A perpendicular bisector runs through the middle of a line segment and splits into

Differentiate both sides with respect to x and solve for the derivative dy/dx :

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[x^2y^2+xy\right] = \dfrac{\mathrm d}{\mathrm dx}[2] \\\\ \dfrac{\mathrm d}{\mathrm dx}\left[x^2\right]y^2 + x^2\dfrac{\mathrm d}{\mathrm dx}\left[y^2\right] + \dfrac{\mathrm d}{\mathrm dx}\left[x\right]y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 2xy^2 + x^2(2y)\dfrac{\mathrm dy}{\mathrm dx} + y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ (2x^2y+x)\dfrac{\mathrm dy}{\mathrm dx} = -2xy^2-y \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{2xy^2+y}{2x^2y+x}[/tex]

This gives the slope of the tangent to the curve at the point (x, y).

If the slope of some tangent line is -1, then

[tex]-\dfrac{2xy^2+y}{2x^2y+x} = -1 \\\\ \dfrac{2xy^2+y}{2x^2y+x} = 1 \\\\ 2xy^2+y = 2x^2y+x \\\\ 2xy^2-2x^2y + y - x = 0 \\\\ 2xy(y-x)+y-x = 0 \\\\ (2xy+1)(y-x) = 0[/tex]

Then either

[tex]2xy+1 = 0\text{ or }y-x=0 \\\\ \implies y=-\dfrac1{2x} \text{ or }y=x[/tex]

In the first case, we'd have

[tex]x^2\left(-\dfrac1{2x}\right)^2+x\left(-\dfrac1{2x}\right) = \dfrac14-\dfrac12 = -\dfrac14\neq2[/tex]

so this case is junk.

In the second case,

[tex]x^2\times x^2+x\times x=x^4+x^2=2 \\\\ x^4+x^2-2 = (x^2-1)(x^2+2)=0[/tex]

which means either

[tex]x^2-1 = 0 \text{ or }x^2+2 = 0 \\\\ x^2 = 1 \text{ or }x^2 = - 2[/tex]

The second case here leads to non-real solutions, so we ignore it. The other case leads to [tex]x=\pm1[/tex].

Find the y-coordinates of the points with x = ±1 :

[tex]x=1 \implies y^2+y=2 \implies y=-2 \text{ or }y=1 \\\\ x=-1\implies y^2-y=2\implies y=-1\text{ or }y=2[/tex]

so the points of interest are (1, -2), (1, 1), (-1, -1), and (-1, 2).

Answer:

Uhm, I see there's a pattern, but there are only 2 green boxes, whole there are 4 orange boxes in every figure.

Using proportions, it is found that the length of the sculpture using the new scale is given by:

D. 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The initial scale is of 1 cm = 2 feet, with a sculpture of 8 feet, hence the length of the drawing is given by:

l = 8/2 = 4 cm.

For the new scale, 1 cm = 5 feet, and you keep the drawing of 4 cm, hence the length of the sculpture is given by:

l = 4 x 5 = 20 feet.

Hence option D is correct.

More can be learned about proportions at https://brainly.com/question/24372153

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9514 1404 393

Answer:

  24 in square by 6 in deep

Step-by-step explanation:

Let x represent the side of the square cut from each corner. Then the dimensions of the base of the box are 36-2x in each direction. The total volume of the box is ...

  V = LWH = (36 -2x)(36 -2x)x = x(4x² -144x +1296)

The volume will be a maximum where dV/dx = 0.

  dV/dx = 12x^2 -288x +1296 = 0

  x² -24x +108 = 0 . . . . divide by 12

  (x -6)(x -18) = 0 . . . . . factor

  x = 6 or 18 . . . . . . x = 18 gives a minimum volume; we want x = 6

Then the dimensions are 36 -2(6) = 24 inches square by 6 inches deep.

Answer:

Step-by-step explanation:

Area of ΔABC is:

We have:

Find CD using Pythagorean:

Find DB using the following identity, coming from ratios of corresponding sides of similar triangles:

Find AB:

Find the area of ΔABC:

Answer:

I would round 5 up and anything below 5 would be rounded down.

10 + 4 + 3 + 8 = x

25 = x

Answer:

Let me know if I explain this wrong but from what I understand, what you would do is 9m5 and 7.5 together ad .5 and .5 are 1. That means 9+1+7. Next is 4.7 and 3.2 The problem with this us that .7 and .2 are .9 however that is important. 4+3 is 7 and we know .9 so it's 7.9. now just add the whole numbers and 7.9 and then you get your perfect answer. this answer was mainly just distributive property. hope I helped

Answer:

Pretty sure you'd be in hell by then 0_0

Step-by-step explanation:

think of it-2,200 ft and your at 0. Your in hell!

Answer:

Polynomial Equation                          Degree                                  Example

Linear Equations                                     1                                    -3x + 1 = 4x + 5

Quadratic Equations                               2                                   x^2 – 6x + 9 = 0

Cubic Equations                                      3                              x^3 – 2x^2 + 3x = -5

Quartic Equations                                   4                                      x^4 – 2x^2 = -4

Step-by-step explanation:

Linear Equations

Linear equations are polynomial equations that have a degree of 1.

ax + b = 0

Solving for solutions for this type of equation will require us to isolate the unknown variable on one side of the equation. Master your craft in solving linear equations here.

Quadratic Equations

Quadratic equations are polynomial equations with a degree of 2.

ax2 + bx + c = 0

There are different ways we can solve quadratic equations – it mostly depends on the form of the quadratic expression on the right-hand side.

We can factor quadratic expressions and apply the zero-property.

Applying special algebraic properties such as the difference of two squares, perfect square trinomial properties, and completing the square.

Lastly, we can also use the quadratic formula to find the zeroes of quadratic equations.

Polynomial Equations (with a degree of 3 or higher)

Here’s the exciting part: what if we need to find the zeros of the solutions of a polynomial equation with degrees that are 3 or higher?

Some cubic and quartic equations can be factored by grouping and be reduced to equations with a smaller degree. There are times, however, that finding the actual factors can be challenging.

9514 1404 393

Answer:

  a = ±2

Step-by-step explanation:

For similar figures, the same scale factor applies to both x and y.

  12 = 3a²

  4 = a²

  a = ±√4 = ±2

Answer:

a = [tex]\frac{2A}{p}[/tex]

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] ap ( multiply both sides by 2 to clear the fraction )

2A = ap ( isolate a by dividing both sides by p )

[tex]\frac{2A}{p}[/tex] = a

Answer:

B

Step-by-step explanation:

i did this a couple years ago should be right if im correct

B: is correctly in my opinion

Answer:

60

Step-by-step explanation:

its the answer

Perimeter is the distance around the rectangle and the formula is 2 x length + 2 x height.

Perimeter = 2 x45 + 2x20

Perimeter = 90 + 40

Perimeter = 130 yards

Answer:

Length = 45 yard

Height = 20 yards

Perimeter

We know that

[tex] \: perimeter = 2(l + b)[/tex]

» Perimeter = 2(45 + 20)

» Perimeter = 2(65)

» Perimeter = 130 yards

Answer:

-60 , -19 , 6.28 , 14

Step-by-step explanation:

Order the number in ascending order, or from least to greatest. Note that the bigger the negative number, the smaller the number. The bigger the positive number, the bigger the number:

-60 , -19 , 6.28 , 14

~

Note: For 6.28, the decimal point results in 6 being in the ones place, 2 being in the tenths place, 8 being in the hundredths place. By the rules regarding the usage of decimals, place values after the decimal point will be significantly less then the place values before the decimal point, and would be used to determine a more exact value.

Answer:

3

Step-by-step explanation:

[tex]log(3x^{3}) - log(x^{2}) = log(\frac{3x^{3}}{x^{2}})\\log(27) - log(x) = log(\frac{27}{x} )\\[/tex]

therefore,

[tex]\frac{3x^{3} }{x^{2} } = \frac{27}{x} \\3x=\frac{27}{x} \\3x^{2} =27\\x= +3\\x=-3[/tex]

however, since logarithms cannot have negative arguments, x can only be +3

i.e. log(-3) is impossible, and will return MATH ERROR on a calculator.

Answer:

plane EBG

Step-by-step explanation:

plane C is also named plane EBG

Answer:

[tex]\\ \sf\longmapsto Plane EBG[/tex]

We can't name it EBF as it is a axis and coplanar points

Also nEF is not a satisfactory name .

So the correct option is C

Answer:

x is 2 and -8

Step-by-step explanation:

[tex] {x}^{2} + 6x - 16 = 0[/tex]

general equation

[tex] {ax}^{2} + (sum)x + product = 0[/tex]

sum is 6, product is -16

for completing squares,

first divide the sum by 2:

[tex] = \frac{6}{2} = 3[/tex]

add the square of the result on (x² + 6x) and subtract it from the product:

[tex] ( {x}^{2} + 6x + {3}^{2} ) - 16 - {3}^{2} = 0 \\ {(x + 3)}^{2} - 25 = 0 \\ {(x + 3)}^{2} = 25[/tex]

take square root:

[tex] \sqrt{ {(x + 3)}^{2} } = \sqrt{25 } \\ x + 3 = ±5 \\ x = ±5 - 3[/tex]

x is either: 5-3 or -5-3

[tex]x = 2 \: \: and \: - 8[/tex]

Answer:

-3.64

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because lot of people love it

Answer:

the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

cosA^2 = 1 - sinA^2

subtitute 1/4 below

= 1 - (1/4)^2

= 1 - 1/16

after calculation

= - 0.9682

Answer:

D

Step-by-step explanation:

When all the members in a domain has only but one member in the do main then function has been satisfied.

considering a situation of,

4 1

6 1

8 2

the domain has only one member in the Co domain hence which makes it a function

9514 1404 393

Answer:

  58 km/h

Step-by-step explanation:

Let s represent James's speed. Then s-24 is Kim's speed. The relationship between time, speed, and distance is ...

  d = st

Since the two were traveling in opposite directions, their distance apart is the sum of the distances they drove. James drove for 1.6 more hours than the 1.8 hours Kim drove, so their total distance is ...

  (1.6 +1.8)s +1.8(s -24) = 258.4

  5.2s -43.2 = 258.4 . . . . . . . . . . . . collect terms

  5.2s = 301.6 . . . . . . . . . . . add 43.2

  s = 58 . . . . . . . . . . . divide by 5.2

James drove at 58 km/h.

<CDE  =  137°

When two triangles are congruent:

Since △JKL and △CDE are congruent, all the corresponding angles are equal.

Therefore, <JKL  =  <CDE   =  137°

Learn more here: https://brainly.com/question/12077512

Answer:

x = 33

AB = 60

Step-by-step explanation:

18 + 2x -6 = x+45

x = 33

AB = 33× 2 -6

= 60

Answer:

[tex]f(x)^{-1}=-x+5[/tex]

Step-by-step explanation:

It looks like the function is f(x)=-x+5.

To find the inverse, first replace f(x) with y.

y=-x+5

Switch the y and x.

x=-y+5.

Solve for y.

x-5=-y

-x+5=y

[tex]f(x)^{-1}=-x+5[/tex]

I hope this helps!

pls ❤ and mark brainliest pls

Answer:

ghhc