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MariettaO [177]
3 years ago
13

Systems of linear equations iready quiz

Mathematics
1 answer:
saw5 [17]3 years ago
7 0

Answer:

<h2>One solution.</h2>

Step-by-step explanation:

The given question is

<em>Does the following system have One Solution, No Solution, or Infinite Solutions.   </em>

<em />y = 4x + 8\\y = -5x + 3<em />

<em />

<em />

To solve this system, we just need to multiply the first equation by -1, and then sum those equations.

-y = -4x - 8\\y = -5x + 3

0=-9x-5\\5=-9x\\x=-\frac{5}{9}

Then, we use this value to find the other one

y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}

As you can observe, the system of equations have a unique solution.

Therefore, the answer is one solution.

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Circumference of the cylinder a cylinder of the base with the diameter of 6cm and height of 12cm
yuradex [85]

Answer:

To find the volume, we must find the area of the circle and multiply it by its height, think of a cylinder as an object made up of MANY circles. So, V=pir^2h... so diameter is 6cm so radius = 3cm...

therefore, Volume = (pi)(3^2)(12) = 108(pi)

where 12 = height 3 = radius

For the surface area, we need to find the area of the 2 circles(top and bottom ) so once again,

2(pi)(r^2) = 2(pi)(9)

for the area of the rectangle(if we unfold the cylindrical can) we get D(pi)(12) where D= Diameter

so the surface area is

SA = (2)(9)(pi) + 6(pi)(12)

SA = 18pi + 72pi = 90pi

7 0
2 years ago
Read 2 more answers
What does the fundamental theorem of algebra illustrate?
UNO [17]

Answer:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

Step-by-step explanation:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

We have to find the roots of this given equation.

If a quadratic equation is of the form ax^{2}+bx +c=0

Its roots are \frac{-b+\sqrt{b^{2}-4ac } }{2a} and \frac{-b-\sqrt{b^{2}-4ac } }{2a}

Here the given equation is 2x^{2}-4x-1 = 0

a = 2

b = -4

c = -1

If the roots are x_{1} and x_{2}, then

x_{1} = \frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}

                       = \frac{4 +\sqrt{24}}{4}

                       = \frac{2+\sqrt{6} }{2}

x_{2} = \frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}

                        = \frac{4 +\sqrt{8}}{4}

                        = \frac{2-\sqrt{6} }{2}

These are the two roots of the equation.

6 0
3 years ago
Help Please!!!!!!! Need Help!!!​
Citrus2011 [14]

Answer:

925

Step-by-step explanation:

In order to solve this summation formula, you need to first understand what it means. The summation symbol is tell you to add the terms in a sequence. Below the summation sign, there is a variable and number; the variable n is the index of summation and the number 1 is the lower limit of summation or the first value of the sequence. The number 25 above the summation sign is the upper limit (so there would be 25 terms, with the first being 1). The polynomial to the right of the summation symbol represents the explicit function for each term. For example, using this, the first term would be (3(1) - 2) and the second (3(2) - 2) and so on. This means the value of that equation is:

(3(1) - 2) + (3(2) - 2) + (3(3) - 2)... + (3(25) - 2)

One way to solve this is to write all 25 of the terms and add them, but since that's tedious, you can solve this by first doing the basic summation of 1 to 25 and then inputting that into the equation:

1 + 2 + 3... + 25 = (25 × 26)/2 (when the first number is one and the rate of change is 1, the sum of the terms in a sequence is (n*(n+1))/2)

= 325

Now, that you know what the sum of the sequence of terms 1 to 25 are, you can multiply this by the constant since if you break up the equation you would be multiplying 3 by 1 then 3 by 2 and so on until 25, or 3 × (1 + 2 + 3... + 25):

3 × 325 = 975

At this point, you just need to add (-2) × 25. You do this because since there are 25 terms, if you subtracted 2 each time, you would subtract 2 twenty-five times:

975 + ((-2) × 25)

= 975 - 50

= 925

3 0
2 years ago
Please help this is almost due soon!
PolarNik [594]

Answer:

6\pi

Step-by-step explanation:

The area of the circumference of a circle is:

C=2\pi r

We know that r is 8, so we can plug that into the formula.

However, there's a problem.  We only want 3pi/4 of the circumference, not the entire circle's circumference.  Therefore, we have to divide by part/whole.  In this case, the part is 3pi/4, and the whole is 2pi (the entire circle is 2pi radians).

C = (\frac{3\pi/4}{2\pi})*(2\pi *8)\\C = (\frac{3}{8})(16\pi)\\C = \frac{48\pi }{8} \\C = 6\pi

6 0
3 years ago
Find x and y this is geometry
Lyrx [107]
Y = 4
X = 12
I’m pretty sure^ I did this last unit btw
6 0
3 years ago
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