If h is instead negative, the curve shifts

19) Albert says that the two systems of equations shown have the same solutions.

k0ka [10]

Answer:

option A) Agree, because the solutions are the same is correct.

Step-by-step explanation:

FIRST SYSTEM

$6x + y= 2$

$-x-y=-3$

solving the system

$\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18$

$\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}$

adding the equation

$-6x-6y=-18$

$+$

$\underline{6x+y=2}$

$-5y=-16$

so the system becomes

$\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

simplify

$y=\frac{16}{5}$

$\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$6x+\frac{16}{5}=2$

subtract 16/5 from both sides

$6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}$

$6x=-\frac{6}{5}$

Divide both sides by 6

$\frac{6x}{6}=\frac{-\frac{6}{5}}{6}$

$x=-\frac{1}{5}$

Therefore, the solution to the FIRST SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

SECOND SYSTEM

$2x-3y = -10$

$-x-y=-3$

solving the system

$\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6$

$\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}$

$-2x-2y=-6$

$+$

$\underline{2x-3y=-10}$

$-5y=-16$

so the system of equations becomes

$\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

Simplify

$y=\frac{16}{5}$

$\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$2x-3\cdot \frac{16}{5}=-10$

$2x=-\frac{2}{5}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\frac{2}{5}}{2}$

Simplify

$x=-\frac{1}{5}$

Therefore, the solution to the SECOND SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

Conclusion:

As both systems of equations have the same solution.

Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.

Hence, option A) Agree, because the solutions are the same is correct.

8 0

3 years ago

I would be so greatful if someone can help me with this

ioda

Same i need to do this

7 0

3 years ago

prism M and pyramid n have the same base area and the same height. cylinder p and prism Q have the same height and the same base

Katen [24]

Answer:

The volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume.

Step-by-step explanation:

The volume of a cylinder having base area 'A' and height 'H' is given by V = AH, and the volume of a cone having the same base area as the cylinder i.e. A and height 3 times the height of the cylinder i.e. 3H is given by $V' = \frac{1}{3} A(3H) = AH$ .

So, V = V'

Hence, the volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume. (Answer)

6 0

3 years ago

a tiny but horrible alien is standing at the top of the empire state building (which is 443443443 meters tall) and threatening t

Aleonysh [2.5K]

The angle for shooting laser gun should be 89.98°.

The vertical height where a tiny but horrible alien is standing is given as 443443443 meters. The horizontal distance of a men in black agent from building is given in the question as 181818 meters. So, let us assume the angle formed to be theta (θ).

Writing the formula for tan theta, that relates the given height and distance

Now, tan θ = vertical height ÷ horizontal distance

Keep the values in above mentioned equation of theta to find the angle.

tan θ = $\frac{443443443}{181818}$

Performing division to find the tan theta and subsequently calculate the angle

tan θ = 2438.94

θ = tan⁻¹ 2438.94

Calculating tan inverse to find the value of theta

θ = 89.98°

Therefore, the angle for shooting laser gun by a men in black agent should be 89.98°.

Learn more about calculation of angle -

brainly.com/question/21865829

#SPJ4

7 0

1 year ago

Solve this question and how to do it

satela [25.4K]

Answer:

Step-by-step explanation:

7/15 + 3/5

I'd multiply 3/5 by 3 so that both of the denominators (bottom number) are the same.

Now all we have to do is add the Numerators tog

7/15 + 9/15ether (the top number)

7/15 +9/15 = 16/15 or 1 1/15

6 0

3 years ago

Read 2 more answers