Answer:
B. y = -3/4x + 5/2
Step-by-step explanation:
Take two points from the graph, let's use (-2, 4) and (2, 1):
Find slope:
m = (y₂ - y₁) / (x₂ - x₁)
= (1 - 4) / (2 - (-2))
= -3/4
Find y-intercept using slope above and anyone point:
y = mx + b
(1) = -3/4(2) + b
1 = -3/2 + b
b = 1 + 3/2
b = 5/2
Equation of line using m and b above:
y = mx + b
y = -3/4x + 5/2
Answer:
The solution to the system of linear equations is:
(x, y) = (-2, 8)
Hence, y - 2x = 12 and x - 2y = -18 has the ordered pair (-2,8) as its solution. Thus, option A is correct.
Step-by-step explanation:
Checking the first system of equations
y - 2x = 12
x - 2y = -18
solving the first system of equations
adding the equations
solving -3x=6 for x
Divide both sides by -3
Simplify
Subtract 8 from both sides
Simplify
Divide both sides by 2
Simplify
Therefore, the solution to the system of linear equations is:
(x, y) = (-2, 8)
Hence, y - 2x = 12 and x - 2y = -18 has the ordered pair (-2,8) as its solution. Thus, option A is correct.
Answer:
n(B') = 15
Step-by-step explanation:
Assumunin U is the universal set.
B = { 7,11,17,19}
B' = natural numbers different form 7,11,17 and 19 = {1,2,3,4,5,6,8,9,10,12,13,14,15,16,18}
Each paper cup is a cone.
The volume if a cone is (1/3) (pi) (radius)² (height)
Notice, in the picture they labeled the <em>diameter</em> of the cup = 8 cm.
But we need the<em> radius</em>. that's 1/2 of the diameter = 4 cm.
So, the volume of these paper cups is
(1/3) (pi) (4cm)² (11 cm) = about <em><u>184 cm³</u></em>
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It says that tons of lemons have been sacrificed, and you have
about 37,850 cm³ of lemonade.
How many cups will that fill ?
37,850 cm³ / 184 cm³ = about <em>205 cups</em>.
========================
How many packs of cups do you need to buy ?
Unfortunately, they only come in packs of 50.
1 pack = 50 cups . . . . . not enough
2 packs = 100 cups . . . not enough
3 packs = 150 cups . . . not enough
4 packs = 200 cups . . . oh so close but still not enough
You need to buy <em>5 packs = <u>250 cups</u></em>.
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It started raining, so you only sold 80% of the lemonade that you had.
80% means 0.80
"of" means "times"
You started out with 37,850 cm³ .
You sold (0.8) x (37,850 cm³) = about <u>30,280 cm³</u> of it.
How many cups did you fill with that much lemonade ?
(Remember, each cup holds about <u>184 cm³</u>.)
30,280 cm³ / 184 cm³ = about <u>164 cups sold</u>.
You bought 250 cups to start out.
You sold 164 cups of lemonade.
You had (250 bought - 164 used) =
<em>86 clean, unused paper cups, still in the wrappers, left over</em>.
If you were to list these numbers in order from greatest to least, it would be 1.29, 1.202, 1.02.
Hope this helps!!