Bill's school is selling tickets to a spring musical. On the first day of ticket sales the school sold
10 senior citizen tickets and 8 child tickets for a total of $170. The school took in $185 on the
second day by selling 10 senior citizen tickets and 11 child tickets. Find the price of a senior
citizen ticket and the price of a child ticket.
A) senior citizen ticket: $13, child ticket: $5 B) senior citizen ticket: $12, child ticket: $7
C) senior citizen ticket: $5, child ticket: $13 D) senior citizen ticket: $21, child ticket: $6

Answer:

2

Step-by-step explanation:

In order to make the equation undefined, you should make the denominator 0. Remember that dividing anything by 0 will become undefined.

[tex]2x-4=0\\\frac{2x=4}{2} \\x=2[/tex]

Answer:

[tex]\boxed{x = 2}[/tex]

Step-by-step explanation:

A rational expression is undefined when Denominator = 0

Here Denominator = 2x-4

So,

=> 2x - 4 = 0

Adding 4 to both sides

=> 2x = 4

Dividing both sides by 2

=> x = 2

Step-by-step explanation:

c^2( c^2-10c+25)

=c^4 - 10c^3 + 25c^2

Answer:

9 = k :)

Step-by-step explanation:

1. distribute 3 to the -1/4 k and to the 3 and get -3/4 k + 9 = 1/4 k

2. add 3/4 k to both sides and get 9 = k

Answer:

20

Step-by-step explanation:

20 + (75% × 20) =

20 + 75% × 20 =

(1 + 75%) × 20 =

(100% + 75%) × 20 =

175% × 20 =

175 ÷ 100 × 20 =

175 × 20 ÷ 100 =

3,500 ÷ 100 =

35;

Answer:

$1.935

Step-by-step explanation:

As the store is offering a 15% discount, you have to calculate the 15% of the price of the game app to find the amount of the discount:

Price of the game app= 12.90

12.90*15%=1.935

According to this, the answer is that the amount of the discount if you buy the game app during the sale is $1.935 and you would have to pay: 12.90-1.935= $10.965.

Answer:

Option (A).

Step-by-step explanation:

[tex]8\frac{4}{5}[/tex] is a mixed fraction and can be written as,

[tex]8\frac{4}{5}=8+\frac{4}{5}[/tex] [Combination of a whole number and a fraction]

When we multiply this mixed fraction by 7,

[tex]7\times 8\frac{4}{5}=7\times (8+\frac{4}{5})[/tex]

          [tex]=(7\times 8)+(7\times \frac{4}{5})[/tex] [Distributive property → a(b + c) = a×b + a×c]

          [tex]=56+\frac{28}{5}[/tex]

          [tex]=56+5\frac{3}{5}[/tex]

          [tex]=56+5+\frac{3}{5}[/tex]

          [tex]=61+\frac{3}{5}[/tex]

          [tex]=61\frac{3}{5}[/tex]

Therefore, [tex]7\times 8\frac{4}{5}=61\frac{3}{5}[/tex] will be the answer.

Option (A) will be the correct option.

Answer:  A) 1       B) [tex]\sqrt5[/tex]

Step-by-step explanation:

[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]

Answer:

Step-by-step explanation:

–3(6 – 2x) ≥ 4x + 12

Expand the terms in the bracket

We have

- 18 + 6x ≥ 4x + 12

Group like terms

that's

6x - 4x ≥ 12 + 18

2x ≥ 30

Divide both sides by 2

x ≥ 15

Hope this helps you

Step-by-step explanation:

no worries

if u multiply by a negative number the sign changes

so it can -18 + 6x <= 4x + 12

take x to one side and others to other side

6x - 4x <= 18 + 12

2x <= 30

x<= 15

so solutions can be from ....-2,-1,0,1,2,3....

Answer:

ADB and ADC

Step-by-step explanation:

SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.

Answer:

ABD and ECD

Step-by-step explanation:

EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.

Answer:

[tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex] will be the answer.

Step-by-step explanation:

The given expression is,

[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]

By solving this expression,

[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]

= [tex]\frac{3n(n-4)}{(n+3)(n-4)}+\frac{5(n+3)}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]

= [tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]

Therefore, fraction given in option (2) will be the answer.

Answer:

AAS

Step-by-step explanation:

Δwzy=Δwzv

to prove the equality:

1- wz is a common side

angle:  wzv=wzy=90 degrees ( height of triangle)

angle v= angle y

Since WZ bisects W, it's good  to say that vwz and zwy

prove one side is equal and two angles

so ASA or AAS is the answer

Answer:

  -0.0062 and 27.5

Step-by-step explanation:

You can write the equation of the line using the 2-point form:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

The given values of the variables are ...

  (h, T) = (10000, -34.5) and (15000, -65.5)

Putting these into the formula, we have ...

  T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)

  T = -31/5000(h -10000) -34.5

  T = -0.0062h +62 -34.5

  T = -0.0062h +27.5

The appropriate choice is ...

  -0.0062 and 27.5

Answer: [tex]-50a^{11}b^{9}[/tex]

Step-by-step explanation:

Any negative exponent can be moved to the other side of the fraction as a positive exponent.[tex]\frac{1}{x^{-3}}=x^3\\ \frac{x^{-3}}{1}=\frac{1}{x^3}[/tex]

Thus, simply move the negative exponents from the bottom into the numerator to get. -10a^2*b^4*5a^9*b^5.  Then, use the exponent rule to get [tex]-50a^{11}b^{9}[/tex]

Hope it helps <3

Answer:

  57°

Step-by-step explanation:

There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:

  m∠K = 90° -m∠J = 90° -33°

  m∠K = 57°

Answer:

y = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 5 when x = 7, then

5 = [tex]\frac{k}{7}[/tex] ( multiply both sides by 7 )

35 = k

y = [tex]\frac{35}{x}[/tex] ← equation of variation

When x = 70, then

y = [tex]\frac{35}{70}[/tex] = [tex]\frac{1}{2}[/tex]

S - a randomly chosen pregnancy result in a successful delivery

C - a randomly chosen pregnancy ending in a C section

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

Answer:

x = 0

Step-by-step explanation:

i) x - 11 + 1 < 15

x - 10 < 15

x < 10 + 15

x < 25

ii) x - 11 + 1 > 15

x - 10 > 15

x > 25

Therefore to compare (i) and (ii)

25 < x < 25

In any case, x = 0

Answer:

11

Step-by-step explanation:

Prime factor: 43659 = 3*3*3*3*7*7*11

Pair: √43659 = √3²×3²×7²×11

11 is odd therefore 11 must be divided by 43659

Answer:

125

Step-by-step explanation:

1 x 1  x 1 = 1

5 x 5 x 5 = 125

125 / 1 = 125

125 is your answer

Answer:

Scale 1: 1 centimeter = 3 meters.

Scale 2: 1 centimeters = 4 meters.

Step-by-step explanation:

your answer should be A

15*3=45

15*4=60

Answer:

A.)Scale 1: 45 m; Scale 2: 60 m

Step-by-step explanation:

bcuz......uhhhhhhh, ummmmmm:/

Answer:

(1.5,-3) and (4.5,-3)

Step-by-step explanation:

Answer:

cos C

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

Answer:

Step-by-step explanation:

[tex]10 + {(2 \times 3)}^{2} \div 4 \times {( \frac{1}{2}) }^{3} [/tex]

To raise a product to a power, raise each factor to that power

[tex] = 10 + 4 \times 9 \div 4 \times {( \frac{1}{2} )}^{3} [/tex]

To raise a fraction to a power, raise the numerator and denominator to that power

[tex] = 10 + 4 \times 9 \div 4 \times \frac{1}{8} [/tex]

Any expression divided by itself equals 1

[tex] = 10 + 1 \times 9 \times \frac{1}{8} [/tex]

Any expression multiplied by 1 remains the same

[tex] = 10 + 9 \times \frac{1}{8} [/tex]

Calculate the product

[tex] = 10 + \frac{9}{8} [/tex]

Write all numerators above the common denominator

[tex] = \frac{80 + 9}{8} [/tex]

Add the numbers

[tex] = \frac{89}{8} [/tex]

Divide

[tex] = 11.125[/tex]

Hope this helps..

Best regards!!

Answer:

11 1/8

Step-by-step explanation:

Okay so I messed up big time. So I had to edit this! I am really sorry if you read mine before. I fixed mine. So this is the right answer. Sorry!

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Answer:

The correct answer is D because we proved that the triangles ΔDBE and ΔADF are congruent so that means that DE = segment A F because of CPCTC.

Step-by-step explanation:

Answer: 24 units

Step-by-step explanation:

MO, NO and LO are radii.

If MO = 13, THEN LO = NO = 13

IF NO = 13 and NP = 8, THEREFORE,

PO = NO - NP

PO = 13 - 8 = 5

USING PYTHAGORAS, WE CAN FIND MP:

MP = Sqrt(MO^2 - PO^2)

MP = sqrt(13^2 - 5^2)

MP = sqrt(169 - 25)

MP = sqrt(144)

MP = 12 units

P is the midpoint of Segment ML,

THEREFORE,

MP = PL

ML = MP + PL

ML = 12 + 12

ML = 24 units

Answer: 24

Step-by-step explanation:

edge

The solution is where the two red lines cross. This is the point (3,-4)

If you knew the equation of each red line, you can plug (x,y) = (3,-4) into each equation. You should find the two equations lead to true statements.

Answer:

Step-by-step explanation:

If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.

If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.

Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].

So the area of the rectangle:  [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]

The area of the kite:

                                  [tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]

No matter the height of the triangles, so no matter the location of the EG

Answer:

Sum of interior angles of 12 sided object = 1800°

Step-by-step explanation:

Formula to calculate the sum of interior angles of a polygon is,

Sum of the interior angles of a polygon = (n - 2) × 180°

Where n = number of sides of the polygon.

If number of sides of a polygon are 12,

For n = 12,

Sum of interior angles = (12 - 2) × 180°

                                     = 10 × 180°

                                     = 1800°

Therefore, sum of interior angles of a 12 sided polygon will be 1800°.

Answer:

im pretty sure its the third one

Step-by-step explanation:

i guessed but it might be right