Answer:
Elliot will make 4 hats and 16 scarves
Step-by-step explanation:
Let x be the number of hats and y be the number of scarves Elliot will make.
Elliott wants to make a total of 20 items, then
x + y = 20
Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then
0.1y = 2(0.2x)
Thus,
0.1y = 0.4x
y = 4x
Substitute it into the first equation:
x + 4x = 20
5x = 20
x = 4
y = 20 - 4
y = 16
Hence, Elliot will make 4 hats and 16 scarves
We are going to define two equations where b means bagels and m will be muffins, First equation: 10*b + 4*m = 13 Second equation: 5*b + 8*m = 14 From the second equation, we can isolate b: b = (14 - 8*m)/5 In the second equation 10*(14 - 8*m)/5 + 4*m = 13 2*(14 - 8*m) + 4*m = 13 28 - 16*m + 4*m = 13 28 -13 = 16*m - 4*m 15 = 12*m m = 15/12 = 1.25 Then b = (14 - 8*m)/5 = (14 - 8*1.25)/5 = 4/5 = 0.8 So one bagel costs $0.8 and one muffin $1.25
Answer:
x (children) = 58
y (students) = 66
z (adults) = 29
Step-by-step explanation:
Step 1: Write system of equations
x + y + z = 153
5x + 7y + 12z = 1100
1/2x = z
The best way to solve the systems of equations is to use an augmented matrix:
Top row: [1 1 1 | 153]
Middle row: [5 7 12 | 1100]
Bottom row: [1/2 0 -1 | 0]
And then put it in RREF form:
Top row: [1 0 0 | 58]
Middle row: [0 1 0 | 66]
Bottom row: [0 0 1 | 29]
The triangle has an only acute angle
In order to draw x ≤ -10 on a number line, first draw a closed dot at -10. This is because we have a ≤ and not a <. If we had a <, it would be an open dot.
Next, since we want x to be smaller, draw an arrow pointing towards all numbers that are smaller. This arrow would point to the left.
