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Maru [420]
3 years ago
12

The table below shows the surface area y, in square feet, of a shrinking lake in x days:

Mathematics
1 answer:
zmey [24]3 years ago
8 0
1A) The points are all on the line y=110-x, so the correlation coefficient is -1.

1B) The slope of the graph everywhere is -1 (square feet per day). This represents the change in area each day (-1 ft²).

1C) The data represents correlation. There is no reason to believe the change in area is caused by the passage of time. Rather, we expect the change to be caused by some process that removes water from the lake. In fact, we expect surface area to increase with time if water is being added (as by rain, for example).


2A) (h+t)(x) = h(x) +t(x) = (5x -2) +(4x +6) = 9x +4

2B) (h·t)(x) = h(x)·t(x) = (5x -2)·(4x +6) = 20x² +22x -12

2C) h(t(x)) = h(4x +6) = 5(4x +6) -2 = 20x +28


3A) 3x²y² -2xy² -8y² = y²(3x² -2x -8) = y²(x -2)(3x +4)
  we made use of the factoring -24 = -6·4 to form factors (3x-6)/3·(3x+4)

3B) x² +10x +25 = (x +5)² . . . . . matches the form for the square of a binomial

3C) x² -36 = (x -6)(x +6) . . . . . . matches the form for the difference of squares


4A) The discriminant is b²-4ac = (-12)² -4(4)(10) = 144 -160 = -16. The radicand is negative, so the solutions will be complex.

4B) A graph shows the solutions to be x ∈ {3, 3.5}.
  The "steps of the method" consisted of typing the expression into a graphing calculator and highlighting the x-intercepts. I chose this method as it requires the least amount of work.

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I don't know what the answer is to divide 180 in a ratio of 4:5:9
Karolina [17]
Hello there,

First you need to add together the numbers.
4+5+9 = 18
Divide the total by this,
180 / 18 = 10
Multiply each number by 10.
40:50:90.

Hope This Helps You!
Good Luck Studying :)
4 0
3 years ago
Read 2 more answers
What is the product of −3 1/4 and −1 1/2? Enter your answer as a mixed number, in simplified form, in the box.
Amiraneli [1.4K]

The product of −3 1/4 and −1 1/2  as a mixed number is 4\frac{7}{8}.

The product of −3 1/4 and −1 1/2  as a simplified form is \frac{39}{8}

<h3>What is products and mixed numbers?</h3>

Thew products between two terms can be described as the multiplication operation of the the two terms to give a term which is been performed by the use of the operation sign (*) between the two terms.

The mixed number can be defined as the numbers that contains whole numbers as well as the denominators and numerator.

It should be noted that the product of −3 1/4 and −1 1/2  can be done as (-3\frac{1}{4}  * -1\frac{1}{2}  = -\frac{13}{4} * \frac{-3}{2}  = \frac{39}{8} = 4\frac{7}{8}

Read more on mixed number here: brainly.com/question/21610929

#SPJ1

7 0
1 year ago
An initial amount of $2000 is invested in an account at an interest rate of 5% per year, compounded continuously. Find the amoun
yulyashka [42]

Answer:

$2,100.00

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).
aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0
3 years ago
Solve the equation<br> x-5=36-7(x+7)
lana66690 [7]

Answer: x = -1

Step-by-step explanation:

1) x - 5 = 36 -7x -49

2) x - 5 = -13 -7x

3) x + 7x =- 13 +5

4) 8x =- 8

5) x = -1

Please mark this as the brainliest answer! :) I hope this helped! <3

6 0
3 years ago
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