You have to understand how piecewise functions first
I hope you do because I won't be explaining it here
1.
if it is continiuous at x=1 then the part of the function that approaches 1 from the left is the same value
so we have f(x)=3-x for x<1, so evaluate it for x=1,
we would get 3-1=2
so
if a=2 and b=3
f(x)=2x²+3x
for x=1, we get 2+3=5
it approaches 2 from the left but equals 5
2≠5
so it is not continuous because it doesn't approach the same value at x=1
2.
alright
so we established that it should approach 2 because we had the f(x)=3-x
so
f(1)=2=ax²+bx
2=a+b
the relationship is 2=a+b
3.
same as before, but use the other function, the one that is defined at x≥2
5x-10, 5(2)-10, 10-10, 0
it approaches 0
so
we must find one such that f(x)=0 for x=2 with the ax²+bx
0=a(2)²+b(2)
0=4a+2b
if we minus 2b both sides
-2b=4a
divide by 2
-b=2a
add b both sides
0=2a+b
4.
2=a+b
0=2a+b
2=a+b
minus b both sides
2-b=a
subsitute
0=2a+b
0=2(2-b)+b
0=4-2b+b
0=4-b
b=4
sub back
2-b=a
2-4=a
-2=a
a=-2
b=4
5.
graph f(x)=-2x²+4x from x=1 to x=2 and put a closed dot at (1,2) and an open dot at (2,0)
The area of the triangle is 90 m²
Explanation:
Given that the base of the triangle is 15 m
The altitude of the triangle is 12 m
<u>Area of the triangle:</u>
The area of the triangle can be determined using the formula,
where b is the base and h is the altitude
Thus, we have,
and 
Substituting the values in the above formula, we get,
Multiplying the terms, we get,
Dividing, we get,
Therefore, the area of the triangle is 90 m²
-2/3(2/2)= -4/6
1/2(3/3)= 3/6
-4/6+3/6= -1/6
The answer is -1/6. Hope this helps!
Answer:
P
(
sum
>
3
and
divisor of
24
)
=
7
18
Explanation:
Possible target sums that meet the given requirements:
XXX
{
4
,
6
,
8
,
12
}
Consider the possible die rolls that can give these sums:
sum
−−−−
xxx
first roll
−−−−−−−
second roll
−−−−−−−−−
4
1
3
2
2
3
1
6
1
5
2
4
3
3
4
2
5
1
8
2
6
3
5
4
4
5
3
6
2
12
−−
6
−
6
−
Giving a total of
14
out of a possible
36
combinations that meet the given requirements.
Step-by-step explanation:
A,B,and C because in when multiplying or dividing, + and - will be negative and if they are + and + or, - and - then the answer will be positive.
