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Komok [63]
1 year ago
11

Solve the system by substitution. 4x+3y=5x=4y+6Options: A. The solution is ____B. There are infinitely many solutions. C. There

is no solution
Mathematics
1 answer:
zvonat [6]1 year ago
5 0

So we have the following system of equations:

\begin{gathered} 4x+3y=5 \\ x=4y+6 \end{gathered}

We need to solve it by substitution. This means that we have to take the expression for x given by the second equation and replace x with it in the first equation:

\begin{gathered} 4x+3y=5 \\ 4\cdot(4y+6)+3y=5 \\ 16y+24+3y=5 \\ 16y+3y=5-24 \\ 19y=-19 \\ y=-\frac{19}{19}=-1 \end{gathered}

So y=-1. If we use this value in the second equation:

\begin{gathered} x=4y+6 \\ x=4\cdot(-1)+6 \\ x=-4+6 \\ x=2 \end{gathered}

So we have x=2 and y=-1 which means that there's one solution. Then the correct answer is A and the solution is (2,-1).

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Joe earns $14 an hour and Blaine earns $18 per hour. Joe receives a raise of $1.75 every six months, and Blaine receives a raise
Katarina [22]

After 4 interval of six months, Joe to earn same hourly rate as Blaine

<em><u>Solution:</u></em>

Given that,

Amount earned by Joe = $ 14 per hour

Amount earned by Blaine = $ 18 per hour

Lets assume the number of six month intervals be "x"

<em><u>Joe receives a raise of $1.75 every six months</u></em>

Therefore,

Joe earning: 14 + 1.75(number of six month intervals)

Equation for Joe earning: 14 + 1.75x ------- eqn 1

<em><u>Blaine receives a raise of $0.75 every six months</u></em>

Therefore,

Blaine earning: 18 + 0.75(number of six month intervals)

Equation for Blaine earning: 18 + 0.75x ------------ eqn 2

The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,

Eqn 1 must be equal to eqn 2

14+1.75x = 18+0.75x\\\\1.75x-0.75x = 18-14\\\\1x = 4\\\\x = 4

Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.

8 0
3 years ago
Translate the following phrase to a mathematical expression: a number times fifteen.
crimeas [40]

Answer:

it could either be n15

15n

because a number multiplied by 5 is

n15

but in mathematics a number comes before a letter when writing a mathematical expression

8 0
3 years ago
Read 2 more answers
If angle 1 = 6n + 1 and angle 4 = 4n + 19, what is the angle 2?
kobusy [5.1K]
Angles 1 and 4 are alternate angles and thus have the same measurement. You will set their equations equal to each other and solve for the variable. 

6n + 1 = 4n + 19

Subtract 1 and 4n from both sides to get variables on one side and constants on the other. 

6n - 4n = 19 - 1

Combine like terms and solve for n.

2n = 18
n = 18 / 2
n = 9

Angles 1 and 2 are congruent as labeled in the graph. 

So angle 2 is also 6n + 1

Plug in for 9 for n

6(9) + 1
54 + 1
55

Option C is your answer. 


7 0
3 years ago
Can some one PLEASE give me brainliest
KIM [24]

Answer:

You gotta deserve it

Step-by-step explanation:

8 0
3 years ago
ANWSER these three questions show ur work, if u can is somewhat optional
Airida [17]

Answer:

1. 35            2. 565.5         3. 12.28

Step-by-step explanation:

1. Triangle 1 & 2: 7x3=21    

You do not have to divide by 2 is since there are two triangles.

 Semi-circle: 14.13

2. Trinagle: 29x19/2 = 275.5

Rectangle: 29x10 = 290

3. Triangle: 3x4/2 = 6

Semi-circle: 3.14x4/2 = 6.28

<em>Took a long time- Please give Brainliest and points!</em>

7 0
3 years ago
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