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3 years ago

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Mathematics

2 answers:

Agata [3.3K]3 years ago

8 0

Answer:

a = 4

Step-by-step explanation:

a^2 + b^2 = c^2

a= ?

b= 3

c= 5 (c is always the hypotenuse)

*plug in given values

a^2 + 3^2 = 5^2

a^2 + 9 = 25

-9 -9

a^2 = 16

*find the square root

sqrt(a) = sqrt(16)

a = 4

Makovka662 [10]3 years ago

3 0

Answer:

a = 4

General Formulas and Concepts:

<u>Pre-Algebra</u>

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

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg
b is another leg
c is the hypotenuse<u> </u>

Step-by-step explanation:

<u>Step 1: Define</u>

Leg <em>a</em> = <em>a</em>

Leg <em>b</em> = 3

Hypotenuse <em>c</em> = 5

<u>Step 2: Solve for </u><em><u>a</u></em>

Substitute in variables [Pythagorean Theorem]: a² + 3² = 5²
[Subtraction Property of Equality] Isolate <em>a </em>term: a² = 5² - 3²
Evaluate exponents: a² = 25 - 9
Subtract: a² = 16
[Equality Property] Isolate <em>a</em>: a = ±4

Since we are dealing with a regular right triangle and not a quadrant triangle, we use the positive root.

∴ a = 4

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Answer:

Step-by-step explanation:

-2/5 - (-9/15) = -2/5 + 9/15.

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Zinaida [17]

Answer:

Step-by-step explanation:

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3 years ago

Al sumar un número entero con el doble de su sucesor, se obtiene un total de 44. ¿De qué número se está hablando?

Vlad [161]

Basado en lo que nos dieron en la pregunta podemos decir que:
1) x sea un numero entero
2)x+1 sea el numero sucesor del anterior
3) los dos seran sumados y el total de la suma es 44
4) el numero sucesor es multiplicado por dos antes de ser sumado con el numero entero

Entonces tenemos:
$x+2(x+1)=44 \\ x+2x+2=44 \\ 3x=42 \\ x=14$

En este caso el numero del cual se esta hablando es 14 para comprobar

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3 years ago

A pile of sand has a weight of 90kg.

ankoles [38]

Answer:

9Kg, 18Kg and 63 Kg

Step-by-step explanation:

Sum the parts of the ratio, 1 + 2 + 7 = 10 parts

Divide the weight of sand by 10 to find the value of one part of the ratio

90 Kg ÷ 10 = 9 Kg ← value of 1 part of the ratio, thus

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3 years ago

What is the area of the shaded region?

Verdich [7]

<h2>Area of Composite Shapes</h2>

To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.

For this triangle, we will need to know the formula to find the area of a triangle:

$A=\dfrac{1}{2}bh$

<h2>Solving the Question</h2>

The given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:

Find the area of the large triangle
Find the area of the little triangle
Subtract the area of the little triangle from the large triangle

<h3>Area of the Large Triangle</h3>

$A=\dfrac{1}{2}bh$

⇒ Plug in the values given for the base and height:

$A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2$

<h3>Area of the Small Triangle</h3>

$A=\dfrac{1}{2}bh$

⇒ Plug in the values given for the base and height:

$A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2$

<h3>Subtract the Area of the Small Triangle from the Area of the Large Triangle</h3>

$30 mm^2-6mm^2\\=24mm^2$

<h2>Answer</h2>

The area of the shaded region is $24mm^2$ .

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