4. Find f(x) - g(x)
4 options to chose from

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

The constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation of direct variation is given by,

y = kx   ....(i)    where "k" is a constant.

Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.

Given that y varies directly with x, and x = 27, then y = 3.

Substitute the values of y = 3 and x = 27 in the direct variation equation and solve for k:

⇒ 3 = 27k

⇒ k = 3/27

⇒ k = 1/9

Substitute the values of k = 1/9 in the direct variation equation :

⇒ y = (1/9)x

Thus, the constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.

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Answer:

61 seconds

Step-by-step explanation:

36 divided by 7 = 5.1 seconds so if you add 5 to 36 five more times you'll get the answer which is 61.

Answer:

x= 10.630145

I hope it's helps you

Answer:

422.39

Step-by-step explanation:

[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]

use a calculator for the above and round

Answer:

OB

Step-by-step explanation:

start counting from 1

Then your significant digit is 6

Answer:

5/2, 7/3, 9/4, 11/5, 13/6, 15/7,17/8

Step-by-step explanation:

Answer:

2/1

2.5

2whole number6/4

Answer:

Step-by-step explanation:

(a + b)² = a² + 2ab + b²

a = 2x   ;  b = 3y

(2x)²= 2x * 2x = 4x²

(3y)²  =3y * 3y = 9y²

(2x + 3y)² = (2x)² + 2 *2x*3y + (3y)²

              = 4x² + 12xy + 9y²

Answer:

17

Step-by-step explanation:

Solve the equation for x then plug that into the 1st expression.

-3 + 4x = -19

4x = -19 + 3

4x = -16

x = -4

then

-3x + 5

-3(-4) + 5 = 12 + 5 = 17

Answer:

the larger one is 183

Step-by-step explanation:

[tex]x + y = 262 \\ x - y = 104 \\ y = 262 - x \\ x - (262 - x) = 104 \\ x - 262 + x = 104 \\ 2x = 104 + 262 \\ 2x = 366 \\ x = 183 \\ y = 262 - 183 \\ y = 79[/tex]

Answer:

a. -2

b. s = 2 and y = -5

c. (2.5, -9)

d. -7x - 2

Step-by-step explanation:

a. In the image, I have used rise over run, which is -8/4 or -2.

b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.

c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).

d. y = mx + b

   5 = (-7)(-1) + b

   5 = 7 + b

   -2 = b

y = -7x - 2  

Answer:

10/100*$x

Step-by-step explanation:

You will multiply the $x by 10%

Answer:

Area equals to 3615.7

Step-by-step explanation:

So first in order to get the area of the triangle you need to have it’s height and base. We know the base is 150m(you can choose another base too), and we need to get the height.

In order to get the height we can see the triangle as two right triangle spreaded by the height. Now looking at the right triangle at the left hand, realized this triangle has a 40, a 90 degree angle and a side of 75.

Next using the law of sines, and plot the numbers in:

a = b(sinα/sinβ)=75(sin(40°)/sin(90°))≈48.20907

Now calculat the area;

Area = 1/2 bh = 1/2 (150x48.20907) ≈ 3615.6765

I attached a graph below that may help to see will all the things go

Answer: 8 books (She will also keep with her a balance of $8)

Step-by-step explanation:

Total amount of money = $28

Cost of 4 books = $10

Sets of books able to be bought with the money = 28/10

                                                                                 = 2 (Reminder will be 8)

Amount of books able to be bought with the money = 2 × 4

                                                                                       = 8 books

Regina can purchase 11 books when she has $28 to spend.

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

A bookstore is selling 4 books for $10 as part of its clearance sale. Regina has $28 to spend.

Let's represent the number of books Regina can purchase x.

The total price for x books at the clearance rate is 10/4x = $2.5x

Since Regina has 28 dollars to spend, she can purchase :

⇒ x = 28/2.5

Apply the division operation, and we get

⇒ x = 11.2 books.

Therefore, she can purchase 11 books.

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Answer:

Option C, 15.14 units²

Step-by-step explanation:

area of the triangle,

6.82×5.04×sin(61.73)/2

= 15.1365001284..

= 15.14 units² (rounded to the nearest tenth)

The required area of the irregular triangle is 15.14 unit². Option C is correct.

Given that,
A figure of the triangle is shown,
Side AB = a =6.82
Side BC = b = 5.04
Angles, ∠A = 45.03°, ∠B = 61.73°.

The triangle is a geometric shape which includes 3 sides and the sum of the interior angle should not be greater than 180°.

Altitude is perpendicular bisector to the side of the triangle from the opposite vertex of the triangle.

The area of the given triangle can be given as,
Area = 1/2 * a * b sinB
       =  1/2 * 6.82 * 5.04 * sin61.73°
       =  1/2 * 6.82 * 5.04 * 0.88
       =  15.14 unit²

Thus, the required area of the irregular triangle is 15.14 units². Option c is correct.

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Answer:

5*sqrt(3)+sqrt(6)

Step-by-step explanation:

sqrt(3)*(5+sqrt(2))=5*sqrt(3)+sqrt(6)

Answer:

(5 x sqrt(3)) + sqrt(6)

Brainliest, please! (Almost an Ace!)

Step-by-step explanation:

Distribute the sqrt(3) through and get:

(5 x sqrt(3)) + (sqrt(3) x sqrt(2))

Next, we simplify.

(5 x sqrt(3)) + sqrt(6)

Hi

1) f(x)= 0.9 x

2) g(x) = x-100

3) f °g. is first apply g then f. so :

f°g = 0.9 ( x-100) = 0.9x-90

4) g°f. is first apply f then g

so g°f = (0.9x) -100 = 0.9x-100

I let you conclude which is the best deal :)

8.6

Answer:

Solution given:

[tex]\bold{\sqrt{74}=8.60232526704≈8.6}[/tex]

Answer:

[tex]8.6[/tex]

Step-by-step explanation:

Step 1:  Find the approximate value of [tex]\sqrt{74}[/tex]

[tex]\sqrt{74}[/tex]

[tex]\sqrt{74}[/tex] ≈ [tex]8.6[/tex]

Answer:  [tex]8.6[/tex]

Answer:

360°

Step-by-step explanation:

The sum of the exterior angles of any polygon = 360°

The sum of the measures of the exterior angles of a convex hexagon will be 360°. Then the correct option is A.

The complete polygonal shape of a regular hexagon has six rotational symmetry and six equal angles. Any periodic polygon has symmetrical sides and angles on all vertices.

The external angle of the regular hexagon will be given as,

External angle = 360° / 6

External angle = 60°

Then the sum of the measures of the exterior angles of a convex hexagon will be

⇒ 60° x 6

⇒ 360°

The sum of the measures of the exterior angles of a convex hexagon will be 360°.

Then the correct option is A.

More about the regular hexagon link is given below.

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Answer:

1) for -1 as x, k(x) would be -8

2) for -3 as x, k(x) would be -18

3) for 0 as x, k(x) would be -3

4) for 1 as x, k(x) would be 2

Answer:

Step-by-step explanation:

Do the subtraction in the numerator first. 6 - 8 = -2. So now we have

[tex]\frac{-2}{-4}[/tex]  negative divided by a negative is a positive and that fraction reduces to

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

Answer:

y= -2x+6

Step-by-step explanation:

General formula :

y=mx+c

m is the gradient

when finding when finding the perpendicular line of another line is will be the negative inverse of the gradient

The perpendicular line will have a gradient of -2 (the negative inverse of 1/2)

so

the line perpendicular to the equation y=1/2x+6

is y= -2x+6

Answer:

x = 3/2

Step-by-step explanation:

Given:

9 - 4x = 2x

Step 1: Addition property of equality

9 - 4x + 4x = 2x + 4x

9 = 6x

Step 2: Division property of equality:

9 = 6x

9/6 = 6x/6

9/6 = x

x = 9/6

= 3/2

x = 3/2

Check:

9 - 4x = 2x

9 - 4(3/2) = 2(3/2)

9 - 12/2 = 6/2

9 - 6 = 3

3 = 3

Answer:

B

Step-by-step explanation:

The slope is zero is the answer

Answer:

t = 1.4 meters

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

2.744 = t^3

Take the cube root of each side

(2.744) ^ 1/3 = t^3 ^ 1/3

1.4 = t

Answer:

7 weeks

Step-by-step explanation:

b​=95+(10+9​)w

Combine like terms

b​=95+(19​)w

Let b = 220

220 = 95 + 19w

Subtract 95 from each side

220-95 = 19w

125 = 19w

Divide each side by 19

125/19 = w

6.578947368

Round up

After 7 week

Answer:

Hello,

[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]

x/2 = -7

=> x = -7 × 2

=> x = -14

Answer:

x=-14

Step-by-step explanation:

[tex]\frac{x}{2} =-7\\\\x=-14\\[/tex]

Answer:

sqrt(2)/2

Step-by-step explanation:

tan(x) and cot(x) are both 1 when x=pi/4 and since 1+1=2, then we just need to evaluate cos(pi/4) which equals sqrt(2)/2.

Answer:

55%

Step-by-step explanation: