Solve each equation by completing the square. Write both answers separately.

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.

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

1) Equation: y = 5x + 1

Missing Value: 51

2) Equation: y = 4x

Missing Value: 28

3) I have no idea for this one... sorry!

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:

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

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.

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)

Answer:

78.5 is the answer

10/2 = 5

5 x 5 = 25

3.14 x 25 = 78.5

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

Answer:

what do i do is this math or science

Step-by-step explanation:

you too ty :)

ilysm and you matter <3

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

Answer:

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.

Answer:

The answer is 4 to the equation

Answer:

3 cups would be left or 1.5 pints.

Step-by-step explanation:

1 pint is equal to 2 cups.

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:

c

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

Answer:

Step-by-step explanation:

Linear function has the form of:

Only one of the choices, B is representing the linear function:

Answer:

ask ur teacher

Step-by-step explanation:

talk

Answer:

1/2

Step-by-step explanation:

Answer:

-0.0056

Step-by-step explanation:

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

Answer:

stretching trifling preheated prejudicial irresistible

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.

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