Solve. Check for extraneous solutions. (x+3)¹/₂-1=x

Using the Pythagorean Theorem, the values of x are given as follows:

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Hence, in the first triangle:

x² + 35² = 37²

x² = 37² - 35²

x² = 144

x = sqrt(144)

x = 12.

On the second triangle, we have two right triangles, hence:

x = a + b.

a² + 8² = 10²

a² = 36

a = sqrt(36)

a = 6.

b² + 8² = 17²

b² = 225

b = sqrt(225)

b = 15.

Hence the value of x is given as follows:

x = a + b = 6 + 15 = 21.

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the option tray days subtract 4 from both sides.

A triangle with an area of 108 square feet has a base length and height equal to 24 feet and 9 feet, respectively.

Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle.

A = 1/2bh

where b is the length of the base

h is the height

If the base of the triangle is 6​ feet more than twice its height, then we have b = 6 + 2h.

A = 1/2bh

A = 1/2(6 + 2h)(h)

A = h^2 + 3h

If the area of the triangle is 108 square feet, then

A = h^2 + 3h

108 = h^2 + 3h

h^2 + 3h - 108 = 0

Getting the roots of the polynomial.

h^2 + 3h - 108 = 0

(h - 9)(h + 12) = 0

h = 9     ;     h = -12

Since h must be a positive number, h = 9 feet.

Substitute the value of h in the equation for b.

b = 6 + 2h

b = 6 + 2(9)

b = 6 + 18

b = 24 feet

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 The rationalized expression in general term is given by: 21√2

 Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

3 √18 +2√72, in this expression we have no values in the denominator, so we must only decompose the square root to reduce the term without altering its value.

3√18 +2√72

3×3√2 + 2×6√2

9√2 + 12√2

21√2

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There are √34 miles between the house and the library

The given parameters are

Distance between house and market, x = 3 miles

Distance between market and library, y = 5 miles

The number of miles between the house and the library is calculated as

Distance = √x² + y²

Substitute the known values in the above equation

So, we have

Distance = √3² + 5²

Evaluate the exponents in the above equation

So, we have

Distance = √9 + 25

Evaluate the sum in the above equation

So, we have

Distance = √34

Hence, there are √34 miles between the house and the library

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Answer: x = 61

Step-by-step explanation:

combine both angles to equal 180 in one formula

2x+3+x-6=180

then add the sides up

3x-3=180

add 3 to both sides

3x=183

divide

x=61

An algebra word problem that can be used to explain the given expression is;

If the cost of a box is $16 and the cost of a bag is $14. Peter decides to buy x number of boxes. If his brother wants to buy bags to be same number as the number of boxes bought by his brother and he spends $8 more than the cost of the bags, how many boxes did peter buy?

We are given the algebraic expression as;

16x = 14x + 8

Algebraic word problems are defined as questions that need translation of sentences to equations, and then solving those equations. It usually has a single variable that represents a quantity in a real-life scenario that is  unknown.

Now, an algebra word problem that can be used to explain the given expression is;

If the cost of a box is $16 and the cost of a bag is $14. Peter decides to buy x number of boxes. If his brother wants to buy bags to be same number as the number of boxes bought by his brother and he spends $8 more than the cost of the bags, how many boxes did peter buy?

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Answer:

11

Step-by-step explanation:

The value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 as required in the task content is; 0.

It follows from the task content that the value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 be determined.

Since, slope, m = (y2-y1) / (x2-x1)

Ultimately, the value of t can be determined as follows;

-2 = (-8-(-4))/(2-t)

-4 +2t = -4

2t = 0

t = 0.

Therefore, the value of t for which the points (t,–4) and (2,–8) fall on a line with a slope of –2 as required in the task content is; 0.

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Answer:

1/3, 2/7, and 3/10

Step-by-step explanation:

2/8 = 0.25

3/8= 0.375

1/3=0.333333

2/7=0.28571

3/10=0.3

Answer:

f(x) = x + 6

Step-by-step explanation:

if the y-intercept is decreased by 3 units in the slope formula where b is the y-intercept, then the answer is x + 6

Answer:

S = 350T - 130, where T is the number of hours and S is the number of pounds.

If T = 11, then S = 3,720 pounds.

Step-by-step explanation:

[tex]m = \frac{2320 - 1445}{7 - 4.5} = 350[/tex]

[tex]2320 = 350(7) + b[/tex]

[tex]2320 = 2450 - b[/tex]

[tex]b = - 130[/tex]

So we have S = 350T - 130. Substituting 11 for T, we have S = 3,720 pounds.

Answer:

[-2,infinitysymbol)

Step-by-step explanation:

If you have a graph to look at, the domain is like you are walking up and down the x-axis (which is actually not up/down but left/right) and you're stating where this graph exists.

If you walked all the way over to -10 and looked up or down, the graph just doesn't exist over there.

The graph exists from -2, including -2, so use the SQUARE bracket [.

On the right side there's an arrow on the graph so it keeps going forever. Thats infinitysymbol.

Always wrap a parenthesis ), around the infinity symbol.

Interval notation uses the [SQUARE] brackets or (parenthesis) and even though it looks like a point, its not. It means

[FromHere, ToHere) and answers the question, where is the graph?

The time that Natasha will be able to finish the last piece of equipment will be 8.15 pm

It should be noted that the following information can be deduced based on the information given:

Steeper = 18 minutes

Treadmill = 25 minutes

Rower = 27 minutes

Bike = 1 hour 5 minutes = 65 minutes

Total minutes = 18 + 25 + 27 + 65 = 135 minutes = 2 hours 15 minutes

It should be noted that there's an interval of 5 minutes between each equipment. The time for all the equipment will be:

= 5 × 3 = 15 minutes

Therefore since the starting time is 5.45 pm, the ending period will be:

= 5.45 + 15 minutes + 2 hours 15 minutes

= 8.15 pm

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Answer:

16

Step-by-step explanation:

The GCF of two non-zero integers, x(16) and y(48), is the greatest positive integer m(16) that divides both x(16) and y(48) without any remainder.

Answer:16

Step-by-step explanation: i did this question on a test before

Answer:

The answer is hotdog you can cook the hotdog and eat it

The logarithmic form of the equation is [tex]log_{3}243=5[/tex] .

We have given an equation 243 = 3⁵ .

Taking log on both sides , we get

   [tex]log(243) =log3^5[/tex]                    ..(1)

Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get

        [tex]log(243) =5log3[/tex]

On rearranging the above equation , we get

         [tex]\frac{log243}{log3} =5[/tex]                          ..(2)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\

  [tex]\frac{log243}{log3}[/tex]   can be written as  [tex]log_{3}243[/tex] using property

Putting in equation (2) , we get

     [tex]log_{3}243=5[/tex]

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Answer:Julia will receive $12 she will have to pay TAXES on that income.An additional cost of this investment includes A BROKER FEE to buy a stock

Step-by-step explanation:

An expression that models the cost of each marker, when the cost of x + 2 markers is x³ + 5 x² + 2 x - 8, is x² + 3 x - 4

Given,

Total number of markers = x + 2

The total cost of markers = x³ + 5 x² + 2 x - 8

An expression to model the cost of each marker can be found by dividing the total cost of markers by the total number of markers.

This implies, the expression can be given as :

(x³ + 5 x² + 2 x - 8) / (x + 2)

               x² + 3 x - 4

          _______________

x + 2 |   x³ + 5 x² + 2 x - 8

            x³ + 2 x²

           ________________

                    3 x² + 2 x

                    3 x² + 6 x

           ________________

                             - 4 x - 8

                             - 4 x - 8

          _________________

                                       0

The quotient of this division is the expression that the cost of each marker.

Therefore, An expression that models the cost of each marker when the cost of x + 2 markers is taken into account. x³ + 5 x² + 2 x - 8, is x² + 3 x - 4

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Answer:
x= 7+y/2

The slope is 2

Step-by-step explanation:

Answer:

It is 6×x 6x-18=45

6x=45-18

=27

6x=27

27 divided by 6 = 4.5

The equation to find the volume in terms of P, n, R , and T is:

[tex]V=\frac{n R T}{P}[/tex]

The ideal gas law is the general gas equation. It is a good approximation to find behavior of gases under different conditions. This law says that the product of pressure in the atmosphere and volume is equal to product of moles and temperature. We generally use an equation to define these relations.

Equation of ideal gas law

P V=n R T

where,

P = pressure measured in atmosphere

V = volume measured in liters

n = number of moles present in gas

T = temperature

R = gas constant

Ideal gas equation shows several direct and indirect variations between the different elements ,  such as in the equation pressure (P) shows direct variation with n and T , and inverse variation with volume (V).

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The Algebraic expression for the final cost of the item using the variable c is 0.7455c

The cost of the item is c

Algebraic expression after discounting the cost by 30%

c - 30%of c

c- 0.3c

0.7c

Now, Algebraic expression after the application of 6.5% of sales tax

0.7c + 6.5%of 0.7c

0.7c +0.065(.7c)

0.7c +0.0455c

0.74.55c

Hence, 0.7455c is the algebraic expression for the final cost of the item using the variable c.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

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Answer:

x = 6

Step-by-step explanation:

multiply by 6 the whole equation to eliminate fractions and convert the coefficients and independent numbers to integers:

[tex]4x-1=3x+5[/tex]

[tex]4x-3x=5+1[/tex]

[tex]x=6[/tex]

Hope this helps

Answer:

[tex]x = 6[/tex]

Step-by-step explanation:

In the equation:

[tex] \frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6} [/tex]

Multiply both sides of the equation by the common denominator which is 6

[tex] \frac{2 \times 6}{3} x - \frac{1 \times 6}{6 } = \frac{1 \times 6}{2} x + \frac{5 \times 6}{6} [/tex]

[tex] ⟹ \frac{12}{3} x - \frac{6}{6} = \frac{6}{2} x + \frac{30}{6} [/tex]

Reduce the fraction

[tex]4x - 1 = 3x + 5[/tex]

Now, collect like terms to find the value of x

[tex]4x - 3x = 5 + 1[/tex]

Therefore:

[tex]x = 6[/tex]

The answer is 4

Step-by-step explanation:

Answer:

4 gallons

Step-by-step explanation:

75/5=15

This means that per gallon gives 15 miles.

15*4=60

1 gallon x 4 = 4 gallons.

Answer = 4 gallons

Hope this helps :)

Step-by-step explanation:

let's write it a little bit nicer

5.7 + 67v = -9.3 + 65v | subtract 65v on both sides

5.7 + 2v = -9.3 | subtract 5.7 on both sides

2v = -9.3 - 5.7 = -15 | divide both sides by 2

v = -7.5

Answer:

y = 1.2x

Step-by-step explanation:

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 4 is an equation.

We have,

Pilar:

Cost of 2 cans of dog food = $2,40

We can write this as an equation:

2 = 2.40 ____(1)

Leo:

Cost of 3 cans of dog food = $3.60

We can write this as an equation:

3 = 3.60 ____(2)

From (1) and (2) we get,

The cost of dog food y is proportional to 1.2 of the cans of dog food x.

y = 1.2x

Thus,

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

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Answer:

32.4! or 9 with the square root of 13!

Step-by-step explanation:

You have to add the outside numbers and keep 13 the same. Then proceed answer that getting 32.4.

Hopefully this answered your question have a nice day! :D

The factor is the solution of zeros of the equation and x + 2 making it zero therefore x + 2 will be the solution of the given polynomial so option (B) will be correct.

Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

Given the polynomial,

x³ + 2x² - 9x - 18

A factor is consist of a solution of zeros of any polynomial.

For example;

x² + 5x + 6 = 0

x(x + 2) + 3(x + 2) = 0

(x + 3)(x + 2) = 0

Here x + 3 and x + 2 are factor and solution is x = -3 and -2

Similarly,

x³ + 2x² - 9x - 18 = 0

The factor must be the solution to this.

By cross-checking option

Option (A) x + 1 = 0 → x = -1

Keeping x = -1

(-1)³ + 2(-1)² - 9(-1) - 18 = -8 ≠ 0 so it is not the factor.

Option (B) (x + 2) = 0 → x = -2

(-2)³ + 2(-2)² - 9(-2) - 18

-8 + 8 + 18 - 18 = 0 = 0 so it will be factor of the polynomial.

Hence " x + 2 will be the solution of the given polynomial".

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the formula for the parabola that passes through the points, y = ax2 + bx + c. The values of a, b, and c are -9, -19,32 respectively.

The intersection of a right circular cone with a plane parallel to an element of the cone creates a plane curve, which is equivalent to a point moving so that its distance from a given point equals its distance from a fixed line.

based on the available facts;

Parabola fundamental: y = ax2 + bx + c

We can plug in three locations for (x, y) to get three equations at once.

(-4, -40):  40 = 4a - 2b + c   {equation 1}

(-3, -13):   -13 = 9a + 3b + c    {equation 2}

(-2,4): 4 = a - b + c        {equation 3}

Solve this system to find the values of a, b, c

Let's first eliminate variable c:

4a - 2b + c = -40   {equation 1}

 a -  b + c = 4   {equation 3}

---------------------  subtract

3a - b = -44

9a + 3b + c = -13    {equation 2}

 a -  b + c = 4   {equation 3}

--------------------  subtract

8a + 4b = -17

We now have two equations with 2 unknowns we can use to find a, b

3a - b = -44         {equation 4}

8a + 4b = -4   {equation 5}

Multiply equation 4 through by 4 and add equations

12a - 4b = -176

8a + 4b = -4

-----------------   add

20a = -180

a = 180/20

a = -9

8a + 4b = -4

4b = -76

b = -19

Plug these 2 values into one of the original equations and solve for c

4 = a - b + c        {equation 3}

4 = -9-19 + c

4 = -28 + c

4+28= c

c = 32

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