A 260-inch pipe is cut into two pieces. One piece is four times the length of the other. Find the lengths of the two pieces.
The short piece is inches long.

Answer:

3²×5

Step-by-step explanation:

Product of its prime numbers its more like having the number in its simplest form by factorising it

Answer:

[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]

Step-by-step explanation:

Differentiate both sides of the equation (consider y as a function of x).

[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]

the derivative of a sum/difference is the sum/difference of derivatives.

[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]

[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]

the function of y^4(x) is the composition of f(g(x)) of the two functions.

the chain rule:

[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]

[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]

apply the power rule:

[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]

return to the old variable:

[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]

apply the power rule once again:

[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]

simplify:

[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]

[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]

[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]

[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]

differentiate the equation:

[tex]( \frac{d}{dx} (16)) = (0)[/tex]

[tex] = \frac{d}{dx} (16) = 0[/tex]

derivative:

[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]

[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]

Answer:

use the formula sn= n(a1+an)/2

Step-by-step explanation:

2982=28(228+an)/2

5964=28(228+an)

5964/28=228+an

213=228+an

an=-15(last term)

to find difference use formula

an = a+(n-1)d

-15=228+(28-1)d

-243=27d

d=-243/27

d=-9

arithmetic sequence  can be found be keep on subtracting 9 from 228

hence the arithmetic sequence is

228, 219, 210, 201, 192, 183, 174........-15

Step-by-step explanation:

find the area of the big semicircle and the small semicircle.minus the area of the small semicircle from the big semicircle.

now find the area of the other semicircle on top of the big semicircle.

add your results

area of semicircle=1/2(pir^2)

Answer:

3. Jaxson added the denominators instead of finding a common denominator and leaving it alone

Step-by-step explanation:

8 3/5 + 7 1/8 = 15 4/3

Get a common denominator

8 3/5 *8/8  + 7 1/8 *5/5

8 24/40 + 7 5/40

15 29/40

The number of students who passed is 234 and the number of students who failed is 39.

To find number of students who passed, and the number of students who failed.

The branch of mathematics dealing with the properties and manipulation of numbers.

Given that:

students enrolled in a freshman-level chemistry class=272

By the end of the semester, 7 times the number of students passed as failed.

Let x is number of students failed.

Then 6x is number of students passed.

So, 6x + x = 273

7x = 273,

∴x = 39

number of students passed= 273 - 39 = 234

So, the number of students who passed is 234 and the number of students who failed is 39.

Learn more about arithmetic here:

https://brainly.com/question/24433122

#SPJ2

Answer:

54

Step-by-step explanation:

6x5=30

3x8=24

30+24=54

Answer:

a = 9

Step-by-step explanation:

7a = 63

Divide 7 on both sides,

=> 7a/7 = 63/7

=> a = 9

Perimeter = the sum of all the sides. In this case, we know the ratio but not what each would be multiplied by, hence the variable.

6x + 8x + 10x = 96

24x = 96

x = 4

6(4) = 24

8(4) = 32

10(4) = 40

Check:

24 + 32 + 40 = 96 cm

Area = (base * height) / 2

Base = 32

Height = 24

(The base and height are interchangeable here, as we just have to make sure we're multiplying the legs of the triangle together and avoiding the hypotenuse.)

(32 * 24) / 2

768 / 2

384

Area = 384 cm^2

Hope this helps!

Answer:

False

Step-by-step explanation:

63 x 42= 2646

216 x 16= 3456

have a great day

Answer:

a^(1+2+3) so a^6

Step-by-step explanation:

Answer:

[tex]b) h) \\ - 5 - ( - 14) \\ = - 5 - - 14 \\ = - 5 + 14( - \times - = + )-5+14=14-5 \\ thank \: you[/tex]

Answer:

-5 + 14

14 - 5

Step-by-step explanation:

Answer:b. a deposit of $278 followed by a withdrawal of $278

Step-by-step explanation:

use a calculator

Answer:

if he work 3 hours and earn 40.50

then the money he earn per hour is 40.50/3=13.5 ans

Answer: -6

Step-by-step explanation:

-18 - (-12)

= -6

none of them

it's actually-6.

Answer:

False

Brainliest, please!

Step-by-step explanation:

+ + = +

- - = +

+ - = -

- + = -

Answer:

False

Step-by-step explanation:

The question doesn't specify whether you are adding positive or negative integers. If you have add 2 positive integers, your answer will be positive. If you add 2 negative integers, the answer will be negative. Here is an example;

1 + 1 = 2

-1 + (-1) = -1 - 1 = -2

Best of Luck!

Answer:

[tex]y=\frac{1}{3} x+6[/tex]

Step-by-step explanation:

[tex](3,7)(-6,4)[/tex]

Step 1. Find the slope (by using the slope-formula)

m = slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-7}{-6-3}[/tex]

[tex]m=\frac{-3}{-9}[/tex]

[tex]m=\frac{3}{9}[/tex]

[tex]m=\frac{1}{3}[/tex]

Step 2. Write the equation (using the slope and the points)

Here's how to do it:

Slope-intercept Formula [tex]y=mx+b[/tex] whrere m = slope and b = y-intercept

Plug in the slope into the Slope-intercept Formula

[tex]y=\frac{1}{3} x+b[/tex]

Find the y-intercept (b) by using a point and substituting their x and y values

[tex]y=\frac{1}{3} x+b[/tex]

Point: (3, 7)

[tex]7=\frac{1}{3} (3)+b[/tex]

[tex]7=1+b[/tex]

[tex]b=7-1[/tex]

[tex]b=6[/tex]

Step 3. Write the equation in Slope-intercept form

[tex]y=mx+b[/tex]

[tex]y=\frac{1}{3} x+6[/tex]

Answer:

x=y

Step-by-step explanation:

There is exactly one value of x for a value of the function by the one-to-one property.

Answer:

min | miles

———|———

1 | 3

2 | 6

3 | 9

4 | 12

5 | 15

6 | 18

Step-by-step explanation:

try putting this into a T-chart like I kind of did here or some other kind of other table.

Answer:

1/8

Step-by-step explanation:

There is a 1/2 probability for each of the three flips to result in the desired outcome. To get 3 desired outcomes in a row, we multiply each of the probabilities together

(1/2)³ = 1/8

Answer: it is D) 2/3

Given Data : Length = (7p - 10q) and Breadth = (2p - 9q)

Calculation :

⟹ Perimeter = 2(Length + Breadth)

⟹ Perimeter = 2(7p - 10q + 2p - 9q)

⟹ Perimeter = 2(9p - 19q)

⟹ Perimeter = 18p - 38q centimetres

The required perimeter of the rectangle is 18p - 38q centimeters.

It is required to find the required perimeter of the rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Given:

width of a rectangle = (2p - 9q) centimeters,

length measures= (7p - 10q) centimeters.

We know that

⟹ Perimeter = 2(Length + Breadth)

By put the value width and length in perimeter we get,

⟹ Perimeter = 2(7p - 10q + 2p - 9q)

⟹ Perimeter = 2(9p - 19q)

⟹ Perimeter = 18p - 38q centimeters

Therefore, the required perimeter of the rectangle is 18p - 38q centimeters.

Learn more about rectangle here:

brainly.com/question/24437900

#SPJ2

Answer:

Step-by-step explanation:

[tex]f(x,y)=arctan(xy)\\\\\dfrac{ \partial f}{ \partial x}=\dfrac{y}{1+x^2y^2} \\\\\dfrac{ \partial f}{ \partial y}=\dfrac{x}{1+x^2y^2} \\\\\dfrac{ \partial ^2 f}{ \partial x^2}=\dfrac{-2xy^3}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial y^2}=\dfrac{-2x^3y}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial x\ \partial y}=\dfrac{1-x^2y^2}{(1+x^2y^2)^2} \\[/tex]

[tex]f(x,y)= f(1,1)+(x-1)\dfrac{\partial f}{\partial x} (1,1)+(y-1)\dfrac{\partial f}{\partial y} (1,1)+\dfrac{(x-1)^2}{2} \dfrac{\partial^2 f}{\partial x^2} (1,1)+(x-1)(y-1)\dfrac{\partial^2 f}{\partial x\ \partial y} (1,1)+\dfrac{(y-1)^2}{2} \dfrac{\partial^2 f}{\partial y^2} (1,1)+...\\\\=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} +(x-1)(y-1)*\dfrac{0}{4}-\dfrac{(y-1)^2}{4} \\\\[/tex]

[tex]\boxed{f(x,y)=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} -\dfrac{(y-1)^2}{4} }\\\\[/tex]

Answer:

256

Step-by-step explanation:

4⁴

= 4 × 4 × 4 × 4

= 16 × 16

= 256

Answer:

Whenever the denom is 0, that's where it's undefined -- or in your case "restrictions"

So factoring 2x^2 + x - 21 gets you (x-3)(2x+7). That means 3 and -7/2 are the restricted values.

To simplify, I'm going to factor it. (Assuming what you wrote is 8x^2 for the numerator)

[(4x-7)(2x+7)] / (x-3)(2x+7)

You can cancel 2x+7 out,

so you get 4x-7/x-3

When we have a given function f(x), the rate of change in a given value x₀ is given by:

[tex]\frac{df(x_0)}{dx} = \lim_{h \to 0} \frac{f(x_0 + h) - f(x_0)}{h}[/tex]

We will find that the rate of change at t = 4s is:

r = -1/3

Now we can't do this if we do not have the function and we only have a text description of the graph, but what we can do is find the average rate of change.

For a function f(x), the average rate of change in an interval (a, b) such that a < b is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Something really nice is that the average rate of change is equal to the exact rate of change if f(x) is a linear equation.

If we want to find the rate of change at t = 4, then we need to find the smallest interval that contains t = 4.

Here we know that the graph passes through the points:

(3,1) to (6, 0)

Because of the statement "a line falling from (3, 1) to (6, 0)" we know that in this segment we have a line, which implies that the average rate of change will be equal to the exact rate of change.

Using the equation of the average rate of change we get:

[tex]r = \frac{d(6) - d(3)}{6 - 3} = \frac{0 - 1}{3} = - 1/3[/tex]

Then the rate of change in the distance at the time t = 4s is -1/3.

If you want to learn more, you can read:

https://brainly.com/question/18904995

Answer:

12:14

Step-by-step explanation: