Answer: the cost of one plate is $4.5
The cost of one cup is $2.1
Step-by-step explanation:
Let x represent the cost of 1 plate.
Let y represent the cost of 1 cup.
5 plates and 4 cups cost 30.90 dollars. It means that
5x + 4y = 30.9- - - - - - - -1
6 plates and 5 cups cost 37.50 dollars. It means that
6x + 5y = 37.5- - - - - - - -2
Multiplying equation 1 by 6 and equation 2 by 5, it becomes
30x + 24y = 185.4
30x + 25y = 187.5
Subtracting, it becomes
- y = - 2.1
y = 2.1
Substituting y = 2.1 into equation 1, it becomes
5x + 4 × 2.1 = 30.9
5x + 8.4 = 30.9
5x = 30.9 - 8.4
5x = 22.5
x = 22.5/5
x = 4.5
Answer: a) 2:1. b) 3. c) Perimeter of ΔEFG=36 Perimeter of ΔHIJ=18. d) 2:1
Step-by-step explanation:
a) Find the ratio of GF and JI. 16:8. Simplify by dividing both by 8 to get 2:1.
b) Set up this equation: 6/16=x/8. Cross-multiply. 6*8=48. Divide by 16. 48/16=3.
c) First find the length of one half of GF by dividing 16 by 2. 16/2=8. Set up the Pythagorean theorem. 8^2+6^2=c^2. Square 8 and 6. 64+36=c^2. Add 64 and 36. 100=c^2. Find the square root of 100. c=10.
EF and EG both measure 10 since they are shown to be congruent. 10+10+16=36.
Next find the length of one half of JI by dividing 8 by 2. 8/2=4. Set up the Pythagorean theorem. Since we know x=3, it will be 4^2+3^2=c^2. Square both 4 and 3. 16+9=c^2. Add 16 and 9. 25=c^2. Find the square root of 25. c=5.
HJ and HI both measure 5 since they are congruent. 5+5+8=18.
d) Find the ratio of the perimeters of ΔEFG and ΔHIJ. 36:18. Simplify by dividing both by 6 to get 6:3. Simplify further by dividing both by 3 to get 2:1.
The new graph would have a less steeper slope than the first graph because slopes with whole numbers have a steeper slope than slopes with fractions
hope this helps:)
Answer:
240π
Step-by-step explanation:
Turbine blade that was 24 inches long is the radius of the circle the bug travels.
So the Circumference is = 2rπ = 2*24*π = 48π
The bug held on for 5 rotations. so the distance that the bug travels = 5*48π = 240π
Answer:
x < 15
Step-by-step explanation:
Let's first expand the parentheses on both sides. Remember that when expanding parentheses, the result will be the sum of the products of the "outside number" with each of the "inside number".
On the left, the parenthetical expression is: -6(x + 4). Here, the outside term is -6 and the inside terms are x and 4. So:
-6(x + 4) = -6 * x + (-6) * 4 = -6x - 24
On the right, the parenthetical expression is: -5(x + 6). Here, the outside term is -5 and the inside terms are x and 6. So:
-5(x + 6) = -5 * x + (-5) * 6 = -5x - 30
Now put these back in:
-6(x + 4) + 9 > -5(x + 6)
-6x - 24 + 9 > -5x - 30
-6x - 15 > -5x - 30
x < 15
Thus the answer is x < 15.
Hope this helps!