Mathematics

Question

Can someone please help me on this?

The swimming team is ordering shirts. The cost (y) in dollars of (x) shirts is calculated by using the rule y=20x+40.
a) Identify the slope and y-intercept
slope:
Meaning:
b) how much will 15 sweatshirts cost?
c) If the bill was $1,000, how many shirts were ordered?


2) Write a rule in slope-intercept form for the linear function that has (1,5) and (4, 11)


3 Y=8x-25
y=6x-5
Solve the system of equations above

5.)which region indicates the intersection of the system 3x+4y>8 and -2x+4y>12



6) Write and solve a system of equations to the following.
Two times Antonio;s age plus Sara's age equals 35. Sarah's age is also 5 times Antonio's age. How old is Sarah?

1 Answer

  • 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.
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