What is the maximum number of turning points the function f(x)=7x^5+6x^3-4x^2+1 , can have

Answers

Answer 1

Answer: The maximum number of turning points of the polynomial is the degree of the polynomial minus 1. In this case the degree is 5, so the maximum number of turning points is 5-1=4.

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Solve for x.

A) 10.5
B) 10
C) 6√3
D) 20

Answers

There are three right triangles in this figure. Set up Pythagorean theorem for each of them.
Let y be the altitude of the largest triangle.
Let z be the left side.
We have for large triangle:
x² + z² = (9+3)²
For left sub-triangle:
y² + 3² = z²
For right sub-triangle:
y² + 81 = x²

So the three equations are
x² + z² = 144
y² + 9 = z²
y² + 81 = x²

Solve last equation for y², plug into second equation, solve that for z² in terms of x², and lastly plug z² into the first equation to find
x² + x² - 72 = 144
2x² = 216
x² = 108
x = √108 = √(36·3) = 6√3

The answer is C) 6√3

A scale drawing of a square has a side length of 5 millimeters. The drawing has a scale of 1 mm : 5 km. Find the actual perimeter and area of the square.

Answers

Answer:

Actual Perimeter = 100 km

Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

1 mm = 5 km

5 mm = 5 × 5 km

= 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

Perimeter of square = 4 × side

= 4 × 25

= 100 km

Area of the square = side × side

= 25 × 25

= 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

2/√3-1 where p and q are integers. Show your working clearly. (b) Express in the form p + √q

Answers

Answer:

Hi,

$1+√(3)$

Step-by-step explanation:

$(2)/(√(3) -1) \n=(2*(√(3) +1))/((√(3) -1)(√(3) +1))\n=(2*(√(3) +1))/(3 -1)\n\n=\boxed{1+√(3) }$

hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Answers

Answer:

$2√(6)$

Step-by-step explanation:

Perimeter of equilateral triangle = 36 inches

Formula of perimeter of equilateral triangle = $3* side$

⇒ $36=3* side$

⇒ $(36)/(3) = side$

⇒ $12= side$

Thus each side of equilateral triangle is 12 inches

Formula of area of equilateral triangle = $(√(3))/(4) a^(2)$

Where a is the side .

So, area of the given equilateral triangle = $(√(3))/(4) * 12^(2)$

= $36√(3)$

Since hexagon can be divided into six small equilateral triangle .

So, area of each small equilateral triangle = $(36√(3))/(6)$

= $6√(3)$

So, The area of small equilateral triangle :

$(√(3))/(4)a^(2) =6√(3)$

Where a is the side of hexagon .

$(1)/(4)a^(2) =6$

$a^(2) =6* 4$

$a^(2) =24$

$a =√(24)$

$a =2√(6)$

Hence the length of a side of the regular hexagon is $2√(6)$

$Perimter\ of\ equilateral\ triangle\ =36\n a- \ side\ of\ triangle\n 36=3a\ |:3\n a=12\n\n Area\ of\ equilateral\ triangle:\n A=(a^2√(3))/(4)\n A=(12^2√(3))/(4)\n A=(144√(3))/(4)=36\sqrt3 \n\n Hegagon\ can\ be\ divided\ into\ 6\ equilateral\ small\ triangles.\nArea\ of\ one\ of\ them: A_s=(A)/(6)=(36\sqrt3)/(6)=6√(3)\n s-side\ of\ equilateral\ =\ side\ of\ small\ triangle\n A_s=(s^2√(3))/(4)=6√(3)\ |*4 \n s^2\sqrt3=24\sqrt3\ |\sqrt3\n s^2=24\n s=√(24)$ $√(24)=√(4*6)=2\sqrt6\n\n Side\ of\ hexagon\ equals\ 2\sqrt6\ inches$

(4,? is on the line below. Find the other half of the coordinate

y=2/7x-3

Answers

(x,y)
we are given (4,?)
basically,
if x=4, then what is y equal to ?
subsitute 4 for x
y=2/7(4)-3
y=8/7-3
y=8/7-21/7
y=-13/7=-1 and 6/7

(4,-13/7)

What is the half of 15

Answers

Half of 15 is

15/2 = 7.5

half means divide by 215/2= 7.5

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