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4 years ago

What is the solution to the system of equations represented by the two equations?

1 answer:

4 0

To solve a system of equations, you must first set the equations to equal "y" (which has already been done in this problem), and then set them to equal each other. This can be done because both of your equations equal"y", so they both equal each other.
-2x + 7 = 1/3x
7 = 1/3x + 2x
2 1/3x = 7
x = ~3
The answer is a long decimal with the first four places 0, so I rounded...
Hope that helps:)

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Edward owes his parents $20 for a new video

Galina-37 [17]

Answer:

it would take Edward 8 to pay back his debt

Step-by-step explanation:

every 2 days he pays his parents 5 bucks so because 5 times 4 equals 20 he would have to multiply the 4 by 2 and that gets you 8 days

3 0

3 years ago

6 dogs are black, 5 dogs are white, and the rest are blue. If there are 15 dogs in total, how many are blue?

Bezzdna [24]

Answer:

4 blue dogs

Step-by-step explanation:

Since there are 6 black dogs and 5 white dogs, there is 11 black and white dogs. There is 15 dogs in total, so you subtract 11 from 15, and that is 4. So, 4 dogs are blue.

6 0

4 years ago

At his lemonade stand, Ishmael has enough lemonade mix to make 3 gallons 2 quarts 1 pint of lemonade. How many 1-cup serving of

Kaylis [27]

For gallons 16 times 3 is 48

2 quarts is 4 pints which is eight more cups and one more pint is 2 more cups

8+2+48

This gives you 58 servings

8 0

3 years ago

Read 2 more answers

At Ezra's restaurant and bakery, each cake is cut into 9 pieces. Let c represent the number of cakes and p represent the total p

zmey [24]

Answer:

C * 9 = P

9C = P

Step-by-step explanation:

Each cake is 9 pieces

Cakes times 9 equals pieces

c * 9 = P

3 0

3 years ago

On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago