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3 years ago

If triangle ABC has sides of lengths 6,10,and x, between which two numbers must the value of x lie

1 answer:

4 0

The sum of two sides of a triangle must be more than the length of the third side. 6+4 = 10 so x must be greater than 4. 6 + 10 = 16, so x must be less than 16
4<x<16
x is between 4 and 16.

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2 years ago

Solve using elimination x-2y=12 and 5x+3y=-44 (4,8) (-4,8) (4,-8) (-4,-8)

Leya [2.2K]

Answer:

(-4, -8)

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
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

x - 2y = 12

5x + 3y = -44

Step 2: Rewrite Systems

x - 2y = 12

[Multiplication Property of Equality] Multiply everything by -5: -5x + 10y = -60

Step 3: Redefine Systems

-5x + 10y = -60

5x + 3y = -44

Step 4: Solve for y

Elimination

Combine 2 equations: 13y = -104
[Division Property of Equality] Divide 13 on both sides: y = -8

Step 5: Solve for x

Define original equation: x - 2y = 12
Substitute in y: x - 2(-8) = 12
Multiply: x + 16 = 12
[Subtraction Property of Equality] Subtract 16 on both sides: x = -4

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2 years ago

An inheritance of $40,000 is divided among three investments yielding $3,500 in interest per year. The interest rates for the th

a_sh-v [17]

Answer:

x = $ 16,000 , y = $13,000 z= $11,000

Step-by-step explanation:

given,

Investment amount $40,000

three investments yielding = $3,500

three investments are 7%, 9%, and 11%

second and third are $3,000 and $5,000 less than the first

0.07 x + 0.09 y + 0.11 z = $ 3,500

x + (x - 3000 ) + (x - 5000) = $ 40,000

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x = $ 16,000

y = 16000 - 3000 = $ 13,000

z = 16000 - 5000 = $ 11,000

the investment by each

x = $ 16,000 , y = $13,000 z= $11,000

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3 years ago