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# Tamara's Responses in WyzAnt Answers

#### What is the answer to (y-3)^2/16 - (x+2)^2/9 in hyperbola form with the center, vertices, foci, asymps, and what a,b, and c equal?

Please show work so I will understand I have been stuck on this one problem.

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Asked by Corey from Charleston, WV
20

Recall the standard form for the equation of a hyperbola is as follows:

Horizontal transverse axis:     (x - h)2/a2  -  (y - k)2/b2  = 1

Vertical transverse axis:     (y - k)2/a2  -  (x - h)2/b2  = 1

The equation of the hyperbola in question is already in standard form:

(y - 3)2/16  -  (x + 2)2/9  = 1

Looking at the equation, we see that the transverse axis is vertical. With this, we can find the center, vertices, foci, and asymptotes.

h = -2 ,   k = 3      ==>     center:   (h, k) = (-2, 3)

a2 = 16     ==>     √a2 = √16     ==>     a = 4

b2 = 9     ==>     √b2 = √9     ==>     b = 3

to find c, use the following formula:      c2 = a2 + b2

c2 = 16 + 9

c2 = 25      ==>      c = 5

Vertices:     (h, k + a)  =  (-2, 3 + 4) = (-2, 7)

(h, k - a)  =  (-2, 3 - 4) = (-2, -1)

Foci:     (h, k + c)  =  (-2, 3 + 5) = (-2, 8)

(h, k - c)  =  (-2, 3 - 5) = (-2, -2)

Asymptotes:     y - k = ± (a/b)(x - h)

y - 3 = ± (4/3)(x + 2)

thus, the asymptotes of this hyperbola have the following equations:

y - 3 = (4/3)(x + 2)          and          y - 3 = -(4/3)(x + 2)

#### Name the property shown by the statement. 9(6n)=(9x6)n

Name the property shown by the statement. 9(6n)=(9x6)n

I am stuck.

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Asked by James from Scarsdale, NY
10

When multiplying three or more real numbers, their product is always the same regardless of their grouping.

For instance, let  a, b, and c  be real numbers then, by the above statement, the following is true:

(a • b) • c  =  a • (b • c)  =  (a • c) • b

This is known as the associative property of multiplication.

Thus,

9 • (6 • n)  =  (9 • 6) • n  =  (9 • n) • 6

#### What is the area of rectangle B?

Right triangle A has base b, height h, and area x. Rectangle B has length 2b and width 2h. What is the area of rectangle B in terms of x?

a) 2x

b) 4x

c) 6x

d) 7x

e) 8x

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Asked by Sun from Los Angeles, CA
30

Given:

Right triangle A:     base = b     ,      height = h     , and     Area = x

Recall that the area (A) of a triangle is given be the following formula:

A = (1/2)bh

Thus, since we are given that the area of triangle A is equal to x, then

(1/2)bh = x

Rectangle B:     length = l = 2b     and      width = w = 2h

Recall that the area (A) of a rectangle is given by the following formula:

A = lw

Thus, the area (A) of rectangle be is as follows:

A = 2b·2h

A = 2·2(bh)

A = 4(bh)

From the area of triangle A, we can solve for bh then substitute this expression in terms of x into the formula of the area of rectangle B above:

area of triangle A:     (1/2)bh = x      multiply both sides of equation by 2 to solve for bh

(1/2)bh = x

bh = 2x

area of rectangle B:     A = 4(bh)     given bh=2x, replace bh in this equation with 2x

A = 4(2x)

A = 8x

Thus, the area of rectangle B in terms of x is 8x

you own a pizza restaurant the selling price is \$12 for each pizza the cost to make each pizza is \$5 you have a fixed labor cost of \$230 and you sell 85 pizzas what is your profit? How many pizzas would need to be sold to make a profit of \$700? How many pizzas would need to be sold if you wanted to make a profit greater than \$1,000?

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Asked by Donna from Citra, FL
20

Recall:     Profit  =  Revenue  -  Cost

P(x)  =  R(x)  -  C(x)   ,     where x is the number of pizzas sold

Revenue, R(x), is given by the following:

R(x) = (selling price)·(# of pizzas sold)

R(x) = 12x

Cost, C(x), is given by the following:

C(x) = (variable cost)·(# of pizzas sold) + fixed cost

C(x) = 5x + 230

Therefore, since    Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = 12x - (5x + 230)

P(x) = 12x - 5x - 230

P(x) = 7x - 230

Thus, the profit of selling 85 pizzas is determined by solving P(x) when x=85:

P(x) = 7x - 230

P(85) = 7(85) - 230

= 595 - 230

= 365

Since   P(85) = 365 ,  selling 85 pizzas yield a profit of \$365.

To find how many pizzas need to be sold to yield a profit of \$700, solve for x when P(x)=700:

P(x) = 7x - 230

700 = 7x - 230

700 + 230 = 7x - 230 + 230

930 = 7x

930/7 = 7x/7

132.86 = x

x ≈ 133

Thus, to make a profit of \$700, 133 pizzas need to be sold.

To find how many pizzas need to be sold to yield a profit greater than \$1000, solve for x when P(x)>1000:

P(x) = 7x - 230

7x - 230 > 1000

7x - 230 + 230 > 1000 + 230

7x > 1230

7x/7 > 1230/7

x > 175.7

x ≥ 176

Thus, to make a profit greater than \$1000, you would need to sell at least 176 pizzas.

#### What is the area of the triangle in cm

7 is on the base of the triangle & 13 is on the right side of the triangle

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Asked by Gavin from Bentonville, AR
10

The area (A) of a triangle given its base (b) and height (h) is defined by the following formula:

Area = (1/2)base·height     ==>     A = (1/2)bh

The triangle in question has the following base and height:

b = 7 cm      and      h = 13 cm

Therefore, its area is:

A = (1/2)(7 cm)(13 cm)

= (1/2)(91 cm2)

A = 45.5 cm2

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