The system of equations to find the value of x, the first number, and y, the second number are;
<em>y = -x + 84</em>
<em>y = x² + 6</em>
<h3>System of equation</h3>
The system of equation are equations that contains more than two equation and unknown.
Let the two unknown numbers x and y
If the sum of two numbers is 84, hence;
x +y = 84
y = -x + 84
If the square of the first number is 6 more than the second number, hence;
x² = y + 6
Substitute equation 2 into 2 to have:
x² = y + 6
x² = (-x+84) + 6
x² = -x+84 + 6
x² +x+84 + 6 = 0
x² +x + 90 = 0
Hence the system of equations to find the value of x, the first number, and y, the second number are;
<em>y = -x + 84</em>
<em>y = x² + 6</em>
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Answer:
48 and 36
Step-by-step explanation:
Let the two numbers be 4x and 3x
or4x+3x=84
or, 7x=84
or, x=84÷7
or, x=12
now,
4x=12×4
=48
3x=3×12
=36
Answer:
The speed of the first car is 60 mph
Step-by-step explanation:
speed = distance/time
Solve the above equation for distance to get
distance = speed * time
or simply
d = st
Now we use this formula for distance to write an equation for each car.
Let s = speed of second car
Then since the speed of the first car is 10 mph faster, the first car's speed is s + 10.
The time the two cars traveled is equal but unknown, so let the time = t.
First car: speed = s + 10; time = t; distance = 120 miles
d = st
120 = (s + 10)t
(s + 10)t = 120 Equation 1
Second car: speed = s; time = t; 100 miles
d = st
100 = st
st = 100 Equation 2
Equations 1 and 2 form a system of 2 equations in 2 unknowns.
(s + 10)t = 120
st = 100
Distribute t in the first equation.
st + 10t = 120
From the second equation we know st = 100, so substitute 100 for st.
100 + 10t = 120
10t = 120
t = 2
The time traveled was 2 hours.
Equation 2:
st = 100
Substitute t with 2.
s * 2 = 100
s = 50
The speed of the second car was 50 mph.
The speed of the first car is s + 10.
s + 10 = 50 + 10 = 60
Answer: The speed of the first car is 60 mph
Part A
The given line passes through (-2,2) and it is parallel to the line

We need to determine the slope of this line by writing it in slope -intercept form.


The slope of this line is

The line parallel to this line also has slope

The equation is

We substitute (-2,2)


The required equation is

PART B
The given line is

The slope of this line is

The slope of the line perpendicular to it is

The equation of the line is

We substitute the point, (-2,2)



The equation of the perpendicular line is
Answer:
The mean number of children is 3.
Step-by-step explanation: