Complete the inequality below to describe the domain of the graph shown. Domain: < x < 4

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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Answer:

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

The measure of the angles are  ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

Supplementary angles are the angles whose sum is equal to [tex]180^{o}[/tex].

According to the question we have been given that the three angles that is ∠A , ∠B and ∠C are the supplementary angles that is their sum is 180°.

Let the measure of ∠A = x = ∠B

and the measure of ∠C = 81 + x

Now,

      ∠A + ∠B + ∠C = 180°

Putting the required values we get

        x° + x° + (81 +x )° = 180°

        2x° + 81° + x° = 180°

             3x° = 99°

               x° = 33°

Hence the measure of three angles are

       ∠A = 33°  ,   ∠B = 33° and   ∠C = 114°

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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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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

a) The Linear equation is,

y = 13.5x + 119.5

b) The annual membership fee at this club is $119.5.

c) The fee that is charged each time a member plays racquetball is $13.5.

What is Linear equation?

The linear equation of a line with slope m is defined as;

y = mx + b

Now, Let the linear equation is;

y = mx + b

For, Jay played racquetball 77 times and payed a total of $1159.

1159 = 77m + b  .... (i)

And, For Sammy played racquetball 37 times and payed a total of $619.

619 = 37m + b ... (ii)

Solve both equation as;

1159 - 619 = 77m - 37m

40 m = 540

m = 13.5

And, b = 119.5

Hence, The Linear equation is,

y = 13.5x + 119.5

So, The annual membership fee at this club is $119.5

The fee that is charged each time a member plays racquetball is $13.5.

Hence,

a) The Linear equation is,

y = 13.5x + 119.5

b) The annual membership fee at this club is $119.5.

c) The fee that is charged each time a member plays racquetball is $13.5.

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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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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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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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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: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:

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 :)

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

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: 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

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:

19

Step-by-step explanation:

The answer stays the same

Answer:

|19|

Step-by-step explanation:

The absolute value of a positive number stays positive.

Answer:

11

Step-by-step explanation:

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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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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Answer:

It is 6×x 6x-18=45

6x=45-18

=27

6x=27

27 divided by 6 = 4.5

Answer:

328 Posters

Step-by-step explanation:

$1000-$180 = $820

$820/$2.50 = $328

To Check Answer:

328 x 2.50 = 820

820 + 180 = 1000

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:

Step-by-step explanation saz mix dururtuuuutruturutrutrtru

Step-by-step explanation:

I don't know what the equations are, but I'll do my best to help

ax² + bx + c

"a" is multiplied by (-4) and (c), as well as 2 in the denominator

"b" is put in front of the equation so, hypothetically speaking, b = -1

-b = -(-1) = 1 so it would turn a positive into a negative and a negative into a positive number.

b is also squared so no matter what it will be positive in √b² - 4ac

"c" is multiplied by (-4) and (a)

If I knew the equations I could help more but this is probably the best I can do.

I hope this helps!

the option tray days subtract 4 from both sides.

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:

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

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 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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