Given that f ( x ) = x 2 + 9 x + 20 f(x)=x 2 +9x+20 and g ( x ) = x + 5 g(x)=x+5, find f ( x ) + g ( x ) f(x)+g(x) and express the result in standard form.

Answer:

Step-by-step explanation:

-14 ft drop

drop is below and its a negative number

Answer:

Her weekly allowance is $18

Step-by-step explanation:

We can use an algebraic equation to solve this problem.

x/2 + 6 = 15

x/2 + 6 ( - 6) = 15 ( - 6)

x/2 ( · 2)= 9 ( · 2)

x = 18

Her weekly allowance is $18

Answer:

If you are asking what the solution to this set of equations is, then they are the same line. They map to the same line.

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

=> 8²

=> 8 × 8

=> 64

Answer:

-ab/1

Step-by-step explanation:

The multiplicative inverse of x/y is y/x, because when multiplied it equals 1.

x/y time y/x = xy/xy, which equals one.

In this case, -1/ab times -ab/1 = -1ab/-1ab, which equals one.

An upper bound on the error that can result from approximating cos(x) by 1−(x^2/2!) + (x^4/4!) over the interval [-0.7, 0.7] is 0.00567.

The Taylor series expansion for cos(x) is given by cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ... . The approximation 1−(x^2/2!) + (x^4/4!) is a truncated version of this series. The error between the actual value of cos(x) and the approximation can be estimated using the Lagrange form of the remainder term, which gives an upper bound on the error.

In this case, the Lagrange remainder term is given by Rn(x) = (f^(n+1)(c)/n+1!) * (x-x0)^(n+1), where f^(n+1)(c) is the (n+1)th derivative of cos(x) evaluated at some point c in the interval [-0.7, 0.7].

The maximum value of Rn(x) over the interval [-0.7, 0.7] occurs when x = ±0.7, and the upper bound on the error is found by evaluating Rn(±0.7).

The resulting upper bound is approximately 0.00567.

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The critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3 and (1, -1) is the only extremum or relative maximum of the function.

To find the relative maximum and minimum values of the function f(x, y) = (\(x^3\))/3 + 2xy +\(y^2\) - 3x + 1, we need to analyze its critical points and classify them using the second partial derivative test.

To find the critical points, we need to compute the partial derivatives of f with respect to x and y and set them equal to zero:

∂f/∂x = \(x^2\) + 2y - 3 = 0

∂f/∂y = 2x + 2y = 0

Solving these equations simultaneously, we find x = 1 and y = -1.

Thus, the critical point is (1, -1).

Next, we need to compute the second partial derivatives and evaluate them at the critical point:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 2

Now, we can use the second partial derivative test to classify the critical point.

The discriminant D = (∂²f/∂x²) × (∂²f/∂y²) - \(\left(\frac{{\partial^2 f}}{{\partial x \partial y}}\right)^2\) = (2)(2) - \((2)^2\) = 0.

Since D = 0, the test is inconclusive.

To determine the nature of the critical point, we can examine the function near the critical point.

Evaluating f at the critical point (1, -1), we find f(1, -1) = \((1^3)\)/3 + 2(1)(-1) + \((-1)^2\) - 3(1) + 1 = -1/3.

Hence, the critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3.

There are no other critical points to consider, so we can conclude that (1, -1) is the only extremum of the function.

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Answer:

intersecting lines will cross at the point

Answer:

x = 30

Step-by-step explanation:

x + 2x + 3x = 180 (Add like terms)

6x = 180 (Divide both sides by 6)

x = 30

Therefore;

x = 30

2x = 60

3x = 90

Explanation

Step 1

to find the total area divide the figure

now, we need to find the area of the triangle

so, we need to find the hypotenuse of the triangle

so, the height of the triangle is 5 cm

Step 2

let

side of the square=6

heigth of the triangle=5

base of the triangle=6

I hope this helps you

These inequalities ensure that Bob buys at least three albums, and no more than 35 individual songs, while staying within his budget of $60.

The system of inequalities that represents the situation is:

x + 10y ≤ 60 (total cost cannot exceed $60)

x ≤ 35 (no more than 35 individual songs)

y ≥ 3 (at least three albums)

Here, x represents the number of individual songs and y represents the number of albums.

The first inequality, x + 10y ≤ 60, ensures that the total cost of Bob's purchases does not exceed $60.

The second inequality, x ≤ 35, ensures that Bob does not buy more than 35 individual songs.

The third inequality, y ≥ 3, ensures that Bob buys at least three albums.

Together, these inequalities ensure that Bob buys at least three albums, and no more than 35 individual songs, while staying within his budget of $60.

Note that this system of inequalities assumes that Bob only buys whole albums, and not individual songs from albums. If he buys individual songs from albums, the system of inequalities would be more complex.

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Answer:

Obtuse.

Step-by-step explanation:

If sides are a b and c, with c the longest:

c^2 = a^2 + b^2 = Right triangle

c^2 < a^2 + b^2 = Acute     ...

c^2 > a^2 + b^2 = Obtuse  ...

33^2 = 1089

25^2 = 625

9^2 = 81

625 + 81 = 706

1089 > 706 so the triangle is obtuse.

Answer:

Obtuse scalene triangle

Step-by-step explanation:

Side 1: 9 cm

Side 2: 25 cm

Side 3: 33 cm

1. Find 9 squared, 25 squared, and 33 squared:

9 squared = 81

25 squared = 625

33 squared: 1089

 Find sum of the squares of 2 smallest sides:

81 + 625 = 706

Longest Side Squared = 1089

706 < 1089

Hence, since 706 < 1089, aka sum of the squares of the smaller 2 sides < longest side squared - you have a obtuse scalene triangle

I used a triangle calculator, so yeah in advance you should probably just use one of those :)

Answer:

90π in²

Step-by-step explanation:

  r = 3 in

  h = 10 in

     \(\sf \boxed{\text{\bf Surface area of cylinder =$\pi r^2h$}}\)

                                                   \(= \pi 3*3*10\\\\= 90 \pi \ in^2\)

In this question it is given that the radius of a cylinder is 3 inches. The height of the cylinder is 10 inches. We are asked to calculate the surface area of the cylinder in terms of π .

Radius = 3 inches

Height = 10 inches

We know,

\( \star \: \small \boxed{\rm{ Surface \: area \: of \: a \: cylinder = πr²h}}\)

Substituting the values we get

\( \small\sf{ Surface \: area \: of \: a \: cylinder = π × 3² × 10}\)

\( \small\rm{ Surface \: area \: of \: a \: cylinder = π × 3 \times 3 × 10}\)

\( \small\rm Surface \: area \: of \: a \: cylinder = π × 90\)

\( \small\sf{ Surface \: area \: of \: a \: cylinder = \bf{90 π \: inches²}}\)

Answer:

See below.

Step-by-step explanation:

-10.75(20x+15.2)

-215x-163.4

-hope it helps

The equivalent expression is,

⇒ - 215x - 163.4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 10.75 (20x + 15.2)

Now, We can simplify as;

⇒ - 10.75 (20x + 15.2)

⇒ - 10.75 × 20x - 10.75 × 15.2

⇒ - 215x - 163.4

Thus, The expression is equivalent to - 215x - 163.4.

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The cost of 45 blank CD's will be equal to $ 14.85.

It is given that 15 blank CD's costs $5.

We have to find out what will be the cost of 45 blank CD's.

What is the unitary method?

The unitary method is a method in which we find the value of a unit and then the value of the required number of units.

As per the question ;

Cost of 15 blank CD's = $5

So ;

The cost of 1 blank CD will be ;

= 5 ÷ 15

= $ 0.33

And

The cost of 45 blank CD's will be ;

= 45 × $0.33

= $ 14.85

Thus , the cost of 45 blank CD's will be equal to $ 14.85.

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Answer:

owes $12.50

Step-by-step explanation:

2.5*5

=12.5

Answer:

-12.5

Step-by-step explanation:

If you do 2.50*5 (because Ms. Ortiz borrows $2.50 every day for 5 days) it equals 12.5, and since it's how much she owes, you have to make it negative, so it's -12.50 or she owes $12.50 (the first one if you are supposed to have the answer be negative, the second one if you have to have it in money form).

The given statement "The diagonal of a parallelogram does not create alternate interior angles" is false because alternate interior angles are formed when two parallel lines are intersected by a transversal, and they are located on opposite sides of the transversal and between the two parallel lines.

In a parallelogram, the opposite angles are congruent, meaning they have equal measures. When a diagonal is drawn in a parallelogram, it creates two pairs of congruent opposite angles, but these angles are not considered alternate interior angles.

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From the question the transformations that non-rigid is dilation. The correct answer is B.

Any transformation of a geometric object that alters the size but not the shape is referred to as a nonrigid transformation. Examples of non-rigid types of transformation include stretching and dilation. Any action taken on a shape is referred to as a metamorphosis.

Rigid transformation is When a figure undergoes a stiff transformation, its size and shape are left unaltered. Because the image is unchanged, stiff transformations include translations, rotations, and reflections.

As a result, a dilation is a non-rigid transformation because the size of the image is changing.

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Answer:

13 + 14 + 15

Step-by-step explanation:

n + (n + 1) + (n +2) =42

n + n + n + 1 + 2 = 42

3n + 3 = 42

(subtract 3 from both sides)

3n = 39

(divide both sides by 3)

n = 13

(solve)

n + (n + 1) + (n +2) =42

13 + (13 + 1) + (13 + 2) = 42

13 + (14) + (15) = 42

13, 14, 15

(Hope this helps, have a nice day!)

If the initial population is 3800. The population of cockroaches after 3 years will be 1603.

Consider the function:

y = a(1 ± r)ⁿ

where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, there is exponential growth happening by r fraction or r%.

If there is a minus sign, there is exponential decay happening by r fraction or r%.

If the population is currently 3,800 cockroaches.

The expression is given as

y = 3800(0.75)ⁿ

The population of cockroaches after 3 years will be

y = 3800(0.75)³

y = 3800 x 0.4218

y = 1603.125

y ≅ 1603

Hence, the population of cockroaches after 3 years will be 1603.

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The complete question is:

Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.

Answer: 21,400 mg

Step-by-step explanation: Multiply the mass value by 1000 .

The correct properties of the Student's t-distribution are: B. The area in the tails of the t-distribution is slightly greater than the area in the tails of the standard normal distribution. D. As the sample size n increases, the density curve of t gets closer to the standard normal density curve.

A. This statement is incorrect. The t-distribution is not necessarily centered at μ (population mean). The center of the t-distribution depends on the degrees of freedom.

B. This statement is correct. The t-distribution has heavier tails compared to the standard normal distribution, which means that the area in the tails of the t-distribution is slightly greater than the area in the tails of the standard normal distribution.

C. This statement is incorrect. The area under the t-distribution curve is not necessarily 1. The area under any probability distribution curve is always equal to 1, but the t-distribution can have varying areas under its curve depending on the degrees of freedom.

D. This statement is correct. As the sample size (degrees of freedom) increases, the t-distribution becomes closer to the standard normal distribution.

E. This statement is incorrect. The t-distribution differs for different degrees of freedom. The degrees of freedom determine the shape and characteristics of the t-distribution, and changing the degrees of freedom results in different t-distributions.

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SOLUTION

The rate at wihich the cartons are packed per hours is

Then we find the rate at which each of the worked per hour.

The number of carton joe parcked=6

The ime taken by Joe =2 hours

Hence

Joe packed 3 cartons per hour

Similarly,

The number of carton Bob packed =17

The time taken by Bob =6 hours

hence

hence

Bob packed 2.83 cartons per hour

Hence

Comparing the number of carton packed per hour by both individuals,

Joe packed the most carton per hour

(4) a reflection over the line y = x, rigid motion would map ABC onto A'B'C

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The graph below shows two congruent triangles, ABC and A'B'C'.

Horizontal translation: g(x)=f(x+c).

The graph is translated c units to the left if c>0 and c units to the right if c<0.

Vertical translation: g(x)=f(x)+k.

The graph is translated k units upward if k>0 and k units downward if k<0.

We have,

ΔABC to ΔA'B'C

The reflection over y = x states that,

(x, y) → (y, x)

Now,

The coordinates of ΔABC.

A = (5, 2)

B = (7, -2)

C = (2, -4)

The coordinates of ΔA'B'C

A' = (2, 5)

B' = (-2, 7)

C' = (-4, 2)

This is a reflection of y = x.

Thus,

The rigid motion is a reflection over y = x.

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Complete question:

Answer:

\( \frac{61}{20} \)

Step-by-step explanation:

\( \frac{3}{4} + ( \frac{4}{3} - \frac{1}{2} + \frac{2}{3} + \frac{4}{5} ) \\ \\ \frac{3}{4} + (( \frac{4}{3} - \frac{1}{2}) - \frac{2}{3} + \frac{4}{5} ) \\ \\ \frac{3}{4} + ( \frac{4 + 3}{3} - \frac{1}{2} + \frac{4}{5} \\ \\ \frac{3}{4} + ( \frac{6}{3} - \frac{1}{2} + \frac{4}{5}) \\ \\ \frac{3}{4} + (2 - \frac{1}{2} + \frac{4}{5} )\\ \\ \frac{3}{4} + \frac{20 - 5 + 8}{10} \\ \\ \frac{3}{4} + \frac{15 + 8}{10} \\ \\ \frac{3}{4} + \frac{23}{10} \\ \\ \frac{15 + 46}{20} \\ \\ \frac{61}{20} \)

The rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

What is the Volume of a Sphere?

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a circular, three-dimensional form. Its form is determined by three axes: the x, y, and z axes. Sports like basketball and football are all instances of spheres with volume.

Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We may use the following formula to get the volume of a sphere whose radius is "r":

Here, In the question, It is given that:

Radius = 4inch.

Rate of increase = 569 cubic inches;

So, using the Volume of Sphere, formula:

\(\begin{aligned}v=\frac{4}{3} \pi r^3 \\\frac{d v}{d t} &=\frac{d}{d t}\left[\frac{4}{3} \pi r^3\right] \\&=\frac{4 \pi}{3}\left(3 r^2\right) \frac{d r}{d t} \\\frac{d v}{d t} &=4 \pi r^2 \frac{d r}{d t}\end{aligned}\)

\(\begin{aligned}&\frac{d r}{d t}=\frac{\frac{d v}{d t}}{4 \pi r^2}\\&\left.\frac{d r}{d t}=\frac{569}{(4 \pi)(4)^2}=\frac{d}{d t}_{r=4}^{d r^2}=569\right]\\&\frac{d v}{d t}=\frac{569}{64 \pi} \sim 2.83\end{aligned}\)

Hence,  the rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

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Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

gimme brainlyest gang

The probability that the interval (x - 15) to (x + 15) contains the true population mean can be determined using the properties of the normal distribution.

In this scenario, the random variable x represents the sample mean. The sample mean is an unbiased estimator of the population mean.

Since the sample mean follows a normal distribution, with a known variance of 3600, we can calculate the standard deviation (σ) by taking the square root of the variance. So, σ = √3600 = 60.

To calculate the probability that the interval (x - 15) to (x + 15) contains the true population mean, we need to find the area under the normal curve between these two values.

Since the normal distribution is symmetric, the probability of the interval (x - 15) to (x + 15) containing the population mean is equal to the probability of the interval (x - 15) to (x) plus the probability of the interval (x) to (x + 15).

Using the standard normal distribution table or a statistical calculator, we can find the probabilities associated with these two intervals. The probability for each interval can be calculated by finding the area under the normal curve.

Given that the sample size is 36, we can use the central limit theorem to assume that the sample mean follows a normal distribution regardless of the shape of the population distribution.

To summarize, to find the probability that the interval (x - 15) to (x + 15) contains the true population mean, we need to find the area under the normal curve for the intervals (x - 15) to (x) and (x) to (x + 15).

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Answer:

The correct option is;

a. Accountant

Step-by-step explanation:

The given data are;

Career,                                                                   Average Salary

Veterinarian,                                                          $56,000

Personal trainer,                                                    $18,000

Accountant,                                                           $43,000

Paralegal,                                                              $34,000

Architect,                                                               $50,000

Photographer,                                                       $19,000

Pharmacist,                                                            $44,000

Secretary,                                                              $30,000

Surveyor,                                                               $36,000

Webmaster,                                                           $49,000

Among the options given, which are, accountant (salary, $43,000), paralegal (salary, $34,000), photographer (salary, $19,000), and surveyor (salary, $36,000), the accountant, with a salary of $43,000, requires the most education.

Answer:

In other words, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. On the other hand, the lateral surface area refers to the area of the sides of a shape , excluding its base and top area.

Step-by-step explanation: