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White raven [17]

2 years ago

14

Megan and Sam were solving a system of equations. They both noticed that the two lines had different slopes. Megan said that bec

ause each line in the system had different slopes, the two lines had to intersect, which meant there was one solution to the system. Sam disagreed, and said they should also look at the y-intercepts. Who is correct?
A. Megan is correct. When two lines have different slopes, they must intersect, producing one solution.
B. Neither person makes a valid argument.
C. Sam is correct. When two lines intersect, their y-intercepts determine how many solutions there will be.

2 answers:

finlep [7]2 years ago

7 0

Answer:

A

Step-by-step explanation:

pochemuha2 years ago

5 0

Your answer is A. Megan is correct. When two lines have different slopes, they must intersect, producing one solution.

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Step-by-step explanation:

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Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly

damaskus [11]

Answer:

The balance be after he has made exactly half of his monthly payments is $56881.4.

Step-by-step explanation:

Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.

To find : What will his balance be after he has made exactly half of his monthly payments?

Solution :

Formula of monthly payment ,

$M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $40,000

Rate r= 4% compounded monthly

$i=\frac{4}{100}=0.04$

Time = 10 years

$n=10\times12=120$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.04)^{-120}}{0.04}$

$D=\frac{1-(1.04)^{-120}}{0.04}$

$D=\frac{1-0.00903}{0.04}$

$D=\frac{0.9909}{0.04}$

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$M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{40000}{24.7725}$

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3 0

2 years ago

Read 2 more answers

An open-top rectangular box is being constructed to hold a volume of 150 in3. The base of the box is made from a material costin

Oksanka [162]

Answer:

minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in

Step-by-step explanation:

given data

volume = 150 in³

base material costing = 5 cents/in²

front cost = 10 cents/in²

remainder sides cost = 2 cents/in²

to find out

the dimensions that will minimize the cost

solution

we consider here length = x and breadth = y and height = z

and

area of base = xy

area of front = xz

and area of remaining side = xz + 2yz .....................1

so

cost of base will be = 5xy

cost of front = 10xz

cost of remaining side = 2 ( xz+ 2yz)

and

total cost will be

total cost TC = 5xy + 10xz + 2 ( xz+ 2yz)

total cost TC = 5xy + 10xz + 2xz+ 4yz

total cost TC = 5xy + 12xz + 4yz ....................2

and total volume will be = xyz

150 = xyz

z = $\frac{150}{xy}$ .......................3

now put z value in equation 2

total cost TC = 5xy + 12xz + 4yz

total cost TC = 5xy + 12x $\frac{150}{xy}$ + 4y $\frac{150}{xy}$

total cost TC = 5xy + $\frac{1800}{y}$ + $\frac{600}{x}$ ...........4

now differentiate TC w.r.t x and y

TC (x) = 5y - $\frac{600}{x^2}$

TC (x) = 5x - $\frac{1800}{y^2}$

now equating with 0 these

5y - $\frac{600}{x^2}$ = 0

x² = $\frac{120}{y}$

and

5x - $\frac{1800}{y^2}$ = 0

x = $\frac{360}{y^2}$

solve we get

y = 10.2598

x = 3.4199

now put x and y value in equation 3

z = $\frac{150}{xy}$

z = $\frac{150}{3.4199*10.2598}$

z = 4.2750

so minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in

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2 years ago

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eimsori [14]

Same as what I explained in your last question.

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Hope this helps!!!

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Artyom0805 [142]

Answer:

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2 years ago