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Fittoniya [83]
2 years ago
9

Solve the following system of equations using a method of your choice.

Mathematics
1 answer:
dusya [7]2 years ago
8 0

Answer:

Step-by-step explanation:

cant remember what this method is called but

change the second equation to be y = something

x + y = 10

y = -x + 10

plug in this y= in the first equation to get x

4x -2(-x + 10) = 4

4x + 2x -20 = 4

6x = 24

x = 4

then plug in the x we found into the original second equation

4 + y = 10

y = 6

so your ordered pair would be (4,6)

hope this helps <3

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A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high
Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0
3 years ago
Jill converted the equation of the line 15 x minus 14 y = negative 2 into slope-intercept form and found the slope and y-interce
fgiga [73]

Answer:

hello! in short the answer is B! i took the test and didnt do very good but id thought id share this to help some people!

much love!~ chi chi

8 0
3 years ago
Read 2 more answers
Please answer quick!
tatuchka [14]
4 * (25 * 1.2) = (4 * 25) * 1.2
3 0
3 years ago
Read 2 more answers
Find the quotient and express it in the simplest form
pychu [463]
2i(4+5i)(4-5i) =82i
4+i nothing more can be done it is at simplest form 

so \frac{82i}{4+i} = \frac{82}{17} + \frac{328}{17} i

so your answer is  \frac{82}{17} + \frac{328}{17} i


5 0
3 years ago
Explain how you can use equivalent fractions to find the quotient of 2 3 ÷ 4.
Virty [35]

Answer:

see below

Step-by-step explanation:

2/3 ÷ 4

We use copy dot flip

The flip means make a reciprocal of the second number

2/3 * 1/4

Multiply the numerators

2*1 = 2

Multiply the denominators

3*4 =12

Put the numerator over the denominator

2/12

Simplify

1/6

8 0
3 years ago
Read 2 more answers
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