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3 years ago

5. The cost of movie tickets at the

Mathematics

2 answers:

vlada-n [284]3 years ago

8 0

Answer:

its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4

zhannawk [14.2K]3 years ago

3 0

B because more adults and children played on saturday.

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Analyze the diagram below and complete the instructions that follow.

Trava [24]

Law of Cosines says

$b^2 = a^2 + c^2 - 2 ac \cos B$

$2 a c \cos B = a^2 + c^2 - b^2$

$\cos B = \dfrac{a^2 + c^2 - b^2}{2 a c}$

$\cos B = \dfrac{16^2 + 16^2 - 11^2}{2(16)(16)} = \dfrac{ 391}{512}$

$B = \arccos \dfrac{ 391}{512} \approx 40.2 ^\circ$

Choice C

5 0

3 years ago

Bernard designs motorized bicycles at Smart Gear Technologies. His total earnings are

olganol [36]

Answer: $43146

Step-by-step explanation:

So his total earning is $54,000. He has to pay $201 for every $1,000 he earns. So 54,000/1,000= 54. So now he has to pay 54*201=10854, 54000-10854=43146. His net income for this year is $43146.

8 0

3 years ago

Simplified form of the expression (x^3+3x^2+6)-(9x^2-5x+7)

JulijaS [17]

$(x^3 + 3x^2 + 6) - (9x^2 - 5x + 7)\\\\x^3 + 3x^2 + 6 - 9x^2 + 5x - 7\\x^3 - 6x^2 + 5x -1$

8 0

3 years ago

Prove the function f: R- {1} to R- {1} defined by f(x) = ((x+1)/(x-1))^3 is bijective.

Eduardwww [97]

Answer:

See explaination

Step-by-step explanation:

given f:R-\left \{ 1 \right \}\rightarrow R-\left \{ 1 \right \} defined by f(x)=\left ( \frac{x+1}{x-1} \right )^{3}

let f(x)=f(y)

\left ( \frac{x+1}{x-1} \right )^{3}=\left ( \frac{y+1}{y-1} \right )^{3}

taking cube roots on both sides , we get

\frac{x+1}{x-1} = \frac{y+1}{y-1}

\Rightarrow (x+1)(y-1)=(x-1)(y+1)

\Rightarrow xy-x+y-1=xy+x-y-1

\Rightarrow -x+y=x-y

\Rightarrow x+x=y+y

\Rightarrow 2x=2y

\Rightarrow x=y

Hence f is one - one

let y\in R, such that f(x)=\left ( \frac{x+1}{x-1} \right )^{3}=y

\Rightarrow \frac{x+1}{x-1} =\sqrt[3]{y}

\Rightarrow x+1=\sqrt[3]{y}\left ( x-1 \right )

\Rightarrow x+1=\sqrt[3]{y} x- \sqrt[3]{y}

\Rightarrow \sqrt[3]{y} x-x=1+ \sqrt[3]{y}

\Rightarrow x\left ( \sqrt[3]{y} -1 \right ) =1+ \sqrt[3]{y}

\Rightarrow x=\frac{\sqrt[3]{y}+1}{\sqrt[3]{y}-1}

for every y\in R-\left \{ 1 \right \}\exists x\in R-\left \{ 1 \right \} such that x=\frac{\sqrt[3]{y}+1}{\sqrt[3]{y}-1}

Hence f is onto

since f is both one -one and onto so it is a bijective

8 0

3 years ago

Find the value of b. Then find the angle measures of the pentagon.

melamori03 [73]

Answer:

b = 90

Step-by-step explanation:

Sum the interior angles of the pentagon and equate to 540

Starting from the top and going clockwise

b + b + 45 + 90 + 2b - 90 + $\frac{3}{2}$ b = 540 ← simplify left side

$\frac{11}{2}$ b + 45 = 540 ( multiply through by 2 to clear the fraction )

11b + 90 = 1080 ( subtract 90 from both sides )

11b = 990 ( divide both sides by 11 )

b = 90

Thus

b + 45 = 90 + 45 = 135

2b - 90 = 2(90) - 90 = 180 - 90 = 90

$\frac{3}{2}$ b = $\frac{3}{2}$ × 90 = 135

The angle measure from the top clockwise are

90°, 135°, 90°, 90°, 135°

7 0

3 years ago