Answer:
x=8
Step-by-step explanation:
We know that the sum of two opposite interior angles equals one exterior angle
So
8x-5+27°=9x+14
8x+22=9x+14
22-14=9x-8x
x=8
1)
a. y=mx+b
m=slope
b=y-intercept
y=20x+40
The slope is 20.
The y-intercept is 40.
b. y =cost
x= # of shirts
y=20x+40
15 sweatshirts would make the equation y=20(15)+40
y=300+40
y=340
15 shirts would cost $340.
c. y=20x+40
$1000 would make the equation 1000=20x+40
1960=20x
98=x
Paying $1000 would get the swim team 98 shirts.
2)
(1,5) (4,11)
(x,y) (x1, y1)
y+y1=m(x+x1)
Pick a point and substitute it into the equation.
y+5=m(x+1)
To find the slope of a line, use the following equatIon:
y-y1/x-x1
11-5/4-1
6/3=2
The slope of the line is 2. Plug it into the equation for m.
y+5=2(x+1)
Solve the equation.
y+5=2x+2
y+3=2x
Put the equation in slope-intercept form.
y=2x-3
3)
y=x-25
y=6x-5
Plug one equation into the other.
x+25=6x-5
Solve.
x+30=6x
30=5x
6=x
Now plug 6 into one of the equations.
y=6x-5
y=6(6)-5
y=36-5
y=31
The answer should be in the form of a point.
(6,31)
5) I'm sorry, don't know how to solve this. You can Google how to graph two inequalities, though.
6)
Antonio's age can be represented by x.
Sarah's age can be represented by y.
2x+y=35
5x=y
Plug 5x into the first equation.
2x+5x=35
Solve.
7x=35
x=5
Antonio is 5 years old.
To find Sarah's age, plug Antonio's age into the equation for Sarah's age.
5x=y
5(5)=y
25=y
Sarah is 25 years old.
Each ticket = an individual student.
322 is the total amount
so the equation you use is $322 divided by $4
WHY: this is so you can find the amount of $4 in $322. This is basically finding the number of students attending the dance.
You just have to make them into a faction. Then you can choose any number then you need to multiply the top number and the bottom number by the same thing. And that's how you can tell if they are equivalent.
Hope this helped :D
Answer:
4
Step-by-step explanation:
• Divide the larger number by the smaller number
• If remainder is 0 then the smaller number is the HCF
• If not repeat with the remainder and smaller number until a remainder of 0 is reached.
1820 ÷ 204 = 8 remainder 188
204 ÷ 188 = 1 remainder 16
188 ÷ 16 = 11 remainder 12
16 ÷ 12 = 1 remainder 4
12 ÷ 4 = 3 remainder 0 ← remainder of 0 reached
Thus 4 is the HCF of 1820 and 204