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Vinvika [58]
3 years ago
6

Matinee movie tickets cost 5$ each for adults and 2$ each for kids. For one showing, 460 tickets where sold, and 1880$ was colle

cted. How many of each type were sold.
Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0
320 adult tickets and 140 kids tickets 
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For which values of the parameter B the following system admits a unique solution [ 1 b 1-b 2 2 0 2–2B 4 0] [x y z] = [1 2 0]
photoshop1234 [79]

Answer: β ≠ ±1

Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,

det \left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right] ≠ 0

Determinant of a 3x3 matrix is calculated by:

det \left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right]

8(1-\beta)-[2(2-2\beta)(1-\beta)]

8-8\beta-4+8\beta-4\beta^{2}

-4\beta^{2}+4\neq 0

\beta^{2}\neq 1

\beta \neq \sqrt{1}

β ≠ ±1

For the system to have only one solution, β ≠ 1 or β ≠ -1.

7 0
3 years ago
Which equation is equivalent to
Aleksandr [31]

Answer:

(4x^2 +9)(4x^2-9) =0

Step-by-step explanation:

16x^4 - 18 = 0

Rewriting

(4x^2)^2 - 9^2 =0

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(4x^2 -9)(4x^2+9) =0

5 0
3 years ago
Read 2 more answers
Which expression is equivalent to 2√98⋅√2?<br> 4√98<br><br> 784<br><br> 14√2<br><br> 28
zhannawk [14.2K]
I am not 100% sure this is right but I believe its 28:)
3 0
3 years ago
Read 2 more answers
The fuel cost per hour for running a ship is approximately one half the cube of the speed (measured in knots) plus additional fi
andrezito [222]

Answer:

6 knots

Step-by-step explanation:

Let the speed be v knots

then time taken to cover 500 M = 500 / v hrs

fuel consumption /hr = 216 + 0.5v^3

let F be the fuel consumption for trip

= [500/v][216 + 0.5v^3]

= 500[216/v + 0.5v^2]

dF/dv = 500[ - 216/v^2 + v]

d^2F/d^2v = 500[432/v^3 + 1] , i.e. +ve

so setting dF/dv will give a minima

500[ -216/v^2 + v] = 0

or v = 216/v^2

or v^3 = 216

solving, we get v = [216]^(1/3) = 6 knots

7 0
3 years ago
Evaluate 2/5 log 32 + (log 9 )/log 3) Please Show Working?
sattari [20]

Simplify the expression

exact form:

log(4)+log(9)/log(3)

Decimal Form:

2.60205999 . . .

Hope this helps! :)

~Zane

6 0
3 years ago
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