Which expressions are equivalent to 9b?
Choose all answers that apply
A. b+2(b+2b)
B. 3b+b
C. 2(2b)​

The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².

The expression given in the task content whose simplest form is to be determined is;

- (4x³ + x²) + 2 (x³ − 3x²)

Hence, upon opening up the parentheses, it follows that;

-4x³ - x² +2x³ -6x²

Upon collection and summing up of like terms; -2x³ -7x².

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Answer:

120

Step-by-step explanation:

10%=12

20%=12x2

100%=12x10

        =120

Answer:

Let the number be x.

Compute 10% of x and equate it to 12 to compute the value of x as follows:

[tex]x[/tex] x [tex]\frac{10}{100} = 12[/tex]

[tex]x[/tex] = 12 x [tex]\frac{100}{10}[/tex]

[tex]x[/tex] = 120

Thus, the number is 120.

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.

The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7

x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

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Answer:

[tex]\frac{5pi}{6}[/tex]

Step-by-step explanation:

Answer:

[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]

Therefore, the value of x in the interval [0, 2π) is:

[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]

Answer:

a) quantitative - continuous

b) qualitative

c) quantitative - discrete

d) quantitative - discrete

Explanation:

A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.

A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.

Answer:

L is not valid.

Step-by-step explanation:

For any triangle, the sum of the two legs must be greater than the hypotenuse. Otherwise the two legs would not be long enough to touch.

Answer:

L

Step-by-step explanation:

to add to the previous basically correct answer :

for a triangle the sum of any 2 sides must be greater than the third side (not just legs and Hypotenuse).

for all other options any combination of sum of 2 sides being bigger than the third side works.

but for L

2 + 5 = 7, which is smaller than the third side (8). so, this cannot be a triangle.

Answer:

slope: 3

y-intercept: (0, -1)

Find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points are: (0, -1), (3, 8)

[tex]\rightarrow \sf slope : \dfrac{8-(-1)}{3-0} = \dfrac{9}{3} = 3[/tex]

When finding y-intercept, the value of x is 0. Here given y is -1 when x is 0.

y-intercept: -1  or  (0, -1)

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If a linear function contains these points: (0,-1) and (3,8), what is its slope and y-int.?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Formula utilised, here [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

Put in the values,

[tex]\bf{\dfrac{8-(-1)}{3-0}}[/tex]  | subtract on top and bottom

[tex]\bf{\dfrac{9}{3}}[/tex] | divide on top and bottom

[tex]\bf{3}[/tex]

The y-intercept is the second co-ordinate of the point (0,-1)

[tex]\bf{Which\;is\;-1}[/tex].

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{\begin{cases} \bf{Slope=3} \\ \bf{Y-int. -1} \end{cases}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1 \theta l}}[/tex]

Answer:

1

Step-by-step explanation:

It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.

Answer: 1

Answer:

It is 98. Just look down for the explanation↓:

Step-by-step explanation:

Log 10 (x + 2) = 2

So, the Inverse log is:

10^2 = x + 2

100 = x + 2

98 = x

[tex](10^4)^4[/tex]

[tex]10^8[/tex]

Therefore in simplified form [tex](10^4)^4[/tex] is [tex]10^8[/tex]

Answer:

• f(g(x)) =  [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65

Step-by-step explanation:

• f(g(x)) = f(x² + 1)

         = [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )

            = [tex](\sqrt{x } + 8)^{2}[/tex] + 1

            =  x + 16[tex]\sqrt{x}[/tex] + 64 + 1

            = 16[tex]\sqrt{x}[/tex] + x + 65

Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]

Step-by-step explanation:

This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.

To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.

Answer:

option c (19.2, -6.7) is correct

Step-by-step explanation:

Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.

if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is

given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]

according to question :

given : end point T(-16.8, 31.7)  and mid point M(1.2, 12.5)

let coordinates of another end point S (a, b)

therefore, using mid point formula

1.2 = (-16.8 + a)/2

2.4= (-16.8 + a)

19.2 = a

and,

12.5 = (31.7 + b)/2

25 = 31.7 + b

-6.7 = b

so the option c (19.2, -6.7) is the correct answer

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Answer: 925

Step-by-step explanation:

This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.

Using the sum of an arithmetic series formula, we get the sum is:

[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]

The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:

f(x) = (x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is:

f(x) = x² + 2x + 3

Completing the squares, we find the equation in vertex form, as follows:

f(x) = (x + 1)² + 2

As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.

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Answer:

log12=log(2.2.3)

=log2+log2+log3

=0.30103+0.30103+0.47712

=0.60206+0.47712

=1.07918

Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.

The break-even point is when the revenue and the costs are equal.

In this problem, the equations are given as follows:

At the break-even point:

R(x) = C(x)

15x = 1.25x + 495

13.75x = 495

x = 495/13.75

x = 36.

36 tickets have to be sold each night to break even.

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A translation 2 units to the left followed by dilation by 1/2.

The correct option is (B).

It states that that two triangles are said to be congruent if they are copies of each other and when superposed, they cover each other exactly.

The complete question is:

Which of the following composition of transformations would create an

image that is not congruent to its original image?

A rotation of 45° followed by a reflection across the x-axis

A translation 2 units to the left followed by dilation by 1/2

A reflection across the y-axis followed by a rotation of 60°

A rotation of 135º followed by a translation of 4 units to the right.

After a translation of 2 units to the left followed by dilation by 1/2 the image will not be congruent to its original image.

All other options are reflection and rotation, which not fit into the situation.

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The critical probability, assuming a confindence level of 58% is 0.79.

From the information given, the confidence level is 58%. The alpha will be:

= 1 - (58/100)

= 1 - 0.58

= 0.42

The critical probability will be:

= 1 - (0.42/2)

= 1 - 0.21

= 0.79

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If we want the slope to be -6/7, then the value of x must be -5.

Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:

[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]

Where on the second line we multiplied and divided the right fraction by 2.

Comparing the fractions, we see that we must have:

9 -x = 14

9 - 14 = x

-5 = x

So the value of x must be -5.

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We can use sine ratio in given right angled triangle.

The sine of ∠Q is represented by ratio 48/73.

Given data:

∠R=90°,

QP = 73,

PR = 48,

RQ = 55

We know that;

The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.

Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.

Thus, we have:

sin Q = PR/PQ

        = 48/73

Thus, the sine of ∠Q is represented by ratio,

48/73.

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Answer:

1. santina drove 14 more miles than carole

2. the owner will need to buy 8 bags this week

Step-by-step explanation:

1. 203-189= 14

2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds

1. 14

2. 8

3. 48

4. 318

5. 23

6. 4

7. a) 10 b) 60 c) 8 d) 107

8. $1,532

9. 1

10. $15.50

11. .95

Step-by-step explanation:

The recursive formula would be: 100 - XN = B.

When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.

X: represents how many weeks

N: represents books per week

B: represents books she has at anytime

So the recursive formula would be: 100 - XN = B

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Answer:

  8 hours 32 minutes

Step-by-step explanation:

Working together, the construction rates add. We can use the given relation to write an equation for the total time when the pair work together.

__

Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

  1/k +1/(k -1) = 1/4

__

Multiplying by 4k(k-1), we have ...

  4(k-1) +4k = k(k -1)

  k² -9k = -4 . . . . . . . . subtract 8k and simplify

  k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

  k -4.5 = √16.25 . . . . . . . . . take the square root

  k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

  0.531129 × 60 min ≈ 31.9 min ≈ 32 min

It would take Kirk about 8 hours 32 minutes to build the wall by himself.

_____

Additional comment

For most "working together" problems the rates of completing work need to be expressed in jobs per unit time. Usually, the rates are given in terms of time per job, as they are here. That is why reciprocals get involved.

It will take Kirk about 8 hours 32 minutes to build the wall by himself.

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

Here, Let k represent Kirk's time (in hours) to build the wall by himself. Then (k-1) is the time it takes for Jeff to build it. Their working-together rate in "walls per hour" is ...

 1/k +1/(k -1) = 1/4

Multiplying by 4k(k-1), we have ...

 4(k-1) +4k = k(k -1)

 k² -9k = -4 . . . . . . . . subtract 8k and simplify

 k² -9k +20.25 = 16.25 . . . . . add (9/2)² to complete the square

 k -4.5 = √16.25 . . . . . . . . . take the square root

 k = 4.5 +√16.25 ≈ 8.531129 . . . hours

The fractional hour is ...

 0.531129 × 60 min ≈ 31.9 min ≈ 32 min

Thus, It will take Kirk about 8 hours 32 minutes to build the wall by himself.

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The Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

A function is a type of relation, or rule, that maps one input to a specific single output.

Given

Base salary = $2500 per month

Commision = 3% on Sales over 48000

Determine the function s(x) for sales over $48000

Let's Represent the total sales in a month with s.

So, the function s(x) is:

s(x)  = Base Amount + Commission x Sales over $48000

s(x) = 2500  + 3% (s - 48000)

s(x) = 2500  + 0.03(s - 48000)

s(x) = 2500  + 0.03s - 1440

s(x) = 0.03s - 1060

Hence, the Function models Jay's total monthly salary s(x) in dollars would be s(x) = 0.03s - 1060.

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The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c

An equation is an expression that shows the relationship between two or more numbers and variables.

The associative property states that when adding or multiplying it can be represented by:

(a + b) + c = a + (b + c)

For multiplication:

a * (b * c) = (a * b) * c

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Answer:

Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45