What is the complete factorization of the polynomial below?
x^3 + 3x^2 + 9x + 27
A. (x-3)(x+3)(x +31)
B. (x-3)(x+31)(x-31)
C. (x+3)(x + 31)(x+31)
D. (x+3)(x+3)(x-31)

The value of variable  x is 15 and the value of RS is 42 unit.

Two find the value of x and RS, just cut the trapezium from median and fold it to right and adjust such that it becomes a rectangle,

Now we have a rectangle that is VV'RU

With that we have,

RS + UT = VW + VW

RS + UT = 2(VW)

3x-4 + 8x + 5 = 2(5x + 8)

11x + 1 = 10x + 16

11x - 10x =  16 - 1

x =  15

When x = 15 the RS,

= 3x - 4

= 3(15) - 4

= 45 - 4

= 42

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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10+12/6+12= 24

you just plug 12 in for b.

12/6= 2

so 10+2+12=24

Answer:

6 is 1/2 of 12

6 is 1/4 of 24

12 × 1/2 = 6

6 × 4 = 24

24

18 is 1/3 of 24

12 is 1/2 of 24

6 is 1/4 of 24

Answer:

0.2 kg per meter

Step-by-step explanation:

5÷25=0.2

The surface area of a regular square pyramid is 332.64 square cm

We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.

surface area of pyramid

= areas of lateral faces of pyramid + area of base of pyramid

We know that the formula for the lateral surface area of regular pyramid is:

A = ½ × P × l

where P is the perimeter of the base and l is slant height

Here, a base of regular square pyramid with has sides of 13. 2 cm

a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm

Using the formula of area of square, the base area of pyramid would be,

B = (13.2)²

B = 174.24 sq.cm.

the perimeter of base is:

P = 4 × 13.2

P = 52.8 cm

So, using the above formula of lateral surface area of pyramid the lateral surface area would be

A1 = 1/2 ×  52.8 × 6

A1 = 158.4 sq. cm.

So, the surface area of the pyramid is:

A = A1 + B

A =  158.4 + 174.24

A = 332.64 square cm

Therefore, the surface area of the pyramid = 332.64 square cm

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Answer:

1.5

Step-by-step explanation:

2/4 = .5

4/4 = 1

1 + .5 = 1.5

Answer:

2/4 + 4/4-(from what I learn when the denominators are the same you add normally thus:)

2+4

-------

4

=6/4 (then you reduce but because the top number is bigger you divide)

6÷4

=1 and 2 remaining

=1 ²/4

I'm not good at explaining but that's what my teacher would've told me

Answer:

(9/5, 8/5)

Step-by-step explanation:

First you want to find the equations of the lines. One line is y = 2x - 2 and the other line is y = 1/3x + 1. Then you want to find the x and y that both work in the two equations.

y = 2x - 2

y = 1/3x + 1

Then you do 2x - 2 = 1/3x + 1

Then you do some maths and you get 9/5, and 8/5

The value of X in the Venn diagram that shows information about the genres of films would be = 26

To determine the value of X, the two variables that are mutually exclusive shows that both of them cannot occur the same time.

That is to solve for X the formula that should be used would be ;

n ( F ∪ R) = n(F) + n(R) – n ( F ∩ R)

Where nF= x-12

nR = 7x

n ( F ∪ R)= 2x-1

n ( F ∩ R) = 5x-15

2x-1 = x-12+7x-5x-15

Bring like terms together;

2x-x-7x+5x= 1-15-12

-x = -26

X= 26

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The value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

We have the following equations -

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 10.1 = 6.49p - 4

2.3p - 10.1 + 4 = 6.49p

2.3p - 6.1 = 6.49p

4.19p = - 6.1

p = - 1.46

Therefore, the value of [p] will be p = - 1.46. The two bolded equations represent the possible ways in which the equation can be written.

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Answer:

Turn one of the plus signs into a 4, making it 545+5=550

Step-by-step explanation:

When the value of x will increase then decay factor will decrease the value of y.

Given that the decay factor describes how an advertisement loses its effectiveness over time.

Exponential decay will tell us the process of reducing an amount by a consistent percentage of rate over a particular period of time. Exponential decay is the reciprocal of exponential growth when a quantity decreases by the same factor in equal intervals of time, the constant coefficient of the exponential decay function is less than 1. This can be expressed as (1 - r) and is called the decay factor.

According to the definition of the decay factor, its say that when the value of x increases then the decay factor of the value of y will decrease.

Hence, the value of x will increase then decay factor will decrease the value of y.

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Answer:

290

Step-by-step explanation:

you add $66 to the ending of $224 and your answer is 290

Answer:

303

Step-by-step explanation:

c-59=244 c=303

Answer:

The y and m2 and the m (0, 2) when x=3

Step-by-step explanation:

The 7 is not a variable because variables are letters. The number seven is a coefficient because they are numbers used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients

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If the lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. the probability that a randomly selected crocodile is more than 12 feet long is  0.5941.

Given :

Mean = 12.5 ft

Standard deviation = 2 .1 ft

Randomly selected crocodile = 12 ft

Hence,

First find Z value, Z = (12 – 12.5) / 2.1

Z =  - 0.5 / 2. 1

Z = - 0.238

Using Z table, we will get the probability :

Probability =  1 – 0.4059

Probability = 0.5941

Therefore we can conclude that the probability is 0.5941.

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Answer:

11 1/4

Hope I helped

Answer:

Step-by-step explanation:

The graph of x = 5 is a solid, vertical line through (x,0).

The graph of x > 5 is a dotted, vertical line through (5,0) , and the area to the right of the dotted line is shaded.

Answer:

2(13a-5)

Step-by-step explanation:

Factor 2 out of both numbers and place it in front

Answer:

A. KE=1/2; B. KE=4; C. KE=24; D. KE=1

Step-by-step explanation:

A. KE=1/2*1*1²=1/2

B. KE=1/2*2*2²=1*4=4

C. KE=1/2*3*4²=1.5*16=24

D. KE=1/2*8*0.5²=4*0.25=1

Answer:

(4x+5)(x-3)

Step-by-step explanation:

You factor this by grouping together the numbers you get from multiplying/subtracting the numbers in the equation.

The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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I think it's D because the y-intercept is (0, -2), and in D the filled in circle is on (0, -2) and it goes up one and right one, which is the slope. Although C does this it ends with only one filled in circle, but D still has the two circles and line in between them.

The parent function of this equation is.

y = 1/x.

This equation is transformed using the following three steps:

Vertical Stretch:

The function is vertically stretched by a factor of 5. As a result, the equation becomes.

\(y = 5(1/x).\)

This transformation changes the height of the graph of the function. The height of the graph of the function is five times higher than the original graph of the function.

Reflection: The equation is reflected over the x-axis. As a result, the equation becomes.

\(y = -5(1/x).\)

This transformation shifts the graph of the function downward by two units. The final graph of the function has the same shape as the original graph.

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The dimension of a rectangle is 17m and 17m.

Here we have to find the area of a rectangle as large as possible.

Data given:

Perimeter = 68m

The formula for the perimeter of the rectangle:

perimeter = 2(length + breadth)

68 = 2( l + b)

l + b = 34

We have to find the largest area, so when we will take the length and breadth same then we get the largest area.

So length = breadth

2 length = 34

length = 17m

length = breadth = 17m

Therefore the dimensions are 17m and 17m.

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According to the question The graphs of the equations intersect at two points: (6, 8) and (-2, 0).

To find the total number of points of intersection between the graphs of the equations \($2x^2 - y^2 = 8$\) and \($y = x + 2$\) , we need to solve the system of equations.

Substituting \($y$\) from the second equation into the first equation, we get:

\(\[2x^2 - (x+2)^2 = 8\]\)

Expanding and simplifying:

\(\[2x^2 - (x^2 + 4x + 4) = 8\]\)

\(\[2x^2 - x^2 - 4x - 4 = 8\]\)

\(\[x^2 - 4x - 12 = 0\]\)

Factoring the quadratic equation, we have:

\(\[(x - 6)(x + 2) = 0\]\)

Setting each factor equal to zero:

\(\[x - 6 = 0 \quad \text{or} \quad x + 2 = 0\]\)

Solving for \($x$\) :

\(\[x = 6 \quad \text{or} \quad x = -2\]\)

Now, substituting these values of \($x$\) back into the equation \($y = x + 2$\)  to find the corresponding \($y$\) values:

When \(\\$x = 6$, $y = 6 + 2 = 8$\).

When \(\\$x = -2$, $y = -2 + 2 = 0$\).

Therefore, the graphs of the equations intersect at two points: (6, 8) and (-2, 0).

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Answer:

3/8 of a pizza or 3 slices

Step-by-step explanation:

First, make the numerator of 3/4 an even number that can be divisible by 2 by multiplying the numerator and denominator by 2.

3/4 = 6/8

Then multiply 6/8 by 1/2 to get 3/8

Answer:

C

Step-by-step explanation:

Recall that the standard form for the explicit formula of a geometric sequence is given by:

\(a_n=a\cdot(r)^{n-1}\)

Where a is the initial term, r is the common ratio, and n is the nth term.

Our sequence is 8, 4, 2, 1, and so on.

Hence, our initial term a is 8.

Each subsequent term is half of the previous one. So, our common ratio r is 1/2.

Therefore, by substitution, we acquire:

\(\displaystyle a_n=8\cdot\left(\frac{1}{2}\right)^{n-1}\)

In conclusion, our answer is C.

Answer: 825

Step-by-step explanation: 44/4 = 11 times he reached the threshold. 11 x 75 = 825

Answer:

825

Step-by-step explanation:

He makes 825 because if you divide 75 by 4 you get 18.75

so technically you get a dollar for every 18.75 money you spend

so then you multiply 44 by 18.75 to get ur answer

44 x 18.75=825

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