In the diagram, AP is a tangent and PBC is a secant in a circle O. If PC = 12 and BC = 9, what is AP?

Answer:

a. (A + S = 200), (8S + 10A = 1760)

b. The school play sold 80 adult tickets, and 120 student tickets.

c. 400$ more would have been collected if the school charged 15$ per ticket instead of 10$

Step-by-step explanation:

a. To begin with, we can refer to S as student tickets, and A as adult tickets. We know that 200 tickets were sold, so we can say that (A + S = 200). We can also say that (8S + 10A = 1760).

b. We can twist the first system of equations and put one variable on the other side. It'll be (A = 200 - S). From there, we will substitute A in the second system of equations. The equation will be

(8S + 10(200 - S) = 1760)

Then you solve for S

(8S + 2000 - 10S = 1760)

-2S = -240

S = 120

Substitute for S in the first system of equations

A = 200 - 120

A = 80

or the second

8(120) + 10A = 1760

960 + 10A = 1760

10A = 800

A = 80

This means that the school play sold 80 adult tickets, and 120 student tickets.

c. (8S + 15A = X)

8(120) + 15(80) = X

X = 2160

2160 - 1760 = 400

400$ more would have been collected if the school charged 15$ per ticket instead of 10$

Answer:

9x

Step-by-step explanation:

x + 3x + 5x = 4x + 5x = 9x

Answer:

the required number is 12

Answer:

Step-by-step explanation:

One third of number is 8 less than the three times of the number

The number is x, then:

Answer:

[tex] x = 4 \sqrt{3} [/tex]

Step-by-step explanation:

By geometric mean theorem and Pythagoras theorem:

[tex] {x}^{2} = { (\sqrt{8 \times 4} )}^{2} + {4}^{2} \\ \\ {x}^{2} = { (\sqrt{32} )}^{2} + {4}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = 4 \sqrt{3} [/tex]

Answer: cage  I

Step-by-step explanation:

Given

43 gm of copper and 7 gram of other metal

Another cage has 83 gram of copper and 17 gm of other metals

Here, the percentage of copper is

For the first case

[tex]\Rightarrow \dfrac{43}{43+7}\times 100=86\%[/tex]

For the second case

[tex]\Rightarrow \dfrac{83}{83+17}\times 100=83\%[/tex]

So, the cage-I has more percentage of copper

Answer:

4up on 5 was missing ok madam

Answer:

240 km.

Step-by-step explanation:

The car travels 200km per hour. so multiply it by 1.2 and you get 240km.

Answer:

1.{2,8}

Step-by-step explanation:

that's my answer

Answer :

1. { 2, 8 }

x² - 10x + 16 = 0

x² - 2x - 8x + 16 = 0

x ( x - 2 ) - 8 ( x - 2 ) = 0

( x - 2 ) ( x - 8 ) = 0

x - 2 = 0

x = 2

x - 8 = 0

x = 8

Therefore,

the solution to the equation x² - 10x + 16 = 0 is { 2, 8 }.

Step-by-step explanation:

Line is passing through the point A (-3, 5) and the point B (0, -16)

a) Slope (m) = (-16 - 5)/(0+3) = - 21/3 = - 7

b) y - intercept (b) = - 16

c) Equation of line

y = mx + b

y = - 7x + (-16)

y = - 7x - 16

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

Explanation:

mpg = miles per gallon

To calculate the mpg, you divide the number of miles traveled over the amount of gallons used.

In Caroline's case, she traveled 410.7 miles and used up 22.2 gallons. Her car's mpg rating is 410.7/22.2 = 18.5 mpg which means that one gallon of gas will allow her to drive 18.5 miles.

Answer: non metals F and H, fluorine has high electronegativity and tend to gain one electron. Hydrogen form she compounds with non-metals and metals.

Metals Cs and K, lose easily one outer electron. Electron is far away from nucleus and atom donates it easily.

The periodic table is composed of metals and nonmetals.

The right wing of the period table contains mostly of nonmetals. However, there are a few metals in the right wing of the periodic table. The periodic table is largely made up of metals and nonmetals.

The two most active metals in the right wing of the periodic table are bismuth and lead while the two most active nonmetals in the right wing of the periodic table are fluorine and chlorine.

Learn more: https://brainly.com/question/25114219?

Answer:

A = 65, B = 75

Step-by-step explanation:

x + x + 10 + 40 = 180

2x + 50 = 180

2x= 130

x = 65

Answer:

∠A = 65°

∠B = 75°

Step-by-step explanation:

The sum of all the angles in a triangle is 180°, so we need to add all of the angles and make them equal to 180, then solve for "x".

x + x + 10 + 40 = 180

2x + 50 = 180

2x = 130

x = 65

Now, we replace "x" with 65 to get ∠A and ∠B.

∠A = x = 65°

∠B = x + 10 = 65 + 10 = 75°

Answer:

$1.50 2/3

Step-by-step explanation:

I hope this helps :)

Answer:

600

Step-by-step explanation:

V = l * w * h

V = 10 * 3 * 20

V = 600

Answer:

V = 600 cm³

Step-by-step explanation:

The volume (V) of a cuboid is calculated as

V = lbh ( l is length, b is breadth, h is height )

Here l = 10, b = 3 , h = 20 , then

V = 10 × 3 × 20 = 600 cm³

Answer:1  0.05806644 2 64.3818067 m2 3 10.8696557 m2 4  80.2682266 m2 0.13935456 m2 and 15.7935168 m2

Step-by-step explanation:

Answer:  465

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Variables mean multiplying and that stonleigh when that multiplies and adds And it will never be even number because it is at 99 sense meaning $50 is greater than Whatever you multiply $3.99 by

Answer:

x = 14

∠ABD = 66

∠DBC = 24

Step-by-step explanation:

The sum of the two angles is 90 degrees, so:

3 (x + 8) + 2x - 4 = 90      (distribute 3)

3x + 24 + 2x - 4 = 90       (simplify)

5x + 20 = 90            (subtract 20 from both sides)

5x = 70            (divide both sides by 5)

x = 14

∠ABD = 3 (x + 8)       (plug in 14)

∠ABD = 3 (14 + 8)      simplify

∠ABD = 3 (22)

∠ABD = 66

∠DBC = 2x - 4       (plug in 14)

∠DBC = 2(14) - 4     (simplify)

∠DBC = 28 - 4

∠DBC = 24

To check, 66+24=90.

Answer:

The answer I got was

3(-26+8) = -54

2(-26)-4 = -56

Step-by-step explanation:

3(x+8)=2x−4

(3)(x)+(3)(8)=2x+−4(Distribute)

3x+24=2x+−4

3x+24=2x−4

Then subtract 2x from each side

Once then you have X substitute that number with X and you should get your answer.

So do 3(-26+8) and then 2(-26)-4 which then

3(-26+8)=

2(-26)-4 =

Answer:

They are parallel because they hold a same gradient which is 3/5

Answer:

option 4= 12/13

Step-by-step explanation:

let us supooae <c is thetha

sin thitha = oppotise side/hyptotenuse

<C= AB/AC

<C=12/13

Answer:

7(9+n)=8

Step-by-step explanation:

I hope this is right :)))

Answer: the bottom is A then C

Step-by-step explanation:

Answer:

Following are the responses to the give question:

Step-by-step explanation:

The [tex]f(x) = x^2 + 4[/tex] model is developed in the interval [tex](-2, 2)[/tex] total equal in a between such a range[tex]= 5[/tex].

Its right endpoint of every rectangle is separated onto n equal parts by the height [tex]= \frac{5}{n}.[/tex]

Height of endpoint [tex]= \frac{5}{n}[/tex] of the k rectangles therefore, the height of the kth rectangle = First rectangle height + K rectangle height

[tex]= -2 +k \times \frac{5}{n}\\\\[/tex]

Answer:

area = 277 units²

Step-by-step explanation:

area = (25 x 5) + (8 x 13) + (8 x 6) = 277 units²

Answer:

Sara bought 5 6 penny nails and 3 10 penny nails

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

p³ - 216q³ ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

p³ - 216q³

= p³ - (6q)³

= (p - 6q)(p² + 6pq + 36q²) → C

Answer:

C. (p - 6q)(p² + 6pq + 36q²)

Step-by-step explanation:

Equation at the end of step 1

[tex](p^{3} ) - (2^{3} 3^{3} q^{3} )[/tex]

Trying to factor as a Difference of Cubes:

Factoring:  p^3 - 216q^3

Theory: A difference of two perfect cubes, a^3 - b^3 can be factored into

(a-b) • (a^2 +ab +b^2)

Proof: [tex](a-b)(a^{2} +ab+b^{2} ) =[/tex]

[tex]a^{3} + a^{2} b+ab^{2} -ba^{2} -b^{2} a-b^{3} =[/tex]

[tex]a^{3} +(a^{2} b-ba^{2} )+(ab^{2} -b^{2} a)-b^{3} =[/tex]

[tex]a^{3} +0+0-b^{3} =[/tex]

[tex]a^{3} -b^{3}[/tex]

Check:  216 is the cube of 6

Check:  p^3 is the cube of p^1

Check:  q^3 is the cube of q^1

Factorization is:

[tex](p-6q)(p^{2} + 6pq+36q^{2} )[/tex]

Trying to factor a multi variable polynomial :

Factoring: p^2 + 6pq + 36q^2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final Result:

(p - 6q)(p² + 6pq + 36q²)

Answer:

X=-4, y=-5

Step-by-step explanation:

Y=2X+3

y=-x-9

substitute by inserting y value of 2nd equation (-x-9) into y value of 1st equation:

-x-9=2x+3

-x-9+9=2x+3+9

-x=2x+12

-3x=12

x=-4

solve for y by inserting x value (2) into either equation

y=2x+3

y=2(-4)+3

y=-8+3

y=-5

check answer by inserting x and y into either equation to make sure they equal:

y=2x+3

-5=2(-4)+3

-5=-8+3

-5=-5

or

y=-x-9

-5=-(-4)-9

-5=-5