All categories

3 years ago

Solve for x for 1 and 2

Mathematics

1 answer:

taurus [48]3 years ago

3 0

Answer:

1. 37.5

2. 8

Step-by-step explanation:

1. the smaller triangle and the bigger triangle are similar, so the sides are also similar.

this means that 16/46 = 20/(x+20)

then, just solve that for x

16/46 = 20/(x+20)

divide both sides by 4

4/46 = 5/(x+20)

multiply both sides by (x + 20)

(x+20) * 4/46 = 5

multiply both sides by 46

4x + 80 = 230

subtract 80

4x = 150

divide 4

x = 37.5

2. do the same thing ( still similar triangles)

the equation would be (3x + 1)/10 = (7x - 1)/22

solve

22(3x + 1) = 10(7x - 1)

66x + 22 = 70x - 10

32 = 4x

x = 8

You might be interested in

There are infinitely many solutions to the following equation:

mihalych1998 [28]

Answer:

True

Step-by-step explanation:

Well let's solve and see!

6x + 8 = 6x + 8

subtract both sides by 8

6x = 6x

subtract both sides by 6x

0 = 0

Now notice, that no matter our x value is, we would still get the same, correct, answer. So there <em>are</em> infinitely many solutions

3 0

4 years ago

Find the distance between (-1,4) and (1,-1)

Alex Ar [27]

Answer:

$d=\sqrt{29}$

Step-by-step explanation:

The trick here is knowing the distance formula:

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

using that equation with (-1,4) and (1,-1), we get:

$d=\sqrt{(1-(-1))^2+((-1)-4)^2}\\d=\sqrt{(1+1)^2+(-1-4)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\$

5 0

4 years ago

Are the graphs of the equations parallel, perpendicular, or neither?x -3y = 6 and x - 3y = 9

seraphim [82]

The equation of a line in Slope-Intercept form, is:

$y=mx+b$

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

By definition:

- The slopes of parallel lines are equal and the y-intercepts are different.

- The slopes of perpendicular lines are opposite reciprocals.

For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".

- Line #1:

$\begin{gathered} x-3y=6 \\ -3y=-x+6 \\ y=\frac{-x}{-3}+(\frac{6}{-3}) \\ \\ y=\frac{x}{3}-2 \end{gathered}$

You can identify that:

$\begin{gathered} m_1=\frac{1}{3} \\ \\ b_1=-2 \end{gathered}$

- Line #2:

$\begin{gathered} x-3y=9 \\ -3y=-x+9 \\ y=\frac{-x}{-3}+(\frac{9}{-3}) \\ \\ y=\frac{x}{3}-3 \end{gathered}$

You can identify that:

$\begin{gathered} m_2=\frac{1}{3} \\ \\ b_2=-3_{}_{} \end{gathered}$

Therefore, since:

$\begin{gathered} m_1=m_2 \\ b_1\ne b_2 \end{gathered}$

You can conclude that: The graphs of the equation are parallel.

3 0

2 years ago

PLEASE SOMEONE!!HELP!! I need the answer right now

GalinKa [24]

Answer:

m = -1, b = 5.

Step-by-step explanation:

We can find the slope, <em>m</em>, by plugging in our coordinates into the slope formula: $\frac{y2-y1}{x2-x1} =\frac{2-7}{3-(-2)}=\frac{-5}{5}=-\frac{5}{5}=-\frac{1}{1}=-1$ . That gives us the slope. Now we can fill that in the slope intercept formula: $y=-1x+b$ . We know one of the coordinates and the slope, which allows to find the y-intercept. We know that for every 1 unit down on the line, we move 1 unit right, and vice versa. Meaning we can just count down (or up in this case), so, (-2, 7), (-1, 6), (0, 5). Therefore, our y intercept is 5.