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2 years ago

Help please !!! (will give thanks )

Mathematics

1 answer:

Anestetic [448]2 years ago

6 0

Answer:

The answer is -a-bc+43

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers

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ms Callahan is building a new dog pen for her dog. she has 24feet of fencing. the pen needs to be a rectangle. what is the lengt

NeX [460]

If Ms. Callahan has 24 feet of fencing, and she is building a pen, the PERIMETER of the pen must be 24 feet. The perimeter is basically the distance around a figure. The perimeter of a rectangle is equal to length plus width plus length plus width, AKA l+w+l+w, or P=2l+2w. In a rectangle, two pairs of sides are of equal length--so the two lengths and the two widths must be equal.

So, the formula is P=2l+2w. P, the perimeter, is 24, so 24=2l+2w. Let's try some values for l and see what we get for w. If the length is 1, l=1. 24=(2*1)+2w. 24=2+2w. 22=2w. w=11. So if length is 1 foot, width is 11 feet.

What if l=2? 24=(2*2)+2w. 24=4+2w. 2w=20. w=10. If l=2, w=10. And l=3? 24=(2*3)+2w. 24=6+2w. 18=2w. w=9. If l=3, w=9. Do you see a pattern? Every time we add 1 to l, we subtract 1 from w. So if l=4, w=8. If l=5, w=7. If l=6, w=6. Here, we start getting similar answers: if l=7, w=5. If l=8, w=4. Since we already know these values work, it doesn't matter whether we call it length or width. So, our answers are below.

Answer: Ms Callahan can make a pen with a length of 1 foot and a width of 11 feet, a length of 2 feet and a width of 10 feet, a length of 3 feet and a width of 9 feet, a length of 4 feet and a width of 8 feet, a length of 5 feet and a width of 7 feet, or a length of 6 feet and a width of 6 feet.

6 0

3 years ago

Express each of the following quadratic functions in the form of f(x) = a (x - h)²+ k.Then,state the minimum or maximum value,ax

Ivan

Given:

The function is:

$f(x)=-2x^2+7x+4$

To find:

Express the quadratic equation in the form of $f(x)=a(x-h)^2+k$ , then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

Solution:

The vertex form of a quadratic function is:

$f(x)=a(x-h)^2+k$ ...(i)

Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

We have,

$f(x)=-2x^2+7x+4$

It can be written as:

$f(x)=-2\left(x^2-3.5x\right)+4$

Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

$f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4$

$f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4$

$f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4$

$f(x)=-2\left(x-1.75\right)^2+6.125+4$

$f(x)=-2\left(x-1.75\right)^2+10.125$ ...(ii)

On comparing (i) and (ii), we get

$a=-2,h=1.75,k=10.125$

Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

Maximum value = 10.125

Axis of symmetry : $x=1.75$

Maximum point = (1.75,10.125)

Therefore, the vertex form of the given function is $f(x)=-2\left(x-1.75\right)^2+10.125$ , the maximum value is 10.125, the axis of symmetry is $x=1.75$ and the maximum point is (1.75,10.125).

8 0

3 years ago

Which answer choices is a run on sentence?

liberstina [14]

A would be the answer John hit the baseball it went over the fence.

7 0

3 years ago

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The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphe

ch4aika [34]

Answer:

0.093 ft/min