Find y.............

Mathematics

2 answers:

sattari [20]3 years ago

7 0

Answer:

We know angle y = 78 degrees

Step-by-step explanation:

y and 78 are alternate exterior angles. Alternate exterior angles are equal if the lines are parallel. AB is parallel to CD so y = 78

Natasha_Volkova [10]3 years ago

3 0

<h3>Answer: y = 78</h3>

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Justification #1: Angle x is 78 degrees as these two angles are corresponding angles (congruent due to the parallel lines). We also know that y = x because they are vertical angles. So by the transitive property, y = 78

Justification #2: The parallel lines mean that the alternate exterior angles are congruent, so y = 78 through one step (instead of multiple steps in the prior justification)

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Read 2 more answers

4x + 5y = 10

Vika [28.1K]

Answer:

For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.

Step-by-step explanation:

Given equations are:

4x + 5y = 10

Ax + By = 16

The general form of linear equation in two variables is given by:

$ax+by = c$

Here a, b and c are constants and x,y are variables.

In the given equations, after comparing with the general form

$a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16$

"In order for a system of equations to have infinity many solutions,

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ "

Putting the values we get

$\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8$