Find the slope of the line that passes through<br> (8,3) and (3, 4)?

The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,22

stiv31 [10]

Answer:

<h3>The answer is option A</h3>

Step-by-step explanation:

Let the price of the room be p

Let the size of the room be s

To find the size of a kitchen that costs $3,824.00 we must first find the relationship between them

The statement

The price of tiling a room varies directly as the size of the room is written as

where k is the constant of proportionality

when

p = $4,224.00

s = 264 square feet

Substitute the values into the expression to find k

That's

4224 = 264k

Divide both sides by 264

k = 16

So the formula for the variation is

when

p = 3824

$s = \frac{p}{16}$

$s = \frac{3824}{16}$

s = 239

The final answer is

239 square feet

Hope this helps you

6 0

3 years ago

17. Admission prices to Cinema I to see a movie are $9.50 for an adult and $6.50 for a child. The admission charge at Cinema II

maksim [4K]

Answer:

a. 9.5x + 6.5(x+c) < 8 when c>0

b. Must be one child more than the no. of adults.

Step-by-step explanation:

For Cinema 1:

for adult = $9.50

for child = $6.50

For Cinema 2:

Per person regardless of age = $8.00

First of all, we will find out the condition when per person rates in both cinema are equal.

Assume x = no. of adults

y = no. of children

Rate per person in Cinema I = Rate per person in Cinema II

(9.5x + 6.5y)/(x+y) = 8

9.5x + 6.5y = 8(x+y)

9.5x + 6.5y = 8x + 8y

9.5x-8x = 8y-6.5y

=> x = y

So rates are equal when no. of adults equals no. of children

For Cinema I to have better rates, no. of children should be atleast 1 more than the no. of adult. In this way the rate per person of Cinema I will be less than 8

Hence we form an inequality when y = x+c and c > 0

9.5x + 6.5(x+c) < 8 when c>0

Hence there must be 1 more children than the no. of adults attending Cinema I for it to be a better deal.

4 0

3 years ago

Read 2 more answers

ordered pairs in which of these formats do not have to represent a function? (Length of side of a square,perimeter of square)

Daniel [21]

Answer:

perimeter of square

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Statements that can be proven by a logical sequence of statements is called a(n)

laila [671]

A)Theorem. every theorem can be proved.

6 0

4 years ago

Read 2 more answers

2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.

likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4 + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

$y = ^+_- \sqrt{-x^2+4x+4} -5$

Thus

$f(x) = \sqrt{-x^2+4x+4} - 5$

$g(x) = -\sqrt{-x^2+4x+4} - 5$

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

$\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0$

The quadratic has roots

$\frac{52 ^+_-\sqrt{1664}}{26}$

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0

3 years ago

Find the slope of the line that passes through (8,3) and (3, 4)?