A red light flashes every 6 seconds
A yellow light flashes every 4 seconds
They both flash at the same time.

After how many seconds will they next both flash at the same time?

Answer:

Last option

Step-by-step explanation:

First method :

Red Line:

Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).

[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]

[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]

                [tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex]                  [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]

Blue Line:

Take coordinates through which the line passes.

Let it be (-4, -12) and (-10, -9).

[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]

[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]

              [tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]

Second Method:

From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b

And check for set of equation whose slope are same.

First set :

[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]

Slopes are not equal.

Second set :

[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]

Slopes are not equal.

Third set :

[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]

Slopes are not equal.

Fourth set :

[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]

Slopes are same.

Answer:

y=-3/4x+3

Step-by-step explanation:

the slope is -3/4

in this case, y=mx+b

so y=-3/4x+b

b is the y intercept, so it would be 3

altogether, y=-3/4x+3

Answer:

154 degrees

Step-by-step explanation:

A quadrilateral has the sum of the interior angles that is 360 degrees

for the tangent theorem we know that the angles where the lines intercept the circumference have a value of 90 degrees

x + 90 + 90 + 26 = 360

x + 206 = 360

x = 360 - 206

x = 154 degrees

Answer:

Diameter, D = 2.65 cm

Step-by-step explanation:

Given the following data;

Circumference of circle = 8.34 cm

To find the length of its diameter;

Mathematically, circumference of a circle is equal to;

C = πD

Where;

Substituting into the formula, we have;

8.34 = 3.142 * D

[tex] D = \frac {8.34}{3.142} [/tex]

Diameter, D = 2.65 cm

Answer:

Step-by-step explanation:

since EG bisects angle DEF

31 = x + 15

31 - 15 = x

x = 16 degree

6x - 4 = 56

6x = 56 + 4

x = 60/6

x = 10

Answer:

8. 16

9. 10

abcdefghijklmnopqrstyvwxyz

Answer:

a. 15%

b. .73

c. 39/100, .39

d. .04, 4%

e. 77/100, 77%

f. 46/100, .46

g. .5, 50%

h. 6/100, 6%

i. 80/100, .8

j. .26, 26%

Step-by-step explanation:

Let's do the Fraction to Percent part first. Since all of the fractions have 100 in the denominator, this should be easy. The first one is 15/100 so this is just 15%, the next one is 73/100 and you can see that it is just 73%. It is the same way going from Percent to Fraction. On part f, we have 46%, so this will be 46/100.

For decimals, I recommend getting the percent first. I will use part f as my example again. You start with 46%. To make this a decimal, you just move the decimal point two spaces to the left. So, you end up with 0.46. To go from decimal to percent, you just move the point 2 spaces to the right.

Answer:

The answer is A

Step-by-step explanation:

This I because the area of a square is =

(length of on side)² = l²

The options there are not perfect squarss except A

which is 64 in²

And we know that 8² will give you 64

so then it means one side is 8 in

So the area =

8² = 8 in × 8 in = 64 in²

Answer:

x = 74.4

Step-by-step explanation:

tan = opp/adj

tan42 = 67 / x

x = 67/tan42

use calculator

x = 74.411038493555922

rounded

x = 74.4

Answer:

aaaaaaaaacvvrcgb

Answer:

b

Step-by-step explanation:

<ABC refers just to angle B. Angle B is on the opposite side of 98 therefore we would have to divide it by two. 98 divided by 2 is 49

Answer:

Step-by-step explanation:

Answer:

x =10

Step-by-step explanation:

3x + 10 = 6x -20

3x - 6x + 10 = -20

-3x + 10 = -20

-3x = -20 -10

-3x = -30

x = -30/-3

x = 10

Check:

3(10) + 10 = 6(10) - 20

30 + 10 = 60 - 20

40 = 40

Answer:

following k is l

before k is j

Sum j + k + l

Step-by-step explanation:

I think there may be something missing from your question.

Answer:

um, K=1?  I think you are missing stuff from your question cuz all you gave us was K. So, before K is 0 and after is 2

Step-by-step explanation:

If K were to equal one, It Would go 0, 1(K), 2

So The Sum Could Be Three ( 3 )

Answer:

b=77

c = 103

Step-by-step explanation:

b and 77 are vertical angles and vertical angles are equal

b= 77

c and 77 are supplemental angles and supplemental angles add to 180

c+77 =180

c = 180-77

c =103

[tex] \large \sf \star \: \blue{Answer} \: \star[/tex]

[tex] \small \sf \mapsto\: b = \fbox{77 °} [/tex]

[tex] \small \sf \mapsto \: c = \fbox{ 103 °}[/tex]

Here,

And,

So, b + c = 180 °

77° + c = 180 ° ... { b = 77 -( vertical angle )}

subtract 77 from each sides

77 - 77 + c = 180 ° - 77 °

c = 103 °

It's the third one I believe. y>1/2x

Answer: 30.26%

Step-by-step explanation:

Answer:

Answer:

circle and two lines that don't touch and are the same length are parrarell

Answer:

See Explanation

Step-by-step explanation:

Given two variables (say x and y); the constant of proportionality is the ratio between these to variables.

Illustration; y is directly proportional to x

The above statement can be represented as:

[tex]y\ \alpha\ x[/tex]

When converted to an equation, you get

[tex]y\ =k x[/tex]

k, in the above equation, represents the constant of proportionality

Divide both sides by x to solve for k

[tex]k = \frac{y}{x}[/tex]

Take for instance: [tex]y = 3x[/tex]

Divide both sides by x

[tex]\frac{y}{x} = 3[/tex] --- 3 is the constant of proportionality

Answer:

100,000

Step-by-step explanation:

I'm pretty sure. hope this helped <3 also I LOVE UR PFP ;)

Given:

Point P is Nine-elevenths of the distance from M to N.

To find:

The ratio in which point P partition the directed line segment from M to N.

Solution:

It is given that, point P is Nine-elevenths of the distance from M to N. So,

[tex]\dfrac{MP}{MN}=\dfrac{9}{11}[/tex]

It can be written as

[tex]\dfrac{MP}{MN}=\dfrac{9}{11}[/tex]

Let the lengths of MP and MN are 9x and 11x respectively. Then,

[tex]PN=MN-MP[/tex]

[tex]PN=11x-9x[/tex]

[tex]PN=2x[/tex]

Now,

[tex]\dfrac{MP}{PN}=\dfrac{9x}{2x}[/tex]

[tex]\dfrac{MP}{PN}=\dfrac{9}{2}[/tex]

[tex]\dfrac{MP}{PN}=9:2[/tex]

It means, point P divides the line segment MN in 9:2.

Therefore, the correct option is A.

Answer:

A . on E  D  G  E

Step-by-step explanation:

trust

Answer and Step-by-step explanation:

Scale factor of 4

x, y: (3, 10)

Translate 3 units right, up 10 units.

#teamtrese #PAW (Plant aNd Water)

Answer:

a=5 days, 3 hours

b= 3 people

Answer:

a right angle

b acute angle

c obtuse angle

d obtuse angle

e acute

f obtuse

Answer:

A. The prevalence of Type II diabetes

Step-by-step explanation:

A. The prevalence of Type II diabetes

B. The number of sugary drinks consumed by a child during a day

C. Both the prevalence of Type II diabetes and the number of sugary drinks consumed by a child during a day

D. There is no dependent variable

The prevalence of Type II diabetes depends on number of sugary drinks consumed by a child each day

If

x = The prevalence of Type II diabetes

y = number of sugary drinks consumed by a child each day

Then,

x depends on y

The dependent variable is The prevalence of Type II diabetes

Answer:

hiii my pic lol (✿^‿^)(✿^‿^)(✿^‿^)(✿^‿^)

Given:

The equation is:

[tex]2y=3x-6[/tex]

To find:

The x-intercept and y-intercept of the graph of the given equation.

Solution:

We have,

[tex]2y=3x-6[/tex]

Substitute [tex]y=0[/tex] to find the x-intercept.

[tex]2(0)=3x-6[/tex]

[tex]0+6=3x[/tex]

[tex]\dfrac{6}{3}=x[/tex]

[tex]2=x[/tex]

So, the x-intercept of the graph of the given equation is 2.

Substitute [tex]x=0[/tex] to find the y-intercept.

[tex]2y=3(0)-6[/tex]

[tex]2y=-6[/tex]

[tex]y=\dfrac{-6}{2}[/tex]

[tex]y=-3[/tex]

So, the y-intercept of the graph of the given equation is -3.

Therefore, the x-intercept is 2 and the y-intercept is -3.

Answer:

5

Step-by-step explanation:

=14 + 6^2 ÷ (-4)

=14 + 36 ÷ (-4)

divide 36 by -4

=14 + (-9)

=14 - 9

=5