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3 years ago

What is the solution for the system of equations

Mathematics

2 answers:

OLEGan [10]3 years ago

3 0

First, it depends how you want to solve the system. The easiest way is to solve by elimination. Eliminate the 2 s. Therefore, 4x = 8. Divide by 4 to find x. After dividing by 4, x=2. To find the y plug in 2 for x in the original equation. Try for the first one. 2 +2y =3. Subtract 2 from both sides of the equation. Then you get 2y =1. Divide by 2 in both sides and you get y = 1/2.

Slav-nsk [51]3 years ago

3 0

I'd immediately add the two given equations together. This produces 4x = 8, so that x = 2. Subbing 2 for x in the first equation results in 2+2y=3, so 2y = 1, and y = 1/2.

Thus, the solution is (2, 1/2).

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If the circumference of a circle is divided by the length of its diameter. whats the result

Mnenie [13.5K]

Answer:

3.14 or π (It's the same thing)

Step-by-step explanation:

If you divide the circumference by its diameter, the constant ratio is called Pi

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3 years ago

Is (x-1) a factor of 2x3 - 15x2 + 22x + 15

Advocard [28]

Answer:

Step-by-step explanation:

If x - 1 is a factor of the cubic, then 1 should result in 0 when you put it in the cubic for x. Does it?

f(1) = 2(1)^3 - 15(1)^2 + 22(1) + 15

f(1) = 2 - 15 + 22 + 15

f(1)= 24.

No the result is not zero. So x - 1 is not a factor.

However there must be something that makes this cubic go to zero. The easiest way to find it is to graph it.

The numbers that do make this zero are -0.5, 3, 5

Which mean that the factors are (2x+1)(x-3)(x - 5)

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2 years ago

What’s the height of the can?

kondaur [170]

Answer:

5 inches

Step-by-step explanation:

The formula to find the surface area of a cylinder is A = 2πrh + 2πr²

Since we need the height we will need to solve for h

First we can subtract 2πr² from both sides to get A - 2πr² = 2πrh
Then we can divide both sides by 2πr to get $h=\frac{A-2\pi r^{2} }{2\pi r}$

Now we can plug in our known values and solve for h

Here we were given the diameter, d, however this formula is in terms of the radius, r.
The diameter is equivalent to double the radius, d = 2r
Therefore the radius is equivalent to half the diameter, $r=\frac{1}{2} d$
Plugging in d to solve for r we get $r=\frac{1}{2}(2)$ which simplifies to r = 1

The two variables for this equation we have no obtained, A = 12π and r = 1, so we can plug them into our equation to solve for the height

$h=\frac{12\pi -2\pi (1)^{2} }{2\pi (1)}=h=\frac{12\pi -2\pi }{2\pi }=\frac{10\pi }{2\pi } =5$
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4 0

3 years ago

Learning Task 4. Solve the problem by applying the sum and product of roots

Delvig [45]

Answer:

<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>

Step-by-step explanation:

For a quadratic equation:

$x^2+bx+c=0$

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

$x^2-18x+80=0$

Factoring by finding two numbers that add up to 18 and have a product of 80:

$(x-10)(x-8)=0$

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x=10, x=8

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2 years ago

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aniked [119]

Answer:

Step-by-step explanation:

When cut in half each side is the same as the other

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2 years ago