Find the x and y intercept of this equation: -2x + 8y =4 write your solutions as a point in the form (x,y)

• 1. If 16 ounces of bulk rice costs $2.50, how much would 24 ounces cost? Solve the problem and then verify your response using

jasenka [17]

$60 hope this helps you!:)

6 0

3 years ago

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A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago

Which expression is equivalent to (2x-5)-5x(x-4)

Murrr4er [49]

2x-5-5x²+20x
-5x+22x-5

7 0

3 years ago

Trigonometry

quester [9]

Answer:

$\frac{9 + 2 \sqrt{3} }{3} \\$

Step-by-step explanation:

$\cosec(30) + \cosec(60) + \cosec(90) \\ \\ = 2 + \frac{2}{ \sqrt{3} } + 1 \\ \\ = \frac{2 \sqrt{3 } + 2}{ \sqrt{3} } + 1 \\ \\ = \frac{2 \sqrt{3} + 2 + \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} + 2}{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} + 2}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{9 + 2 \sqrt{3} }{3}$

4 0

3 years ago

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In geometry words describe a way to seperate triangles Into other triangles

Alja [10]

Start at one of the vertices and draw a line from there to a point on the oposite side, not ending at another vertex

6 0

3 years ago

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