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3 years ago

Solve the system by using elimination 3x+3y=-9 3x-3y=21

Mathematics

2 answers:

LekaFEV [45]3 years ago

6 0

Answer:

$\large\boxed{x=2,\ y=-5\to(2,\ -5)}$

Step-by-step explanation:

$\underline{+\left\{\begin{array}{ccc}3x+3y=-9\\3x-3y=21\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad6x=12\qquad\text{divide both sides by 6}\\.\qquad\qquad\boxed{x=2}\\\\\text{Put the value of x to the first equation}\\\\3(2)+3y=-9\\6+3y=-9\qquad\text{subtract 6 from both sides}\\3y=-15\qquad\text{divide both sides by 3}\\\boxed{y=-5}$

e-lub [12.9K]3 years ago

3 0

Answer:

y=-5

x=2

Step-by-step explanation:

3x + 3y=-9

3x - 3y=21

0+6y=-30

6y=-30

y=-5

3x-15=-9

x=2

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the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to retu

Snowcat [4.5K]

It takes 4.3 seconds for the rocket to return to earth.

The equation is:
$0=-9.8t^2+v_0t+h_0$
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:

$0=-9.8t^2+42t$

We will use the quadratic formula to solve this. The quadratic formula is:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Plugging in our information we have:
$t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)}
\\
\\=\frac{-42\pm \sqrt{1764-0}}{-19.6}
\\
\\=\frac{-42\pm \sqrt{1764}}{-19.6}
\\
\\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6}
\\
\\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6}
\\
\\=4.3\text{ or }0$

x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

8 0

3 years ago

NOT GRADED. <br>FIND THE MEASURE OF THE INDICATED ANGLE IN EACH TRIANGLE.

Setler [38]

Answer:

The angle in the box is always 50 and that other acute angle is 46

Hope this helps

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Solve for m <br>-2(m +5) +14 =-6

Westkost [7]

Answer:

m=5

Step-by-step explanation:

-2m-10+14=-6

-2m+4=-6

-2m=-10

m=5

6 0

3 years ago

Help! If you know this can you tell me how to do it?

aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:

$[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?$

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

$\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?$

Put everything over the common denominator now:

$\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?$

Since $sin^2(x)+cos^2(x)=1$ , we will make that substitution:

$\frac{1}{sin(x)cos(x)}$

We could separate that fraction into 2:

$\frac{1}{sin(x)}$ × $\frac{1}{cos(x)}$

$\frac{1}{sin(x)}=csc(x)$ and $\frac{1}{cos(x)}=sec(x)$

Therefore, the simplification is

sec(x)csc(x)

5 0

3 years ago

a sphere has a diameter of 7 centimeters what is the surface area is 3.14 to approximate Pi round to the nearest hundredth if ne

Over [174]

Good idea to look up the formula for "surface area of a sphere" and to write it down for later reference. It is A=4 pi r^2, where r is the radius of the sphere.
If the given sphere has a diameter of 7 cm, what is the radius of this sphere?

Write your answer inside the parentheses, below:

Sphere surface area = 4 pi (r)^2, or (in this case), A = 4(3.14)( )^2

8 0

3 years ago