Algebra 1 connections answers

Author: Matthew David

Algebra 1 connections answers

Introduction to algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. In this article we shall discuss for need help with algebra 1 math.   (Source: Wikipedia)

Sample problem for need help with algebra 1 math

Need help with algebra 1 math problem 1:

Solve the given linear equation

8x+ 8y = 24,

8y +8 z = –40,

8z + 8x = 16.

Solution:

The given equations can be written as

8x + 8y = 24 ----------- (1)

8y + 8z = –40 -------- (2)

8z + 8x =   16 ----------- (3)

Adding all the equations,

8x + 8y + 8z = 24 + (–40) + 16

Or          8(x + y + z) = 0

In the above equation is divided by 2 we get

8x +8 y +8 z = 0 ----------- (4)

Substituting 8y + 8z = 16 in equation (4) we get

8x + (–40) = 0

8x = 40

X = 5

Substituting 4x + 4y = 12 in equation (4) we get

4y + 20 = 12

4y = –8

Y = -2

Substituting x = 5 in equation (3) we get

8z + 8x = 16

8z + 8*5 = 16

8z = 16–40

8z = -24

z = –3

The solution is x = 5, y = –2, z = –3.

Need help with algebra 1 math problem 2:

Solve the given linear equation

10x+ 10y = 32,

10 y +10 z = –50,

10z + 10x = 20.

Solution:

The given equations can be written as

10x + 10y = 32 ----------- (1)

10y + 10z = –50 -------- (3)

10z + 10x = 20 ----------- (3)

Adding all the equations,

20x + 20y + 20z = 32 + (–50) + 20

Or          20(x + y + z) = 0

In the above equation is divided by 2 we get

10x + 10y + 10z = 0 ----------- (4)

Substituting 10x + 10y = -50 in equation (4) we get

10x - 50= 0

10x = 50

X = 5

Substituting 10z + 10x = 20 in equation (4) we get

10y + 20= 0

10y = –20

Y = -2

Substituting x = 5 in equation (3) we get

10z + 10*5 = 20

10z = 20–50

10z = -30

z = –3

The solution is x = 5, y = –3, z = –3.

Algebra 1 connections example problem 1:

Solve the linear function y = 2 - x and x - y = 10

Solution:

Given equations are,

y = 2 - x --------- (equation 1)

x - y = 10 -------- (equation 2)

Substitute the equation 1 into equation 2, we get

x - (2 - x) = 10

Rearrange the above equation, we get

x - 2 + x = 10

2x - 2 = 10

Add 2 on both the side of the equation, we get

2x = 12

Subtract the above equation by 2, we get

x = 6

Substitute x = 6 in equation 1, we get

y = 2 - 6

y = - 4

Answer:

The final answer is x = 6, y = - 4.

Algebra 1 connections example problem 2:

Simplify the given [removed]4x + 43) + 12x = 52 - 2x

Solution:

Given expression is (4x + 43) + 12x = 52 - 2x

Expand the above expression, we get

4x + 43 + 12x = 52 - 2x

16x + 43 = 52 - 2x

Subtract (52 - 2x) on both the side of the equation, we get

18x - 9 = 0

Add 9 on both the sides, we get

18x = 9

Divide the above equation by 18, we get

x = `(9 / 18)`

Answer:

The final answer is x = `(1 / 2)`

Algebra 1 connections example problem 3:

Find the x intercept of the given polynomial equation f (x) = x2 - 225

Solution:

The given polynomial equation is f (x) = x2 - 225

Plug f (x) = 0, for finding x intercept

0 = x2 - 225

Rearrange the above equation, we get

x2 - 225 = 0

Add 225 on both the sides of the equation, we get

x2 = 225

Take square root on both the sides, we get

x = ± 15

Answer:

The final answer is x = ± 15

Practice problems for algebra 1 connections answers

Algebra 1 connections practice problem 1:

Solve the linear function y - 2 = x and 4x + y = 22

Answer:

The final answer is x = 4, y = 6

Algebra 1 connections practice problem 2:

Factorize the equation x2 + 22x + 40 = 0

Answer:

The final answer is x = - 20 and x = - 2

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