A circle C has center at the origin and radius 5 . Another circle K has a diameter with one end at the origin and the other end at the point (0,15) . The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,θ) be the polar coordinates of P , chosen so that r is positive and 0≤θ≤2 . Find r and θ .

By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.

In this question we know the lengths of two sides of the right triangle. By Pythagorean theorem we get the length of the missing side:

a² + b² = c²

b² = c² - a²

b = √(c² - a²)

b = √(37² - 12²)

b = 35

By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.

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Answer:

3

Step-by-step explanation:

Numbers of beads used in making triangles:

3, 6, 10, 15, 21, 28, 36, ...

We need to pick a few numbers from those above that add to 41.

3 + 10 + 28 = 41

Answer: 3 triangles

Answer:

The answer to your question is C.n ≥ 7

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

D

Step-by-step explanation:

Sequence A is increasing using + 6

Sequence B is decreasing using - 6

Sequence C is decreasing using - 6

Sequence D is increasing using x 3

D is the odd one out

(In c) * 1/c = 0.0604 is the change in the function.

According to the statement

y = (In x)^2 on interval [1,4]

By mean value theorem

we use this formula to find a change f '(c)= [f(b) - f(a)] / (b - a)

Let it f(y) = (In x)^2

Now, f(4) = (In 4)^2

f(4) = (0.602)^2

f(4) = 0.3624

and

f(1) = (In 1)^2

f(1) = (0)^2

f(1) = 0

Now, f'(c) = 2 (In c) * 1/c

Substitute all these values in a formula

2 (In c) * 1/c = 0.3624 - 0 / 4 - 1

2 (In c) * 1/c = 0.3624/3

2 (In c) * 1/c = 0.1208

(In c) * 1/c = 0.0604

So, (In c) * 1/c = 0.0604 is the change in the function.

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The set of all three-digit binary numbers as required in the task content includes; 100,101,110,111.

A binary number by definition is one which is made of a combination of numbers 0 and 1.

On this note, it follows that the three digits binary numbers in discuss include; 100,101,110,111.

Binary numbers are most often used in computer programs to represent data.

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The sum of the first five terms is 11/2

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

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

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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The inverse statement is:

¬q ⇒ ¬p

Which is true.

Here we have the biconditional statement:

A number is negative if and only if it is less than zero.

Where:

So we can write the statement as:

p ⇔ q

The inverse statement is:

if not q, then not p.

or

¬q ⇒ ¬p

Replacing p and q, we have:

"if a number is not less than zero, then the number is not negative".

This is true, if the number is not less than zero, then the number is 0 or larger, so that number is not negative.

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Answer:

D.

∼p↔∼q

and

G.

The inverse of the statement is true.

Step-by-step explanation:

The slope of restaurant B is twice that of restaurant A

The tables of values are given as

           X(Bill)     Y(Tip)                          X(Bill)        Y(Tip)

Rest A     10           1                  Rest B      25            5    

Rest A     20          2                 Rest B      50            10

Rest A     30          3                 Rest B      75             15

The slopes are calculated using

Slope = (y2 - y1)/(x2 - x1)

Using the table of values, we have:

Rest A = (2 - 1)/(20 - 10)

Rest A = 0.1

Rest B = (10 - 5)/(50 - 25)

Rest B = 0.2

By comparing the slopes, we have:

Rest B = 2 * Rest A

This implies that the slope of restaurant B is twice that of restaurant A

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answer: 200, 2 hundred, two hundred

The missing coordinates are listed below:

According to the polar coordinate system, a vector in standard position is defined by this parametric formula:

(x, y) = (r · cos t, r · sin t), where t is in radians.

If we assume that r = 1, then we proceed to determine the location of the seven points remaining:

(x₁, y₁) = (cos π/2, sin π/2)

(x₁, y₁) = (0, 1)

(x₂, y₂) = (cos 3π/4, sin 3π/4)

(x₂, y₂) = (- √2 /2, √2 /2)

(x₃, y₃) = (cos π, sin π)

(x₃, y₃) = (- 1, 0)

(x₄, y₄) = (cos 5π/4, sin 5π/4)

(x₄, y₄) = (- √2 /2, - √2 /2)

(x₅, y₅) = (cos 3π/2, sin 3π/2)

(x₅, y₅) = (0, - 1)

(x₆, y₆) = (cos 7π/4, sin 7π/4)

(x₆, y₆) = (- √2 /2, √2 /2)

(x₇, y₇) = (cos 2π, sin 2π)

(x₇, y₇) = (1, 0)

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Using proportions, they must win 22 games to maintain to the ratio of wins to losses.

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

Considering the next 28 games, we have that:

To keep the same proportion, we have that:

[tex]\frac{33}{42} = \frac{33 + x}{70}[/tex]

Applying cross multiplication:

42(33 + x) = 33 x 70

Simplifying by 14:

3(33 + x) = 33 x 5

3x = 33 x 5 - 33 x 3

3x = 33 x 2

3x = 66

x = 66/3

x = 22.

They must win 22 games to maintain to the ratio of wins to losses.

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The equation is in direct variation and have constant of variation is 2.

According to the statement

we have given equation is 3x - 6y = 0 and find that the equation is direct variation of not.

Direct variation is the mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.

So, to find the direct variation equate the given equation equal to zero and solve it.

So, 3x - 6y = 0

3x=6y

or

x/ y=2 or x=2⋅y

here x is directly proportional to the y by 2 times.

∴x∝y

So, this equation in direct variations and constant of variation is 2.

From above this is clear that the equation is in direct variation and have constant of variation is 2.

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Answer:

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

Step-by-step explanation:

=18÷[7+2{7+2(7-6)}+2]

=18÷[7+2{7+2×1}+2]

=18÷[7+2×9+2]

=18÷[7+18+2]

=18÷27

=[tex] \frac{18}{27} [/tex]

=9 two is 18 and 9 three is 27

So,

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

Answer:

slope intercept form: y = mx + b

6x - 4y = 24

4y = 6x - 24

y = 3/2x - 6

slope: 3/2

y intercept: - 6

Answer:

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Step-by-step explanation:

6x-4y = 24

The slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

We need to solve the equation for y

6x-4y =24

Subtract 6x from each side

6x-4y-6x =-6x+24

-4y = -6x+24

Divide each side by -4

-4y/-4 = -6x/-4  + 24/-4

y = 3/2 x -6

The slope is 3/2 and the y intercept is -6

Answer:
[tex]\pi[/tex][tex]14^{2}[/tex] or [tex]\pi 196\\[/tex]

Step-by-step explanation:

  The circle V has the radius of 14 (r=14)
The formula of area is (A=[tex]\pi r^{2}[/tex])

So we insert the value of (r=14)
[tex]A=\pi 14^2[/tex]
[tex]A=\pi 196[/tex]
And that's the answer, The exact value is 615.752...

Answer: 196 pi

Step-by-step explanation:

The maximum amount of water that can be used by each house on a daily basis is 100 liters.

4,500 = 500 + 40x

4,500 - 500 = 40x

4,000 = 40x

x = 4,000 / 40

x = 100 liters

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Answer: SAS

Step-by-step explanation:

There are two pairs of congruent angles and the pair of angles formed by these sides are congruent.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

In the given figure, one angle and two adjacent sides of Triangle AFB is equal to corresponding angle and sides of the Triangle DFC.

So, we can conclude that,

Triangle AFB and Triangle DFC are congruent by :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: $4600

Step-by-step explanation:

The value of x is 78

Given:

[tex]\frac{m}{FCD}=x+48\\\\ \frac{m}{BCD} =x+17\\\\\frac{m}{BCD} =95^0[/tex]

From the given equations, two of them are exactly equivalent

The equivalent equations are compared below

x  +  17   =  95

x  =  95  -  17

x  =  78

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True

Personally, when I see the line underneath the equality sign, I know I've got to draw a dotted line. That's how I remember the difference between drawing a solid / dotted line.

Hope this helps!

Step-by-step explanation:

all the details are in the attachment; the solution are is filled with purple color.

Answer:

7.5. hours

Step-by-step explanation:

Trust me

12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that it took 8 hours for 5 men to build a storeroom. The time required by 12 men to do the same work will be calculated as below:-

Time taken by one man  = 8 x 5 = 40 hours

Time is taken by 12 men will be = 40 / 12 = 3.34 hours

Therefore, 12 men will take 3.34 hours to build a similar storeroom if they work at the same rate.

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Answer:

You will need 187 80 pounds bags of concrete.

Step-by-step explanation:

12x14x(2/3) x 0.6 = 186.666 or 187

Answer:

10 hours

Step-by-step explanation:

The rate x time of the first day + the rate x time of the second day equal the distance of 180 miles.

Let t = time

10t + 8t = 180

18t = 180

t = 10

Answer:

the product is 1.32057606543E32

Answer:

x = 10

Step-by-step explanation:

∆RSE ~ ∆FGE

SE/ GE = RE/ FE

45/ 12x-3 = 55/ 143

3/ 3(4x - 1) = 11/ 143

11(4x-1) = 429

44x-11 = 429

44x = 440

x =10