Adding and subtracting polynomials

The sum of three consecutive integers is 114. what are the three integers?

RSB [31]

Answer: 37, 38, and 39

Step-by-step explanation: This problem states that the sum of 3 consecutive integers is 114 and it asks us to find the integers.

3 consecutive integers can be represented as followed.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since the sum of our 3 consecutive integers is 114, we can set up an equation to represent this.

X + X + 1 + X + 2 = 114

We can simplify on the left side by combining the X's and the numbers.

3x + 3 = 114

-3 -3 ← subtract 3 from both sides of the equation

3x = 111

÷3 ÷3 ← divide both sides of the equation by 3

X = 37

X ⇒ first integer = 37

X + 1 ⇒ second integer = 38

X + 2 ⇒ third integer = 39

Therefore, our 3 consecutive integers are 37, 38, and 39.

5 0

3 years ago

Read 2 more answers

A piece of wire 28 ft long is cut into two pieces. One piece is used to form a square, and the remaining piece is used to form a

marusya05 [52]

Answer:

Wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

Step-by-step explanation:

Length of the wire = 28 ft has been cut in two pieces.

One piece is used to form a square and remaining piece to form a circle.

Let the length of the wire which forms the square is 'l' ft.

Area of the square = (side)²

Perimeter of the square = 4(side) = l

Length of one side = $\frac{l}{4}$

So, the area of the square = $\frac{l^{2}}{16}$ ft²

Now length of the remaining part = perimeter of the circle = (28 - l) ft

2πr = (28 - l)

r = $\frac{28-l}{2\pi }$

Area of the circle formed = πr²

= $\frac{\pi(28-l)^{2} }{4(\pi )^{2} }$

= $\frac{(28-l)^{2}}{4\pi }$

Combined area of the square and circle

= $\frac{l^{2}}{16}$ + $\frac{(28-l)^{2}}{4\pi }$

Now to maximize the area we will find the derivative of the area with respect to l.

$\frac{dA}{dl}=\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28-l)^{2}}{4\pi}]$

= $\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28)^{2}+l^{2}-56l }{4\pi }]$

= $\frac{2l}{16}+\frac{(2l-56)}{4\pi }$

Now equate the derivative to zero.

$\frac{2l}{16}+\frac{(2l-56)}{4\pi }$ = 0

$(2l-56)=-\frac{2l}{16}\times 4\pi$

$(2l-56)=-\frac{\pi l}{2}$

$2l+\frac{\pi l}{2}=56$

$\frac{(4l+l\pi )}{2}=56$

l(4 + π) = 112

l(4 + 3.14) = 112

l = $\frac{112}{7.14}$

l = 15.69 ft

Length of the other part = 28 - 15.69 = 12.31 ft

Therefore, wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

8 0

3 years ago

Please help!! I have no idea how to this

Blababa [14]

D.)

-75x +57 = -75x + 57

3 0

3 years ago

Read 2 more answers

Katie uses a copy machine to enlarge her rectangular design that is 6in. wide and 8in. long. The new width is 10in.What is the n

nadya68 [22]

If it added 4in. to the width and the width was 6in. now 10in. then you should add 4in. to the length the answer must be 14in

4 0

3 years ago

2. A contractor is building a set of stairs out of concrete. Each stair is exactly the same length, width, and height.

adoni [48]

Answer:

we may do perfect concreate do this stairs

5 0

3 years ago