Abby can buy an 8 pound of dog food for 7.40 or a 4 pound bag of the same dog food for 5.38. Which is the better buy

-Dominant- [34]

We know that

in the triangle TQS
applying the Pythagorean theorem
QS²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1

in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2

in the triangle QTR
TQ²=TR²+36-----------> equation 3

I substitute 1 and 2 in 3
18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units

the answer is
TS=6√6 units
6 is the square root of 6 units

6 0

3 years ago

Read 2 more answers

The upper-left coordinates on a rectangle are (-5, 6)(−5,6)left parenthesis, minus, 5, comma, 6, right parenthesis, and the uppe

sammy [17]

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

The upper-left coordinates on a rectangle are (−5,6) and the upper-right coordinates are (−2,6). The rectangle has a perimeter of 16units. Draw the rectangle on the coordinate plane below.

If the coordinates of the top of the triangle (breadth) is (−5,6) and (−2,6), we can calculate the breadth of the rectangle by taking the difference between the two points using the formula:

D = √(y₂-y₁)²+(x₂-x₁)²

Given x₁ = -5, y₁= 6, x₂ = -2 and y₂ = 6

D = √(6-6)²+(-2-(-5))²

D = √0²+3²

D = √9

D = 3 units

Breadth = 3 units

Given the Perimeter to be 16 units and the formula for calculating the perimeter of rectangle t be P = 2(L+B), we can get the length of the rectangle.

16 = 2(3+L)

16 = 6+2L

16-6 = 2L

2L = 10

L = 10/2

L = 5 units.

Hence the length of the rectangle is 5 units and the breadth is 3 units. Find the diagram in the attachment.

7 0

2 years ago

Please help Please help

bekas [8.4K]

The answer is A. I looked it up for you on an surface area calculator.

5 0

2 years ago

Find the slope of the given line, if it is defined.

il63 [147K]

Answer: A. The slope is $-\dfrac{4}{3}$ .

Step-by-step explanation:

The slope of a line helps to specify the direction of the line.

The slope of a line that passes through (a,b) and (c,d) is given by :-

$\text{Slope}=\dfrac{d-b}{c-a}$

Then the slope of a line passes through origin i.e. (0,0) and (-9,12) is given by :-

$\text{Slope}=\dfrac{12-0}{-9-0}\\\\\Rightarrow\ \text{Slope}=\dfrac{12}{-9}\\\\\Rightarrow\ \text{Slope}=-\dfrac{4}{3}$

Hence, the slope is $-\dfrac{4}{3}$ .

8 0

2 years ago

Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p

Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0

2 years ago