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3 years ago

How does writing a function rule as an equation help you solve problems with more than one situation or parameter?

Mathematics

1 answer:

Paha777 [63]3 years ago

7 0

Because then you can replace the variables with the actual value and see of the equation is true.

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How do I solve #14????

Tcecarenko [31]

All the measures in a triangle are equal to 180 degrees.

Let the unknown angle= x.

40+89+x= 180

Combine like terms.

129+x= 180

Subtract 129 from both sides.

x= 51

The angle is equal to 51.

I hope this helps!
~kaikers

5 0

4 years ago

A water tank contains 100 fluid Ounces of water. Jacob fills up cups that hold 8 fl. oz. each. How many cups has he filled when

Kamila [148]

7 and a half cups.

Step-by-step explanation:

Dvide 60 by 8

8 0

3 years ago

Find the slope and y-intercept of the line.

balandron [24]

Answer:

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

= (2 - 0) / (0 - (-3)

= 2/3

Y intercept 2

4 0

3 years ago

a family buys a new home for $212,500 and pays a 20% down payment ($42,500). if the mortgage is for 15 years at 5.75% interest w

diamong [38]

Answer:

Their monthly house payment is of $2,184.65.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

A family buys a new home for $212,500 and pays a 20% down payment ($42,500).

This means that the loan is of 212,500 - 42,500 = $170,000, that is, $P = 170,000$

Value of the loan in 15 years:

15 years means that $t = 15$

5.75% interest means that $r = 0.0575$

Compounded yearly, so $n = 1$

Then

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

$A(15) = 170000(1 + \frac{0.0575}{1})^{15}$

$A(15) = 393237$

Monthly payment:

Total of $393,237 in 15*12 months. So

$M = \frac{393237}{15*12} = 2184.65$

Their monthly house payment is of $2,184.65.

5 0

3 years ago

The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the

sweet-ann [11.9K]

Answer:

24 cm wide by 36 cm high

Step-by-step explanation:

The poster with the smallest area will have an aspect ratio that makes the margin dimensions the same percentage of overall dimension in each direction.

Since the ratio of margin widths is 6:4 = 3:2, the poster and printed area will have an aspect ratio of 3:2. That is, the width is ...

width of printed area = √(2/3·384 cm²) = 16 cm

Then the width of the poster is ...

width = left margin + printed width + right margin = 4cm + 16 cm + 4 cm

width = 24 cm

The height is 3/2 times that, or 36 cm.

The smallest poster with the required dimensions is 24 cm wide by 36 cm tall.

_____

If you need to see the calculus problem, consider the printed area width to be x. Then the printed height is 384/x and the overall dimensions are ...

(x + 8) by (384/x + 12)

We want to minimize the area, which is the product of these dimensions:

a = (x +8)(384/x +12) = 384 +12x +3072/x +96

a = 12x + 3072/x +480

This is a minimum where its derivative is zero.

a' = 12 -3072/x^2 = 0

a' = 1 -256/x^2 = 0 . . . . . . divide by 12; true when x^2 = 256

This has solutions x=±16, of which the only useful solution is x=16.

7 0

4 years ago