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blsea [12.9K]
3 years ago
11

A teenager pulls a rope to the left with a force of 12 N. A child pulls on the other end of the rope to the right with a force o

f 7 N. The child's firend adds a force of 8 N, also pulling to the right. What will happen?
A. The net force will be 3 N to the right
B. The net force will be 15 N to the left
C. The net force will be 12 N to the right
D. The net force will be 27 N to the left
Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0
The net force will be 3 N to the right.  

12N - 8N = 4N - 7N= -3N.  3N is the net force to the right.  
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The product of two consecutive even numbers is 224. What are these two numbers?
Stells [14]

Answer:

14 and 16

Step-by-step explanation:

They are the ONLY  consecutive even numbers

And also

x and (x+2)

x(x+2)=224 ( product of a number and the consecutive of that number)

x ²+  2x-224=0

(x+16)(x-14) =0

x=-16 or 14

In this case 14 and (14+2)    14 and 16

 

 

The  integers are either 14 and 16 or -14 and -16.

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3 years ago
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enot [183]

Answer:

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3 0
2 years ago
The range of y = - 32x ^ 2 + 90x + 3
mariarad [96]

Given:

The given function is:

y=-32x^2+90x+3

To find:

The range of the given function.

Solution:

We have,

y=-32x^2+90x+3

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is f(x)=ax^2+bx+c, then the vertex of the quadratic function is:

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-32,b=90,c=3.

\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}

\dfrac{-b}{2a}=\dfrac{-90}{-64}

\dfrac{-b}{2a}=\dfrac{45}{32}

The value of the given function at x=\dfrac{45}{32} is:

y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3

y=\dfrac{2121}{32}

The vertex of the given downward parabola is \left(\dfrac{45}{32},\dfrac{2121}{32}\right). It means the maximum value of the function is y=\dfrac{2121}{32}. So,

Range=\left\{y|y\leq \dfrac{2121}{32}\right\}

Range=\left(-\infty, \dfrac{2121}{32}\right ]

Therefore, the range of the given function is \left (-\infty, \dfrac{2121}{32}\right ].

8 0
3 years ago
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chubhunter [2.5K]

Answer:

(2, 0 )

Step-by-step explanation:

Given the 2 equations

5x - 2y = 10 → (1)

x + 4y = 2 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the y- term

10x - 4y = 20 → (3)

Add (2) and (3) term by term to eliminate y

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Substituting into (1)

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solution is (2, 0 )

4 0
3 years ago
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