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3 years ago

(08.03)A set of equations is given below:

Mathematics

2 answers:

Andreyy893 years ago

8 0

Hello : the system is :
y = 6x + 9
y = 6x + 2
6x+9=6x+2
9=2 false
conclusion ; no solution

alexandr1967 [171]3 years ago

7 0

These are parallel lines.
You can tell because the slope is the same but the y-intercept is different, meaning that the lines will never intercept.
When you have parallel lines, there are no solutions.
This is because solutions are where lines intercept.
No interception = No solution.

So the answer is B. No solution.

Hope this helps!

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Find the area bounded by the given curves: y=2x−x2,y=2x−4

Andrej [43]

Answer:

$A = [\frac{32}{3}]$

Step-by-step explanation:

Given

$y_1 = 2x - x^2$

$y_2 = 2x - 4$

Required

Determine the area bounded by the curves

First, we need to determine their points of intersection

$2x - x^2 = 2x - 4$

Subtract 2x from both sides

$-x^2 = -4$

Multiply through by -1

$x^2 = 4$

Take square root of both sides

$x = 2$ or $x = -2$

This Area is then calculated as thus

$A = \int\limits^a_b {[y_1 - y_2]} \, dx$

Where a = 2 and b = -2

Substitute values for $y_1$ and $y_2$

$A = \int\limits^a_b {(2x - x^2) - (2x - 4)} \, dx$

Open Brackets

$A = \int\limits^a_b {2x - x^2 - 2x + 4} \, dx$

Collect Like Terms

$A = \int\limits^a_b {2x - 2x- x^2 + 4} \, dx$

$A = \int\limits^a_b {- x^2 + 4} \, dx$

Integrate

$A = [-\frac{x^{3}}{3} +4x](2,-2)$

$A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)]$

$A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}]$

$A = [\frac{16}{3}] - [\frac{-16}{3}]$

$A = [\frac{16}{3}] + [\frac{16}{3}]$

$A = [\frac{16 + 16}{3}]$

$A = [\frac{32}{3}]$

Hence, the Area is:

$A = [\frac{32}{3}]$

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4 years ago

A triangle has angles that measure 49° and 84°.

BaLLatris [955]

A plat angle measure 180° it means that A+B+C=180 Then if A=49° and B=84. ,A+B=133 Then if we make 180-133 we we would have 47

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3 years ago

Given the lines a and b are parallel and that m 2= 68, find m 5.

skelet666 [1.2K]

M<2 and M<6 are corresponding angles, that means they have the same degree. M<6 and M<5 are supplementary angles, that means they have together a sum of 180. So all you need to do is 180 - 68 = 112. D is the answer.

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Alexxx [7]

Answer:

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Step-by-step explanation:

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in this problem,

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3 years ago

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