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3 years ago

How do you simplify algebraic expressions?

1 answer:

7 0

There are many reasons one may want to simplify, rearranging to find specific values - or maybe just making it simpler
Well, let's do some examples:
y(x(3+2)) +2 = -2y +2 y(3x+2x) + 2 = - 2y +2
3xy + 2xy + 2 = -2y +2
5xy + 2 = -2y +2 <-- the +2's dissapear because they cancel out
5xy = -2y

And there we have it, that long expression has been simplified to something really simple.

Another example:
3(4(x+3(2 +z)) - 5)= 3y <- you can start where ever, I like starting in the middle
3 * (4 * (x + 3*(2 + z)) - 5 ) = 3y <- here it is spaced out, we get a much better view
3 * (4 * (x + 6 + 3z) - 5 ) = 3y
3 * (4x + 24 + 12z - 5) = 3y <- divide both sides by 3 ..
4x + 24 + 12z - 5 = y <- much better

Note: Simplify means solving to a degree, but you can't solve it because it has unknowns

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5s + 2z = 1.32 3s + 1z = 0.75 what would the answer be?

Sphinxa [80]

Answer:

Step-by-step explanation:

7 0

3 years ago

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit c

Lera25 [3.4K]

Answer:

Claim is false

Step-by-step explanation:

Claim : A credit reporting agency claims that the mean credit card debt in a town is greater than $3500.

$H_0:\mu \leq 3500\\H_a:\mu = 3500$

n = 20

Since n <30

So we will use t test

Formula : $t =\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

s = standard deviation = 391

x = 3600

n = 20

$t =\frac{3600-3500}{\frac{391}{\sqrt{20}}}$

$t =1.14$

Degree of freedom = n-1 = 20-1 = 19

α=0.10

So, using t table

$t_({\frac{\alpha}{2},d.f.})$ = 1.72

t critical > t calculated

So we accept the null hypothesis

Hence we reject the claim that the mean credit card debt in a town is greater than $3500.

7 0

3 years ago

Rectangle WXYZ is shown on a coordinate plane. On a coordinate plane, a rectangle has 4 points. Point W is (1, 1), point X is (1

Temka [501]

Answer:

the length of the side XY is 4 units

Step-by-step explanation:

To find the length of side XY, what we do is to find the distance between the points X and Y

To find this distance, we employ the use of the formula for finding the distance between two points on a Cartesian plane.

Mathematically, the distance d which represents the length XY is given by;

d = √{(x2-x1)^2 + (y2-y1)^2}

Where point X represents the coordinates (x1,y1) = (10,1) while point Y represents the coordinates (x2,y2) = (10,-3)

Plugging these values into the formula, we have;

d = √{(10-10)^2 + (-3-1)^2}

d = √{(0)^2 + (-4)^2}

d = √(0 + 16)

d = √(16)

d = ± 4

but since distance cannot be negative, we ignore the -4 and thus we choose 4 units as the length between the points XY

4 0

4 years ago

Find the value of sin(a/2) if cosa= 12/13

daser333 [38]

Answer: sin $\frac{a}{2}$ = ± $\frac{1}{\sqrt{26} }$

Step-by-step explanation:

We very well know that,

cos2A=1−2sin²A

⟹ sinA = ± $\sqrt{(1-} \frac{cos2A}{2} )$

As required, set A = $\frac{a}{2}$ & cos a= $\frac{12}{13}$ ,thus we get

sin $\frac{a}{2}$ =± $\sqrt{\frac{1-cos a}{2} }$

∴ sin $\frac{a}{2}$ =± $\sqrt{\frac{1-\frac{12}{13} }{2} }$ = ± $\frac{1}{\sqrt{26} }$

since ,360° < $\frac{a}{2}$ <450°

,180° < $\frac{a}{2}$ <225°

Now, we are to select the value with the correct sign. It's is obvious from the above constraints that the angle a/2 lies in the III-quadrant where 'sine' has negative value, thus the required value is negative.

hope it helped!

5 0

3 years ago

Item 19 A cylindrical container of four rubber balls has a height of 20 centimeters and a diameter of 5 centimeters. Each ball i

Lady_Fox [76]

First you need to find the volume of the cylinder. Then find the volume of all 4 rubber balls (spheres). Subtract the cylinder's volume by the spheres' volumes.

Volume of cylinder: πr²h
π2.5²(20) = 392.7 cm³

Volume of sphere: 4/3πr³
4/3π2.5³ = 65.45 cm³

392.7 - 65.45 = 327.25

The amount of space in the container unoccupied by the rubber balls is 327 cm³.

7 0

4 years ago

How do you simplify algebraic expressions? ￼￼￼￼￼ ￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼

How do you simplify algebraic expressions?