Circle Theorems 1! need help

Answer:

The volume is maximum when the height is 3 cm.

Step-by-step explanation:

let the side of the removed potion is x.

length of the box = 18 - 2 x

width of the box = 18 - 2 x

height = x

Volume of box

V = Length x width x height

[tex]V = (18 - 2 x)^2 \times x\\\\V = x(324 + 4x^2 - 72 x)\\\\V = 4 x^3 - 72 x^2 + 324 x \\\\\frac{dV}{dx} = 12 x^2 - 144 x + 324 \\\\So,\\\\ \frac{dV}{dx} =0\\\\x^2 - 12 x + 27 = 0 \\\\x^2 -9 x - 3 x + 27 =0\\\\x (x - 9) - 3 (x -9) = 0\\\\x = 3, 9[/tex]

Now

[tex]\frac{d^2V}{dx^2}=24 x - 144 \\\\Put x = 3 \\\\\frac{d^2V}{dx^2}=24\times 3 - 144 = - 72\\\\Put x = 9\\\\\frac{d^2V}{dx^2}=24\times 9 - 144 = 72\\[/tex]

So, the volume is maximum when x = 3 .

Hey there! There are 1000 thousands in a million.

If this helps, please mark ME as brainliest!

Have a wonderful day :)

9514 1404 393

Answer:

   C.  y = 1/2x +2

Step-by-step explanation:

The magnitude of the slope is the measure of "steepness." The slope is the coefficient of x in these equations. Here those values are ...

  4, 3/4, 1/2, 10

Of these, 1/2 is the smallest (least steep). 1/2 is the slope in the equation ...

  y = 1/2x +2

Answer:

x2-4

Step-by-step explanation:

Answer:

hope it helps

Answer:

A

Step-by-step explanation:

the first one in the picture

16:52

Hope this helps! :)

Answer:

DL/dt = 529 miles/h

Step-by-step explanation:

The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t  point C) shape a right triangle wich hypothenuse L is:

L²  =  d² + x²

d is the constant distance between the plane and the ground

Then differentiation with respect to time on both sides of the equation

2*L*dL/dt  = 2*d* Dd/dt  + 2*x*dx/dt

But   Dd/dt  =  0

L*dL/dt  =  x*dx/dt

x =  5 miles       dx/dt  =  570 m/h        L  = √ d² + x²    L  √ (5)² + (2)²

L = √29      L  = 5.39 m

5.39 *DL/dt  =  5*570 m/h

DL/dt  =   5*570/5.39   miles/h

DL/dt  =  528.76  miles/h

DL/dt = 529 miles/h

Answer:

156 degrees

Step-by-step explanation:

Bisects meand to cut into two equal halves.

That means 4x-2=3x+18.

Subtracting 3x on both sides gives x-2=18

Adding 2 on both sides gives x=20

If x=20, then 4x-2 equals 4(20)-2=78.

The other half is also 78 since the two angles were comgruent.

The whole angle is 78+78=156.

9514 1404 393

Answer:

  d = kw/p

Step-by-step explanation:

When d varies directly with w, the equation is ...

  d = kw

When d varies inversely with p, the equation is ...

  d = k/p

When d does both, the equation is ...

  d = kw/p

Answer:

the magnitude of a real number without regard to its sign.

Step-by-step explanation:

For example, |-3| would just be a 3 in general, no negative sign in the front.

hope this answers your confusion.

Hello!

3a = 7b =>

=> 3 × a = 7 × b =>

=> a/b = 7/3

Good luck! :)

Answer:

see below

Step-by-step explanation:

3x - 6(5x + 3) = 9x + 6

Distribute

3x -30x-18 = 9x+6

Combine like terms

-27x - 18 = 9x+6

Add 27x  to each side

-27x+27x-18 = 9x+27x+6

-18 = 36x+6

Subtract 6 from each side

-18-6 = 36x+6-6

-24 = 36x

Divide by 36

-24/36 = 36x/36

Simplify

-2/3 = x

Answer:

[tex]\small \sf x = \frac{2}{-3} \\ [/tex]

Step-by-step explanation:

3x - 6(5x + 3) = 9x + 6.

Use the distributive property to multiply -6 by 5x + 3.

3x - 30x - 18 = 9x + 6

Combine 3x and -30x to get -27x.

-27x - 18 = 9x + 6

Subtract 9x from both sides.

-27x - 9x - 18 = 9x - 9x + 6

-36x - 18 = 6

Add 18 to both sides.

-36x - 18 + 18 = 6 + 18

-36x = 24

Divide both sides by -36.

[tex]\small \sf \frac{ -36x}{ -36} = \frac{24}{-36} \\ [/tex]

Reduce the fraction [tex]\frac{24}{-36} [/tex] to lowest terms by extracting and canceling out 12.

[tex]\small \sf x = \frac{2}{-3} \\ [/tex]

Answer:

Option A

Step-by-step explanation:

If the quadrilateral ABCD is dilated by a scale factor 'k' to form quadrilateral A'B'C'D',

Scale factor = [tex]\frac{\text{Length of one side of the Image}}{\text{Length of one side of the original}}[/tex]

k = [tex]\frac{BA'}{BA}[/tex]

Distance between B(2, -5) and A(-1, -1) = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                               = [tex]\sqrt{(2+1)^2+(-5+1)^2}[/tex]

                                                               = 5 units

Distance between B(2, -5) and A'(-5.5, 5) = [tex]\sqrt{(-5.5-2)^2+(5+5)^2}[/tex]

                                                                    = [tex]\sqrt{(-7.5)^2+(10)^2}[/tex]

                                                                    = 12.5 units

Scale factor 'k' = [tex]\frac{12.5}{5}[/tex]

k = [tex]\frac{5}{2}[/tex]

Therefore, ABCD is dilated by a scale factor [tex]\frac{5}{2}[/tex] about point B.

BA and it's image BA' are on the same line and passes through center of dilation B.

Similarly, lines CD and C'D' will be parallel because they do not pass through center of dilation.

Therefore, Option (A) will be the correct option.

Answer:

3

Step-by-step explanation:

From the diagram

AD = 9 units and AB = 3 units , then

[tex]\frac{AD}{AB}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

A is that answer

A) y<2x-3

Answer:

(x-4) (x-5)

Step-by-step explanation:

* means multiply

first you figure out what 2 numbers

when added make 9

when multiplied make 20

those are 4 and 5

(x  4) (x  5)

in this case

-4 -5 make -9

-4 * -5 make 20

(x-4) (x-5)

Answer:

(x-4)(x-5)

Step-by-step explanation:

Firstly you need to use the second equation formula to get the value of x.

x= [tex]\frac{-(-9)+- \sqrt{(-9)^{2}-4*1*20 } }{2*1}[/tex]

x= [tex]\frac{9+- \sqrt{81-80 } }{2}[/tex]

x= [tex]\frac{9+-1}{2}[/tex]

so,

x=[tex]\frac{9+1}{2}[/tex]      x=5

and

x=[tex]\frac{9-1}{2}[/tex]      x=4

When writing the factor, we have to change signs of 5 and 4. So it will be -5 and -4.

That's why the awnser is (x-4)(x-5)

Hope it helps!

Answer:

x = -3 +/- square root(22)

Step-by-step explanation:

x = -b +/- square root(b^2 - 4ac) / 2a

ax^2 + bx + c = 0

these are both the quadratic formula but one is solved for the x and another for 0

a= 1

b= 6

c = -13

x= -6 +/- square root( 6^2 - 4(1)(13)) / 2(1)

x = -6 +/- sqrt( 36 + 52) / 2

x= -6 +/- sqrt (88) / 2

sqrt of 88 = 2 x sqrt (22)

divide 2 on each

x= -3 +/- sqrt (22)

Answer:

39

Step-by-step explanation:

you just put it in a calculator

Answer:

The expression is not factorable with rational numbers.

2x^2+19x+12

Step-by-step explanation:

Answer:

A=W, B=X, C=Y, D=Z, AB=WX, BC=XY, CD=YZ, AD=WZ

(The second answer down)

Step-by-step explanation:

Answer:

a)  c) μ = 16.4.

b)  d) μ > 16.4.

c) a) μ < 16.4.

d) c) μ ≠ 16.4.

e)  d) right; left; both.

Step-by-step explanation:

Question a:

Test if it is getting worse, so at the alternative hypothesis we test if the mean is of greater than 16.4 inches, but at the null hypothesis we test if it is still of 16.4 options, so option C.

Question b:

At the alternative hypothesis we test if the mean is of greater than 16.4 inches, as said above, so the answer is given by option d.

Question c:

Dying down, so if the mean is lower than 16.4 inches, so option a.

Question d:

Don't know, so just test if it is different, which includes both lower or greater, so the correct answer is given by option c.

Question e:

Test if more -> right, so on question b) is a right tailed test.

Test if less -> left, so on question c) is a left tailed test.

Different -> both sides, so on question d) it is a two-tailed test.

Thus the correct answer is given by option d.

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{3^3 \times 5^4}[/tex]

[tex]\mathsf{3^3}[/tex]

[tex]\mathsf{= 3\times3\times3}[/tex]

[tex]\mathsf{= 9\times3}[/tex]

[tex]\mathsf{= \bf 27}[/tex]

[tex]\mathsf{5^4}[/tex]

[tex]\mathsf{= 5\times 5\times5\times 5}[/tex]

[tex]\mathsf{= 25\times25}[/tex]

[tex]\mathsf{= \bf 625}[/tex]

[tex]\mathsf{27 \times625}[/tex]

[tex]\mathsf{= \bf 16,875}[/tex]

[tex]\mathsf{2\times5^3\times11}[/tex]

[tex]\mathsf{5^3}[/tex]

[tex]\mathsf{= 5\times 5\times5}[/tex]

[tex]\mathsf{= 25\times 5}[/tex]

[tex]\mathsf{\bf = 125}[/tex]

[tex]\mathsf{2\times125\times11}[/tex]

[tex]\mathsf{= 250\times11}[/tex]

[tex]\mathsf{\bf = 2,750}[/tex]

[tex]\large\textsf{Find the Greatest Common Factor (GCF) of 16,875 \& 2,750}[/tex]

[tex]\large\textsf{16,875: 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 625, 675, 1,125,}\\\\\large\textsf{1,875, 3,375, 5,625, \& 16,875}[/tex]

[tex]\large\textsf{2,750: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 125, 250, 275, 550, 1,375, \& 2,750}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: the GCF is \bf 125 }}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

0.0105 = 1.05% probability that no more than 3 of the entry forms will include an order.

Step-by-step explanation:

For each entry form, there are only two possible outcomes. Either it includes an order, or it does not. The probability of an entry including an order is independent of any other entry, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.

This means that [tex]n = 16[/tex]

They know that the probability of receiving a magazine subscription order with an entry form is 0.5.

This means that [tex]p = 0.5[/tex]

What is the probability that no more than 3 of the entry forms will include an order?

At most 3 including an order, which is:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{16,0}.(0.5)^{0}.(0.5)^{16} \approx 0[/tex]

[tex]P(X = 1) = C_{16,1}.(0.5)^{1}.(0.5)^{15} = 0.0002[/tex]

[tex]P(X = 2) = C_{16,2}.(0.5)^{2}.(0.5)^{14} = 0.0018[/tex]

[tex]P(X = 3) = C_{16,3}.(0.5)^{3}.(0.5)^{13} = 0.0085[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0002 + 0.0018 + 0.0085 = 0.0105[/tex]

0.0105 = 1.05% probability that no more than 3 of the entry forms will include an order.

Answer:

Yes

Step-by-step explanation:

If you replace each x with -3 and each y with 2 you get:

1) 2<-4*(-3)

2<12

True

2) -3+8*2>7

13>7

True

Therefore the point is part of the solution set

Answer:

916.67 (corrected to 2 decimal places)

Hope I'm right, fingers crossed

Step-by-step explanation:

[tex]55 \times 50 = 2750 \div \frac{3}{4 } = 916.6666667[/tex]

Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Answer:

I don't know the answer to ur question. LOL

Answer:

stop being desperate

nobody is gonna fall in love with some desperate weirdo