I need help simplifying this

Answer:

Answer:

1/2

Step-by-step explanation:

Answer:

c

.......................

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

Subtraction is a mathematical operation that reflects the removal of things from a collection. The number of students who climbs the rock wall is 4.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The total number of students in the class is 48, out of these 48 students, 24 students choose to play volleyball. Therefore, the remaining students are 24 (48-24).

Students remaining after volleyball

  = Total number of students - Number of students who play volleyball

  = 48 - 24 = 24

Now, The teacher then divides the remaining students into as many groups of 5 as possible to shoot baskets. Therefore, the teacher divides the remaining 24 students into 4 groups of 5 people. After this, the number of students that are remaining is 4(24-20).

Students remaining after basketball

  = Total number of students - Number of students who shoot basketball

  = 24 - (4x5)

  = 24 - 20 = 4

Further, the remaining students go for climbing the rock wall.

Hence, the number of students who climbs the rock wall is 4.

Learn more about Subtraction:

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Answer:

72 words per minute

Step-by-step explanation:

[tex]\frac{1}{y}= \frac{42}{3024}[/tex]

42 × y = 1 × 3024

42y = 3024

42y ÷ 42 = 3024 ÷ 42

y = 72

Answer:

what do i do is this math or science

Step-by-step explanation:

Answer:

stretching trifling preheated prejudicial irresistible

Answer:

11n611  and -n6-n6

Step-by-step explanation:

Step-by-step explanation:

sec X = WX/XY = 37/12 = 3 1/12

or 3.083

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

Answer:

2(x+3)(x-1)

Step-by-step explanation:

Because 2x^2+4x-6 can be divided by 2, you can divide them by two. This would make the equation 2(x^2+2x-3). To factor this, you have to find two equation that would make it true. The equation have to be _+_=2 and _x_=-3. The two blanks would be 3 and -1. 3+-1=2 and 3x-1=-3. This means that the equation is 2(x-1)(x+3).

If you need an explanation tell me but if this answer helped you, pls mark as brainliest

Answer:

[tex]k =(2,1)[/tex]

[tex]JK = 2[/tex]

Step-by-step explanation:

Given

[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]H = (1,-2)[/tex] --- [tex](x_2,y_2)[/tex]

[tex]I = (3,-2)[/tex] --- [tex](x_3,y_3)[/tex]

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

[tex]\frac{1}{2}(I + J) = \frac{1}{2}(H+K)[/tex]

[tex]\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)[/tex]

[tex]\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)[/tex]

[tex]\frac{1}{2}(3,-1) = \frac{1}{2}(1+x,-2+y)[/tex]

Multiply through by 2

[tex](3,-1) = (1+x,-2+y)[/tex]

By comparison:

[tex]1 + x = 3[/tex]

[tex]-2 + y = -1[/tex]

Solve for x and y

[tex]x = 3 - 1 =2[/tex]

[tex]y = -1 +2 = 1[/tex]

So, the coordinates of k is:

[tex]k =(2,1)[/tex]

The length of JK is calculated using distance (d) formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]

[tex]J = (0,1)[/tex] ---- [tex](x_1,y_1)[/tex]

[tex]k =(2,1)[/tex] ---- [tex](x_2,y_2)[/tex]

So:

[tex]d = \sqrt{(0 - 2)^2 + (1 - 1)^2[/tex]

[tex]d = \sqrt{(- 2)^2 + (0)^2[/tex]

[tex]d = \sqrt{4 + 0[/tex]

[tex]d = \sqrt{4[/tex]

[tex]d = 2[/tex]

Hence:

[tex]JK = 2[/tex]

Answer:

-0.0056

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php

you too ty :)

ilysm and you matter <3

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)

The distance from library and the park is 12 miles.

"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".

For the given situation,

Jaime ride her bike in north = 5 miles

Jaime ride her bike in east = 13 miles

The distance from library and the park be x.

The below diagram shows about the Jaime's riding.

The distance from library and the park can be find by using Pythagoras theorem,

[tex]Hypotenuse^{2} = Perpendicular^{2} + base^{2}[/tex]

On substituting the above values,

⇒ [tex]13^{2} = 5^{2}+x^{2}[/tex]

⇒ [tex]x^{2} =169-25[/tex]

⇒ [tex]x^{2} = 144[/tex]

⇒ [tex]x=\sqrt{144}[/tex]

⇒ [tex]x=12[/tex]

Hence we can conclude that the distance from library and the park is    12 miles.

Learn more about trigonometric ratios here

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Step-by-step explanation:

Note 12 is the difference between the numbers..

hope it helps

Answer:

d

Step-by-step explanation:

hope this helps

Answer:

150+93=241

Step-by-step explanation:

I'm not sure if this is correct but i guess because she got 95 and deposited it into her checking she has 95 and judging on if she spent 2 dollars from her savings or checking i assumed it was savings which leaves it with 148 from 100 after depositing 50 - 2 = 148 so basically

edit: nvm i saw the note now im sure but something i dont understand is that if she made 95 how come the answer choices dont say 93 in checking so im guessing you meant 150+43=193

193 is your answer sorry lol took me a while to work this out or Answer choice C

Answer:

3 cups would be left or 1.5 pints.

Step-by-step explanation:

1 pint is equal to 2 cups.

Answer:

The answer is 4 to the equation

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

Answer:

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:

Answer:

12/2.54 ≈ 4.72 inches

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.