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3 years ago

Bryce has 135 feet of rope. He wants to cut it into pieces that are each 9 feet long. How many pieces of rope will Bryce have?

Mathematics

2 answers:

GarryVolchara [31]3 years ago

8 0

He will have 15 pieces of rope. hope this help c:

jeka57 [31]3 years ago

8 0

He will have 15 pieces of rope because if you divide 135 by 19 you get 15! Hope this helped! tell me if u need help on anything else

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Q3: Identify the graph of the equation and write and equation of the translated or rotated graph in general form. (Picture Provi

natta225 [31]

Answer:

b. circle; $2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0$

Step-by-step explanation:

The given conic has equation;

$x^2-5x+y^2=3$

We complete the square to obtain;

$(x-\frac{5}{2})^2+(y-0)^2=\frac{37}{4}$

This is a circle with center;

$(\frac{5}{2},0)$

This implies that;

$x=\frac{5}{2},y=0$

When the circle is rotated through an angle of $\theta=\frac{\pi}{3}$ ,

The new center is obtained using;

$x'=x\cos(\theta)+y\sin(\theta)$ and $y'=-x\sin(\theta)+y\cos(\theta)$

We plug in the given angle with x and y values to get;

$x'=(\frac{5}{2})\cos(\frac{\pi}{3})+(0)\sin(\frac{\pi}{3})$ and $y'=--(\frac{5}{2})\sin(\frac{\pi}{3})+(0)\cos(\frac{\pi}{3})$

This gives us;

$x'=\frac{5}{4} ,y'=\frac{5\sqrt{3} }{4}$

The equation of the rotated circle is;

$(x'-\frac{5}{4})^2+(y'-\frac{5\sqrt{3} }{4})^2=\frac{37}{4}$

Expand;

$(x')^2+(y')^2-\frac{5\sqrt{3} }{2}y'-\frac{5}{2}x'+\frac{25}{4} =\frac{37}{4}$

Multiply through by 4; to get

$4(x')^2+4(y')^2-10\sqrt{3}y'-10x'+25 =37$

Write in general form;

$4(x')^2+4(y')^2-10x'-10\sqrt{3}y'-12 =0$

Divide through by 2.

$2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0$

8 0

3 years ago

Find the remaining factors of x^3+6x^2-4x+3 given (x+2)

satela [25.4K]

Answer:

y=(x+6)(x−2)(x+2)

Step-by-step explanation:

4 0

1 year ago

Elena has some bottles of water that each hold 17 fluid ounces.

Svet_ta [14]

Answer:

17b = w

Step-by-step explanation:

17 times the number of bottles = the number of ounces of water

Then you just plug in the numbers you are given

17(51) = w

17 x 51 = 867

51 bottles of water holds 867 ounces

17b = (51)

divide both sides by 17

51/17 = 3

b = 3

It would take 3 bottles of water to hold 51 ounces

6 0

2 years ago

Compound inequalities 3>11+k/4>-3

Marat540 [252]

Answer:

−56<k<−32

Step-by-step explanation:

this is the right one

5 0

2 years ago

Let f(x) = x + 3 and g(x) = 1/x The graph of (gºf)(x) is shown below what is the range of ( gof) (x) .

charle [14.2K]

Answer:

The range of the function $(g\°f)(x)$ is

B. is all real numbers except $y=0$

Step-by-step explanation:

Given functions:

$f(x)=x+3$

$g(x)=\frac{1}{x}$

To find the range of $(g\°f)(x)$ .

Solution:

In order to find $(g\°f)(x)$ , we will plugin $f(x)$ in function $g(x)$ .

$(g\°f)(x)=g(f(x))$

$(g\°f)(x)=\frac{1}{x+3}$

The graph of the function $(g\°f)(x)$ shows that

1) As $x$ approaches -3 (but never touches the line $x=-3$ ), $y$ tends to positive or negative infinity.

2) As $y$ approaches 0 (but never touches the line $y=0$ ) , $x$ tends to positive or negative infinity.

Thus, the range of the function is all real numbers except $y=0$

4 0

3 years ago