Mathematics College

The graph of y=√x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph off(x)?$ 10-10-88 10 x

Answers

Answer 1

Explanation

We must apply some transformations to the function:

[tex]y=g(x)=\sqrt[3]{x}.[/tex]

(1) A reflection across the y-axis is given by the transformation:

[tex]g(x)\rightarrow h(x)=g(-x)=\sqrt[3]{-x}=-\sqrt[3]{x}.[/tex]

(2) A translation down 2 units is given by the transformation:

[tex]h(x)\rightarrow f(x)=h(x)-2=-\sqrt[3]{x}-2.[/tex]

Plotting the function f(x), we get the following graph:

Answer

Related Questions

Please help me solve this problem it’s my last question on my hw

Answers

To solve this problem, we will use the following expression:

[tex]\frac{favorable\text{ outcomes}}{total\text{ outcomes}}.[/tex]

In this case:

[tex]\begin{gathered} Total\text{ outcomes}=21+6+6=33, \\ favorable\text{ outcomes}=6. \end{gathered}[/tex]

Substituting the above values in the expression, we get:

[tex]\frac{6}{33}.[/tex]

Finally, simplifying the above result, we get that the probability that his shirt number is from 67 to99 given that he weighs at most 210 pounds is:

[tex]\frac{2}{11}.[/tex]

Answer:

[tex]\frac{2}{11}.[/tex]

For each system to the best description of a solution if applicable give the solution

Answers

System A

[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]

solve the first equation for x

[tex]x=4+4y[/tex]

replace in the second equation

[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]

The system has infinitely many solutions, They must satisfy the following equation

[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]

System B

[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]

solve for x for the first equation

[tex]x=6+2y[/tex]

replace in the second equation

[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]

The system has no solution.

Find the orthogonal trajectories of the family of curves. y^2=6KX^3

Answers

Y4 =9KX is your answer

The orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

What is the orthogonal trajectory?

An orthogonal trajectory of a family of curves is any curve that forms right angles with each member of the family. The curve does not always have to cross each member of the family.

It is given that,

y² = 6Kx³

Differentiate both sides we get,

[tex]\rm 2y = 6k(3x^2) \frac{dy}{dx} \\\\ \frac{dy}{dx} =\frac{2y}{18Kx^2}[/tex]

Substitute the value of K as

[tex]\rm K = \frac{y^2}{6x^3}[/tex]

[tex]\frac{2y}{18(\frac{y^2}{6x^3})x^2} = \frac{dy}{dx} \\\\ \frac{dy}{dx} = \frac{2x}{3y}[/tex]

Consider the negative reciprocal to find the perpendicular slope.

[tex]\frac{-3y}{2x} =\frac{dy}{dx} \\\\ - \int {\frac{1}{2x} \ dx = \int \frac{1}{3y} dy \\\\[/tex]

[tex]-\frac{x^2}{4}+C = \frac{y^2}{6}[/tex]

Simplify,

[tex]\rm 6(-\frac{x^2}{4}+C)= y^2 \\\\ y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

Thus, the orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]

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Hi, can you help me with this exercise please, Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.

Answers

From the given figure , we will use the Sine function in order to find segment x .

Sin 70 ° = opposite /hypotaneus

Sin 70 ° =x /7

∴x = 7* Sin 70°

x = 6.5778

x ≈6.6 ...( rounded to the nearest 10 )

How do I solve the missing verticals angles for L2 and L3?

Answers

The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:

Then, if we apply this theorem to the figure shown we can say that

[tex]\begin{gathered} L1=L3 \\ L2=L4 \end{gathered}[/tex]

This means that:

[tex]\begin{gathered} L2=110.6 \\ L3=69.4 \end{gathered}[/tex]

A linear function is shown on the graph
6
What is the domain of the function?
O(x10≤x≤4)
O(x10 Oy 12sy≤6)
0012 Question 1 (Answered)

Answers

The coloured dots in the graph means that it is in a closed interval .

x is between 0 in the y axis and 4 this intervals are included because the colour dots at the end of the straight line mean so

MATHEMATICALLY we say

[tex]0 \leqslant x \leqslant 4[/tex]

THAT IS THE DOMAIN OF THE GRAPH

THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.

Evaluate each function in the table at f (3).
Enter the correct answers in the boxes in the table.
Σ
Functions
Function
f(x) = 3x + 5
f(x)=x²-1.5
3
f(x) = 2x
ƒ(3)

Answers

The answer to the given functions are:

1) f (3) = 3 × 3 + 5 = 14

2) f( 3 ) = (3)² - 1.5 = 7.5

3) f (3) = 3×2 = 6

What are functions ?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

A function is a type of rule that produces one output for a single input.. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Given : Functions are f(x) = 3x + 5 ------- 1

f(x)=x²-1.5 --------- 2 and f(x) = 2x -----------3

Thus when we put x = 3 we will get the following values that is ;

1 becomes f (3) = 3 × 3 + 5 = 14

and 2 becomes f( 3 ) = (3)² - 1.5 = 7.5

And 3 becomes f (3) = 3×2 = 6

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write the quadratic equation whose roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable

Answers

The quadratic equation is y = 4. (x + 2)(x - 1).

Given,

The roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable.

To Write the Quadratic Equation by using above given:
Now, According to the question:

Roots are -2 and 1

Leading Coefficient is = 4

Using Variable is = x

Formulate the equation of polynomial function is

y = 4. (x + 2)(x - 1)

Hence, The quadratic equation is y = 4. (x + 2)(x - 1).

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URGENT!!) Which of the following served as the primary route for transporting cotton to Georgia's only sea port? (5 points)

a

The Savannah River

b

The Chattahoochee River

c

The Oconee River

d

The Suwanee River

Answers

Answer:

Correct answer:

a. The Savannah River

7.4.PS-15 Question Help Juanita has 3 rectangular cards that are 7 inches by 8 inches. How can she arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter? How will the area of the polygon compare to the combined area of the 3 cards? The perimeter of the polygon is 58 in. (Type a whole number.) How will the area of the polygon compare to the combined area of the 3 cards? O A. The areas will be equal. OB. The area of the polygon will be greater than the combined area of the cards. OC. The area of the polygon will be less than the combined area of the cards. OD. This is impossible to determine with the given information. Click to select your answer and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 8 of 10 Back Next →

Answers

Since there is no overlapping the area of the polygon must be equal to the combined area of the cards.

Match the one-to-one functions with their inverse functions.

Answers

Matching the following function

What is a Function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The function of f^(-1)(x) = 5x is:

f(x)= x / 5

The function of f^(-1)(x) = x^3 / 2 is:

f(x)=3√2x

The function of f^(-1)(x) = x+10 is:

x - 10

The function of f^(-1)(x) = 3(x + 17) / 2 is:

(2x / 3) - 17

Hence, These are the Match of one-to-one functions with their inverse functions.

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Can’t find the correct answer pls help

Answers

(14,-18) to get to 0 to 7 is 7 points and 3 to -8 is -10 points so you add that to ST (7,-8) and that’s gives u (14,-18)

Lashonda, Josh, and Brian sent a total of 90 text messages during the weekend, Lashonda sent 10 more messages than Josh. Brian sent 2 times as manymessages as Josh. How many messages did they each send?Number of text messages Lashonda sent:Number of text messages Josh sent:Number of text messages Brian sent:

Answers

Defining:

Number of messages of Lashonda = L

Number of messages of Josh = J

Number of messages of Brian = B

We know that:

L+J+B=90 (Equation 1)

We also know:

L = J+10 (Equation 2)

B=2J (Equation 3)

Now, we can substitue the values for L and B in the first equation

L+J+B=90

J+10 + J + 2J = 90

4J=90-10

4J=80

J=80/4

J=20

Since you found how many messages Josh sent, we can return to Equation 2 and 3:

L = J+10

L = 20 + 10

L = 30

B=2J

B=2*20

B=40

ANSWER:

Number of text messages Lashonda sent: 30

Number of text messages Josh sent: 20

Number of text messages Brian sent: 40

Find the range and mean of each data set. Use your results to compare the two data sets.Set A:Set B:2 10 8 19 2314 16 15 17 16

Answers

Range of a Data Set :

The range of a set of data is the difference between the highest and lowest values in the set

MEAN :

The mean is the mathematical average of a set of two or more numbers

Set A: 2, 10, 8, 19, 23

Arrange the data of set A in ascending order;

Set A : 2, 8, 10, 19, 23

For range; the highest term is 23, lowers term is 2

Range = highest - lowest

Range = 23 - 2

Range = 21

for Mean; the sum of all entries divided by the total number of entries in data set.

In data A, total number of entries are : 5

[tex]\begin{gathered} \text{ Mean = }\frac{2+8+10+19+23}{5} \\ \text{Mean}=\frac{62}{5} \\ \text{Mean}=12.4 \end{gathered}[/tex]

Thus, mean of set A is 12.4

Now, for set B;

Set B : 14 16 15 17 16

Arrange the elements of set B in the ascending order;

Set B : 14, 15, 16, 16, 17

For range; the highest term is 17, lowers term is 14

Range = highest - lowest

Range = 17-14

Range = 3

Thus, range of set B is 3

for mean of set B;

The sum of all entries divided by the total number of entries in data set.

In data B, total number of entries are : 5

[tex]\begin{gathered} \text{ Mean = }\frac{14+16+15+17+16}{5} \\ \text{Mean}=\frac{78}{5} \\ \text{Mean}=15.6 \end{gathered}[/tex]

Thus, the mean for set B is 15.6

Answer : The mean of set A is 12.4 and range is 21

The mean of set B is 15.6 and range is 3

Write in point-slope form an equation of the line through the pair of points (2,0) and (6,10). Type an equation of the line in point-slope form using one of the given points.

Answers

The point-slope form of a line is

[tex]y-y_1=m(x-x_1)_{}[/tex]

where (x_1, y_1) are the coordinates of a point on the line.

From the given point we find the slope m.

[tex]m=\frac{10-0}{6-2}=2.5[/tex]

With the value of the slope in hand, we now use one of the points given to write down the point-slope form:

[tex]\textcolor{#FF7968}{y-10=2.5(x-6)}[/tex]

where we have used the point (6, 10).

The area of the triangle below is40 square meters. What is the length of the base?Express your answer as a fraction in simplest form.

Answers

Given the area of the triangle:

[tex]A=\frac{3}{40}m^2[/tex]

You can identify in the figure provided in the exercise that the height of the triangle is:

[tex]h=\frac{1}{5}m[/tex]

The area of a triangle can be calculated using this formula:

[tex]A=\frac{bh}{2}[/tex]

Where "A" is the area, "b" is the base, and "h" is the height.

If you solve for "b", you obtain this formula:

[tex]\begin{gathered} 2A=bh \\ \\ b=\frac{2A}{h} \end{gathered}[/tex]

Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:

[tex]b=\frac{(2)(\frac{3}{40})}{\frac{1}{5}}[/tex][tex]b=\frac{\frac{6}{40}^{}}{\frac{1}{5}}[/tex][tex]b=\frac{6\cdot5}{40\cdot1}[/tex][tex]b=\frac{30}{40}[/tex][tex]b=\frac{3}{4}m[/tex]

Hence, the answer is:

[tex]b=\frac{3}{4}m[/tex]

"An orchestra of 120 players take 70 minutes to play Beethoven's 9th symphony," "How long would it take for 60 players to play the symphony?"Answer the question an explain*

Answers

Beethoven's 9th symphony

We have that in 70 minutes 120 players of an orchestra play Beethoven's 9th symphony because it always lasts 70 minutes.

The lenght of a musical piece does not depend in the number of musicians playing it. The orchestra could have 2 violinists more or less and they still will play the same 70 minutes musical piece.

Then, an orchestra of 60 players would take the same 70 minutes to play Beethoven's 9th symphony.

Answer: 70 minutes

Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge $41 per hour and painters charge $16 per hour.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

Answers

A) The inequality for the situation is 41x + 16y < 6900

B) The painter can work less than 97 hours without exceeding the budget of Hanson.

Given,

The total money spend by Hanson = < $6900

The charge for carpenters = $41 per hour

The charge for painters = $16 per hour

A) We have to find an inequality for this situation.

Lets take,

Carpenters working hours = x

Painters working hours = y

So, the inequality will be like:

41x + 16y < 6900

B) Now, we have to find the number of hours the painter can work without exceeding his budget if he hires carpenter.

Carpenters working hours = 50

Then, the charge will be = 50 × 41 = 2050

Then,

6900 - 2050 = 4850

The balance amount will be less than 4850.

So, the working hours of painter:

y < 4850 / 50

y < 97

That is, the painter can work less than 97 hours without exceeding the budget of Hanson.

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The question is incomplete. Completed question is given below:

Hanson is fixing up his home and must spend less than $6,900 to hire carpenters and painters. Carpenters charge$41 per hour and painters charge $16 per hour.

Part A: Write an inequality to represent the situation.

Part B: If he hires a carpenter for 50 hours, what is the maximum number of hours the painter can work without exceeding his budget?

What is the slope of the line passing through the points (0, 5) and (4,2) ^ prime

Answers

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]

An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 75%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 52%.

Answers

1. The probability that they win both contract will be 23.4%.

How to calculate the probability?

It should be noted that probability simply means the likelihood that an event will occur.

The probability of winning the contract will be:

= Probability of A winning × Probability of B winning

= 45% × 52%

= 0.45 × 0.52

= 0.234

= 23.4%

The probability is 23.4%

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What is the simplified form: (8m + 1)^2

Answers

Answer

(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1

Explanation

The question simply wants us to simplify the expression

(8m + 1)^2

= (8m + 1)²

= (8m + 1) (8m + 1)

= 8m (8m + 1) + 1 (8m + 1)

= 64m² + 8m + 8m + 1

= 64m² + 16m + 1

Hope this Helps!!!

grant is rolling a six sided number die eight times. How many possible outcomes are there?

Answers

The die has 6 faces

[tex]\begin{gathered} \text{ In n number of throws, the number outcomes is given by 6}^n \\ ^{} \end{gathered}[/tex][tex]\begin{gathered} \text{ In 8 throws, the possible outcomes will be 6}^8 \\ =1679616 \end{gathered}[/tex]

Bea is asked to graph this system of equations: 8x - 6y= 3 -3y + 4x = 4 How many times will the lines intersect?

Answers

Given the system of equations:

8x - 6y = 3

-3y + 4x = 4

To find how many times the lines will intersect. let's solve the system of equation using substitution method.

8x - 6y = 3 ........................................1

-3y + 4x = 4 ......................................2

From equation 1, make x the subject:

8x - 6y = 3

8x = 3 + 6y

[tex]\begin{gathered} x=\frac{3}{8}+\frac{6}{8}y \\ \\ x=\frac{3}{8}+\frac{3}{4}y \end{gathered}[/tex][tex]\text{Substitute (}\frac{3}{8}+\frac{3}{4}y)\text{ for x in equation 2}[/tex]

We have:

[tex]\begin{gathered} -3y+4(\frac{3}{8}+\frac{3}{4}y)=4 \\ \\ -3y+\frac{3}{2}+3y=4 \\ \\ \end{gathered}[/tex]

Multiply through by 2 to eliminate the fraction:

[tex]\begin{gathered} -3y(2)+\frac{3}{2}(2)+3y(2)=4(2) \\ \\ -6y+3+6y=8 \end{gathered}[/tex]

[tex]\begin{gathered} -6y+6y=8-3 \\ \\ 0=5 \end{gathered}[/tex]

Since we have 0 = 5, it means the system of equations has no solution.

Therefore, the lines will not intersect, because this system has no solution.

ANSWER:

A. The lines will not intersect, because this system has no solution.

For the following exercises, evaluate the function f at the indicated values.
a. f(-3) b. f(2) c. f(-a) d. -f(a)
4. f(x)=2x-5
5. f(x)=−5x²+2x−1
6. f(x)=x-1-x+1

Answers

After we evaluate the function f at the indicated values the results are

a. (4) −11, (5) −52, (6) 0

b. (4) -1, (5) −17, (6) -5

c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a

d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a

What is function?

A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.

Lets evaluate the function a. f(-3)

4. f(-3) = 2(-3)-5

= −11

5. f(-3) = −5(-3)²+2(-3)−1

= −52

6. f(-3) = -3-1-(-3)+1

= 0

Lets evaluate the function b. f(2)

4. f(2) = 2(2)-5

= −1

5. f(2) = −5(2)²+2(2)−1

= −17

6. f(2) = -3-1-(2)+1

= −5

Lets evaluate the function c. f(-a)

4. f(-a) = 2(-a)-5

= −2a−5

5. f(-a) = −5(-a)²+2(-a)−1

= −5a² −2a−1

6. f(-a) = -3-1-(-a)+1

= −3+a

Lets evaluate the function d. -f(a)

4. -f(a) = -(2(a)-5)

= −2a+5

5. -f(a) = -(−5(a)²+2(a)−1)

= 5a² −2a+1

6. -f(a) = -(-3-1-(a)+1)

= 3+a

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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.48 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 3% and the bottom 3%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.

Answers

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.

Some of their significance comes from the main limit theorem. This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution tends to become more normal as the number of samples increases. Because of this, the distributions of physical quantities, like misspecification, which are thought to be the consequence of hundreds of distinct processes, are frequently close to normal.

First we will find the bottom 3% such that P(X ≤ x) = 0.03

⇒ [tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03[/tex]

⇒[tex]P(Z\leq \frac{x-5.48}{0.07} )=0.03[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348[/tex]

Now we will find the same for the top part of the distribution.

[tex]P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97[/tex]

Now we will use the normal table to calculate the corresponding z-score.

[tex]\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612[/tex]

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

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Among the following which is the best
example for unlike terms?
O8x, 9t
O 9x-2x
О 3р. 5р
All of the choices

Answers

Answer 8x, 9t

The variable X and T are different and cannot be combined.

Hope this helps :)

Pls help asap

Find the product of 5.3 x 10^12 and 5.12 x 10^9. Write the final answer in scientific notation.

2.7136 x 10^21

2.7136 x 10^22

27.136 x 10^21

27.136 x 10^22

Answers

Answer:

B. 2.7136 x 10^22

Step-by-step explanation:

Hope this helps :))

TRIG ANALYSIS- THE LAW OF SINES- THE AMBIGUOUS CASERecall that your triangle should be set up so that angside b, and angle C is opposite side c.PLEASE HELP. WILL MARK BRAINLIEST

Answers

The sine law is described by the equation

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using

[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]