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1 year ago

Number 11 and 12. Solve for x and y. Please and thank you.

Mathematics

1 answer:

vlada-n [284]1 year ago

4 0

Answer:

11. x=18, y=5

12. x=17, y=9

Step-by-step explanation:

Use the angle property https://www.proprofs.com/quiz-school/story.php?title=angle-properties-parallel-lines (REFER TO THIS LINK)

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Which expression is equivalent to the expression below? Select all that apply.

katen-ka-za [31]

Answer:

2 and 3

Step-by-step explanation:

To simplify this expression, you will need to use the distributive property.

Multiply -2/5 by 15 = - 6, -2/5 by -20d = 8d, and -2/5 by 5c = -2c.

you can switch these around to get -6 + 8d - 2c and -2c + 8d - 6.

Hope this helps :)

3 0

2 years ago

Tickets for the theater are $5 for the balcony and $10 for the orchestra. If 600 tickets were sold and the total receipts were $

kherson [118]

5x+10y=4750
x+y=600

x=250
y=350

250 theater tickets
350 orchestra tickets

4 0

3 years ago

I need help with these two trigonometry problems.

Sloan [31]

Answer:

$B \approx 32.1\°; A \approx 39.0\°$

Step-by-step explanation:

Sine theorem: in any triangle, the ratio between a side and the sine of the opposite angle is constant

$\frac{sin\ \alpha}a = \frac{sin\ \beta}b =\frac{sin\ \gamma}c$

In our case, for the left triangle,

$\frac {sin\ 103\°}{11} =\frac{sin\ B} 6 \rightarrow sin\ B = \frac6{11} sin\ 103\°$

Time to grab a calculator and crunch numbers. Double check your calculator is in degrees and not in radians (plug in sin 30°, if you're getting 0.5 you're good) and you will get

$sin\ B \approx 0.53 \rightarrow B \approx 32.1\°$

Same difference with the right triangle. With the same calculations

$sin\ A = \frac{26}{41} sin 83\° \approx 0.68 \rightarrow A \approx 39.0\°$

5 0

1 year ago

Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma

Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}$

The total surface area is,

$\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}$

Volume is,

$\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}$

Now, differentiate with respect to x,

$\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}$

Now,

$\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}$

Now, differentiate (1) with respect to x again,

$\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}$

Since, the double derivative is negative.