If ABCD is a square, and the area covered by the blue equilateral triangle is 49√3cm², what will be the area covered by the yellow region (in cm²)?
a. 139
b. 98
c.42
d. 154
no spam answers please!
49√3 = √3/4 a²
49×4 = a²
a = 7×2
a = 14 cm
Side of equilateral triangle = Side of square ABCD = 14cm
Area of square ABCD = a²
A = 14×14
A = 196 cm²
Now diameter of circle = side of square = 14cm
Radius = D/2 = 7 Cm
There are two half circle in the square = one whole circle
Area of circle = πr²
A = 3.14 ×7 ×7
A = 153.86
Area of yellow region = Area of square - Area of circle
Area of yellow region = 196 - 153.86 = 42.14 Cm²
The area covered by the yellow region (in cm²) in the given diagram is 42cm². The correct option is c.42
From the question, the area of the blue equilateral triangle in the given diagram is 49√3cm².
The area of an equilateral triangle can be calculated by finding half the product of the square of a side (all sides are equal in an equilateral triangle) and sin 60° (each interior angle of an equilateral triangle is 60°)
Hence, the area of the blue triangle is given by
[tex]A = \frac{1}{2}/AB/^{2}sin60\°[/tex]
Where A is the area
Therefore,
[tex]49\sqrt{3} = \frac{1}{2}/AB/^{2}sin60\°\\2 \times 49\sqrt{3} = /AB/^{2} \times \frac{\sqrt{3} }{2}[/tex]
[tex]2 \times2 \times 49\sqrt{3} = /AB/^{2} \times \sqrt{3}[/tex]
[tex]196 \sqrt{3} = /AB/^{2} \times \sqrt{3}[/tex]
∴ [tex]/AB/^{2} = \frac{196 \sqrt{3} }{\sqrt{3} }[/tex]
[tex]/AB/^{2} = 196[/tex]
∴ [tex]/AB/ = \sqrt{196}[/tex]
[tex]/AB/ = 14cm[/tex]
Hence, the length of a side of the square is 14 cm and the diameter of the circle is also 14 cm (since the length of a side of the square cuts the circle into equal halves, hence it is the diameter)
Area covered by the yellow region = Area of the square - ( sum of the areas of the two semicircles)
Sum of the areas of the two semicircles = Area of one circle
Area of a circle is given by the formula
[tex]A = \pi r^{2}[/tex]
But r = d/2
where r is radius and d is diameter
∴ r = 14/2 cm
r = 7cm
Hence
Area of the circle = [tex]\pi \times 7^{2}[/tex]
A = [tex]49\pi[/tex]
Taking π = 22/7
∴ A = [tex]49 \times \frac{22}{7}[/tex]
A = 154cm²
This is the sum of areas of the two semicircles
Now, for the area of the square
Area of the square = /AB/²
∴ Area of the square = 196 cm²
Now, as stated earlier,
Area covered by the yellow region = Area of the square - ( sum of the areas of the two semicircles)
∴ Area covered by the yellow region = 196 cm² - 154cm²
Area covered by the yellow region = 42cm²
Hence, the area covered by the yellow region (in cm²) in the given diagram is 42cm²
The correct option is c.42
Learn more on area of shapes here: https://brainly.com/question/24220654
WILL GIVE BRAINLIEST!
Ify is floating freely in outer space. The gravitational forces pulling on her body are negligible except for the forces from a nearby asteroid (a) the nearest planet (p) and the nearest star (s) The asteroid, planet, star, and Ify all lie in the same plane.
a= (2,4)
p=(-1.-3)
s=(8,2)
Answer:
The magnitude of the net gravitational force acting on Ify is 9.1 newtons.
Ify is getting pulled in a direction of 6.2 radians.
Step-by-step explanation:
The vector g = (9,-1) describes the net gravitational force acting on Ify.
We can find the magnitude of g, using the Pythagorean theorem.
PLEASE HELP IM GIVING 70 POINTS Figure A is a scale image of Figure B, as shown Х 3 Figure A Figure B The scale that maps Figure A onto Figure B is 1:7- 4
Answer:
stretching trifling preheated prejudicial irresistible
write -5.6 x 10^-3 in standard form?
Answer:
-0.0056
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php
Logic puzzle ANSWER AS QUICKLY AS POSSIBLE PLS!
Answer:
what do i do is this math or science
Step-by-step explanation:
You spin a spinner labeled 1-10 evenly. what are the chances you will get an odd number?
Answer:
1/2
Step-by-step explanation:
Veronica and Helga both have collections of trading cards.
Veronica has 752 trading cards.
Veronica has 16 times as many trading cards as Helga.
If Veronica and Helga put their cards together, how many cards would there be?
Lori had $126.89 in her bank account. She deposited $21.49 into it and then wrote a check for her car repairs for $156.61.
What was the ending balance in her account?
O -$51.21
O $8.23
O $8.23
O $51.21
What is the answer?
Answer:
-8.23
Step-by-step explanation:
If Lori had $126.89 in her bank account and she deposited $21.49, she would be adding that to the amount of money in her bank account.
126.89+21.59= 148.48
Then subtract the amount of money the repairs costed.
148.48 - 156.61 = -8.23
Therefore Lori would have a balance of -$8.23.
Answer:
Lori had $126.89 in her bank account.
She deposited $21.49 into it and then wrote a check for her car repairs for $156.61
126.89+ 21.49=148.38
148.38-156.61=−8.23
the answer is -8.23
State six ordered pairs for this function.
f(x)=4^x
Answer:
Step-by-step explanation:
x y = 4^x (x, y)
-2 1/16 (-2, 1/16)
-1 1/4 (-1, 1/4)
0 1 (0, 1)
1 4 1, 4
3 64 3, 64
5 1024 (5, 1024)
Solve the system by eliminating one of the variables by addition or subtraction
2x-y=4
3x+y=6
Answer:
(2,0)
Step-by-step explanation:
2x-y=4 equation 1
3x+y=6 equation 2
5x=10 eliminate y by adding equations
x=2
solve for y
2x-y=4
2(2)-y=4
4-y=4
-y=0
y=0
check answer:
3x+y=6
3(2)+0=6
6=6
Which equation is equal to 4a + 2b = 10?
options:
b = -2a + 10
b = 2a + 10
b = -2a + 5
b = 2a + 5
Can someone help pls
Answer:
Age of Sean = 15
Age of Ricki = 10
[tex]Ratio \ of \ their \ age = 15 : 10 = 3 : 2[/tex]
[tex]Sum \ of \ the \ ratio = 5[/tex]
[tex]Let \ number\ of sweets \ be \ x[/tex]
[tex]Number \ of \ sweets \ Sean \ got = \frac{3}{5} * x\\\\48 = \frac{3}{5} * x\\\\x = \frac{48*5}{3} = 80[/tex]
[tex]Total \ number \ of \ sweets = 80\\Sean \ got \ 48\\Number \ of \ sweets \ Ricki \ got = 80 -48 = 32[/tex]
Ans : a) 3 : 2
b) 32 sweets
c) 80 sweets
3x-8y=24
y=x-8
Please show
work
Answer:
3x - 8y = 24 --------(1)
y = x - 8 ---------(2)
substitute y in (1)
3x - 8( x - 8) = 24
3x - 8x + 64 = 24
-5x = 24 - 64
-5x = -40
5x = 40
x= 8
substitute x in (2)
y = 2 - 8
y = - 6
Answer:
x = 8, and y = 0
Step-by-step explanation:
We can solve this by taking y as (x-8), as it states there.
Since y is equal to x-8, we can rearrange the system of equations into one single equation.
We can multiply y by 8, as it shows in the first equation, which is something like 8x-64.
Since it is a negative 8 being multiplied by y, it would be the inverse of 8x-64, which is -8x+64.
We can now organize our equation here.
3x - 8x + 64 = 24.
We can use subtraction property of equality by subtracing 64 from both sides to get rid of it.
We will get something like:
3x - 8x + 64 - 64 = 24 - 64.
Simplify by solving like terms like the x value and the integers.
-5x = -40
Divide both sides with division property of equality:
-5/5x = -40/5
x = 8
We can then plug the 8 back into x, lets use the second equation because I'm lazy and it looks the easiest to solve for.
y = (8) - 8
y = 0
Therefore, x = 8, and y = 0.
Which equation is a linear function?
Answer:
B. y = xStep-by-step explanation:
Linear function has the form of:
y = mx + bOnly one of the choices, B is representing the linear function:
y = xgood luck on finals week :)
you too ty :)
ilysm and you matter <3
Find the value of x in the triangle shown below.
ac
5
What is the area of the following circle?
Either enter an exact answer in terms of 7 or use 3.14 for TT and enter your answer as a decimal.
d=10
units?
Answer:
78.5 is the answer
10/2 = 5
5 x 5 = 25
3.14 x 25 = 78.5
Janet is comparing prices of bottled drinks. She finds one bottle of water that costs $1.92 and contains 12 ounces. She then finds one bottle of soda that costs $2.40 and contains 16 ounces. Which bottle costs less per ounce?
it a short answer response
Answer:
1 ounces of water= $0.16
1 ounces of soda= $0.15
Water costs $0.16 per ounces while soda costs $0.15 per ounces which means soda costs less than water per ounces.
Plz answer i'll give brainliest but it has to be right.
Practice test question, help please
Answer:
ask ur teacher
Step-by-step explanation:
talk
Please help me quick please solve in inequality form
Answer:
Answer OPTION C
AT LEAST... means that she needs 80% and more
Meaning its must be equal to 80% or greater than 80%
Average has to do with Mean.
Her mean would have to be
The sum of the 3 last algebra tests plus the unknown one she's supposed to have to complete 80%
So
Thatll be
80+75+86 + x /(4) ≥ 80
241 + x/(4) ≥80
Option C
3800 divided by 4, I know it’s 950 but I need to know how to get 950
Which expresion is equivalent to -5 -(-7)?
HURRY 20 POINTS
Answer:
2 (the answer should have a positive sign.)The equivalent to -5-(-7) is -5+7.Step-by-step explanation:
To solve this problem, use the order of operations.
PEMDAS
Parentheses
Exponents
Multiply
Divide
Add
Subtract
[tex]\sf{-5-(-7)=-5+7}[/tex]
[tex]\sf{-5+7}[/tex]
Add or subtract.
Solve.
[tex]-5+7=2[/tex]
[tex]\large\boxed{2}[/tex]
So, the correct answer is 2.
Answer:3+(px6)
Step-by-step explanation:
Someone help!
If there are 365 days in a year and you buy 365 $15 Starbucks gift cards. How much will that cost?
Answer:
If you buy a 15 dollar gift card every day for a year, it will cost $5,475.
Just take the price, multiply it by the amount.
Answer:
$5475
Step-by-step explanation:
365 X 15 =
(365 x 10) + (365 x 5) =
3650 + 1825 =
$5475
1/5(6+3+1){2
answer the question
Answer:
The answer is 4 to the equation
I need help! would appreciate it
Answer:
stay safe healthy and happy....Gisella has 4 pints of chicken broth. She uses 5 cups of the broth to make soup.
How much chicken broth is left?
Answer:
3 cups would be left or 1.5 pints.
Step-by-step explanation:
1 pint is equal to 2 cups.
Given the following equation, solve for x.
y = mx+b
Answer:
c
.......................
Tan?cos? Sin? What is the m
Answer:
45º
Step-by-step explanation:
Since we know the relatiionship of a 45-45-90 degree triangle, we can go two ways. Either we can use this to find CA and get the tangent of (6/6) or we can go straight to it. The hypotenuse in a 45-45-90 is always 6√2 and we know it is a right triangle so we can confirm this. So, measure of angle B is 45º.
Marking brainliest if you answer all 3 of them n
1) Equation: y = 5x + 1
Missing Value: 51
2) Equation: y = 4x
Missing Value: 28
3) I have no idea for this one... sorry!