If f(x) = x³ + 14x² + 61x + 84, which of the following is not a factor of f(x)?

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Given:

The parent function is

represented by graph A. Graph A is transformed to get graph B and graph C.

Required:

To find the function B and C by using the graph.

Explanation:

The graph B represents the function g(x) :

Here the graph shifts 2 units down.

So

The graph C represents the function h(x) :

Here the transformed function have horizontal compression of 2 units.

Final Answer:

Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

The equivalent of the products given = 3√7

A perfect square root is said to be a number that gives rise to an integer when it's square root is carried out. Examples are √16, √9 which is 4 and 3 respectively.

√3 × √21

But √a ×√b = √ a×b

Find the prime factors which when multiplied would give 21 = 3 and 7.

Therefore,

\( \sqrt{3 \times 3 \times 7} \)

\( \sqrt{9 \times 7} \)

\( 3 \sqrt{7} \)

Therefore, the equivalent of the products of √3 × √21 =

3√7

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Answer:

4+2/3-1 = 3

Step-by-step explanation:

hopefully it helped

In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming \(a\neq o\)

First, subtract c from both the sides to get:

\(y-c=ax^{2}\)

then, divide both sides by \(a\) and transpose to get:

\(x^{2} =\frac{y-c}{a}\)

So, \(x\) must be a square root of \(\frac{y-c}{a}\)  and we can deduce:

\(x=\) ± \(\sqrt \frac{y-c}{a}\)

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Answer:

The answer is C.

Step-by-step explanation:

This is because that shape only has the top and bottom lines which are parallel. The sides are not vertical and leaning outwards, which are not parallel. Leaving that shape to only have one pair of parallel sides.

Answer:

C.

Step-by-step explanation:

A & B both have 2 pairs of parallel lines, so they're not a choice. D has three sides, making it a triangle. Meaning it has no pairs of parallel lines. That leaves us with C. The reason why C is the answer is because, we can see that both top and bottom lines are parallel to each other. However, the left and right lines are not.

I hope this helped!

Step-by-step explanation:

\(c = 40 \\ b = 180 - 90 - 40 = 50\)

\( \cos(40) = \frac{a}{12} \\ 0.766 = \frac{a}{12 } \\ a = 9.19\)

The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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The function end behavior of ln(x + 1 ) is \(\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:\)

From the question, we have the following parameters that can be used in our computation:

f(x) = ln(x + 1)

The end behavior of a function f(x) describes the behavior of the function as x approaches \(+\infty\) and as :x approaches \(-\infty\)

Calculate f(∝) and f(-∝)

So, we have

f(∝) = ln(∝ + 1) = +∝

f(-∝) = ln(-∝ + 1) = +∝

Using the above as a guide, we have the following:

The function end behavior of ln(x + 1 ) is \(\quad \mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:\)

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Answer:

area of ABC=1/2 b×h=1/2×20×6=30m²

Answer:

60 m^2

Step-by-step explanation:

( Base * Hight / 2 = Area)

20 * 6 = 120

120 / 2 = 60

Answer:

1/3

Step-by-step explanation:

hello,

probability of 1 = 1/6

probability of 2 = 1/6

probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0

so the answer is 2/6=1/3

Answer:

x ≤ 1

Step-by-step explanation:

In the graph shown, the blue arrow is facing to the left, so we know that the inequality is some kind of less-than inequality (x < number).

We can also see that the blue arrow starts at a filled-in circle, so we know that the inequality will use the less-than-or-equal-to relator (≤).

Finally, the filled-in dot is at 1, so we can construct the equation:

x ≤ 1

Note that you could replace x with any other variable or even a blank space, since it isn't specified by the number line.

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes n key comparisons, in unsuccessful case.

The BST (Binary Search Tree) is a tree where all nodes on the left and right sides of a given node are larger and less than each other.

The nodes of the BST are not kept in a continuous location because it is a non-linear data structure. The element is absent from the list in the best-case scenario, making it a worst-case scenario.

The worst-case temporal complexity for linear structures is O. (n).

In the worst scenario, there will be n key comparisons.

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The right question is:

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes.......................... key comparisons, in unsuccessful case.

Answer:

42

Step-by-step explanation:

(5+3) x 8 -22

8 x 8 -22

64 - 22

42

Answer:

42

Step-by-step explanation:

You Use PEMDAS

Answer:

Step-by-step explanation:

148 people

To completely solve the problem, Karim should convert the product back into standard decimal notation.

We cannot directly apply the product of powers property because the binomial is not raised to a power itself.

(1) To convert a number from scientific notation to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).

0.0258 × \(10^{-8\)  = 0.0258 × 0.00000001

                         = 0.000000000000258

(2) The product of powers property states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.

In the expression \((3z + y)^3\), we have a binomial term (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.

To simplify the expression, we need to expand it using the binomial theorem or by applying the concept of binomial expansion.

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Answer:

1.4

Step-by-step explanation:

when we add -1.4 and 1.4 we get zero so its the opposite

The area of the cross section after the dilation has a value of  484 square units

When a square pyramid is dilated, all of its dimensions, including the base area and height, are multiplied by the same factor.

In this case, the base of the pyramid was dilated with a factor of k=0.55.

Therefore, the new area of the base can be calculated as:

New base area = k^2 * old base area

Plugging in the values given in the problem, we get:

New base area = (0.55)^2 * 1600

New base area = 484 square units

So, the new base area is 484 square units

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Answer:

C

Step-by-step explanation:

The slope of the line will be (2) and the equation will be C

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\stackrel{\textit{we'll be using this one}}{\downarrow }~\hfill }{log_a a^x = x\qquad \qquad a^{log_a x}=x} \end{array}\)

\(\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(2^{0.5x}=10\implies \log_2\left( 2^{0.5x} \right)=\log_2(10)\implies 0.5x=\log_2(10) \\\\\\ \cfrac{x}{2}=\log_2(10)\implies x = 2\log_2(10)\implies x = \log_2(10^2)\implies x = \log_2(100) \\\\\\ \stackrel{\textit{using the change of base rule}}{x = \cfrac{\log(100)}{\log(2)}\implies x = \cfrac{2}{\log(2)}}\implies x\approx 6.644\)

as far as the domain, or namely what values "x" can take on safely, I don't see any constraints, so it must be (-∞ , +∞).

The surface areas of the figures are 336, 82 and 836

From the question, we have the following parameters that can be used in our computation:

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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Answer:

\(3\)

Step-by-step explanation:

\(10 \div ( \frac{ {3}^{2} + 1 }{5 - 2} )\)

\( \frac{10(5 - 2)}{ {3}^{2} + 1} \)

\( \frac{10 \times 3}{ {3}^{2} + 1 } \)

\( \frac{30}{ {3}^{2} + 1 } \)

\( \frac{30}{9 + 1} \)

\( \frac{30}{10} \)

\(3\)

Answer:

12/5 or 2.4

Step-by-step explanation:

Form the equation:

5x - 2 = 10

^     ^     ^

^     ^    "is ten" which adds a equal sign to it

^   minus two

five times a number  

Solve:

5x - 2 = 10

     +2    +2

-----------------

5x = 12

----   ----

5      5

x = 12/5 or 2.4

Let the number be x

Then ATQ

5x - 2 = 10

5x = 10+2

x = 12/5

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

a)= 5x+10

b)= 7y-6

c)= 6x-6

d)= 2x^2+8x-5

e)= 6x+9

f)= 4xy-4y^2+8y

g)= -12y^2+10y

h)= 6x+154

i)= 6x+21

h)= 2x^2+16