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lana [24]
3 years ago
12

What is 2x + 3y = 13 x = 2 + 3y

Mathematics
2 answers:
IgorC [24]3 years ago
4 0

Answer:

Step-by-step explanation:

Given that

2x+3y=13. Equation 1

x=2+3y. Equation 2

Using substitution method

Substitute x in equation 2 to equation 1

2x+3y=13

2(2+3y)+3y=13

4+6y+3y=13

4+9y=13

9y=13-4

9y=9

y=9/9

y=1.

To get x, substitute y=1 into equation 2

x=2+3y

x=2+3(1)

x=2+3

x=5

Then, x=5 and y=1 is the solution to the simultaneous equation

Zanzabum3 years ago
3 0

Answer:

y = 1

x = 5

Step-by-step explanation:

Substitute:

2(2 + 3y) + 3y = 13

Simplify:

4 + 6y + 3y = 13

Combine terms:

4 + 9y = 13

Subtract 4 from each side:

9y = 9

Divide by 9:

y = 1

Substitute:

x = 2 + 3(1)

Simplify:

x = 2 + 3

Combine terms:

x = 5

Check with original equation:

2(5) + 3(1) = 13

Simplify:

10 + 3 = 13

Combine terms:

13 = 13

It works!

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For what value of c does x^2−2x−c=4 have exactly one real solution?<br> PLEASE HELP!!!!!!!
Paul [167]

Answer:

-5

Step-by-step explanation:

Moving all terms of the quadratic to one side, we have

x^2-2x-(c+4)=0.

A quadratic has one real solution when the discriminant is equal to 0. In a quadratic ax^2+bx+d, the discriminant is \sqrt{b^2-4ad}.

(The discriminant is more commonly known as \sqrt{b^2-4ac}, but I changed the variable since we already have a c in the quadratic given.)

In the quadratic above, we have a=1, b=-2, and d=-(c+4). Plugging this into the formula for the discriminant, we have

\sqrt{(-2)^2-4(1)(-(c+4)).

Using the distributive property to expand and simplifying, the expression becomes

\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.

Setting the discriminant equal to 0 gives

2\sqrt{c+5}=0.

We can then solve the equation as usual: first, divide by 2 on both sides:

\sqrt{c+5}=0.

Squaring both sides gives

c+5=0,

and subtracting 5 from both sides, we have

\boxed{c=-5}.

3 0
3 years ago
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lesya692 [45]

Answer:

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6 0
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GarryVolchara [31]

Answer:

a) 29

b) 0

c) 7

d) 3/8

Step-by-step explanation:

Whenever you're facing a clock maths problem, the solution always have to be < to the number of hours in the given clock.  If it's > the number of hours of the given clock, you subtract the number of hours until you get a result <= the number of clock hours.

If the result is negative, you add the clock hours.

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b) 13 * 4 = 52,  then do 52 - 52 = 0, since answer has to be < 52.

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7 0
3 years ago
What compass heading represents 20° north of east?​
sleet_krkn [62]

Answer:

45°

Step-by-step explanation:

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scoray [572]
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