In a parallelogram ABCD, prove that (AC)2 + (BD)2= 2[(AB)? +(BC)?].​

To solve this question, we have to find the equation of the circle with given center and where it passes. Doing this, we get that the equation of the circle is:

[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]

Equation of a circle:

The equation of a circle with center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Center at (16, 30)

This means that [tex]x_0 = 16, y_0 = 30[/tex]

Thus

[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]

Passes through the origin:

We use this to find the radius squared, as this means that [tex]x = 0, y = 0[/tex] is part of the circle. Thus

[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]

[tex](0 - 16)^2 + (0 - 30)^2 = r^2[/tex]

[tex]r^2 = 16^2 + 30^2 = 1156[/tex]

Thus, the equation of the circle is:

[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]

For another example to find the equation of a circle, you can look at https://brainly.com/question/23719612

Answer:

x = 6

Step-by-step explanation:

s = 6

t = 4

x = 4 + s - t

Substituting s and t in equation,

x = 4 + 6 - 4

x = 6

Answer:

6

Step-by-step explanation:

s=6

t=4

x= 4+6-4

x=10-4

x=6

Therefore; the final result is 6

Answer:

1. 3x^3 - 2x^2 - x

2. -4x^2 + x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.

c^2 = a^2 + b^2

c = 2.77

a = 2.5

b = 1/2 the side of the heptagon.

2.77^2 = 2.5^2 + b^2

7.6729 =6.25 + b^2

7.5629 - 6.25 = b^2

b^2 = 1.4229

b = sqrt(1.4229)

b = 1.1928

But the side is twice that long

s = 2.3857

Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.

Area of the triangle so formed is

Area = 1/2 * b * h

b = 2.3857

h = 2.5

Area = 1/2 * 2.5 * 2.3857

Area = 2.982

There are 7 such triangles.

Answer: 7 * 2.982

Answer: 20.87

Tan=24/10 ≈ 2.4

using Pythagoras theorem

x²=(24)²+(10)²

x²=576+100

x²=57600

x=√57600 => 240

Therefore

sina=24/240 => 0.1

cota=1/tana => 1/(24/10) => 10/24

Answer:

2x^4+4x^2+2

Step-by-step explanation:

f(x) = x^2+1

g(x) = 2x^2

g(f(x))=

Replace x in the function g(x) with the function f(x)

         =2( x^2+1)^2

         = 2( x^2 +2x^2 +1)

         = 2x^4+4x^2+2

Answer:

x= 2/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's write that out completely:

[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.

e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):

[tex]e^7=x[/tex] choice C.

Answer:

b^27

Step-by-step explanation:

Answer:

A. b^27

You multiply 9x3 and you get 27 with the base "b"

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

Let the gladiolas Mr Haas has be x

We know that Mrs Albert has 3 times as many gladiolas as Mr. Haas, so Mrs Albert has:

3x gladiolas

Together they have 128 gladiolas, so:

x + 3x = 128

4x = 128

x = 128/4

x = 32

Therefore Mr Haas has 32 gladiolas & if Mrs. Albert has 3 times more than him she has (32x3) = 96 gladiolas.

answered by g a u t h m a t h

Answer:

60

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2+25^2 = 65^2

a^2 +625 = 4225

a^2 = 4225-625

a^2=3600

Taking the square root of each side

sqrt(a^2) = sqrt(3600)

a = 60

Answer:

Step-by-step explanation:

Hypotenuse: 65

Leg: 25

Let Hypotenuse be c, and leg be a

[tex]a^{2}[/tex] + [tex]b^{2} = c^{2}[/tex]

[tex]a^{2} + 25^{2} = 65^{2}[/tex]

[tex]a^{2} + 625 = 4225\\[/tex]

[tex]a^{2}[/tex] = 4225 - 625

[tex]a^{2}[/tex] = 3600

3600 is the exponential value of a, meaning we need to apply the opposite of squaring to get the value of b. Which is square rooting.

a = [tex]\sqrt{3600\\}[/tex]

a = 60

Therefore a is equal to 60 feet

Answer:

The length of the shortest side of the triangle is 10.

Step-by-step explanation:

Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :

6 = 15

4 = X

4 x 15/6 = X

10 = X

Therefore, the length of the shortest side of the triangle is 10.

Hey there!

At first, Josh has 30 keys.

Then, he loses 3 keys.

30 keys - 3 keys = 27 keys

After that, Josh finds 7 keys.

27 keys + 7 keys = 34 keys

Josh will have a total of 34 keys.

Hope this helps! Have a great day!

The solution to the continuous linear relation is: (2,-7)

The data on the table can be presented as:

Relation A

[tex](x_1,y_1) = (-8,-5)[/tex]

[tex](x_2,y_2) = (-3,-6)[/tex]

Relation B

[tex](x_1,y_1) = (-8,-15)[/tex]

[tex](x_2,y_2) = (-3,-11)[/tex]

Plot the points of each relation and draw a line through the points (see attachment)

Write out the point of intersection of the two lines.

[tex](x,y) = (2,-7)[/tex]

Hence, the solution to the continuous linear relation is: (2,-7)

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Answer:

22 mm

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

cause it will be more faster just because it is in a solid phase or it is solid

The time taken to hit the ground is 6.25 sec.(Option B)

How to calculate time?

It is given that penny follows the trajectory:

[tex]y = -4.9x^2 + 32x + 425[/tex]

Differentiating it we get:

[tex]\dfrac{dy}{dx} =-9.8x+32[/tex]

At y=425, it is obvious that x=0

So dy/dx at x=0 is 32.

Now the vertical component of the velocity is 32sinФ (where Ф is the angle at which penny is thrown).

Ф[tex]=\tan^{-1}(32)[/tex]

Vertical component=[tex]32*\sin(\tan^{-1}(32))[/tex]=31.98 ft/sec

Now applying the equation of motion: acceleration=-32ft/sec^(2)

u=31.98ft/sec   s=-425   t=?

[tex]s=ut+\frac{1}{2} at^{2}[/tex]

[tex]-425=31.98t-16t^2[/tex]

[tex]16t^2-31.98t-425=0[/tex]

Solving the quadratic equation we get:

t=6.249 sec≅6.25 sec

Therefore, the time taken is 6.25 sec.

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Answer:

Step-by-step explanation:

The shape cam be split into a triangle and a trapezoid

✔️Area of the trapezoid = ½(a + b)h

Where,

a = 12.5 ft

b = 16.7 ft

h = 11.6 ft

Plug in the values

Area of the trapezoid = ½(12.5 + 16.7)*11.6

Area of trapezoid = 169.36 ft²

✔️Area of the triangle = ½*b*h

b = 16.7 ft

h = 19.2 - 11.6 = 7.6 ft

Area of the triangle = ½*16.7*7.6

= 63.46 ft²

✔️Area of the shape = 169.36 + 63.46

= 232.82 ft²

Answer:

off topic

Step-by-step explanation:

Answer:

y =x^2 +8x +15

factories form

y =( x+5 )( x+3 )

x intercept where the graph meet the x axis

y = x^2 +8x +15

let y =0

0 = x^2 +8x +15

0 = ( x + 5) (x+3)

o = x+5 or 0 = x+3

-5 = x or x = - 3

x intercept

(-5;0)

(-3 ;0)

axis of symmetry : where you will cut the graph into two half

x = - b/2a

x = - 8/2(1)

x = - 8/2

x = - 4

Domain

XER

Range

y > -1

Answer:

75% of the specials served were salmon fillets

Step-by-step explanation:

We have that:

15 + 5 = 20 specials were served.

Of those, 5 were salmon fillets.

What percentage of the specials served were salmon fillets?

15*100%/20 = 75%

75% of the specials served were salmon fillets

Answer:

15 weeks

Step-by-step explanation:

Let the number of weeks = x.

At the end of x weeks,

Jeremy has 120 + 14x,

and Katie has 180 + 10x

We want to know when their amounts are equal.

120 + 14x = 180 + 10x

4x = 60

x = 15

Answer: 15 weeks

Answer:

15 weeks

Step-by-step explanation:

One is given the following information:

Jeremy

Katie

Let the parameter (x) represent the number of weeks passed. Parameter (y) is the amount in the account, (S) represents the amount in the account to start with and (A) represents the amount added to the account every week. One can use the following general equation to represent the situation:

y = S + Ax

Substitute the given information into the equation for each person:

Jeremy: y = 120 + 14x

Katie: y = 180 + 10x

One is asked to find the point in time when the two account have the same amount of money. Therefore, set the two equations equal to each other and solve:

y = 120 + 14x = 180 + 10x

Inverse operations,

120 + 14x = 180 + 10x

4x = 60

x = 15

15 weeks will pass before Katie and Jeremy have the same amount of money in their accounts.

Answer:

A' (-3,12)

B' (9,6)

C' (-6,-6)

Answered by GAUTHMATH

Answer:

[tex]\left(\dfrac{8}{7} , \ \dfrac{17}{35} \right)[/tex]

Step-by-step explanation:

The given system of equations is presented as follows;

[tex]\dfrac{s}{2} + 5 \cdot t = 3[/tex]

3·t - 6·s = 9

Making t the subject of both equations, gives;

In the first equation; t = (3 - s/2)/5

In the second equation; t = (9 + 6·s)/3

Equating both values of t to find the the values that satisfies both equations, gives;

(3 - s/2)/5 = (9 + 6·s)/3

3 × (3 - s/2) = 5 × (9 + 6·s)

9 - (3/2)·s = 45 + 30·s

45 - 9 = (30 + (3/2))·s

36 = (63/2)·s

s = 36/(63/2) = 8/7

t = (3 - s/2)/5

∴ t = (3 - (8/7)/2)/5 = 17/35

Therefore, the ordered pair is (8/7, 17/35)

Answer:

66%

Step-by-step explanation:

[tex]-10x\:+\:\left(20\cdot \left(1-x\right)\right)=\:0[/tex]

x = [tex]\frac{2}{3}[/tex] = .666 = 66%

Answer:

x = -2

[tex](2/3)^{(x-1)} = \frac{27}{8}[/tex]  

Step-by-step explanation:

you have to use logs here

[tex]ln((2/3)^{x} ) =ln(27/8)\\x ln((2/3) ) =ln(275/8)\\\\[/tex]

x-1  =ln(27/8)/ ln(2/3)

x -1  = -3

x = -2

Answer: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

tangent of ∠PLM = [tex]\frac{opposite}{adjacent} =\frac{4}{3}[/tex]

Answer:

PLM=4/3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The value of x is 3 if the volume of the triangular prism is 54 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that  volume of the triangular prism is 54 cubic units.

We have to find the value of x

The volume of the prism with triangular base is 54 unit³.

The base is a triangle with,

base = 4 units

height = x units

height of the prism = 3x

V= 6x²

54= 6x²

Divide both sides by 6

x² = 9

x=3

Hence, the value of x is 3 if the volume of the triangular prism is 54 cubic units.

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Answer:

See below & pic.

Step-by-step explanation:

Start by plotting the given point. Then use the slope to find two more points. From the given point go up 2 and right 4. GO back to the given point. Go down 2 and left 4. Now you have 3 points. Connect them with a line.

Answer:

Step-by-step explanation:

You are given most of the equation that you need to solve. To find the number of years it will take to have 2000, sub in 2000 for A and solve:

[tex]2000=1000(1.0512)^t[/tex] and begin by dividing away the 1000 on both sides to get

[tex]2=(1.0512)^t[/tex] now we have to take the natural log of both sides:

[tex]ln(2)=ln(1.0512)^t[/tex]. Taking the natural log allows us to bring the t down out front:

ln(2) = t ln(1.0512) and now divide both sides by ln(1.0512):

[tex]\frac{ln(2)}{ln(1.0512)}=t[/tex] and do this on your calculator to get

t = 13.9 years

Answer:

T = 13.9

Step-by-step explanation:

A = 1,000 · 1.0512^T

Let A = 2000

2000 = 1,000 · 1.0512^T

Divide each side by 1000

2000/1000 =  1,000/1000 · 1.0512^T

2 =  1.0512^T

Take the log of each side

log 2 =  log 1.0512^T

We know log a^b = b log a

log 2 =  T log 1.0512

Divide each side by log 1.0512

log 2 / log 1.0512 = T

T=13.88172

Rounding to the nearest tenth

T = 13.9