Solve for x:

[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]


A. -2

B. 2

C. no solution

D. 4

Answer:

b=98 and a=82

Step-by-step explanation:

b and 98 are corrisponding angles which means that they are both 98

a+b=180 because it is a straight line

a+98=180 subtract 98 from both sides a d you get a=82

Answer:

range

Step-by-step explanation:

The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.

Adjacent rectengular corral has length and width with area formula as below.

A = L × W

Given:

Because the dimension of adjacent rectangular corrals are the same, so:

W = 4x

L = 3y

3y + 4x = 200

[tex]y = \frac{200 - 4x}{3} [/tex]

There are two adjacent rectangular corrals, so:

A = 2×L×W

[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]

A = ⅓(400x–8x²)

We can differentiate to get the maximum area:

⅓×(400x–8x²) = 0

400–16x = 0

16x = 400

x = 25 feet

Substitute x value (width) to get y value (length):

y = (200–4(25)) ÷ 3

y = (200–100) ÷ 3

y = 100 ÷ 3

y = 33⅓ feet

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The translation T due to the transformation is (5,3)

Translation can be defined as movement in a straight line

Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means  (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.

From the figure, the value of  (x, y) can be read i.e. (x, y) = (2,2)

Thus the translation will be:

(x,y) → (x + 3, y + 1)

(2,2) → (2 + 3, 2 + 1) = (5, 3)

Therefore, the  translation T of the transformation shown in the graph is (5, 3)

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Answer: $2.08

Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)

=2.08

The unit rate of change , d with respect to t is =  1.6  .

In the question,

it is given that ,  the relationship between d and t is proportional

also given that "  increase of 5 units in t corresponds to increase of 8 units in d ".

which is represented as 5t = 8d

Divide both sides of the equation  5t = 8d by "5" ,

t = 8/5d

t = 1.6d

next we plot the graph of t = 1.6d

we see that the above equation is a proportional linear equation

and A proportional linear equation is represented as

t = md , Where m represents the unit rate .

So , after comparing , we get

m = 1.6

Therefore , The unit rate of change of d with respect to t is 1.6  .

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Answer:

Nathan

Step-by-step explanation:

4.76 / 2.5

= (476/100) / (25/10)

= (476/100) * (10/25)

= 238/125

= 1.904

Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19

The width, labelled x in the figure is 162.5 meters

From the question, we have the following parameters that can be used in our computation:

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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The value of the variables in the equation are as follows:

1. x = -4 / 9

2. t = -8

3. x = -54

4. x = -3

5. x = 1 / 6

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Let's find the solution of the equations. The solution of the equation is the value of the variable x. A variable is a number represented by a letter in an equation.

Therefore,

1.

-4  = 9x

divide both sides of the equation by 9

x = - 4 / 9

2.

−32=4t

divide both sides of the equation by 4

t = - 32 / 4

t = - 8

3.

x − 18 = −72

add 18 to both sides of the equation

x - 18 + 18 = -72 + 18

x = -54

4.

−18 = x − 15

add 15 to both sides of the equation

-18 + 15 = x - 15 + 15

-3 = x

x = -3

5.

−24x = −4

divide both sides of the equation by - 24

x = - 4 / -24

x = 1 / 6

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Answer:

-5 with the exponet of 11

Answer:

-1/5 or -0.2 if you are going by fraction or decimal

Answer:

The graph is a function.

Step-by-step explanation:

The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

Given,

In the question:

f(x) = [tex]x^{2}[/tex]

To find the value of g(x)

To see the graph and analysis

Now, According to the question:

We know that:

g(x) = k f(x) = k[tex]x^{2}[/tex]

In the graph, The value are given as:

Plug (4,1) into g(x):

1 = k. [tex]4^2[/tex]

k = 1/16

=> g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex])

Hence, The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

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The equation can be given as X+20 = 60

Wyatt needs to save $40 to buy the new game.

What is an equation?

An equation is an expression which has an equality symbol in it.

We are given that, Wyatt is saving up money for a new game. It costs $60,

including tax.

He has already saved $20. At least how much more money, X, does he need to save

Hence the equation can be given as

X + 20 = 60

On solving the equation X = 40

Hence Wyatt needs to save $40 to buy the new game

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If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.

Probability of getting two of each sweet:

P( Liquorice) = (12/20)×(11/19)

P (Liquorice) =132/380

P (mints) =(5/20)×(4/19)

P (mints)  =20/380

P (Humbugs) =(3/20)×(2/19)

P (Humbugs) =6/380

Probability that two sweets will be the same

P(same) =132/380+20/380+6/380

P(same) =158/380

Hence,

Probability that two sweets will not be the same

P(not same) = 1- (158/380)

P(not same) =380 -158 /380

P(not same) = 222 /380

P(not same) =111 /190

Therefore the probability is 111/190.

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Answer:

Step-by-step explanation:

first you need to find the nth term

that would be -4n+28

then you just need to substitute 20 into the position of n

-4*20 = -80

-80+28=-52

Answer: x=3

Step-by-step explanation:

5x+2=7x-4
-5x +4    -5x +4
2x=6
divide both sides by 2
x=3

Check the picture below.

The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

As per the given,5280ft

It is known that 1 ft = 12 inches.

5280ft = 5280 x 12 inches

It is known that 1 inch = 2.54 cm

5280 x 12 inches = 5280 x 12 x 2.54 cm

It is known that 1 cm = 0.01 meter

5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter

⇒  1609.344 meters

Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".

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Considering the figure the unknown angles are

Using the angle in a straight line are supplementary we have

60 + a + 55 = 180

a + 115 = 180

a = 180 - 115

a = 65

applying sum of angles in a triangle equal to 180, b is calculated as follows

a + b + 90 = 180 right angle triangle

substituting for a

65 + b + 90 = 180

b + 155 = 180

b = 180 - 155

b = 25

applying vertical angle theorem

angle c = angle b

angle c = 25

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Answer:

24,278

Step-by-step explanation:

The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x

From the question, we have the following parameters:

Dimension of sheet = 8 inches by 12 inches

Also from the question, we understand that:

He cuts equal squares from each corner.

The cut-out length from the sheet would represent the height of the box

Represent this cut-out length with x

So, we have

Height = x

The width and the length are then represented as

Width = Initial width - 2x

Length = Initial length - 2x

So, we have

Width = 12 - 2x

Length = 18 - 2x

The volume of a box is the product of its dimensions

In this case, we have

Width = 12 - 2x

Length = 18 - 2x

Height = x

So, we have

Volume = Width * Length * Height

Substitute the known values in the above equation So, we have the following equation

V = (12 - 2x)(18 - 2x)x

So, the volume function is V = (12 - 2x)(18 - 2x)x

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Answer: 23%

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given sequence, 20 - n²

The 20 - n² represents the nth term of the sequence.

Thus a(n) = 20 - n²

For the third term n = 3

a(3) = 20 - (3)²

a(3) = 20 - 9 = 11

Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".

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The area of the tile in square centimeters is 929cm2

The area in square centimeters is calculated as follows

First, let convert the tile measures 12 inches on each side into centimeters

1 inch = 2.54 centimeters

= 12 x 2.54
= 30.48 centimeters

Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters

= 929.0304

= 929 square centimeters (rounded)

So, the area of the tile in square centimeters is 929 square centimeters

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Answer:

The area of the tile in square centimeters is 929cm2

Step-by-step explanation:

I took the exam and got it right