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Mars2501 [29]
3 years ago
10

Rachel really wants to purchase a new skateboard and her mother has agreed to give her a weekly allowance that she can save unti

l she has $220 (enough to buy the skateboard). Rachel’s mother is a math teacher and presents two different plans for paying her weekly allowance
Plan 1: a fixed weekly payment of $25


Plan 2: a 120 initial plus payment $10 per week


Part 1: write an equation for each plan explain what information the variables and numbers represents


Part 2: which plan requires number of weeks to save enough money for the kateboard? Explain or show your work
Mathematics
1 answer:
Anna11 [10]3 years ago
7 0

Please mark brainliest!

Part 1:

Plan 1: y = 25x

Plan 2: y = 120 + 10x

x = number of weeks

y = total money

Part 2:

Plan 1 requires 8.8 weeks.

220/25 = 8.8

Plan 2 requires 10 weeks.

220 - 100 = 100

100/10 = 10 weeks

Plan 1 is best since the money is earned faster.

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Solve by substitution <br> X^2= 2y + 10<br> 3x-y = 9
Viefleur [7K]

Answer:

x=-4\\ x=-2\\ y=-21\\ y=-15

Step-by-step explanation:

x^{2} =2y+10

y=-9+3x

x^{2} =2(-9+3x)+10

x^{2} =-18+6x+10

x^{2} =6x-8

x^{2} -6x+8

x=-4, -2

y=-9+3(-4)

y=-9-12

y=-21

y=-9+3(-2)

y=-9-6

y=-15

8 0
3 years ago
Read 2 more answers
A grasshopper has a length of 5X +2 inches a spider has a length of 2X -1 inches how much longer is the grasshopper
Temka [501]
The grasshopper is 5X+2-(2x-1)=3x+3 inches longer than the spider.
8 0
3 years ago
2(x-3)^2+10=82 solve by isolating x
Leviafan [203]
We have the following equation:
 2 (x-3) ^ 2 + 10 = 82
 We must clear x.
 We pass the constant terms to one side of the equation:
 2 (x-3) ^ 2 = 82 - 10
 2 (x-3) ^ 2 = 72
 (x-3) ^ 2 = 72/2
 (x-3) ^ 2 = 36
 Square root to both members:
 x-3 = +/- root (36)
 x-3 = +/- 6
 The solutions are:
 x1 = 6 + 3 = 9
 x2 = -6 + 3 = -3
 Answer:
 
x1 = 9
 
x2 = -3
7 0
3 years ago
You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until y
Luba_88 [7]
Current amount in account
P=36948.61

Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n

Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11

We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000

We can solve this by trial and error.


The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000.  It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.

So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.

So it takes 15.00 years to reach the goal of 280000 years.
8 0
3 years ago
Not sure if i got this right?
aleksandrvk [35]

Answer:

The effect it will have on the volume is;

The volume will be 8 times larger

Step-by-step explanation:

The dimensions of the given prism are;

The length of the prism, l = 5 in.

The breadth of the prism, b = 5 in.

The slant height of the prism,  = 4 in. by 5 in.

The height of the prism, h = 7 in.

The shape of the prism = Parallelepiped

The volume of a parallelepiped = Area of Base × Height of the prism

The base area of the parallelepiped = The length × Breadth of the parallelepiped

∴ The base area of the given parallelepiped = 5 in. × 5 in. = 25 in.²

The volume of the given parallelepiped, V₁ is found as follows;

V₁ = 5 in. × 5 in. × 7 in. = 25 in.² × 7 in. = 175 in.³

When a scale factor of 2 in applied to the dimensions of the prism, we have;

The new volume, V₂ =  2 × 5 in. × 2 × 5 in. × 2 × 7 in.

∴ V₂ = 2 × 2 × 2 × 5 in. × 5 in. × 7 in. = 8 × 5 in. × 5 in. × 7 in. = 8 × V₁

Therefore;

V₂ = 8 × V₁

The volume of the image of the object, V₂ after applying a scale factor of 2 is 8 times larger than the volume of the object, V₁.

5 0
3 years ago
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