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2 years ago

Find the intersection between thelines 2x + 3y = 5 and 3x + 4y = 6

1 answer:

4 0

An intersection point, is a shared coordinate. If the equations share a coordinate we can say they are "equal". There are two ways (algebraically) to find this point. Substitution or linear combination. Because the coefficients are different, let's use linear combination

First stack the equations on top of each other.

2x + 3y = 5
3x + 4y = 6

Next let's manipulate one or both of the equations to get coefficients that are equal, but opposite. For this I'm going to turn the coefficient of x into 6 and -6 respectively by multiplying the first equation by 3 and the second by -2 to get

6x + 9y = 15
-6x -8y = -12

Now we can combine the equations with addition and the x's will cancel leaving a single variable (which we can solve)

y = 3

Now plug this back into either original equation to find the x coordinate.

2x + 3(3) = 5

2x + 9 = 5

2x = -4

x = -2.

So your intersection point is (-2,3)

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A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra

S_A_V [24]

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

Compounds money quarterly

Double your money in 10 years

Step:1

Formula to calculate future investment with compounded quarterly,

$A =P(1+\frac{r}{n} )^{nt}$ ...............................(1)

Where, A - Future amount

P - Initial investment\

r - Rate of interest

n - No. of compounding in a year

t - No. of years

Step:2

Let, P = X

A = 2X ( Double your money )

From given, n - 4 ( for compounding quarterly )

t - 10 years

From equation (1)

$2X =X(1+\frac{r}{4} )^{(4)(10)}$

$\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

$2 =(1+\frac{r}{4} )^{40}$

Take root $40^{th}$ root on both side,

$\sqrt[40]{2} = (1+\frac{r}{4} )$

$1.017479692 = (\frac{4+r}{4} )$

$(1.017479692)(4) = (r+4)$

$4.06992=(r+4)$

$r = 4.06992 -4$

$r =( 0.06992)(100)$

r = 6.992 %

Result:

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

3 0

2 years ago

Which transfromations tranforms the graph of f(x)=x^2 to the graph of g(x)=(x+4)^2?

wariber [46]

Greetings from Brasil...

In function F(X) = X², if we replace X with X + 4 we will have exactly function G(X) = (X + 4)²

So, just replace X for X + 4..... This will be responsible for translating 4 units to the left, because:

F(X) = X²

F(X + 4) = (X + 4)²

F(X + 4) ⇔ F(X + k) see below

We know that the translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

see more:

brainly.com/question/17163323

4 0

2 years ago

Jeff is saving to purchase a new basketball that will cost at least $88. He has already saved $32. At least 7) Jeff is saving to

Mariulka [41]

The answer is 224
becs 32*7=224

4 0

2 years ago

Mitchell currently sells stoves for company a at a salary of $12,000 plus $150 commission for each stove he sells Company B offe

ipn [44]

Answer:

Mitchell needs to sell 120 stoves for the options to be equal.

Step-by-step explanation:

Company A gives Mitchell $12000 salary plus $150 commission per stove selling and Company B is offering Mitchell $24000 salary plus $50 commission per stove selling.

So, if Mitchell sells x number of stoves such that both the plans become equal, then we can write

12000 + 150x = 24000 + 50x

⇒ 100x = 12000

⇒ x = 120

Therefore, Mitchell needs to sell 120 stoves for the options to be equal. (Answer)

5 0

2 years ago

Please help me!!!!!!!!!!i need to finish by tonight!!

Viktor [21]

Number 3.
opens up
vertex (1,2)
idk maybe because it is on the right side. its positive

number 4.
opens up as well
Vertex (-2,0)
no because it is negative and on the left. Idk just a guess for this one

4 0

2 years ago