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3 years ago

7

Which are the solutions of x2 = -5x + 8?

1 answer:

Oksana_A [137]3 years ago

6 0

Answer:

1.27, -6.27 to the nearest hundredth,

or if you require it in exact form,

-2.5 + √14.25, -2.5 - √14.25.

Step-by-step explanation:

x^2 = -5x + 8

x^2 + 5x = 8

Competing the square:

(x + 2.5)^2 - 6.25 = 8

(x + 2.5) = 14.25

x + 2.5 = +/-√14.25

x = -2.5 + √14.25, -2.5 - √14.25

x = -2.5 + 3.77, -2.5 - 3.77

= 1.27, -6.27.

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A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inc

Bond [772]

The relationship is that two times the volume of cylinder is volume of cone

<em><u>Solution:</u></em>

Given that, cylinder and a cone have the same diameter: 8 inches

Diameter = 8 inches

Radius is diameter divided by 2

$radius = \frac{diameter}{2}\\\\radius = \frac{8}{2} = 4$

Radius = 4 inches

<u><em>Let us find the volume of cylinder and cone</em></u>

<u><em>Volume of cylinder:</em></u>

$volume = \pi r^2 h$

Radius = 4 inches

The height of the cylinder is 3 inches

height = 3 inches

Substituting the values, we get

$volume = 3.14 \times 4^2 \times 3\\\\volume = 3.14 \times 16 \times 3\\\\volume = 150.72$

Thus volume of cylinder is 150.72 cubic inches

<em><u>Volume of cone:</u></em>

$volume = \frac{\pi r^2h}{3}$

Radius = 4 inches

The height of the cone is 18 inches

height = 18 inches

Substituting the values, we get

$volume = \frac{3.14 \times 4^2 \times 18}{3}\\\\volume = 3.14 \times 16 \times 6\\\\volume = 301.44$

Thus volume of cone is 301.44 cubic inches

<em><u>What is the relationship between the volume of this cylinder and this cone?</u></em>

Volume of cylinder is 150.72 cubic inches

Volume of cone is 301.44 cubic inches

On observing the volume of cylinder and cone, we find that two times the volume of cylinder is volume of cone

$2 \times \text{Volume of cylinder} = \text{Volume of cone}$

$2 \times 150.72 = 301.44\\\\301.44 = 301.44$

Thus the relationship between the volume of this cylinder and this cone is that two times the volume of cylinder is volume of cone

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4 years ago

Find the slope of the line y=5x+4

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Answer:

Slope = 5

Step-by-step explanation:

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6 0

3 years ago

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aivan3 [116]

<span>3m^-2 3n^3
--------- = -----------
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3 years ago

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1. Find the area of the polygon

zhannawk [14.2K]

Answer:

1. A = 40 units²

2. A = 72 units²

3. B) 45

Step-by-step explanation:

1. This shape comprises 4 congruent triangles with base of 5 units and height of 5 units.

Area of a triangle = 1/2 x base x height

Therefore, area of polygon = 4(1/2 x 5 x 4)

= 40 units²

2. This shape comprises two pairs of congruent triangles.

Area of a triangle = 1/2 x base x height

Therefore, area of polygon = 2(1/2 x 2 x 6) + 2(1/2 x 10 x 6)

= 72 units²

3. Count the number of shaded squares:

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 units²

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2 years ago

1. Construct a table of values of the following functions using the interval of 5

Morgarella [4.7K]

Complete Question:

Construct a table of values of the following functions using the interval of -5 to 5.

$g(x) = \frac{x^3 + 3x - 5}{x^2}$

Answer:

See Explanation

Step-by-step explanation:

Required

Construct a table with the given interval

When $x = -5$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(-5) = \frac{-5^3 + 3(-5) - 5}{-5^2}$

$g(-5) = \frac{-125 -15 - 5}{25}$

$g(-5) = \frac{-145}{25}$

$g(-5) = -5.8$

When $x = -4$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(-4) = \frac{-4^3 + 3(-4) - 5}{-4^2}$

$g(-4) = \frac{-64 -12 - 5}{16}$

$g(-4) = \frac{-81}{16}$

$g(-4) = -5.0625$

When $x = -3$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(-3) = \frac{-3^3 + 3(-3) - 5}{-3^2}$

$g(-3) = \frac{-27 -9 - 5}{9}$

$g(-3) = \frac{-41}{9}$

$g(-3) = -4.56$

When $x = -2$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(-2) = \frac{-2^3 + 3(-2) - 5}{-2^2}$

$g(-2) = \frac{-8 -6 - 5}{4}$

$g(-2) = \frac{-19}{4}$

$g(-2) = -4.75$

When $x = -1$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(-1) = \frac{-1^3 + 3(-1) - 5}{-1^2}$

$g(-1) = \frac{-1 + 3 - 5}{1}$

$g(-1) = \frac{-3}{1}$

$g(-1) = -3$

When $x = 0$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(0) = \frac{0^3 + 3(0) - 5}{0^2}$

$g(0) = \frac{0 + 0 - 5}{0}$

$g(0) = \frac{- 5}{0}$

<em>g(0) = undefined</em>

When $x = 1$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(1) = \frac{1^3 + 3(1) - 5}{1^2}$

$g(1) = \frac{1 + 3 - 5}{1}$

$g(1) = \frac{-1}{1}$

$g(1) = 1$

When $x = 2$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(2) = \frac{2^3 + 3(2) - 5}{2^2}$

$g(2) = \frac{8 + 6 - 5}{4}$

$g(2) = \frac{9}{4}$

$g(2) = 2.25$

When $x = 3$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(3) = \frac{3^3 + 3(3) - 5}{3^2}$

$g(3) = \frac{27 + 9 - 5}{9}$

$g(3) = \frac{31}{9}$

$g(3) = 3.44$

When $x = 4$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(4) = \frac{4^3 + 3(4) - 5}{4^2}$

$g(4) = \frac{64 + 12 - 5}{16}$

$g(4) = \frac{71}{16}$

$g(4) = 4.4375$

When $x = 5$

$g(x) = \frac{x^3 + 3x - 5}{x^2}$ becomes

$g(5) = \frac{5^3 + 3(5) - 5}{5^2}$

$g(5) = \frac{125 + 15 - 5}{25}$

$g(5) = \frac{135}{25}$

$g(5) = 5.4$

<em>Hence, the complete table is:</em>

x ---- g(x)

-5 --- -5.8

-4 --- -5.0625

-3 --- -4.56

-2 --- -4.75

-1 --- -3

0 -- Undefined

1 --- 1

2 -- 2.25

3 --- 3.44

4 --- 4.4375

5 --- 5.4

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3 years ago