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3 years ago

The inverse of Fx) is a function. True or False

Mathematics

2 answers:

olga2289 [7]3 years ago

8 0

It is true because it passes the horizontal line test

pickupchik [31]3 years ago

5 0

Answer:

The answer would be true

Step-by-step explanation:

Since there is only one y for every value of x and only one x for every value of y, both this graph and it's inverse would both be functions.

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Write a real-world problem for each problem.<br> 1. 5x - 10 = 40<br> 2. 3x + 4 = 13

Yuki888 [10]

1. I have 5 times some number of shoes. I give 10 away and now have 40. How many shoes did I originally start with?

2. I have 3 times some number of apples. I get 4 more apples. What amount of apples did I originally<span> start with? </span>

6 0

3 years ago

The height of a triangle is 7 ft more than its base. If the area of the triangle is 30 ft2, what is the length of the base?

SSSSS [86.1K]

Answer:

see below

Step-by-step explanation: 5 27 7 16

area = 1/2 bh

height of a triangle is 7 ft more than its base

base = b

height = b + 7

area = 30

area = 1/2 b(h)

30 = 1/2 b(b + 7)

30 = 0.5(b²+ 7b)

30 = 1/2 b²+ 3.5b solve for b

1/2 b²+ 3.5b = 30

1/2 b²+ 3.5b - 30 = 0

b²+ 7b - 60 = 0 factor

(b +12)(b - 5) = 0 when b = -12 or 5 base length can't be negative

b = base = 5

area = 1/2 bh 1/2×2(9) = 9

area = 1/2 bh 1/2×5(12) = 60

area = 1/2 bh 1/2×9(16) = 56

area = 1/2 bh 1/2×12(19) = 114

5 0

3 years ago

Simplify 5a+6a2+7a-4a2-9a

Mice21 [21]

Answer:

2a to the second power + 3a

Step-by-step explanation:

8 0

3 years ago

If f(x) = x3 - 12x2 + 44x - 48, which of the following is not a factor of f(x)? O (x + 4) O (x - 6) O (x - 2) O (x - 4)

denis-greek [22]

Answer:

(x + 4)

Step-by-step explanation:

x - 2 = 0, so x = 2

x - 4 = 0, so x = 4

x - 6 = 0, so x = 6

8 0

3 years ago

A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0

3 years ago