Two angles in a triangle measure 102 degrees and 67 degrees. What is the measure of the third angle?

Mathematics

1 answer:

Nat2105 [25]3 years ago

3 0

Answer:

11 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees.

From 180 degrees we subtract the sum of 102 degrees and 67 degrees, obtaining 11 degrees (first answer choice)

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What is an equation of the line that passes through the points (0, 3) and (5, -3)?

shepuryov [24]

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -\frac{6}{5} x+3$

Step-by-step explanation:

1) First, use the slope formula $m =\frac{y_2-y_1}{x_2-x_1}$ to find the slope of the line. Substitute the x and y values of the given points into the formula and solve:

$m =\frac{(-3)-(3)}{(5)-(0)} \\m = \frac{-3-3}{5-0}\\m = \frac{-6}{5}$

So, the slope is $-\frac{6}{5}$ .

2) Now, use the slope-intercept formula $y = mx + b$ to write the equation of the line in slope-intercept form. All you need to do is substitute real values for the $m$ and $b$ in the formula.

Since $m$ represents the slope, substitute $-\frac{6}{5}$ for it. Since $b$ represents the y-intercept, substitute 3 for it. (Remember, the y-intercept is the point at which the line hits the y-axis. All points on the y-axis have an x-value of 0. Notice how the given point (0,3) has an x-value, too, so it must be the line's y-intercept.) This gives the following equation and answer:

$y = -\frac{6}{5} x+3$

3 0

3 years ago

Chris and Josh have a total of 1,800 stamps in their collections, Josh and Jessica have a total of 2,200 stamps, and Jessica and

LiRa [457]

Answer: 3000 stamps

Step-by-step explanation:

Given

Chris and Josh have 1800 stamps

Josh and Jessica have 2200 stamps

Jessica and Chris have 2000 stamps

Suppose Chris, Josh, and Jessica have $x,y, \text{and}\ z$ stamps

$\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000$