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vladimir1956 [14]
2 years ago
5

The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, cal

culate the area and perimeternof the shaded region.​ PLEASE HELP!

Mathematics
1 answer:
dolphi86 [110]2 years ago
7 0

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\  \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = \frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = \frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

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Elizabeth is selling jam at a farmers market, and she earns $5.00 for each jar of jam that she sells. Her goal for the weekend i
Musya8 [376]

Answer:

66 jars of jam

Step-by-step explanation:

Elizabeth is selling jam at a farmers market.

She earns $5 for each jar of Jan that she sells

Her goal is to earn $450 during the weekend.

Elizabeth has already made $95 from the sale of her jams and $24 from leading a demonstration

Therefore the total amount that has been made is

= $95 + $24

= $119

Since her target is $450 and she has already made $119 then the amount remaining to complete the target can be calculated as follows

= $450 - $119

= $331

The minimum number of jars that Elizabeth must sell to realize her goal can be calculated as follows

= 331/5

= 66

Hence Elizabeth must sell 66 jars of jam to reach her goal.

7 0
3 years ago
one tank is filling at a rate of 3/4 per gallon per 2/3 minute .a second tank is at a 5/8 gallon per 1 half gallon per 1/2 minut
Bingel [31]
recall\ that\implies \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus
\\ \quad \\

\cfrac{\frac{3g}{4}}{\frac{2m}{3}}\implies \cfrac{3g}{4}\cdot \cfrac{3}{2m}\implies \cfrac{\square ?}{\square ?}
\\-------------\\
\cfrac{\frac{5g}{8}}{\frac{1m}{2}}\implies \cfrac{5g}{8}\cdot \cfrac{2}{1m}\implies \cfrac{\square ?}{\square ?}

so... you tells us, which filling rate is the bigger and thus faster one?

6 0
3 years ago
What are the coordinates of the x-intercepts of the parabola y = x² - 8x + 15?
tamaranim1 [39]

Answer:

(3, 0) and (5, 0)

Step-by-step explanation:

we have

y=x^{2}-8x+15

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

x^{2}-8x+15=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^{2}-8x+15=0  

so

a=1\\b=-8\\c=15

substitute in the formula

x=\frac{-(-8)\pm\sqrt{-8^{2}-4(1)(15)}} {2(1)}

x=\frac{8\pm\sqrt{4}} {2}

x=\frac{8\pm2} {2}

x=\frac{8+2} {2}=5

x=\frac{8-2} {2}=3

so

x=3, x=5

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4 0
2 years ago
Emily and Sarah had a total of $80. after Sarah spent 1/3 of her money and Emily spent $17, Emily had twice as much money as Sar
Phoenix [80]
<span> SO in total, Emily and Sarah had a total of 80 dollars in which Emily had twice as much as Sarah.
Let’s solve to find out how much their Money is.
=> Since the ratio of the given data is 2:1, 2 + 1 =3, so let’s divide 80 by 3
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=> Emily has twice as this.
=> 26.667 * 2 = 53.33
=> Sarah has 26.67
Now, Sarah spent 1/3 of her money
=> 26.67 / 3 = 8.89 – her remaining money
Emily spent 17 dollars of her money
=> 53.33 – 17 = 36.33</span>



3 0
2 years ago
Please Help Part C Final Part Thanks
alexandr402 [8]

3 blue + 3 yellow = 6 total marbles.

The probability of picking a blue one first would be 3/6 ( 3 blue out of 6 total marbles).

3/6 reduces to 1/2.

After picking the first marble, there would be 5 marbles left in the bag.

The probability of picking a yellow one would be 3/5 ( 3 yellow and 5 total marbles left).

The probability of picking a blue then a yellow then becomes:

1/2 x 3/5 = 3/10 = 0.30 = 30%

4 0
3 years ago
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