Question 1 of 10
f(x) = 3x³ - 2x² + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).

Answer:

D) x = 8

Step-by-step explanation:

The information given states that ABCD is similar to RSTU.

Line BC is similar to Line ST. ST is 2 times larger that BC.

Line AB is similar to Line RS. RS must be 2 times larger than AB as well, so multiply 4 x 2 to get x = 8.

Hope it helps!!!

Answer:

Step-by-step explanation:

I believe its

(-2,-6)

Answer:

11, 13, 17, 19

Step-by-step explanation:

A) Find the prime #'s less than 30.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

2) See which #'s add and is less than 30 but, equal to 8.

17.

B) Find prime #'s between 30 & 60

31, 37, 41, 43, 47, 53, 59

2) See which #'s add and is add to 10.

37.

The lakefront company should make the investment as in 5 years they'll have a profit of 10000.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, the lakefront company is considering investing in a new dock that will cost 560,000.

So, a Capital cost of 10% is (560000/10) = 56000

The company's borrowing rate is 8%.

∴ SI = (560000×8×5)/100.

SI = 5600×8×5.

SI = 224000.

So, The total cost is (560000 + 56000 + 224000) = 840000.

After 5 years they can sell it for 300000.

And has a cash flow of 110000, so in 5 years it is 550000.

So, total earnings is (300000 + 550000) = 850000.

Total profit is (850000 - 840000) = 10000 so it is profitable.

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Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

Explanation:

Given that three out of every fourteen trick-or-treaters were dressed as pirates

The proportion of the tick-or-treaters that were not dressed as pirates is the subtraction of the proportion of the people d

Dressed as pirates = 3/14

Not dressed as pirates = 14/14 - 3/14

= 11/14

Answer:

(B)The expression (5n)(9-p) is the product

(D)The expression 9-p has exactly two terms

Step-by-step explanation:

In the expression;

\(m+(5n)(9-p)-6-r^2\)

The coefficient of m is 1, therefore Option A is not true

The product of 5n and 9-p is (5n)(9-p), therefore Option B is true.

The expression 9-p has exactly two terms,9  and p.

Therefore, Options B and D are true.

Answer:

Hey, it is B and D! It is right on khan.

Given: Ben goes to the grocery store at a rate of 3 times a week.

Required: To determine how often Ben would be expected to go to the grocery store in 10 weeks.

Explanation: Let Ben goes x times to the grocery store in 10 weeks. It is given that Ben goes three times to the grocery store in 1 weeks. It can be translated to proportions as

Solving the above proportion gives,

Final Answer: Translate to proportion-

x=30 times in 10 weeks.

Answer:

\(\mathbf{E(p) = 1 - 3p}\)

the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%

Step-by-step explanation:

Given that:

the number of units demanded \(q = pe^{-3p}\)

Taking differentiations ; we have,

\(\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})\)

\(\dfrac{dq}{dp}=(1-3)e^{-3p}\)

Now; the price elasticity of demand using the differentials definition of elasticity  is:

\(E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}\)

\(E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}]\)

\(\mathbf{E(p) = 1 - 3p}\)

(b)   Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.

The estimate of the percentage change in price is :

\(=\dfrac{2.10-2.00}{2.00}*100 \%\)

= 5%

From (a)

\(\mathbf{E(p) = 1 - 3p}\)

Now at p = $2.00

E(2) = 1 - 3 (2.00)

E(2) = 1 - 6

E(2) = -5

The percentage change in q = -5 × 5%

The percentage change in q = -25%

Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%

The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

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

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

See below

Step-by-step explanation:

Given function is ,

=> f(x) = 4x + 7.

Replace f(x) with y ,

=> y = 4x + 7

For finding the inverse , interchange x and y ,

=> x = 4y + 7

Now solve for y ,

=> 4y = x - 7

=> y = x-7/4

Replace y with f-¹(x) ,

=> f-¹(x) = (x-7)/4

These are the required steps .

The ASA congruence theorem, Triangle TSR is congruent to Triangle QRS.

Triangle TSR is congruent to Triangle QRS, we can use the following steps:

We know that Angle TSR is congruent to Angle QRS because they are both right angles.

In Euclidean geometry, all right angles are congruent.

We are given that Angle T is congruent to Angle Q.

This is an additional angle congruence.

We know that Line segment SR is congruent to line segment RS.

This is due to the reflexive property, which states that any geometric figure is congruent to itself.

By combining the information from steps 1, 2, and 3, we have Angle TSR congruent to Angle QRS, Angle T congruent to Angle Q and Line segment SR congruent to RS.

According to the Angle-Side-Angle (ASA) congruence theorem, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

We have Angle TSR congruent to Angle QRS, Angle T congruent to Angle Q and Line segment SR congruent to RS.

Triangle TSR is congruent to Triangle QRS based on the given information and the ASA congruence theorem.

Congruence of triangles:

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

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The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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No, a triangle cannot be constructed with sides of 2in 3in and 6in For three line segments to be able to form any triangle you must be able to take any two sides, add their length and this sum be greater than the remaining side

9514 1404 393

Answer:

  y = ∛(x -4) -1

Step-by-step explanation:

The transformation ...

  g(x) = f(x -h) +k

translates the graph of f(x) h units to the right and k units up. Here, the cube root function is translated 4 units right and 1 unit down, so h=4 and k=-1. Putting those into your equation gives ...

  y = ∛(x -4) -1

Answer: Length = 40 inches

Width = 20 inches

Step-by-step explanation:

Let the width of the package be represented by x.

Since the length of the package must be twice its width, therefore the length will be: = 2 × x = 2x

Since the sum of the dimensions equals 60 inches. This will then be:

x + 2x = 60.

3x = 60

x = 60/3

x = 20

Therefore, the width = 20 inches

Length = 2x = 2 × 20 = 40 inches

The dimensions should be 40 by 20 inches.

Answer:2

Step-by-step explanation:{[(30-60) ÷ (-30)1²-15} = (-7)=2

Hours, h Total Cost

1 14

2 18

3 22

4 26

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.

Here,

To find the total cost of renting the golf clubs for h hours, we can use the expression:

Total Cost = 10 + 4h

We can use this expression to complete the table as follows:

Hours, h Total Cost

1 10 + 4(1) = 14

2 10 + 4(2) = 18

3 10 + 4(3) = 22

4 10 + 4(4) = 26

Therefore, the completed table is:

Hours, h Total Cost

1 14

2 18

3 22

4 26

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Answer: Symmetric Property

Step-by-step explanation: In this problem, notice that we're simply switching

the two sides of an equation and this idea is called the symmetric property.

The symmetric property allows us to switch the left and right

side of an equation which is why we can change n = -3 to -3 = n.

The correct ordered pair for the data is (1, 2), (2, 4), (3, 6), and (4, 8). The correct option is A.

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.

Number of Boxes of Popcorn     Cost ($)

1                                                          2

2                                                         4

3                                                         6  

4                                                         8  

The ordered pair of the data is,

(1, 2),

(2, 4),

(3, 6),

(4, 8),

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Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

Answer:

Step-by-step explanation:

30.8%

Explanation- Did the maths

Answer:

9000/10=900

Explanation:

We can find this by cancelling zeros

this is what it looks like

9000

---------

 10

900

------

  1

the answer to any division fraction with the denominator as 1 has the numerator as the answer

The speed of the rabbit in miles per hour is 50.33 mi/h.

We know that the speed of the jackrabbit is:

1.35 km/min.

Now we need to use the relations:

1 hour = 60 minutes.

So, in one hour, the rabit runs 60 times the distance that it runs in one minute, then:

1.35 km/min = 60*(1.35 km/h) = 81km/h

Now we need to change kilometers for miles.

1km = 0.6214 mi

Then we can rewrite:

81km/h = 81*0.6214mi/h = 50.33 mi/h

The speed of the rabbit in miles per hour is 50.33 mi/h.

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Answer:

We conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.

Step-by-step explanation:

We need to determine the expression for the amount of sugar Freed needs to make 1/2 batch.

Let 'x' be the batch and 'y' be the amount of sugar

Suger needed for a full batch = 3/4 cup of a sugar

so

But, Farid is making 1/2 of the batch.

Thus, multiply both sides by 1/2

\(x\times \frac{1}{2}\:=\:\frac{3}{4}y\times \frac{1}{2}\)

\(\frac{x}{2}=\frac{3y}{8}\)

Therefore, we conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.

The correct statement regarding the values is given as follows:

The values are opposite from each other, and they are both 5/2 units from zero.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

The values for this problem are given as follows:

The numbers are the same, with the opposite signal, hence they are opposites.

Additionally, both numbers have the same absolute value of 5/2, hence they are both at a distance of 5/2 units from the origin.

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