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3 years ago

Please help explanation needed 42 points

Mathematics

2 answers:

kodGreya [7K]3 years ago

6 0

Alternate interior angles means the angles across from another are equal. If you follow the line up 85 is directly across from 2x+1
then you can say
85 = 2x +1
85 -1 = 2x
84 = 2x
84/2 = x
42 = x

supplementary angles make a straight line so they must add to equal 180 degrees.
That means the other angle 3y+5 = 180-85
3y +5 = 95
3y = 95-5
3y = 90
y = 90/3
y = 30

sveta [45]3 years ago

5 0

Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure.

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Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

3 years ago

The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteri

Nady [450]

Do you notice anything strange about those points ?

(0, 1),
(1, 2),
(2, 4),
(3, 8).

The y-coordinate of each point is (2) raised to the power of the x-coordinate.

First point:   x=0, y=2⁰ = 1
Second point: x=1, y=2¹ = 2
Third point:    x=2, y=2² = 4
Fourth point: x=3, y=2³ = 8

The equation of the curve appears to be

   y = 2 ^ x .

So, after 10 hours, x=10, and y = 2¹⁰ = 1,024 .

3 0

3 years ago

Read 2 more answers

Does anyone know the answer to this!?

PolarNik [594]

Answer:

$|A_y|=\left|\begin{array}{cc}12&7\\ \\17&-51\end{array}\right|$

Step-by-step explanation:

You can use these Cramer's formulas to solve for x and y:

$x=\dfrac{|A_x|}{|A|},\\ \\y=\dfrac{|A_y|}{|A|},$

where

$|A|=\left|\begin{array}{cc}12&-13\\ \\17&-22\end{array}\right|\\ \\ \\|A_x|=\left|\begin{array}{cc}7&-13\\ \\-51&-22\end{array}\right|\\ \\ \\|A_y|=\left|\begin{array}{cc}12&7\\ \\17&-51\end{array}\right|$