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ANEK [815]
3 years ago
5

Find the solution to the system of equations.y=2x+3 and y=-3x+3

Mathematics
1 answer:
iragen [17]3 years ago
6 0

Answer:

x = 0 and y = 3

Step-by-step explanation:

Using elimination method, we can solve for x and y in the simultaneous equation

y = 2x + 3   .................................eqn 1

y = -3x + 3  .................................eqn 2

multiply equation 1 by 3 and equation 2 by 2, then we will have

(y = 2x + 3) × 3

(y = -3x + 3) × 2

3y = 6x + 9   ...............................eqn 3

2y = -6x + 6 ................................eqn 4

Add eqn 3 and 4 together and we will eliminate x and have

5y = 15

Divide both sides by 5, and we will have

y = 3

To solve for x, substitute 3 for y in eqn 1

y = 2x + 3

3 = 2x + 3

collect like terms

3 - 3 = 2x

0 = 2x

Therefore x = 0

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A projectile is launched from ground level with an initial velocity of v 0 feet per second. Neglecting air​ resistance, its heig
Over [174]

Answer:

After 3 seconds while going up and 6 seconds while coming down

Step-by-step explanation:

Since projectile is launched from ground level with an initial velocity of v 0 feet per second, initial height =0

Height is given by

h(t) = -16t^2+144t where v0 = initial velocity = 144

a) When h =288 ft.

288 = -16t^2+144t\\t^2-9t+18 =0\\t=6 or 3

At t= 3 or 6 seconds the projectile would be at height 288 ft.

So while going up after 3 seconds it wouldbe at a height of 288 ft and while coming after 6 seconds.

4 0
2 years ago
A rectangular prism has dimensions of 4 cm by 3 cm by 2 cm.
EastWind [94]

Answer:

HN

Step-by-step explanation:

6 0
3 years ago
The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\
600 = (x+5)(x+4)\\
600 =  x^{2} + 9x + 20


Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\
x^{2} + 9x - 580 = 0\\
(x + 29)(x - 20) = 0\\
x + 29 = 0, \:\: x - 20 = 0\\
x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
8 0
3 years ago
Read 2 more answers
In a triangle, one of the angle measures 70°
Tanya [424]

Answer:

the two angles are 55° each

Step-by-step explanation:

Let the two equal angles be y each

Therefore,

70° + y + y = 180°

Collect like terms

2y = 180 — 70

2y = 110

Divide both side by the coefficient of y i.e 2

y = 110/2

y = 55°

Therefore, the two angles are 55° each

4 0
3 years ago
Write the Taylor Series for f(x) = sin (x)center<br> 4x^4+3x^3+2x^2 x 8 centered at a 2
algol [13]

Answer:

attached images

Step-by-step explanation:

8 0
3 years ago
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