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3 years ago

14

Katie wants to hang a painting in a gallery. The painting and frame must have an area of 45 square feet. The painting is 6 feet

wide by 7 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

1 answer:

Luda [366]3 years ago

5 0

Each side should increase by 2x (left & right, and up & down) so that to match the condition :
7+2x)(6+2x) = 45
Solving it will give you: 4x² + 26x - 3

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I NEED HELP ASAP!!!!!!!!

andreev551 [17]

Step-by-step explanation:

$slope = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 7 - 13}{5 - ( - 3)} \\ = \frac{ - 20}{8} \\ = \frac{ - 2 \times 10}{2 \times 4} \\ = \frac{ - 10}{4} \\ = \frac{ - 2 \times 5}{ 2 \times 2} = \frac{5}{2}$

7 0

3 years ago

Find the probability:

Vikki [24]

Part 1:

3+2+1 = 6 total units

There is only 1 history book.

1/6 total.

Part 2:

6-1 (we've lost the history book) = 5 total units

3 novels. = 3/5

Part 3:

1/6 * 3/5 = 3/30 or 1/10

3 0

3 years ago

Read 2 more answers

A small regional carrier accepted 16 reservations for a particular flight with 12 seats. 8 reservations went to regular customer

wolverine [178]

Answer:

a) 32.04% probability that overbooking occurs.

b) 40.79% probability that the flight has empty seats.

Step-by-step explanation:

For each booked passenger, there are only two possible outcomes. Either they arrive for the flight, or they do not arrive. The probability of a passenger arriving is independent of other passengers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Our variable of interest are the 8 reservations that went for the passengers with a 48% probability of arriving.

This means that $n = 8, p = 0.48$

A) Find the probability that overbooking occurs.

12 seats, 8 of which are already occupied. So overbooking occurs if more than 4 of the reservated arrive.

$P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{8,5}.(0.48)^{5}.(0.52)^{3} = 0.2006$

$P(X = 6) = C_{8,6}.(0.48)^{6}.(0.52)^{2} = 0.0926$

$P(X = 7) = C_{8,7}.(0.48)^{7}.(0.52)^{7} = 0.0244$

$P(X = 8) = C_{8,5}.(0.48)^{8}.(0.52)^{0} = 0.0028$

$P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2006 + 0.0926 + 0.0244 + 0.0028 = 0.3204$

32.04% probability that overbooking occurs.

B) Find the probability that the flight has empty seats.

Less than 4 of the booked passengers arrive.

To make it easier, i will use

$P(X < 4) = 1 - (P(X = 4) + P(X > 4))$

From a), P(X > 4) = 0.3204

$P(X = 4) = C_{8,4}.(0.48)^{4}.(0.52)^{4} = 0.2717$

$P(X < 4) = 1 - (P(X = 4) + P(X > 4)) = 1 - (0.2717 + 0.3204) = 1 - 0.5921 = 0.4079$

40.79% probability that the flight has empty seats.

4 0

3 years ago

I need help with this question

PSYCHO15rus [73]

Answer:

3/28

Step-by-step explanation:

6 0

3 years ago

Please help! question attached

Svetradugi [14.3K]

Answer:

36. y=x

37. x=4

38. y=3x-10

39. y=-25x+49

40. $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. y=-x+3

Step-by-step explanation:

36. Parallel lines have the same slope. The slope of the line $y=x+42$ is $m=1,$ so the equation of a parallel line is

$y=x+b$

This line passes through the point (2,2), so its coordinates satisfy the equation:

$2=2+b\\ \\b=0$

and the equation of the line is $y=x$

37. The line $x=03$ is vertical ine, so parallel line is also vertical line with equation $x=a.$ Substitute the coordinates of the point (4,3):

$4=a$

hence the equation is $x=4$

38. Parallel lines have the same slope. The slope of the line $y=3x+24$ is $m=3,$ so the equation of a parallel line is

$y=3x+b$

This line passes through the point (2,-4), so its coordinates satisfy the equation:

$-4=3\cdot 2+b\\ \\b=-10$

and the equation of the line is $y=3x-10$

39. Parallel lines have the same slope. The slope of the line $y=-25x+35$ is $m=-25,$ so the equation of a parallel line is

$y=-25x+b$

This line passes through the point (2,-1), so its coordinates satisfy the equation:

$-1=-25\cdot 2+b\\ \\b=49$

and the equation of the line is $y=-25x+49$

40. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=18x+26$ has the slope $m_1=18,$ perpendicular line has the slope $m_2 =-\dfrac{1}{18}.$

The equation is

$y=-\dfrac{1}{18}x+b$

This line passes through the point (1,-5), so its coordinates satisfy the equation:

$-5=-\dfrac{1}{18}\cdot 1+b\\ \\b=-5+\dfrac{1}{18}=-\dfrac{89}{18}$

and the equation of the line is $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=x+2$ has the slope $m_1=1,$ perpendicular line has the slope $m_2 =-1.$

The equation is

$y=-x+b$

This line passes through the point (4,-1), so its coordinates satisfy the equation:

$-1=-4+b\\ \\b=3$

and the equation of the line is $y=-x+3$

4 0

3 years ago