mathematics

1 answer:

ad-work [718]2 years ago

8 0

Answer:

3/5 is the number that can be distributed across two terms inside parentheses.

you might not need it but:

x = 5

Step-by-step explanation:

3/5(x - 10) = 18 - 4x - 1

using distributive property, open the parentheses:

3/5x - 6 = 18 - 4x - 1

Simplify:

3/5x + 4x = 17 + 6

4⅗x = 23

x = 5

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204, 200,196,... find the 31st term

rewona [7]

Answer:

31st term = 84

Step-by-step explanation:

Given:

204, 200,196,...

Find:

31st term

Computation:

204, 200,196,...

First term a = 204

Difference d = a3 - a2

Difference d = 196 - 200

Difference d = -4

An = a + (n-1)d

A31 = 204 + (31-1)(-4)

A31 = 204 - 120

A31 = 84

6 0

2 years ago

Read 2 more answers

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S.

sweet-ann [11.9K]

Answer:

2.794

Step-by-step explanation:

Recall that if G(x,y) is a parametrization of the surface S and F and G are smooth enough then

$\bf \displaystyle\iint_{S}FdS=\displaystyle\iint_{R}F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})dxdy$

F can be written as

F(x,y,z) = (xy, yz, zx)

and S has a straightforward parametrization as

$\bf G(x,y) = (x, y, 3-x^2-y^2)$

with 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\frac{\partial G}{\partial x}= (1,0,-2x)\\\\\displaystyle\frac{\partial G}{\partial y}= (0,1,-2y)\\\\\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y}=(2x,2y,1)$

we also have

$\bf F(G(x,y))=F(x, y, 3-x^2-y^2)=(xy,y(3-x^2-y^2),x(3-x^2-y^2))=\\\\=(xy,3y-x^2y-y^3,3x-x^3-xy^2)$

and so

$\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2$

we just have then to compute a double integral of a polynomial on the unit square 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\int_{0}^{1}\displaystyle\int_{0}^{1}(2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2)dxdy=\\\\=2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}ydy+6\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^4dy+\\\\+3\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}x^3dx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}y^2dy$

=1/3+2-2/9-2/5+3/2-1/4-1/6 = 2.794

5 0

2 years ago

How to describe an inequality in your own words

emmasim [6.3K]

An inequality: a number sentence with ≤, ≥, <, >, = or ≠
≤ means: "less than or equal to"
≥ means: "greater than or equal to"
< means: "less than"
> means: "greater than"
≠ means: "not equal to"
= means: "equals"

8 0

3 years ago

Renaldo increased the image size on the computer screen by 20%. By

BartSMP [9]

Answer:

44%

Step-by-step explanation:

100 + 20 = 120/100

(1.2)^2=1.44

144 - 100 = 44%

3 0

2 years ago

PPPPLLLLEEEEZZZZ HHHEEELLLLPPP!!!!!!!. When a number x is multiplied by 9, the result is 35.

timama [110]

The x value is 3.888888 (the eight repeats, goes on forever) hope this helps :)

8 0

2 years ago

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