In 3 hours, a car travels 120 miles. What is the speed of the car

A student borrows a total of $5400 in student loan from two lenders. Bank One charges 4.3% simple

g100num [7]

9514 1404 393

Answer:

$1400

Step-by-step explanation:

Let x represent the amount borrowed from Bank 1. For each loan, the interest is given by I=Prt, where P is the principal borrowed at rate r for t years.

Then the total interest over 3 years is ...

3(4.3%·x +5.9%(5400 -x)) = 888.60

-1.6%·x +318.60 = 296.20 . . . . . . . . . . . divide by 3, simplify

-1.6%·x = -22.40 . . . . . . . . . . . subtract 318.60

x = 22.40/0.016 = 1400

The student borrowed $1400 from Bank 1.

8 0

2 years ago

An open box is to be made from a square piece of cardboard measuring 15 inches on a side by cutting a square from each corner an

vodomira [7]

Answer:

Dimensions are;

2.5 inches height

Base: 10 inches by 10 inches

Max volume; 250 Sq.in

Step-by-step explanation:

Let each side of the square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60

Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

6 0

3 years ago

If the area of a rectangle is 12cm2 what could its length be and its width?

lawyer [7]

Hello,

We know that th formula for the area of a rectangle is: $A=b*h$
Now, the problem in this excercise is that there is no restriction on the values that b and h can take, so, they can take any value provided that it meets: $b*h=12 cm^{2}$
for example:
$lenght= \frac{12}{3}cm \,\,\,\,\,\,and\,\,\,\,width= 3 cm \\ \\ A=\frac{12}{3}cm*3cm \\ A=12 cm^{2}$

But if they can only take intenger values, what we have to do is to descompose 12, and then we can analyze the possible solutions.

12 | 2
6 | 2
3 | 3
1

12= 2 *2*3

first option:
12=4*3

Answer: lenght= 4cm and width= 3cm or vice versa

second option:
12=2*6

Answer: lenght= 6cm and width= 2cm <span>or vice versa</span>

7 0

3 years ago

Si el dividendo es 800 el cociente es 160 y el residuo es 0 ¿cuál es el divisor?<br><br>ayudaaa

atroni [7]

Answer:

Él dividendo seria 5

Step-by-step explanation:

Por que si dividimos 800 ÷ 5 = 160 y no nos quedan residuos

ESPERO Y TE AYUDE ;)

5 0

3 years ago

Ginny’s favorite cookie recipe requires 1 1/2 cups of sugar to make 24 cookies. How much sugar does Ginny need to make 36 of the