Answer:
(-1, 0), (2, 0), (3, 0)
Step-by-step explanation:
x-intercept of a line is defined by a point where y = 0.
So the point in the form of (x, 0) will be the x-intercept of the given continuous function.
From the table attached,
For x = -1, f(-1) = 0
For x = 2, f(2) = 0
For x = 3, f(3) = 0
Points (-1, 0), (2, 0) and (3, 0) are the x-intercepts of the continuous function f(x).
Answer:
A, B, C, and D, all options are correct.
A is correct because,
∠2 and ∠3 are corresponding angles.
B is correct because,
∠5 and ∠7 are corresponding angles.
C is correct because,
∠2 and ∠4 are corresponding angles.
D is correct because,
∠5 and ∠6 are alternate interior angles.
Note,
If two lines parallel, then
- Corresponding angles are equal.
- Alternate interior angles are equal.
Part A: each tricycle has three wheels, so with 48 wheels the number of tricycles was a =48/3=16 tricycles.
t=w/3 (the number of tricycles is the number of wheels divided by 3)
Part B:
The number of seats:
24=b+a (so b=24-a)
The number of seats is the sum of one seat per bicycle and one seat per a tricycle
also, 61=2a+3b (the number of wheels)
So we have:
24=b+a
b=24-a
We can substitute this for b:
61=2a+3(24-a)
and solve:
61=2a+3*24-3a
61=72-a
a=72-61
a=11
There were 11 bicycles!!
and there were 24-11 tricycles, so 13 tricycles.
Part C: each of the bikes has only one front-steering handlebar, so there were a total of 144 vehicles:
a+b+c=144
There were 378 pedals. And the number of pedals is:
2a+2b+4c=378 (the numbers 2,2,4 represent the number of pedals per vehicle)
divide by 2:
a+b+2c=189
Now, we have
a+b+2c=189
and
a+b+c=144
and we can subtract them from each other:
a+b+c-(a+b+2c)=144-189
-c=45
c=45, so there were 45 tandem bicycles!
(this also means that a+b=144-45, that is a+b=99)
now the wheels:
3a+2b+2c=320
Let's substitute c:
3a+2b+90=320
which is
3a+2b=240
We also know that a+b=99, so we can substract this from this equation:
3a+2b+-a-b=240-99
2a+b=141
and again:
2a+b-a-b=141-99
a=42 - there were 42 trycicles!!!
And the bicycles were the rest:
99-42=57 bycicles
Answer:
<h3>
<u>Given Question</u></h3>
If
Given pair of equations are
and
On dividing by 2, we get
On multiply equation (1) by 3 and (2) by 4, we get
and
On Subtracting equation (3) from (4), we get
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
<h3>
<u>Concept Used :- </u></h3>
There are 4 methods to solve this type of pair of linear equations.
1. Method of Substitution
2. Method of Eliminations
3. Method of Cross Multiplication
4. Graphical Method
We prefer here Method of Eliminations :-
To solve systems using elimination, follow this procedure:
<h3>
<u>The Elimination Method</u></h3>
Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.
Step 2: Subtract the second equation from the first to eliminate one variable
Step 3: Solve this new equation for other variable.
Step 4: Substitute the value of variable thus evaluated into either Equation 1 or Equation 2 and get the value other variable.
Y=mx+b
m=slope
b=y intercept or where the line crosses the y axis
slope=rise/run, from left to right
so
1.
ok, so we see it is going throught (-2,1) and (-1,4)
so it hits (-2,1) and then goes up 3 and right 1
so sloe=3/1 or 3
y intercept, it hits at y=7 so
y=3x+7 is equation
2.
we gots a hit at (0,2) and (5,6) about
so goes up 4 and to the right 3 so
4/3 is slope
hits y axis at about y=2
y=(4/3)x+2
