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Nostrana [21]
3 years ago
13

Y=7x+3 7x-6y=-18 substitution

Mathematics
2 answers:
Lynna [10]3 years ago
6 0

Answer:

x=0

y=3

Step-by-step explanation:

y =7x+3       equation 1

7x-6y=-18   equation 2

using equation 1 in equation 2 we have:

7x-6(7x+3)= -18

7x -42x -18 = -18

-35x -18 = -18

-35x = -18 +18

-35x=0

x=0

so we have:

y =7x+3  

y= 7(0) +3

y = 3

Andre45 [30]3 years ago
3 0

Answer:

y=3

x=0

Step-by-step explanation:

we have the following system of equations:

y=7x+3\\7x-6y=-18

the substitution method requires that we take one of the variables of one equation, and substitute that value in the other equation.

in this case taking advantage of the fact that in the first equation the value of y is already cleared, we substitute it in the second equation:

7x-6(7x+3)=-18

and then we solve for x:

7x-42x-18=-18\\-35x-18=-18\\-35x=-18+18\\-35x=0\\x=0

and since x=0 substituting this into the first equation of the system to find the value of y:

y=7(0)+3\\y=3

the answer is y=3 and x=0

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Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = bla
Alika [10]

Answer:

Events D and C are mutually exclusive.

Step-by-step explanation:

Two events D and C are mutually exclusive if

Pr(D\cup C)=Pr(D)+Pr(C)

Find these probabilities. In a standard deck of 52 playing cards there are 13 diamond cards and 13 club cards.

The probabilty of chosing diamond is

Pr(D)=\dfrac{13}{52}=\dfrac{1}{4}

The probabilty of chosing club is

Pr(C)=\dfrac{13}{52}=\dfrac{1}{4}

The probabilty of chosing diamond or club is

Pr(D\cup C)=\dfrac{13+13}{52}=\dfrac{1}{2}

Since

\dfrac{1}{2}=\dfrac{1}{4}+\dfrac{1}{4},

events D and C are mutually exclusive.

6 0
3 years ago
Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa
sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0
3 years ago
Can anyone help please?
VMariaS [17]

Answer:

A. a = 60

B. x = 30

C. x = 70

D. a = 30

E. x = 190

Have a great evening!

3 0
2 years ago
How do I solve for x??
timurjin [86]

Answer:

x=40 degrees

Step-by-step explanation:

3x=120 (vertical angles)

solve: 3x=120

x=40

4 0
3 years ago
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kvasek [131]
56 would be your answer because it’s the lowest number
8 0
2 years ago
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