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3 years ago

Factor each expression.

Mathematics

2 answers:

anygoal [31]3 years ago

4 0

3x^2 – 5x – 12 = (3x+4)(x-3)
x^2 -9 = (x-3)^2
8x^3+ 12x^2 - 2x - 3 = (4x^2 - 1)(2x + 3)
12x^2 +16x -3= (6x - 1)(2x + 3)
x^2 + 8x - 9= (x + 9)(x - 1) (I can not see who it can all be positive ;_; )
3(x + y) + a(x + y)= (3x + 3y) + (ax + ay)

geniusboy [140]3 years ago

4 0

7. 3x² - 5x - 12
    3x² - 9x + 4x - 12
    (3x + 4)(x - 3)

8. x² - 9
    x² + 3x - 3x - 9
   (x - 3)(x + 3)

9. 8x³ + 12x² - 2x - 3
    (8x³ + 12x² - 2x - 3)
    (4x² - 1)(2x + 3)

10. 12x² + 16x - 3
      12x² + 18x - 2x - 3
    (6x - 1)(2x + 3)

11. x² + 8x + 9
      (x² + 9x - x + (-9))
      (x - 1)(x + (-9))

Extra Credit: 3(x + y) + a(x + y)
   3(x) + 3(y) + a(x) + a(y)
   3x + 3y + ax + ay
   3x + ax + 3y + ay
   (3 + a)x + (3 + a)y

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3 years ago

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A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

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3 years ago

How do you divide 1.25 by 24

GREYUIT [131]

Answer:

Step-by-step explanation:

The awnser to this problem is +19.20 because since 24 is bigger than 1.25 it goes on the inside of the house and 1.25 goes on the outside because its smaller.

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3 years ago

6x-5y=15 x=y+3 find x and y

arlik [135]

Answer:

(0, -3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Coordinates (x, y)
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

6x - 5y = 15

x = y + 3

Step 2: Solve for y

Substitution

Substitute in x: 6(y + 3) - 5y = 15
Distribute 6: 6y + 18 - 5y = 15
Combine like terms: y + 18 = 15
[Subtraction Property of Equality] Subtract 18 on both sides: y = -3

Step 3: Solve for x

Define original equation: x = y + 3
Substitute in y: x = -3 + 3
Add: x = 0

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3 years ago

Someone sold 20 bottles. White water for 1 dollar and the black ones for 2 dollars each. He earned 35 dollars. How many of each

aivan3 [116]

Answer:

20+1+2+35= 58

Step-by-step explanation:

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2 years ago