Which answer gives statements that should be used to prove angles 2 and 7 are supplementary angles?

Options A and B are correct. If Katarina asks Dacia how she can derive the formula r= x²+y², then the following statements should be Dacia's reply.

Given the equation by Katarina expressed as:

r = √x²+y²

One of the ways Katarina can derive the equation is to use the Pythagoras theorem which states that the sum of the square of the hypotenuse is equal to the sum of the other two sides. Let:

r be the length of the hypotenuse

x and y be the other two sides

According to the theorem:

r² = x² + y²

Take the square root of both sides

√r² = √x² + y²

r = √x² + y²

Also, Katarina can use the trigonometry identity. According to a right triangle where:

sinθ = y/r

Cosθ = x/r

According to trigonometry identity, sin²θ+cos²θ = 1

(y/r)² + (x/r)² = 1

y²/r² + x²/r² = 1

(y²+x²)/r²  = 1

y²+x²  = r²

Swap

r²=y²+x²

This shows that the first two options are correct.

Because r is the hypotenuse of a right triangle, with legs x and y, you can use the Pythagorean theorem to determine 'r

r is a straight line distance from the point and can be projected onto x and y axes where x = rcosθ, y = rsinθ. Writing sinθ = y/r, Cosθ = x/r and using the identity sin²θ+cos²θ = 1

Learn more here: https://brainly.com/question/15610639

Answer:

$1,856.25

Explanation:

To find the square yards, multiply length and width

7.5 * 5 = 37.5

Then, since each square yard costs $49.50, multiply the square yards and the cost

37.5 * 49.50 = 1,856.25

Thus the answer is $1,856.25

The carpet for the room will cost $1,856.25.

This is the product of the unit cost per square yard multiplied by the area of the room.

The area of the room is = 37.5 square yards (Length x Width)

Length of the room = 7.5 yards

Width of the room = 5 yards

Therefore, the total area of the room = 37.5 square yards (7.5 x 5)

Thus, the total area of the room is 37.5 square yards and since each square yard costs $49.50, the total cost for buying the carpet will cost $1,856.25 ($49.50 x 37.5).

Learn more about area of a space at https://brainly.com/question/16758524

Answer:

5

Step-by-step explanation:

5y=10

y=10-5

so,

y=5

and thats the answer

Answer:

smallest:100000, and largest:999999

Answer:

94,237,108?

Step-by-step explanation:

Answer:

Playing with Numbers

∵ 31 z5 is divisible by 3. ∴ ( 9 + z) must be divisible by 3. since, z is a digit. ∴ Possible values of z are 0, 3, 6 or 9.

Hey there! Here is your answer:

102,600 would be in a group. 19 would not be in a group.

Step-by-step explanation:

We can figure this out by doing 102,619 divided by 57. This gives us:

1,800 R 19

Now we need to multiply 1800 by 57 to see how many residents there are:

1,800 x 57 = 102,600

Our remainder tells us how many residents would not fit into a group. Since our remainder is 19, 19 would not be in a group.

I hope this helps!

Answer:5.9

Step-by-step explanation:

Answer:

5.9

Step-by-step explanation:

You round when the numbers are 5 and above

If it is lower than 5 you keep

Nearest 10th = to the 10th place in the decimal form so the 5 is the whole number, the 8 is in the tenths place and the 9 is in the hundredths place

Answer:

Step-by-step explanation:

m+np

Now

Answer:

2x^2 +16x=0

=>2 x(x+8)=0

=>2x=0 or x+8=0

=>x= 0 or x=-8

Step-by-step explanation:

Answer:

4.735 x 10^9 i believe

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

[tex] \frac{2}{4} + \frac{3}{6} =\frac{1}{2} + \frac{1}{2} [/tex]

[tex] \frac{1 + 1}{2} = \frac{2}{2} [/tex]

[tex] = 1[/tex]

Answer:

[tex] \frac{7}{8} - \frac{2}{3 } \\ \frac{7 \times 3}{8 \times 3} - \frac{2 \times 8}{3 \times 8 } \\ \frac{21 - 16}{24 } \\ = \frac{5}{24} [/tex]

Step-by-step explanation:

7/8-2/3

(7*3)/(8*3)-(2*8)/(3*8)

(21-16)/24

5/24

is the answer ...plzz add it to brainliest

Answer:

W = 90 ft

Step-by-step explanation:

1 acre = 43,560 ft^2

A (area) = L (length) x W (width),

L = 484

A = 43560

W = A/L

= 43560/484

= 90 ft

Answer:

Step-by-step explanation:

r = d/t

r = miles / hour

r = 495 / 15

r = 33 miles / hour

Answer:

[tex]\mid x-6 \mid \geq 0[/tex]

Step-by-step explanation:

We have two options for x; it is either 6 or greater than 6:

If [tex]x=6\\[/tex], [tex]\mid x-6 \mid = \mid 6-6 \mid = \mid 0 \mid = 0\\[/tex].

If [tex]x > 6[/tex], [tex]\mid x-6 \mid > \mid 6-6 \mid[/tex] => [tex]\mid x-6 \mid > 0[/tex].

(for example, if [tex]x=7\\[/tex], [tex]\mid x-6 \mid = \mid 7-6 \mid = \mid 1 \mid = 1 > 0[/tex])

So, [tex]\mid x-6 \mid = 0[/tex] or [tex]\mid x-6 \mid > 0[/tex]; [tex]\mid x-6 \mid \geq 0[/tex].

Step-by-step explanation:

If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left

Answer:

If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.

Hope you got it

If you have questions just ask me

Answer:

9+x = 2y+14

Step-by-step explanation:

It says 9 plus a number, so plug in x for 'a number', and it says 'is twice a number plus 14'. Plug in '=' for is another variable for 'a number', and last but not least, just put +14 for plus 14

my guess is "15m" is it correct ?

Explanation:

Apply the pythagorean theorem to find the missing side.

[tex]a^2 + b^2 = c^2\\\\x^2 + 20^2 = 25^2\\\\x^2 + 400 = 625\\\\x^2 = 625-400\\\\x^2 = 225\\\\x = \sqrt{225}\\\\x = 15[/tex]

The horizontal leg of the right triangle is 15 meters long. This is the distance from the base of the tree to the base of the building.

Side note: This right triangle is based off the 3-4-5 right triangle. It has been scaled up by a factor of 5.

Answer:

The perimeter of the figure is 14.71 ft

Step-by-step explanation:

The outer perimeter of the figure is the sum of the boundary dimensions.

The missing outer dimension is the length of the arc or half circumference.

Length of arc formula/half circumference = 1/2 πr = 1/2 x 3.14 x 3 ft = 4.71 ft

The other dimensions are 5ft and 5ft.

Therefore, the outer perimeter of the figure is:

4.71 ft + 5 ft + 5 ft = 14.71 ft

Answer:

[tex]2 {x}^{2} - 25 = 73 \\ 2 {x}^{2} = 73 + 25 \\ 2 {x}^{2} = 98 \\ {x}^{2} = 98 \div 2 = 49 \\ {x}^{2} = 49 \\ x = \sqrt{49} = 7 \\ x = 7 \\ thank \: you[/tex]

Step-by-step explanation:

$1660-$580= $1,080

Answer:

1660 minus 580

Step-by-step explanation:

they have already raised 580. so get 1660 is to subtract 1660 to 580

Answer:

b² + 10b + 21

Step-by-step explanation:

First: b²

Outer: 7b

Inner: 3b

Last: 21

b² + 7b + 3b + 21 =

b² + 10b + 21

Answer:

[tex](b + 3)(b + 7) \\ b(b + 7) + 3(b + 7) \\ b {}^{2} + 7b + 3(b + 7) \\ b {}^{2} + 7b + 3b + 21 \\ b {}^{2} + 10b + 21[/tex]

hope this will help u :)

Answer:

as all the other identical copies : 2

Answer:

Step-by-step explanation:

a) points not on the plane will be somewhere other than on the shaded area representing plane P. Z and W are two such points.

__

b) The name can consist of any three points not on the same line. That means names RVX, RSU, TUV are not allowed, but any other combination of these letters, along with the letter Q, can be used. A couple of possible names are ...

 QRS, STU

Answer:

44

Step-by-step explanation:

Let S = strawberry count

Chocolate = 1/4 * 80 = 20

Vanilla = 1/5 * 80 = 16

Total = C + V + S

80 = 20 + 16 + S

80 - 20 - 16 = S = 44

Answer:

Yes

Step-by-step explanation:

Cross multiply

6/9 = 10/15

6 x 15 = 90

10 × 9 = 90

so yes they consist of equivalent fractions. cross multiplying is a simple way to find out if fractions are equivalent.

Answer:

[tex]94/99[/tex] Or [tex]0.94[/tex] as a repeating decimal

Step-by-step explanation: