Help please thank you!

Part A: Create a system of linear equations with no solution. In two or more complete sentences, explain the specific characteri

Dmitrij [34]

Part A.
You need two equations with the same slope and different y-intercepts.
Their graph is parallel lines. Since the lines do not intersect, there is no solution.

y = 2x + 2
y = 2x - 2

Part B.
We use the first equation as above. For the second equation, we use an equation with different slope. Two lines with different slopes always intersect.

y = 2x + 2
y = -2x - 2

In the second equation, y = -2x - 2. We now substitute -2x - 2 for y in the first equation.

-2x - 2 = 2x + 2

-4x = 4

x = -1

Now substitute -1 for x in the first equation to find y.

y = 2x + 2

y = 2(-1) + 2

y = -2 + 2

y = 0

Solution: x = -1 and y = 0

6 0

3 years ago

What is x and y math help

Readme [11.4K]

<h3>Answer:</h3>

20 cans of cola
10 cans of root beer

<h3>Step-by-step explanation:</h3>

x and y are whatever you want them to be.

It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:

... x = # of cans of cola

... y = # of cans of root beer

Then the problem statement tells you ...

... x + y = 30 . . . . . . . 30 cans total were bought

... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer

_____

This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.

... (2y) +y = 30 . . . . . put 2y where x was

... 3y = 30 . . . . . . . . collect terms

... y = 10 . . . . . . . . . divide by 3

... 2y = x = 20

You're not done yet. You need to answer the question the problem asks.

Jared bought 20 cans of cola and 10 cans of root beer.

_____

Comment on x and y

You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.

Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.

Comment on problems of this type

When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.

Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).

8 0

2 years ago

HELP ASAP!!!

Umnica [9.8K]

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(a)/(a^2-16)+(2/(a-4))-(2/(a+4))=0

Simplify ————— a + 4 Equation at the end of step 1 : a 2 2 (—————————+—————)-——— = 0 ((a2)-16) (a-4) a+4 Step 2 : 2 Simplify ————— a - 4 Equation at the end of step 2 : a 2 2 (—————————+———)-——— = 0 ((a2)-16) a-4 a+4 Step 3 : a Simplify ——————— a2 - 16 Trying to factor as a Difference of Squares :

3.1 Factoring: a2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4
Check : a2 is the square of a1 

Factorization is : (a + 4) • (a - 4)

Equation at the end of step 3 : a 2 2 (————————————————— + —————) - ————— = 0 (a + 4) • (a - 4) a - 4 a + 4 Step 4 :Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

 The left denominator is : (a+4) • (a-4)

 The right denominator is : a-4

Number of times each Algebraic Factor
 appears in the factorization of: Algebraic
 Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a+4 101 a-4 111

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

4.2 Calculate multipliers for the two fractions

 Denote the Least Common Multiple by L.C.M
 Denote the Left Multiplier by Left_M
 Denote the Right Multiplier by Right_M
 Denote the Left Deniminator by L_Deno
 Denote the Right Multiplier by R_Deno

 Left_M = L.C.M / L_Deno = 1

 Right_M = L.C.M / R_Deno = a+4

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. a —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a+4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) Adding fractions that have a common denominator :

4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a + 2 • (a+4) 3a + 8 ————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) Equation at the end of step 4 : (3a + 8) 2 ————————————————— - ————— = 0 (a + 4) • (a - 4) a + 4 Step 5 :Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

 The left denominator is : (a+4) • (a-4)

 The right denominator is : a+4

Number of times each Algebraic Factor
 appears in the factorization of: Algebraic
 Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} a+4 111 a-4 101

Least Common Multiple:
(a+4) • (a-4)

Calculating Multipliers :

5.2 Calculate multipliers for the two fractions

 Denote the Least Common Multiple by L.C.M
 Denote the Left Multiplier by Left_M
 Denote the Right Multiplier by Right_M
 Denote the Left Deniminator by L_Deno
 Denote the Right Multiplier by R_Deno

 Left_M = L.C.M / L_Deno = 1

 Right_M = L.C.M / R_Deno = a-4

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (3a+8) —————————————————— = ————————————— L.C.M (a+4) • (a-4) R. Mult. • R. Num. 2 • (a-4) —————————————————— = ————————————— L.C.M (a+4) • (a-4) Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions

(3a+8) - (2 • (a-4)) a + 16 ———————————————————— = ————————————————— (a+4) • (a-4) (a + 4) • (a - 4) Equation at the end of step 5 : a + 16 ————————————————— = 0 (a + 4) • (a - 4) Step 6 :When a fraction equals zero : 6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

a+16 ——————————— • (a+4)•(a-4) = 0 • (a+4)•(a-4) (a+4)•(a-4)

Now, on the left hand side, the (a+4) • (a-4) cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
a+16 = 0

Solving a Single Variable Equation :

6.2 Solve : a+16 = 0

Subtract 16 from both sides of the equation :
 a = -16

One solution was found :

a = -16

4 0

3 years ago

PLEASE PLEASE HELP ME

Galina-37 [17]

Answer:

1. 110°

Step-by-step explanation:

Given angle - 610°

Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:

-610° + 2*360° = -610° + 720° = 110°

Correct option is 1.

7 0

2 years ago

Can someone help me with this math homework please!

alisha [4.7K]

Answer:

X1 = 2 Y1 = -5

Step-by-step explanation:

math simple slope

5 0

3 years ago