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oee [108]
3 years ago
6

The function f(x) = 3x² + 12x +11 can be written in

Mathematics
1 answer:
Viktor [21]3 years ago
6 0

Answer:

3)  f(x) = 3(x + 2)^2 - 1.

Step-by-step explanation:

f(x) = 3x² + 12x +11

f(x) = 3(x^2 + 4x) + 11        Completing the square:

f(x) =  3[(x + 2)^2 - 4] + 11

f(x) = 3(x + 2)^2 -+3*-4 + 11

f(x) = 3(x + 2)^2  - 12 + 11

f(x) = 3(x + 2)^2 - 1.

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Is it possible to make a quadrilateral with any four dots as corners?
Elden [556K]

Answer:

Yes it is possible, given with 4 dots, lets say were set anywhere within a page or anywhere upon a circumference of a circle even. We can draw 4 straight lines to meet each corner and call this a quadrilateral.

Step-by-step explanation:

Squares, Rectangles and Rhombuses are all Parallelograms and squares and rectangles are regular quadrilaterals!

So any other 4 sided shape that is quadrilateral could be made.

The picture below shows all branches of quadrilaterals.

7 0
3 years ago
Read 2 more answers
Help! It says that I need to determine If both equations represent lines which are parallel, perpendicular, or none...
12345 [234]
    4x + 2y = 8     (1)
    8x + 4y = -4y  (2)

A) Two lines are parallel if they have the same gradient
       - putting both equations into the gradient- intercept form ( y = mx + c                where m is the gradient)
            (1) 4x + 2y = 8
                          2y = 8 - 4x
                            y = -2x + 4
             
            (2) 8x + 4y = -4y
      <span>                    </span>8x = -4y - 4y
                            y = \frac{-8x}{-8}
                            y = -x
   <span>Thus the gradient of the two equations are different and as such          the two lines are not parallel
</span>
B)  When two lines are perpendicular, the product of their gradient is -1
                   m_{1} * m_{2} = p
                                             p = (-2) * (-1)
                                             p =  2
<span>          ∴ the two lines are not perpendicular either.</span>

Thus these lines are SKEWED LINES

4 0
2 years ago
INFO: The chairs are evenly spaced around
lana66690 [7]

Answer: About 72 feet

The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).

======================================================

Explanation:

Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.

  • M = center of the circle
  • N = location where the cable is anchored to the ground

We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.

The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.

-----------------

What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.

It turns out that the chord length c is connected to the radius r and central angle theta like so:

c = 2*r*sin(0.5*theta)

where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.

If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces

Those five spaces could be written as

  1. The jump from L to A
  2. The jump from A to B
  3. The jump from B to C
  4. The jump from C to D
  5. The jump from D to E

Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.

There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.

-----------------

Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.

c = 2*r*sin(0.5*theta)

80 = 2*r*sin(0.5*5pi/6)

80 = 2*r*sin(5pi/12)

80 = 2*r*0.9659258

80 = 2*0.9659258*r

80 = 1.9318516r

1.9318516r = 80

r = 80/1.931 8516

r = 41.4110483

The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.

-----------------

Now that we know the radius, we can determine how long chord JF is.

The central angle for chord JF is angle JMF

If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.

So,

c = 2*r*sin(0.5*theta)

c = 2*41.4110483*sin(0.5*2pi/3)

c = 71.7260397

Chord JF is roughly 71.7260397 feet long.

When rounding to the nearest foot, that's about 72 feet.

6 0
2 years ago
Evaluate cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5.
Andre45 [30]

Answer:

Option d)  5 to the power of negative 5 over 6 is correct.

\dfrac{\sqrt[3]{\bf 5} \times \sqrt{\bf 5}}{\sqrt[3]{\bf 5^{\bf 5}}}= 5^{\frac{\bf -5}{\bf 6}}

Above equation can be written as 5 to the power of negative 5 over 6.

ie, 5^\frac{\bf -5}{\bf 6}

Step-by-step explanation:

Given that cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5.

It can be written as below

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}} \times 5^{\frac{1}{2}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}+\frac{1}{2}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{2+3}{6}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5}{6}} \times 5^{\frac{-5}{3}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5-10}{6}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{5^5}= 5^{\frac{-5}{6}}

Above equation can be written as 5 to the power of negative 5 over 6.

7 0
3 years ago
Solve for x:<br> -3(2x+1) + 3x = 6x + 3<br> Help!!
djverab [1.8K]

Answer:

b  x =-2/3

Step-by-step explanation:

-3(2x+1) + 3x = 6x + 3

Distribute

-6x -3 +3x =6x+3

Combine like terms

-3x-3 = 6x+3

Add 3x to each side

-3x+3x-3 = 6x+3x+3

-3 = 9x+3

Subtract 3 from each side

-3-3 = 9x+3-3

-6 = 9x

Divide by 9

-6/9 = 9x/9

-2/3 =x

8 0
3 years ago
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