Answer:
(-4, -8)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
x - 2y = 12
5x + 3y = -44
<u>Step 2: Rewrite Systems</u>
x - 2y = 12
- [Multiplication Property of Equality] Multiply everything by -5: -5x + 10y = -60
<u>Step 3: Redefine Systems</u>
-5x + 10y = -60
5x + 3y = -44
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Elimination</em>
- Combine 2 equations: 13y = -104
- [Division Property of Equality] Divide 13 on both sides: y = -8
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: x - 2y = 12
- Substitute in <em>y</em>: x - 2(-8) = 12
- Multiply: x + 16 = 12
- [Subtraction Property of Equality] Subtract 16 on both sides: x = -4
Answer:
Hence the probability that she paid cash is 0.105
Step-by-step explanation:
P(cash) = 0.3
P(credit card ) = 0.3
P(debit card ) = 0.4
P ( more than $50 | cash ) = 0.2
P (more than $50 | credit card ) =0.9
P (more than $ 50 |debit card ) = 0.6
P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )
= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4
= 0.57
P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)
= 0.2* 0.3 / 0.57
= 0.105
Answer:
x = -1 and y = -1.
Step-by-step explanation:
The given system of equations are :
y = 4x + 3 ....(1)
y = -x - 2 ....(2)
From equation (1) and (2) :
4x + 3 = -x - 2
Taking like terms together,
4x + x = -3 -2
5x = -5
x = -1
Put the value of x in equation (1)
y = 4(-1) + 3
= -1
The solution is also shown in the attached figure. Hence, the solution is x = -1 and y = -1.
Answer:
C.
Step-by-step explanation:
We are given that
In I year, number of participants=88
In V year, number of participants=115
We have to find the equation of the trend line that can be generated by using the data from years 1 and 5.
Rate of change of participants =
Rate of change of participants,m=6.75
Point-slope form:
Where m=Rate of change of participants per year
By using the formula
Substitute the values then we get
Hence, option C is true.
