Answer:
Step-by-step explanation:
The two inside angles will sum to 180°.
The top to angles are equal.
Think about this as what if both of the parallel lines were intersected by a perpendicuar line. Every angle would be a right triangle 90°. The inside angles will sum to 180° and the opposite angles are again equal.
(2x + 18) + (8x + 12) = 180
10x + 30 = 180
10x = 150
x = 15
-------------------------
(3y - 18) = (8x + 12) x = 15
(3y - 18) = (8(15) + 12)
(3y - 18) = (120 + 12)
(3y - 18) = 132
3y = 132 + 18
3y = 150
y = 50
Answer:
6. 141
7. 28
Step-by-step explanation:
Time to rewrite the expressions!
6. (8 + 45/9)² - 14(2)
First, we need to solve what's in the parentheses.
45/9 is 5. So 8 + 5 is 13. 13² - 14(2)
Now, the exponent. 13² = 169 (nice)
169 - 14(2) Multiply 14 and 2...
169 - 28 = 141
Now to rewrite 7.
12 + 36/2 - 3(1)²
Exponents first...
3² = 9 (the 1 isn't included 'cause 3 multiplied by 1 is still 3.)
12 + 36/2 - 12
Divide... 36/2 = 18
12 + 18 - 2
30 - 2
28
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)
Answer:
7
Step-by-step explanation:
