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4 years ago

Match the following items.

Mathematics

1 answer:

shusha [124]4 years ago

6 0

Step-by-step explanation:

The following match

* a² + 2ab + b² and (a + b)²

* a² - b² and (a - b)(a + b)

* a² - 2ab + b² and (a - b)²

* a³ - b³ and (a - b)(a² + ab + b²)

* a³ + b³ and (a + b)(a² - ab + b²)

* y = 10x Direct variation

* xy = 18 Algorithm

* y = 4xz Joint variation

* y = 4x/z Inverse variation

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Solve for y in the following equation.

Tju [1.3M]

Answer:

$y = \frac{z^2 - x}{2}$

Step-by-step explanation:

Given:

$\sqrt{x + 2y} = z$

Required:

Solve for y (make y the subject of the formula)

SOLUTION:

$\sqrt{x + 2y} = z$

Square both sides

$(\sqrt{x + 2y})^2 = z^2$

$x + 2y = z^2$

Subtract both sides by x

$2y = z^2 - x$

Divide both sides by 2

$y = \frac{z^2 - x}{2}$

5 0

3 years ago

Select the two values of x that are roots of this equation.<br> X2 + 2x - 5 = 0

LenaWriter [7]

Answer:

$x=-1+\sqrt{6 }$

$x=-1-\sqrt{6 }$

Step-by-step explanation:

$x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}$

Ignore the A before the ±. It wouldn't let me type it correctly.

x² + 2x - 5 = 0

a = 1

b = 2

c = - 5

$x=\frac{-2±\sqrt{2^{2}-4((1)(-5)) } }{2(1)}$

$x=\frac{-2±\sqrt{4-4((1)(-5)) } }{2(1)}$

$x=\frac{-2±\sqrt{4+20 } }{2(1)}$

$x=\frac{-2±\sqrt{24 } }{2}$

$x=\frac{-2±\sqrt{(2)(12) } }{2}$

$x=\frac{-2±\sqrt{(2)(2)(6) } }{2}$

$x=\frac{-2±\sqrt{(2)(2)(2)(3) } }{2}$

$x=\frac{-2±(\sqrt{2} )(\sqrt{2})(\sqrt{(2)(3) )} }{2}$

$x=\frac{-2±2\sqrt{6 } }{2}$

Two separate equations

$x=\frac{-2+2\sqrt{6 } }{2}$

$x=\frac{-2-2\sqrt{6 } }{2}$

$x=-1+\sqrt{6 }$

$x=-1-\sqrt{6 }$

7 0

3 years ago

Meiko is hanging a picture collage on her wall. The dimensions of the collage are shown in the diagram. She plans to cover

alexira [117]

Answer: $\frac{A_{collage}}{15.75\ in^2}$

Step-by-step explanation:

Since you did not attach the diagram and I don't know the dimensions of the collage, I will give you a general explanation of the procedure you need to use in order to solve the exercise:

1. You need to use the formula for calculate the area of a rectangle:

$A=lw$

Where "l" is the length and "w" is the width.

2. Using the formula, you must calculate the area of an small picture.

You know that its length is 4.5 inches and its width is 3.5 inches. Therefore, its area is:

$A_{picture}=(4.5\ in)(3.5\ in)\\\\A_{picture}=15.75\ in^2$

3. Calculate the area of the collage using the formula:

$A_{collage}=(l_{collage})(w_{collage})$

4. Finally, divide the area of the collage by the area of an small picture in order to find the number of small pictures that will fit within the collage:

$\frac{A_{collage}}{15.75\ in^2}$

5 0

3 years ago

Read 2 more answers

Write as equation.

Svetach [21]

$\huge\color{red}\boxed{\colorbox{black}{60 = 5+b}}$