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3 years ago

A farmhouse shelters 10 animals, some are pigs, and some are ducks. Altogether there are 36 legs. How many pigs are there

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

4 0

Answer:

8 Pigs.

Step-by-step explanation:

~ P = the number of pig

~ D = the number of ducks

p + d = 10

4p + 2d = 36

4(10 - d) + 2d = 36

40 - 4d + 2d = 36

40 - 2d = 36

-40 = -40

-2d = -4

-2 -2

d = 2 ducks

p + d = 10

p + 2 = 10

Therefore, 8 pigs. :)) hope this helped you :))

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Can someone please help me

Vsevolod [243]

The restrictions for the equation is that the denominator can not be zero. So the restrictions for x would be what values make the denominator zero.

7x^2 + 6x = 0
factor
x(7x + 6) = 0
multiply any number by 0 and you get 0. So either x = 0 or 7x+6 = 0
since there's a x in the numerator x/x = 1 so this will not be a restriction. Then the only restriction is:
7x+6 = 0
7x = -6
x = -6/7

5 0

3 years ago

Find the zeros of y = x2 – 6x – 4 by completing the square.

katrin [286]

Answer:

The solutions to the quadratic equations are:

$x=\sqrt{13}+3,\:x=-\sqrt{13}+3$

Step-by-step explanation:

Given the function

$y\:=\:x^2\:-\:6x\:-\:4$

substitute y = 0 in the equation to determine the zeros

$0\:=\:x^2\:-\:6x\:-\:4$

Switch sides

$x^2-6x-4=0$

Add 4 to both sides

$x^2-6x-4+4=0+4$

Simplify

$x^2-6x=4$

Rewrite in the form (x+a)² = b

But, in order to rewrite in the form x²+2ax+a²

Solve for 'a'

2ax = -6x

a = -3

so add a² = (-3)² to both sides

$x^2-6x+\left(-3\right)^2=4+\left(-3\right)^2$

$x^2-6x+\left(-3\right)^2=13$

Apply perfect square formula: (a-b)² = a²-2ab+b²

$\left(x-3\right)^2=13$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solve

$x-3=\sqrt{13}$

Add 3 to both sides

$x-3+3=\sqrt{13}+3$

Simplify

$x=\sqrt{13}+3$

now solving

$x-3=-\sqrt{13}$

Add 3 to both sides

$x-3+3=-\sqrt{13}+3$

Simplify

$x=-\sqrt{13}+3$

Thus, the solutions to the quadratic equations are:

$x=\sqrt{13}+3,\:x=-\sqrt{13}+3$

4 0

3 years ago

At the end of an experiment, a rat weighed 3.1 times its original weight. If the rat originally weighed 5.8 ounces, about how mu

forsale [732]

Answer:

Step-by-step explanation:

5.8 multiplied by 3.1 equals 17.98, and you can round to 18 ounces.

5 0

3 years ago

Read 2 more answers

What is the equation in point-slope form of the line passing through (0, 6) and (1, 3)?

NeX [460]

Answer:

3 - 6 = -3(1 - 0)

Step-by-step explanation:

To write an equation of point-slope from two points, first you need the slope.

To find slope, find the change in y over the change in x.

(0,6) y = 6 and x = 0
(1,3) y = 3 and x = 1

The change in y over change is x means (y2 - y1) / (x2 - x1)

change in y: -3

change in x: 1

slope = -3/1 or -3

Now that we have slope we can start the point-slope equation.

Point-slope equation: y2 - y1 = m(x2 -x1)

[<em>m</em><em> </em>means slope]

Finally, the point slope equation for these points is: 3 - 6 = -3(1 - 0)

5 0

3 years ago

2 1/4 ft 9 ft 4ft. The base is a square? b. The volume of the rectangular prism is 81 cubic feet? c. The area of the base is 36

natita [175]

Answer:

We have a rectangular prism of measures:

(2 + 1/4)ft by 9ft by 4ft

Let's analyze each one of the statements:

a) The base is a square?

A square has the same length as the width, this prism would have a square base if at least two of the dimensions are equal, but we can see that are all different, so we can conclude that the base can not be a square.

b) The volume of the rectangular prism is 81 cubic feet?

The volume will be equal to the direct product of the 3 dimensions, then the volume is:

V = (2 + 1/4)ft*9ft*4ft = 81 ft^3

This statement is true.

c) The area of the base is 36 square feet.

We know the dimensions, but we do not know which ones describe the base.

In the usual notation, the first two measures will describe the base of the figure, and the third one is the height.

Then the area of the base is:

(2 + 1/4)ft*9ft = 20.25 ft^2

The area of the base is not 36 ft^2

d) if you doubled the height, the volume would be the same:

Of course if we double one of the dimensions the volume will change, but let's calculate this.

The original height is 4ft, if we double this, the new heights Is 2*4ft = 8ft

Then the new volume will be:

V = (2 + 1/4)ft*9ft*8ft = 162 ft^3

The volume changes.

6 0

3 years ago