Solve the inequality
x²(x + 2)(x-7) ≥0

Answer:

It is 6×x 6x-18=45

6x=45-18

=27

6x=27

27 divided by 6 = 4.5

Answer:

33

Step-by-step explanation:

You do 6 x 2 and you get 12 times that by 3 and get 36 and subtract that by 3 and get 33.

Answer:

Step-by-step explanation:

6 x 6 = 36
3(4) is just 3x4 which is 12
so 36 - 12 = 24

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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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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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: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 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:

Step-by-step explanation saz mix dururtuuuutruturutrutrtru

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

Solve for x by factoring. Obtain the roots of the expression. Solve the quadratic form and obtain the complex solutions. Equate the expression to zero and divide by the common factor 4, and factor out x.

4x^3-8x^2+16x

4x^3-8x^2+16x = 0

x(x^2-2x+4) = 0

x =0

x^2-2x+4 = 0

by quadratic formula,

x =  (-b±√(b²-4ac))/(2a)

x= (--2±√((-2)²-4(1x4))/(2)

x =  (2±√(4-16))/(2)

x =  (2±√-12)/(2)

Let √-12 = i , a complex root

x =   (2±i)/(2)

x =  (2+i)/(2)

x =  (2-i)/(2)

Thus,

x = 0

x =  (2+i)/(2)

x =  (2-i)/(2)

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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

 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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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 equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

A bisector divides segments or angles into two equal halves.

Given the data in the question;

Since AC is bisected at point E and we know that a bisector divides segments or angles into two equal halves.

AC = 2 × AE

Hence

40 = 2( 4x + 2 )

Rewrite the equation such that x will be at the left side.

2( 4x + 2 ) = 40

To solve for x, remove the parenthesis using distributive property.

2( 4x + 2 ) = 40

2×4x + 2×2 = 40

Rewrite the equation such that x will be at the left side.

8x + 4 = 40

Subtract 4 from both sides.

8x + 4 - 4 = 40 - 4

8x = 36

Divide both sides by 8

8x/8 = 36/8

x = 36/8

x = 4.5

Therefore, the equation setup up to solve for x is 2( 4x + 2 ) = 40 and the numerical value of x is 4.5.

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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 :)

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:

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:

(-∞, 4]

Step-by-step explanation:

Domain: x-axis

(-∞, 4]

Graph type: √-x

I hope this helps!

Answer:

8x^2 + 13.

Step-by-step explanation:

(f o g)(x) is found by replacing the x in f(x) by g(x).

= 4(2x^2 + 3) + 1

= 8x^2 + 12 + 1

= 8x^2 + 13.

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!

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit. If Khalid makes an investment at 4% simple interest. at the end of 1 year, the total value of the investment is $1560. Then the original investment is $1500.

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

Percent to decimal 4%=4/100=0.04

A=P(1+rt)

where A is the final amount

P is initial principle balance, t is time and r rate of interest.

1560=P(1+0.04)

1560=1.04P

P=1560/1.04

P=1500

Therefore $1500 is originally invested.

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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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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 average weekly change in your running time bases on the information will be 4 seconds.

It should be noted that the mean simply means the average of the numbers that are given.

It should be noted that in this case, the person approve your time running a course by 5 seconds in week one, by three seconds in week two in by four seconds in week three.

Therefore, the average weekly change in your running time will be:

= Total seconds / Number of weeks

= (5 + 3 + 4) / 3

= 12 / 3.

= 4 seconds

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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

the option tray days subtract 4 from both sides.

Answer:

11

Step-by-step explanation:

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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