What are the operations used to
solve this equation5/6x-2=-2/3x+1

Answer:

A

Step-by-step explanation:

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Hello!

[tex]\sf 7n^{2} -6n+10=0\\\\x = \dfrac{-b~\±~\sqrt{b^{2} -4ac} }{2a} \\\\\\x = \dfrac{-(-6)~\±~\sqrt{(-6)^{2} -4~\times~7~\times~10} }{2~\times~7}\\\\\\x =\boxed{\dfrac{6\±\sqrt{-244} }{14} }[/tex]

Final answer:

The area of a kitchen measuring 3.75 meters by 4.2 meters is calculated by multiplying these dimensions, resulting in an area of 15.75 square meters.

Explanation:

The question asks for the area of a kitchen with dimensions 3.75 meters by 4.2 meters. To find the area of a rectangle, you multiply its length by its width. Therefore, the calculation for the area of the kitchen is as follows:

Area = Length × Width= 3.75 m × 4.2 m

= 15.75 square meters

Thus, the area of the kitchen is 15.75 square meters. This calculation is a basic application of geometry, specifically dealing with areas of rectangles.

Answer with explanation:

The given functions in x are

1. f(x)=4 x² + 9 x

2. h(x)= 2 x

3. g(x)=18 x

To check whether the function is increasing or not , there are two ways

1. The graph of function is sloping Upwards.

2. For, two real x number ,that is if , a ≥ b, then , f(a) ≥ f(b).

All the three given function in x, are increasing because ,for increasing , x , value of function increases.

For Integral numbers,

⇒Function 1

f(x)=4 x² + 9 x

f(1)=4×1²+9×1

    =4 +9

   =13

f(2)=4×2²+9×2

    =4 × 4 +18

     =16 +18

   = 34

f(2) - f(1)=34 - 13

           = 21

→→Function B

h(x)= 2 x

h'(x)=2

Rate of change of function is constant, which is equal to 2.

→→Function C

g(x)=18 x

g'(x)=18

Rate of change of function is constant, which is equal to 18.

≡⇒→Rate of change of function ,f(x) is maximum among three functions.That is, f(x)=4 x² + 9 x , has highest rate of increasing, for increasing value of, x.

The percentage of Melanie's walls that still needed to be painted is 55 % and the number of walls is 231 feet²

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage of Melanie's walls that still needed to be painted be A

Now , the equation will be

The total number of walls = 420 feet²

The percentage of Melanie's walls that are painted = 45 %

So , the remaining percentage A = 100 - percentage of Melanie's walls that are painted

The percentage of Melanie's walls that still needed to be painted A = 55 %

And , the number of walls that needed to be painted = percentage of Melanie's walls that still needed to be painted A x total number of walls

On simplifying , we get

The area of walls that needed to be painted = ( 55/100 ) x 420

The area of walls that needed to be painted = 231 feet²

Hence , the area of Melanie's wall to be painted is 231 feet²

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Final answer:

The expression ax²-ay-bx²+cy+by-cx² can be factored by first combining like terms to get (a-b-c)x² + (b+c)y - ay and then refactoring to x²(a-b-c) + y(b+c-a).

Explanation:

The student has given the expression ax²-ay-bx²+cy+by-cx² to factor. To factor this expression, we must first combine like terms and then group the terms in a way that allows us to factor by grouping.

Combining like terms gives us: (a-b-c)x² + (b+c)y - ay. We can then factor out common factors from each group. Notice that x² terms can be grouped together, as well as the y terms.

The refactored expression is x²(a-b-c) + y(b+c-a). Depending on the specific values of a, b, and c, further factoring may be possible, but with the given information, this is the factored form of the expression.

Final answer:

To factor the expression ax² - ay - bx² + cy + by - cx², group the terms based on their factors and factor out the common factors. The factored form of the expression is x²(a - b - c) - y(a - c + b).

Explanation:

To factor the expression ax² - ay - bx² + cy + by - cx², we can group the terms based on their factors. Group ax² - bx² - cx² together, and -ay + cy + by together. Factoring out the common factors from each group, we get:

x²a - b - c) - y(a - c + b)

Thus, the factored form of the expression is x²(a - b - c) - y(a - c + b).

Final answer:

To find out how many 3/7 foot pieces can be made from 7/2 feet of rope, divide the total rope length by the length of one piece, resulting in 8 whole pieces with a small amount left over.

Explanation:

The question asks how many pieces of rope, each measuring 3/7 of a foot, can be made from a total length of 7/2 feet. To find the answer, you need to divide the total length of the rope (7/2 feet) by the length of each piece (3/7 foot), which is a division problem involving fractions:

(7/2) ÷ (3/7) = (7/2) × (7/3) = 49/6.

This means you can cut the rope into 49/6 pieces. Since you can't have a fraction of a physical piece of rope, the practical answer is that you can make 8 whole pieces of rope, each 3/7 of a foot long, with a little bit of rope left over.

You can make 8 full pieces of rope that are each 3/7 of a foot long from 7/2 feet of rope, with a small leftover piece.

The question asks how many pieces of rope measuring 3/7 of a foot each can be made from 7/2 feet of rope. To find this, we divide the total length of rope by the length of one piece:

Total length of rope: 7/2 feet
Piece length: 3/7 foot

We divide 7/2 by 3/7, which is the same as multiplying 7/2 by the reciprocal

of 3/7 (which is 7/3):

(7/2) * (7/3) = 49/6

This simplifies to 8 1/6, which means you can make 8 full pieces of rope that are each 3/7 of a foot long, with a small piece leftover.

Answer:

a number 12 less than g

Step-by-step explanation:

g -12 is a number 12 less than g

Please find the attached file for a better understanding of the solution provided here:

ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.

Now, we know that the length is 8 yards shorter than twice it's width. Thus,

l=2w-8

Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.

Thus, area of the region A'B'QP is (2w+4)x6=12w+24

Likewise, the area of the region D'C'RS will similarly be 12w+24 too.

Now, the area of the region BB'C'C will be 6 x w=6w

Similarly, the area of the region AA'D'D will be 6 x w=6w

Therefore, the total area of the walk way will be:

[tex] 2(12w+24)+2\times 6w=570 [/tex]

[tex] 24w+48+12w=570 [/tex]

[tex] 36w+48=570 [/tex]

[tex] \therefore w=14.5 [/tex]

Therefore, length, l will be:

[tex] l=2w-8=2\times 14.5-8=29-8=21 [/tex]

Therefore, the dimensions of the swimming pool are:

Length, l= 21 yards and Width, w=14.5 yards

Since Wanda's height represents 100% and Will is 23% taller, then Will's height is 123% of Wanda's height.

The question tells us that Will is 23% taller than Wanda. In terms of understanding this percentage in relation to Wanda's height, it helps to see Wanda's height as 100% because 100% represents a whole, in this case, Wanda's entire height. If Will is 23% taller, then his height is 100% of Wanda's plus an additional 23%. Thus, Will's height is 123% of Wanda's height.

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Answer:

I believe it may be A.

Step-by-step explanation:

The formula looks complicated so I'm going to simplify it.

SA = 1/2 (4 * side of base * height) + side of base^2

Using this, we can get our answer.

1/2 (4 * 4 * 6) + 4^2

1/2 * 96 + 16

48 + 16

64

Thus the answer should be 64in. ^2

The surface area of the pyramid is 64 inch².

A three-dimensional shape's surface area is the sum of all of its faces. To calculate the surface area of a shape, we add the areas of each face.

Here the pyramid has 4 triangles and one square.

Side of base square = 4 inch

Height of Triangle = 6 inch

Then, area of base

= side²

= 4²

= 16 inch²

and, Area of Triangle = 1/2 x base x height

                                       = 1/2 x 4 x 6

                                       = 12 inch²

So, the Surface Area of pyramid

SA = 1/2 (4 x t) + side²

     = 12 x 4 + 16

     = 48+ 16

     = 64 inch²

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