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3 years ago

Find the values of a and b

Mathematics

2 answers:

nikdorinn [45]3 years ago

6 0

The values of a and b are as follows :
A=109
B=65

lisabon 2012 [21]3 years ago

5 0

Answer:

a = 115, b = 71

Step-by-step explanation:

The figure has one pair of parallel sides and is a trapezium.

Using a property of trapeziums

• each lower base angle is supplementary to the upper base angle on the same side.

a = 180 - 65 = 115

b = 180 - 109 = 71

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4 years ago

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How to find the percentage of a number

Dovator [93]

Answer:1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y

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4 years ago

For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinite

nignag [31]

Answer:

Equation 1 has exactly one solution.
Equation 2 has infinitely many solutions.
Equation 3 has no solution.

Step-by-step explanation:

We are given three equations to solve. First, let's solve the equations for x.

Equation 1

$\displaystyle{6x+8=7x+13}\\\\7x + 13 = 6x + 8\\\\x + 13 = 8\\\\\bold{x = -5}$

Therefore, we determined that for the first equation, x = -5. We can check our solution by substituting it back into the original equation.

$\displaystyle{6(-5)+8=7(-5)+13}\\\\-30 + 8 = -35 + 13\\\\-22 = -22 \ \checkmark$

Since we got a true statement, there are no other values of x for which we get a true statement. Let's test this with the opposite value: positive 5.

$6(5)+8=7(5)+13\\\\30 + 8 = 35 + 13\\\\38 = 48 \ \text{X}$

Therefore, for Equation 1, there is exactly one solution.

Equation 2

$6 x + 8 = 2 ( 3 x + 4 )\\\\6x + 8 = 6x + 8\\\\0 + 8 = 8\\\\8 = 8 \ \checkmark$

We get a true statement by solving for x (which ends up canceling out of the equation entirely). Therefore, we can check any value in place of x to see if we get a true statement. For this instance, I will use -3.

$6(-3) + 8 = 2 ( 3(-3) + 4 )\\\\-18 + 8 = 2(-9+4)\\\\-18 + 8 = 2(-5)\\\\-18 + 8 = -10\\\\-18 = -18 \ \checkmark$