Answer and show work #38

Solve the system of equations using the Substitution Method (show work)

FromTheMoon [43]

Since both equations have 3y, we will substitute 3y.
2x-3y = 20 eq 1
rearrange
2x - 20 = 3y
sub the value of 3y into eq2
11x + (2x-20) = -1
11x + 2x - 20 = -1
13x = 19
x =19/13

sub value of x into any equation
2(19/13) - 3y =20
38/13 - 20 = 3y
-222/13 = 3y
y = -74/13

3 0

3 years ago

Two composite numbers with one factor tree

Nonamiya [84]

I can't make a tree very easily but I will still answer you question

a composite number, if you did not already know, is a number that can be divided by a diffarent whole number and still get a whole number (exg. 4/2=2=composite 5/2=a decimal=prime)

so one composit number is 16
the factored out tree is 2*8
         2*4
   2*2

another is 24
the factor tree is 2*12
      2*6
   2*3
hope you can see the tree as I typed it out

6 0

3 years ago

Read 2 more answers

Please help with this Question, I've been having trouble with. As soon as possible, thanks

vazorg [7]

I believe it is 12
tell me if i was wrong

6 0

3 years ago

The equation of three lines are given below

kotykmax [81]

Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = $\frac{2}{5}$ x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y = $\frac{5}{2}$ x + $\frac{6}{2}$

I.e y = $\frac{5}{2}$ x + 3

So, slope of this line = $m_1$ = $\frac{5}{2}$

Again , From Line 2

y = $\frac{2}{5}$ x - 1

So, slope of this line = $m_2$ = $\frac{2}{5}$

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - $\frac{6}{4}$ - $\frac{10}{4}$ x

I.e y = - $\frac{5}{2}$ x - $\frac{6}{4}$

So, Slope of this line = $m_3$ = - $\frac{5}{2}$

Now, If the lines are parallel , then the slope of the lines are equal

And If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

$m_2$ × $m_3$ = $\frac{2}{5}$ × ( - $\frac{5}{2}$ )

I.e $m_2$ × $m_3$ = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2 , Line 1 and Line 3 Answer

6 0

3 years ago

A laser travels from glass to water at an angle of 35° with the normal, Θ1. If water has an index of refraction of 1.33 and glas

umka2103 [35]

When light moves from one medium to another, it is refracted. If it moves from a medium with refractive index n1 to one with refractive index n2, with an incidence angle to the surface normal of θ1, the refraction angle θ2 can be calculated from Snell's law.

The Snell's law states that the ratio of the sines of the angles of incidence and refraction of a wave (in this case beam/light) are constant when it passes between two given media.

$n_1\sin\theta_1=n_2\sin\theta_2$

Given that a laser travels from glass to water at an angle of 35° with the normal, $\theta_1$ . If water has an index of refraction of 1.33 and glass has an index of refraction of 1.52, then we have:

 $1.52\sin35^o=1.33\sin\theta_2 \\ \\ \Rightarrow\sin\theta_2= \frac{1.52\sin35^o}{1.33} =0.6555\therefore\theta_2=\sin^{-1}0.6555\approx41^o$

7 0

3 years ago