X : 18 : 30 =36 : 27 : y, find the value of x and y

Find the arc length of AB⌢. Round your answer to the nearest hundredth.

gizmo_the_mogwai [7]

Answer:

3.14 ft

Step-by-step explanation:

The arc AB is the minor arc of the given circle. The length l of the minor arc of a circle is given as

l = Ф°/360° × 2πr

where

Ф is the angle of the arc at the center of the circle

r is the radius of the circle and

π is a mathematical constant equivalent to 22/7

r = 8/2 = 4 ft

Hence

l = 45°/360° × 2 × 22/7 × 4

= 22/7 ft

= 3.14 ft

5 0

3 years ago

Please help I will mark you brainalist

liq [111]

Answer:

EASY. y = 4/7x+3

Step-by-step explanation:

7 0

3 years ago

At a local high school football game, twice the number of students attended as adults. If student tickets were $6.50, adult tick

lesantik [10]

Answer:

454

Step-by-step explanation:

set up a system of equation

let y be the number of students

let x be the number of adults

because there are twice the amount of students attended as adults, we can use y=2x as one equation

the other equation will be 6.5y+9x=4972 because this represents the total amount of money

plug 2x for y : 6.5(2x)+9x=4972 : x=226

plug 226 in for the first equation : y=2(226) : y=452

8 0

3 years ago

By selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50.

valentina_108 [34]

Let the actual value of the stool be x.

So if the carpenter sells the stool x rupees he neither loses, now wins anything.

67.50 is the value x - 10% of x, that is:

67.50=x-0.1x
67.50=0.9x

x=67.50/0.9=75 (rupees) is the actual value of the stool.

Selling the stool for 82.50 rupees, the carpenter clearly would make a profit, say of y% of that actual value, that is y%*75.

So using the same method:

82.50=75+y%*75

y%*75=82.50-75=7.5

we can make the calculations, but clearly 7.5 is 10% of 75

Answer: 10% gain.

8 0

3 years ago

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago