Answers: x = 13 and y = 11
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Let's focus on the angle expressions that have x in them.
They are adjacent angles and they form a straight line. So we consider them a linear pair. All linear pair angles always add to 180
(3x+89)+(7x-39) = 180
(3x+7x) + (89-39) = 180
10x+50 = 180
10x = 180-50
10x = 130
x = 130/10
x = 13
We'll use the same idea to find y
(3y+19)+(4y+84) = 180
(3y+4y) + (19+84) = 180
7y+103 = 180
7y = 180-103
7y = 77
y = 77/7
y = 11
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Extra info (optional section)
Let's find the measures of the four angles based on the x and y values we found.
- 3x+89 = 3*13+89 = 128
- 7x-39 = 7*13-39 = 52
- 3y+19 = 3*11+19 = 52
- 4y+84 = 4*11+84 = 128
It's not a coincidence that the 3x+89 and 4y+84 angles are equal (to 128). These are vertical angles which are always congruent. The other pair of congruent vertical angles are the 3y+19 and 7x-39 angles.
Note how 128+52 = 180 to help further confirm we have the correct values.
Another thing to notice is that all four angles add up to 360 degrees.
Answer:
87 packages
Step-by-step explanation:
First we need to find the volume of the cone-shaped vase.
The volume of a cone is given by:
V_cone = (1/3) * pi * radius^2 * height
With a radius of 9 cm and a height of 28 cm, we have:
V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3
Each package of sand is a cube with side length of 3 cm, so its volume is:
V_cube = 3^3 = 27 cm3
Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:
V_cone / V_cube = 2375.044 / 27 = 87.9646 packages
So we can use 87 packages (if we use 88 cubes, the vase would overflow)
This is the concept of arithmetic:
fraction of:
Protein+healthy fats=1/2
carbohydrates=2/3×1/2=1/3
sugary treats=1-(1/3+1/2)= 1/6
thus the percentage of sugary treats in the current diet will be:
(fraction of sugary treats)×(percentage of the diet)
=1/6×10
=10/6
=1 2/3 %