How do you find x in this question?

Answer:

[tex]b = 2[/tex].

Step-by-step explanation:

By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].

Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:

[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].

Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:

[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].

Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:

[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].

[tex]b = 2[/tex].

Answer:

The answer to writing this graph in fully simplified slope-intercwpt form is y = 1/5x - 7.

Answer:

[tex]p =[/tex] [tex]7\sqrt{2}[/tex]

Step-by-step explanation:

The side length ratio for a 45-45-90 angle triangle is [tex]1:1:\sqrt{2}[/tex]

The length of the bottom adjacent side of the 90-degree angle is 7, so p would be [tex]7\sqrt{2}[/tex]

The mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.

The mean is the average of a set of data or numbers.

It is a typical value that averagely represents the dataset.

The mean can be computed by dividing the total by the number of data values.

Atlanta                     $163

Minneapolis            $125

Boston                       177

New Orleans            167

Chicago                    166

New York                245

Cleveland                126

Orlando                    146

Dallas                       123

Phoenix                   139

Denver                    120

Pittsburgh               134

Detroit                     144

San Francisco         167

Houston                  173

Seattle                    162

Los Angeles           160

St. Louis                 145

Miami                     192

Washington, D.C. 207

Total = $3,181

Mean = $159.05 ($3,181/20)

What is the mean hotel room rate?

Thus, the mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.

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Answer:

Note that #1 starts at #3 and #3 on this list ends at #5 on your page.

Answer:

119.32

Step-by-step explanation:

[tex]A = 2 * 3.14 * 19 = 119.32[/tex]

Answer:

AOC = 124°

Step-by-step explanation:

Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;

This can be written like so:

(3x + 94) + (x + 30) + (2x - 4) = 180

This equation can be solved to find x:

6x + 120 = 180

6x = 180 - 120

6x = 60

x = 10

AOC = 3(10) + 94

= 30 + 94

= 124

Answer:

angle AOC = 124

Step-by-step explanation:

3x + 94 + x + 30 + 2x - 4 = 180 ( ^'s on a STR line)

6x = 180 - 120

6x = 60

x = 10

sub x into 3x + 94

3(10) + 94 = 124

Answer:

w represents the width

w + 2 represents the length

2(w + w +2) = 76     formula for perimeter

w + w + 2 = 38        divide both sides by 2

2w + 2 = 38             combine like terms

2w = 36                    subtract 2 from both sides

w = 18                      divide both sides by 2

Using the t-distribution, it is found that the desired measures are given as follows:

At the null hypotheses, it is tested if the mean is of 63.5, that is:

[tex]H_0: \mu = 63.5[/tex]

At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:

[tex]H_1: \mu < 63.5[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given as follows:

[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]

t = -4.29.

We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.

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0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.

Step-by-step explanation:

=> greater than 0.1 and smaller than 0.12

You can also choose any other numbers too.

Irrational Number :

Answer:

jump equation

bu multiplying by a conjugate

Answer:2/3 < 3/4

Step-by-step explanation: 3/4 is greater than 2/3.

Answer:

3/1/4

That's the expression represents Lena's speed in miles per hour

Answer:

Tom: £166

Ben: £581

Step-by-step explanation:

     In the ratio 2 : 7 there are 9 portions total (2 + 7 = 9).

£747 / 9 = £83

     For Tom:

£83 * 2 = £166

     For Ben:

£83 * 7 = £581

Checking our work:

      Since the decimals are the same, this means the ratios are equal.

2/7 = 0.2857

166/581 = 0.2857

Answer:

(-0.6, 8.4)

Step-by-step explanation:

so first, we have to find out what x is. because y is equal to itself, we can substitute to get

[tex]x+9=-4x-6\\5x+9=6\\5x=-3\\x=-\frac{3}{5}[/tex]

now we can plug in the value of x to find y

[tex]y=-\frac{3}{5} +9\\y=8\frac{2}{5}=8.4[/tex]

your answer is written in the form (x,y) so the answer is (-0.6, 8.4)

Answer: Heyaa! ~

Your Answers are... (-0.6, 8.4)

Step-by-step explanation:

Hopefully this helps you!

~ Lets solve:

Use one equation to find an expression for one of the variables in terms of the other variable. Then substitute that expression in place of that variable in the second equation. You can then solve this equation as it will now have only one variable.

The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.

A perpendicular bisector of a line segment is a line segment that is perpendicular to and passes through the middle of the line segment (left figure). A line segment's perpendicular bisector can be drawn using a compass by drawing circles centred at and with radius and connecting their two intersections.

The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.

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Answer:

32000000

Step-by-step explanation:

3.2 x 10 = 32

you will have 10^6 left

32 x 10^6 = 32000000

just add 6 zeroes

Answer:

32, 000, 000.

Step-by-step explanation:

3.2 x 10^7      <======= move the decimal 7 places to the right

32,000,000.

Answer:

The answer is 1/24

Step-by-step explanation:

1stepout of the 12 is the 5th so 1/12 and divid by 2 because you want it to land on heads.

Answer:

The answer is Graph C.

Step-by-step explanation:

Both the equation of each other are the same in Graph C..

Answer:

B. Graph C

The lines are together, so every point they pass is a solution

Answer:

-20x-48

Step-by-step explanation:

7x-(15x +6)-6(7+2x)

7x-(15x+6)-(42+12x)

7x-15x-6-42-12x

(7x -15x-12x)+(-6-42)

=-20x-48

Answer:

-20x - 48

Step-by-step explanation:

7x - 3(5x  +2) - 6*(7 + 2x) = 7x  + (-3)*5x + (-3)*2  + (-6)*7 + (-6)*2x

                                        = 7x - 15x - 6 - 42 - 12x

                                        = 7x - 15x - 12x  - 6 -42  {Combine like terms}

                                        =  -20x  - 48

Answer:

Step-by-step explanation:

Given equation:

On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3

To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.

[tex]~[/tex]

[tex] \\ \: \: \dashrightarrow \: \: \: \sf {b}^{2} - 4ac = 0 \\ \\ \\\: \: \dashrightarrow \: \: \: \sf (2)² - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 12 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf {\underline{\boxed{\sf{\purple{ -8 > 0}}}}} \\ \\ [/tex]

The discriminant is smaller than 0.

Answer:50,000 x 0.04 x 20=40,000

The total saving after 20 years 50,000+40,000=90,000$

Answer:

3 inches

Step-by-step explanation:

48 - 45 = 3

Step-by-step explanation:

24.

AC = 12 = cos(angle) × AB = cos(angle) × 13

imagine a circle with center in A and radius 13.

that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.

cos(angle) = 12/13 = 0.923076923...

angle = 22.61986495...°

so, B is the right answer.

25.

we have a right-angled triangle.

from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.

at this ground point there is the right angle.

at the ladder ground point we have 70°.

so, the angle at ladder/wall point is

180 - 90 - 70 = 20°.

remember, the sum of all angles in a triangle is always 180°.

the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).

the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.

we can use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being always opposite of the associated angles.

so, we have

20/sin(90) = 20/1 = 20 = height/sin(70)

height = 20×sin(70) = 18.79385242... ft

so, D is the right answer.

Step-by-step explanation:

1.77 would be closer to 2

To solve this problem, we need to use the theorem which states that the sum of angles in a triangle is equal to 180 degrees. The value of m<FED is equal to 120 degrees. From the diagram given, m<CBD is complimentary with m<BED

The value of m<FED can be calculated by summing the entire entity and equating to 180 degrees.

Data;

[tex]35+(16x-8)+(2x+9) = 180[/tex]

Reason: The sum of angles in a triangle is equal to 180 degrees.

But we would need to solve for the value of x.

[tex]35+(16x-8)+(2x+9) = 180\\35 + 16x - 8 + 2x + 9 = 180\\36+ 18x = 180\\180 - 36 = 18x\\18x = 144\\x = \frac{144}{18} \\x = 8[/tex]

Let's substitute the value of x into m<FED

[tex]m < FED = 16x - 8\\x = 8\\m < FED = 16(8) - 8 \\m < FED = 128 - 8\\m < FED = 120^0[/tex]

The value of m<FED is equal to 120 degrees.

From the diagram given, m<CBD is complimentary with m<BED

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Answer:

A = $14,745.544

Step-by-step explanation:

The equation for compound interest is 

A = P (1+i)t 

A = final value

P = amount invested (principal) (10000)

i = interest rate, expressed as a decimal (.05)

t = number of years invested (8)

This formula assumes annual compounding.

Plugging in what we know.

A = 10000(1.05)^8

A = 10000 (1.47745544)

A = $14,745.544

The conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

The conditional probability P(A|B) is calculated using:

P(A | B) = P(A and B)/P(B)

Using the above formula and the data in the complete question (see attachment), we have the following computations:

P(D | F) = 6/34

P(E | D) = 7/25

P(D | E) = 7/18

P(F | E) = 8/18

P(E | F) = 8/34

By comparing the above computations with the options, the conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

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Answer:

A, B, D

Step-by-step explanation:

yw :)