Mathematics High School

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

Part A: Find (f + g)(x). Show your work. (3 points)

Part B: Find (f ⋅ g)(x). Show your work. (3 points)

Part C: Find f[g(x)]. Show your work. (4 points)

Answers

Answer 1
A:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31


Related Questions

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?


f(x) = − one fourth (x − 1)2 + 1

f(x) = − one fourth (x − 1)2

f(x) = one fourth (x − 1)2 + 1

f(x) = one fourth (x − 1)2

Answers

alright,
directix is y=something so it opens down or up

we use
(x-h)²=4p(y-k)
the vertex is (h,k)
and p is distance from focus to vertex
if focus is above directix, p is positive
if focus is below directix, p is negative

so we gts

focus=(1,1)
directix is y=-1
1>-1
focus is above

oh, vertex is in middle of focus and directix
so
beteeen (1,1) and y=-1 is, hmm
that is a distance of 2 vertically
2/2=1
1 down from (1,1) is (1,0)
vertex is (1,0)
p=1

so
(x-1)²=4(1)(y-0)
solving for y to get into f(x)=something form
(x-1)²=4y
y=1/4(x-1)²
f(x)=1/4(x-1)²

4th option

Of the 30 girls who tried out for lacrosse team 12 were selected. Of the 40 boys that tried out 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? Explain.

Answers

Girls;

Total number of girls who tried out = 30

Number of girls who got selected = 12

Ratio of girls on team to girls who tried out = [tex] \frac{12}{30} = \frac{2}{5} [/tex] = 2 : 5

Boys;

Total number of boys who tried out = 40

Number of boys who got selected = 16

Ratio of boys on team to boys who tried out = [tex] \frac{16}{40} = \frac{2}{5} [/tex] = 2 : 5

Hence, the ratios are the same.

If x and y are both negative when is x-y positive

Answers

When multiplying two negative numbers the answer is positive
hmm

let's try some numbers

we have 3 scenarios
x>y
x=y
x<y

x>y
x=-1 and y=-2
x-y=-1-(-2)=-1+2=1
it's positive when x>y

x=y
x=-1, y=-1
-1-(-1)=-1+1=0
nope

x<y
x=-2 and y=-1
-2-(-1)=-2+1=-1
nope


x-y is positive when 0>x>y

You invest a total of $5800 in two investments earning 3.5% and 5.5% simple interest. Your goal is to have a total annual interest income of $283. Write a system of linear equations that represents this situation where x represents the amount invested in the 3.5% fund and y represents the amount invested in the 5.5% fund. Solve this system to determine the smallest amount that you can invest at 5.5% in order to meet your objective.

Answers

The annual interest that can be earned through investment of an amount at a simple interest can be calculated through the equation,
                I  = P x (i)
where I is interest, P is the principal amount, and i is the decimal equivalent of the interest. 

Let x be the amount deposited with 3.5% interest. With this representation, the amount deposited with 5.5% is 5800 - x. 

The linear equation that would represent the given scenario is,
        x(0.035) + (5800 - x)(0.055) = 283

Simplifying the equation,
 
       0.035x + 319 - 0.055x = 283

Combining like terms,
           -0.02x = -36
Dividing by -0.02,   
               x = 1800
             $5800 - x = $5800 - $1800 = y
                   y = $4000

Hence, the value that should be deposited to the 5.5% is $40000.   

If g is the variable, which mathematical sentence expresses the information below? "The number of gallons of gas in the tank plus 7 more adds up to 12 gallons."

Answers

An equation for the sentence would be g + 7 = 12, where g is the unknown number of gallons.

Answer: [tex]g+7=12[/tex]

Step-by-step explanation:

The given statement : The number of gallons of gas in the tank plus 7 more adds up to 12 gallons.

Given variable : 'g'

if g represents the number of gallons of gas in the tank, then for the given statement we have the following expression:-

[tex]g+7=12[/tex]

Hence, the mathematical sentence expresses the given information :-

[tex]g+7=12[/tex]

The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945

Answers

A = P(1+r)^(t/5) A = 500000(1+0.05)^(15/5) A = 500000(1.05)^(15/5) A = 500000(1.05)^3 A = 500000*1.157625 A = 578812.5 Telling us that the population will be about 578,812 people in the year 2005

HELP! Algebra!
The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job:


Based on the table, how many students have both a cell phone and a part-time job?
Answers:
A- 10
B- 40
C- 50
D- 100

Answers

The table shows that of those who have a part time job, 40 students have a cell phone, and 10 do not.  The correct answer is B, or 40.  40 students out of 100 have both a cell phone and a part-time job.

The number of students have both a cell phone and a part-time job is 40.

The correct option is (B)

What is algebra?

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

Given table shows that,

The students having whether having cell phones or not and whether the students are having part time job or not.

As we can see from the Column I shows students having cellphones and the first row shows students having part time job. which is 40.

Hence, the students have both a cell phone and a part-time job is 40.

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The curve y = x/(1 + x2) is called a serpentine. find an equation of the tangent line to this curve at the point (2, 0.40). (round the slope and y-intercept to two decimal places.) y =

Answers

Final answer:

The equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is given by y = -0.24x + 0.88, rounded to two decimal places.

Explanation:

The subject of the question refers to calculus, specifically the concept of finding the equation of a tangent line to a curve. This process typically involves finding the derivative of the function (which gives the slope of the tangent), and then using the point-slope form of the line equation.

The derivative of y = x/(1 + x2) can be found using the quotient rule for differentiation and is given by y' = (1 - x2)/(1 + x2)2. Evaluating this at x = 2 gives a slope of about -0.24 (rounded to two decimal places).

The equation of the line is usually written in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Since we know that the line passes through the point (2, 0.40), we can substitute these values into the equation and solve for b. This yields a y-intercept of about 0.88 (rounded to two decimal places).

Therefore, the equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is approximately y = -0.24x + 0.88.

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Carlos graphs the equations y = 0.5x^2 + 3 and y = –4x^2 + 24x – 35 and generates the graph below. Which conclusion is supported by the graph?

A. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no solutions.
B. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has one solution.
C. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has two solutions.
D. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has three solutions.

Answers

 A is the correct answer because the parabolas never touch.

Answer: The correct option is A. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no solutions.

Explanation:

The given equations are,

[tex]y=0.5x^2+3[/tex]

[tex]y=-4x^2+24x-35[/tex]

Since the above equations are quadratic equations, therefore they area parabola.

The coefficient of first equation is a positive therefore it is an upward parabola. The coefficient of second equation is a negative therefore it is an downward parabola.

From given figure it is noticed that the vertex of first parabola is (0,3) and the vertex of second parabola is (3,1).

The vertex is the extreme point of the parabola. So for first equation [tex]y\geq 3[/tex] and for second equation [tex]y\leq 1[/tex]. Therefore the parabolas will never intersect each other.

Since there is no intersection between parabolas therefore the equation

[tex]0.5x^2+3=-4x^2+24x-35[/tex] has no solution and the correct option is A.

(06.01)Which point on the scatter plot is an outlier?
Point H
Point I
Point J
Point K

Answers

point I is the outlier because it is furthest away from the graph's natural slope
*Hint: An outlier is something that is detached from the original group.

Since Point I seems the only point away from the group of points, that would be the outlier. 

Point I is the answer.

how many cookies will tony have if he bakes 5 more batches y=90+ 14 (x)

Answers

replace x with 5

y=90+14(5)

14*5 =70

90+70 =160

y=160

 he will have 160 cookies

Answer:

Given the equation:

[tex]y = 90+14x[/tex]               .....[1]

where,

y represents the total number of cookies  and

x represents the number of batches bake.

From the statement:

we have;

x = 5

Substitute in [1] we have;

[tex]y = 90+14 \cdot 5 = 90+70 = 160[/tex]

Therefore, 160 cookies will tony have if he bakes 5 more batches

A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class.

Answers

13 +5 =18

360/18=20

13*20 = 260

5*20 =100

260 economy & 100 business

Do as follows:

13 +5 =18

360/18=20

13*20 = 260

5*20 =100

260 economy & 100 business

Solve and check the inequality
|8m+4|<12

Answers

This is the concept of algebra, to solve the inequality we proceed as follows;
|8m+4|<12
given that the absolute value is represented by positive and negative values, we shall have:
-(8m+4)<12
-8m-4<12
-8m<12+4
-8m<16
thus;
m>16/(-8)
m>-2

also:
8m+4<12
8m<12-4
8m<8
m<8/8
m<1
hence the answer is -2<m<1

Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answers

You only have two observations to work the equation for the velocity.

You only can assume a linear relation.

Part a.

Calling x the independent variable (time in hours) and y the dependent variable (velocity in km/h) =>

x (time in hours)         y (velocity in km/h)

1                                  5
2                                  3

Now you use the linear relation:

slope: (3 - 5) km/h/ (2 - 1)h = - 2 km/1h^2 = - 2 km/h ^2

Equation:

y - 3 = slope * (x - 2)

=> y - 3 = - 2 ( x - 2)

=> y - 3 = - 2x + 4

=> y = 3 - 2x + 4

=> y = - 2x + 7

that is the slope-intercept form.

the standard form is y + 2x - 7 = 0

part B.

to draw the graph you can make a table with the points for the first four hours:

x (time in hours)            y (velocity in km/h)
                                        -2x + 7

1                                      -2(1) + 7 = 5

2                                      -2(2) + 7 = 3

3                                      -2(3) + 7 = 1

4                                     -2(4) + 7 = - 1

The graph, of course, is a straight line, because we started from that assumption.

The table and the graph below each show a different relationship between the same two variables, x and y:

How much more would the value of y be on the graph than its value in the table when x = 12?
Please just help me understand, do not give me the answer! thank you

Answers

Notice how both the table and the graph are lines. Moreover, they pass through the origin, so you could find y = a * x in each case, then substitute x=12, and compare each value. It says how much more, so the correct thing is to subtract. If it were how many times, then divide. Is that all you need? You don;t want the solution

help will mark brainliest

Answers

First find the slope:
(0-6)/(2-0)
-6/2
-3

Then find the y intercept (the value of y when x=0)
6

Plug both numbers into slope intercept form
y=-3x+6

Add an inequality symbol. It should me more than because the line is dashed and it is shaded above.

Final answer: y>-3x+6

three consecutive even numbers have a sum where one half of the sum is between 84 and 96

Answers

86 *2 = 172

172/3 = 57.33

54 + 56 +58 =168

168/2 =84


56 + 58 +60 = 174

174/2 =87

58 +60 +62 = 180

180/2 = 90

60 +62 +64 = 186

186/2 = 93


62 +64+66 = 192

192/2 = 96


 there are 3 sets of numbers that fall between 84 & 96

 1 set equals 84 and 1 set equals 96

 so if you are counting those there are 5 sets

 

The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y


****PLEASE HELP********

Answers

We start with football =basketball +30 of x=y+30
Add 10 so that 3/2=(f+10)/(y+10) 
Now let's use substitution to get 3/2=(y+30+10)/(y+10) or 3/2=(y+40)/(y+10) 
Now cross multiply so 3(y+10)=2(y+40) or 3y+30=2y+80. Solve to get y=50, meaning x must be 80.
Now let's check to make sure it would be 3/2 if each gets 10 new members. Football would then have 90 and basketball would have 60, so yes, it works!!

Evaluate 5x + (-2x 2) for x = 3.

Answers

5x + (-2x^2) for x = 3
5(3)+ (-2(3^2)) = 15 - 18 = -3

hope it helps
The answer to the expression is -3.

Which of the following equations has the solution x =  all real numbers? Select one: a. 4(3 - x) + 6x = 3x + 12 - x b. 4(3 - x) + 6x = 3x + 10 - x c. 4(3 - x) + 6x = 3x + 12 + 2x d. 4(3 - x) + 6x = x + 12 - 3x

Answers

a. 4(3-x) + 6x = 3x + 12 - x
    12 - 4x + 6x = 2x + 12
      2x + 12 = 2x + 12...infinite solutions <=== this one
    

b. 4(3 - x) + 6x = 3x + 10 - x
    12 - 4x + 6x = 2x + 10
    2x + 12 = 2x + 10...not this one...no solutions

c. 4(3 - x) + 6x = 3x + 12 + 2x
    12 - 4x + 6x = 5x + 12
     2x + 12 = 5x + 12....not this one...one solution

d. 4(3 - x) + 6x = x + 12 - 3x
    12 - 4x + 6x = -2x + 12
    2x + 12 = -2x + 12...not this one...one solution

The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.

Check all the options in order to determine which of the following equations has the solution x = all real numbers.

A) 4(3 - x) + 6x = 3x + 12 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 3x + 12 - x

       = 2x + 12

LHS = RHS means there is an infinite number of solutions.

B) 4(3 - x) + 6x = 3x + 10 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 2x + 10

LHS [tex]\neq[/tex] RHS means that there are no solutions.

C) 4(3 - x) + 6x = 3x + 12 + 2x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 5x + 12

LHS [tex]\neq[/tex] RHS means that there are no solutions.

D) 4(3 - x) + 6x = x + 12 - 3x

Simplify the above equation separately that is:

LHS = 12 + 2x

RHS = 12 - 2x

LHS [tex]\neq[/tex] RHS means that there are no solutions.

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Enter the degree of the polynomial below

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

A. 11
B. 10
C. 6
D. 7

Answers

The degree of a polynomial expression is the highest power in the expression

Rewriting the expression we have
[tex] 7x^{7} + 10x^{4}+ 4x^{3}-5 x^{11} -10 x^{6} -6 x^{7} [/tex]

We can see that the highest power is 11, hence the degree of the polynomial is 11

Correct answer: A

Assuming that n 1 , rewrite the compound interest equation B t 900 1.185 t in the general form.

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\\ t=year \end{cases}[/tex]

[tex]\bf 1.185\implies 1+0.185\qquad\quad and\quad n=1 \\\\\\ A=P\left(1+\frac{r}{n}\right)^{nt}\implies A=P\left(1+0.185\right)^{nt}\implies A=P\left(1+\frac{0.185}{1}\right)^{1\cdot t}[/tex]

so, the percentage of the rate is 0.185, what's that as a percentage? well, 0.185 * 100, 18.5%.

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –3 + (n – 1)(–2.2)

Answers

A(n) = a1 + (n - 1) * d
A(n) = -3 + (n - 1) * -2.2
n = term to find
a1 = first term = -3
d = common difference = -2.2

we can already see that the first term is -3 <==

4th term..
A(4) = -3 + (4 - 1) * -2.2
A(4) = -3 + 3(-2.2)
A(4) = -3 - 6.6
A(4) = - 9.6 <== 4th term

10th term...
A(10) = -3 + (10 - 1) * -2.2
A(10) = -3 + 9 * - 2.2
A(10) = -3 - 19.8
A(10) = - 22.8 <===10th term

Final answer:

The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.

Explanation:

The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.

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Write 14/42 in simplest form

Answers

7/6!!!!!!!!!!!!!!!!!!!!!!
7/6 should be your answer

Which expression can be used to determine the average rate of change in f(x) over the interval [2,9]
a) f(9-2)
b) f(9)-f(2)
c) f(9-2)/9-2
c) f(9)-f(2)/9-2

Answers

The correct answer is the second c or what I assume you meant to be d
f(9)-f(2)/9-2

Answer:

D. f(9-2)/9-2   on Edg2020

Step-by-step explanation:

Hope this helps!!! Have a great day!!!    : )

What is the sum of the two vectors (2,-1) and (3,3)?

Answers

Answer: (5, 2)

We simply add up the corresponding coordinates. The x coordinates of the two vectors are 2 and 3. They add to 2+3 = 5

The y coordinates are -1 and 3. They add to -1+3 = 2

So overall, 
(2,-1) + (3,3) = (2+3, -1+3) = (5,2)
is the answer
(5,2)is the answer to this question

Let u = <-9,4>, v = <8, -5>. Find u - v.

Answers

I am guessing vectors :)

(-17, 9)

or in polar form

√370, -27°53'50"

To find the difference between vectors u and v, subtract corresponding components.

Given vectors u = <-9,4> and v = <8, -5>, to find the difference u - v, subtract corresponding components:

Subtract the x-components: -9 - 8 = -17

Subtract the y-components: 4 - (-5) = 9

Therefore, u - v = <-17, 9>.

What is the following product

Answers

The answer is choice C. The work is shown in the attached image. 

if the lines a and b in the diagram below are parallel why do angles 1 nd 8 measure 120 degree angles

A) Because they are alternate interior angles.
B) Because they are corresponding angles.
C) Because they are alternate exterior angles.
D) Because they are same-side interior angles.

Answers

The pairs of angles on opposite sides of the transversal but outside the two lines are called alternate exterior angles.

C) Because they are alternate exterior angles.

A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?

Answers

wrong the correct answer is eight times 8
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