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3 years ago

What is the area of the rectangle?

Mathematics

1 answer:

STatiana [176]3 years ago

4 0

Answer:

9x^2 25x+14

Step-by-step explanation:

using FOIL:

(x+2)(9x+7)

9x^2 +7x + 18x +14

9x^2 25x+14

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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

Please solve for all three parts of the question.

neonofarm [45]

Answer:

f(-5) = 25

f(0) = -2

f(5) = 16

Step-by-step explanation:

Given the functions;

To get f(-5), we will use the function of x where x is less than 0 since -5 is less than zero

at where x < 0, f(x) = x^2

f(-5) = (-5)^2

f(-5) = 25

b) For f(0), where the point where x = 0, f(x)= -2

Hence the value of f(o) = -2

c) For f(5), the function where x > 5 is f(x) = 2x+6

f(x) = 2x+6

f(5) = 2(5)+6

f(5) = 16

5 0

2 years ago

Q ,# 13 Graph the function<br>Y = - X + X ^2

GalinKa [24]

We have the following function that is a quadratic function:

$y=-x+x^2$

So the graph of this function is shown in the figure below. This is a <em>parabola</em> as you can see. The roots of this functions, that is, the x-intercepts are:

$y=-x+x^2 \\ y=x(x-1) \\ \\ x_{1}=0 \ and \ x_{2}=1$

As you can see in the figure. This function decreases from $(-\infty,0.5)$ and increases from $(0.5, \infty)$

Finally, another thing we can see from the graph is that the vertex is the point:

$V(0.5,-0.25)$