Which is a factor of 4x2 + 36x + 72?

I need help 6x-2y=10 x-2y=-5 solve by elimination

dem82 [27]

<h3><u>Explanation</u></h3>

Given the system of equations.

$\begin{cases} 6x - 2y = 10 \\ x - 2y = - 5 \end{cases}$

Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.

To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.

$\begin{cases} 6x - 2y = 10 \\ - x + 2y = 5 \end{cases}$

There as we can get rid of the y-term by adding both equations.

$(6x - x) + ( - 2y + 2y) = 10 + 5 \\ 5x + 0 = 15 \\ 5x = 15 \\ x = \frac{15}{5} \longrightarrow \frac{ \cancel{15}}{ \cancel{5}} = \frac{3}{1} \\ x = 3$

Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.

$x - 2y = - 5 \\ 3 - 2y = - 5 \\ 3 + 5 = 2y \\ 8 = 2y \\ \frac{8}{2} = y \\ y = \frac{8}{2} \longrightarrow \frac{ \cancel{8}}{ \cancel{2}} = \frac{4}{1} \\ y = 4$

Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.

Answer Check by substituting both x and y values in both equations.

<u>First</u><u> </u><u>Equation</u>

$6x - 2y = 10 \\ 6(3) - 2(4) = 10 \\ 18 - 8 = 10 \\ 10 = 10 \longrightarrow \sf{true} \: \green{ \checkmark}$

<u>Second</u><u> </u><u>Equation</u>

$x - 2y = - 5 \\ 3 - 2(4) = - 5 \\ 3 - 8 = - 5 \\ - 5 = - 5 \longrightarrow \sf{true} \: \green{ \checkmark}$

Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)

<h3><u>Answer</u></h3>

$\begin{cases} x = 3 \\ y = 4 \end{cases} \\ \sf \underline{Coordinate \: \: Form} \\ (3,4)$

8 0

3 years ago

If the lines x+y=5 and 2x +2y+6=0 are parallel, find the distance between them

kobusy [5.1K]

Pretty sure the distance is 8 units

5 0

3 years ago

1 times 10 to the 21st power

balandron [24]

Answer:

I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.

7 0

3 years ago

A triangle has angle measures 23° and 35°. What is the measure of the third angle ?

frozen [14]

23 + 35 + A=180
58 + a =180
-58 -58
-------------------
A = 122 degrees

7 0

3 years ago

Read 2 more answers

Two cruise ships leave the same port with a 35° angle between their path. Cruise A is traveling at 18 miles per hour and Cruise

GuDViN [60]

Answer:

$20\:\mathrm{miles}$

Step-by-step explanation:

After travelling two hours, the two cruise ships form a triangle. One of the legs of this triangle will be the distance Cruise A travelled, and another will be the distance Cruise B travelled. We can find the distance they travel using:

$s=\frac{d}{t}, d=s\cdot t$

Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:

$d=s\cdot t=18\cdot 2=36\:\mathrm{miles}$

Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:

$d=s\cdot t=15\cdot 2=30\:\mathrm{miles}$

Because we are given the angle between these legs, we can use the Law of Cosines to find the third leg. The Law of Cosines is given by:

$c^2=a^2+b^2-2ab\cos C$ , where $a$ , $b$ , and $c$ are interchangeable. Let $c$ represent the distance between the two cruises. We have:

$c^2=36^2+30^2-2\cdot36\cdot30\cdot \cos 35^{\circ},\\c^2=426.63,\\c\approx \fbox{$20\:\mathrm{miles}$}$ (one significant figure).

8 0

3 years ago

Read 2 more answers