Mathematics Middle School

HELP NEEDED

Use the functions h(x) = 5x − 2 and t(x) = 4x + 6 to complete the function operations listed below.

Part A: Find (h + t)(x). Show your work.

Part B: Find (h ⋅ t)(x). Show your work.

Part C: Find h[t(x)]. Show your work.

Answers

Answer 1
Part A: Find (h + t)(x). Show your work. 
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h + t)(x) = 5x − 2 + 4x + 6
(h + t)(x) = 9x +4



Part B: Find (h ⋅ t)(x). Show your work. 
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h ⋅ t)(x) = (5x − 2) (4x + 6)
(h ⋅ t)(x) = 20x^2 + 30x - 8x - 12
(h ⋅ t)(x) = 20x^2 + 22x - 12



Part C: Find h[t(x)]. Show your work. 
h(x) = 5x − 2 and t(x) = 4x + 6
so
h[t(x)] = 5(4x + 6) − 2
h[t(x)] = 20x + 30 - 2
h[t(x)] = 20x + 28

hope all help.


Related Questions

watts,volts and amps are used to measure electricity. there is a formula that shows the relationship between watts,volts and amps. volts times amps = watts . if the volts are 120 and the amps are 5 how many watts are there?

Answers

VA=W
120(5)=W
600=W
600 Watts
Final answer:

The number of watts for a circuit with 120 volts and 5 amps is 600 watts.

Explanation:

The formula for calculating the power in an electrical circuit is: Power (P) = Voltage (V) × Current (I).

To calculate the number of watts, we can substitute the given values into the formula:
Volts (V) = 120
Amps (I) = 5

Therefore, the number of watts (P) = 120 V × 5 A = 600 W.

Which characteristics best describe an obtuse isosceles triangle? I. One angle is greater than 90°. II. All side lengths are equal. III. Two sides meet at a 90° angle. IV. Two sides are equal in length. A. I and IV B. II and III C. I and II D. III and IV

Answers

An obtuse triangle is a triangle that has an angle greater than 90 degrees, so 1. One angle is greater than 90 degrees is correct.

An obtuse isosceles triangle is defined as a three-sides triangle shape that has one angle (out of three angles) more than 90 degrees and whose two sides are always congruent that includes obtuse angle in between. So it will follow :-

⇒ Obtuse means "one angle is greater than 90 degrees".

⇒ Isosceles means "Two sides are equal in length".

So, option A is correct, i.e. statements I and IV.

which values are outliers ?

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

select all correct answers

Answers

5.8 0.8 5.9 6.1 and 10.9 are all correct answers.

Hope this Helped!

;D
:D
:)
;)
XD
:'D

Answer:

0.8 and 1.1 are outliers of the given data set.

Step-by-step explanation:

The given data set is

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

Arrange the data set in ascending order

0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9

Divide the data in four equal parts.

(0.8, 1.1), 4.9,( 5.2, 5.8), 5.9,( 6.1, 6.1), 7.4, (10.2, 10.9)

From the above division we get,

[tex]Q_1=4.9[/tex]

[tex]Median=5.9[/tex]

[tex]Q_3=7.4[/tex]

The interquartile range of the data is

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=7.4-4.9=2.5[/tex]

If all the data elements lies in the interval [Q₁-1.5(IQR),Q_3+1.5(IQR)], then the data set has no outliers.

[tex][Q_1-1.5(IQR),Q_3-1.5(IQR)]=[4.9-1.5(2.5),7.4-1.5(2.5)]=[1.15,11.15][/tex]

Since all the elements lie in the interval [1.15,11.15] except 0.8 and 1.1, therefore 0.8 and 1.1 are outliers.

The area of this rectangle is 5x2. What does the coefficient 5 mean in terms of the problem?

Answers

5 represents one of the dimensions of the rectangle, either length or width.

Answer: The length is 5 times the width


Step-by-step explanation:

Given: The area of rectangle = [tex]5x^2=(5x)(x)[/tex]

Here x must be a positive real number since it can not be negative.

Also for area of rectangle =[tex]length \times width[/tex]

And length is always greater than width of rectangle, therefore in the given expression 'x' must be width and '5x' must be length of rectangle .

[∵ for every positive x , 5x>x]

Hence, the coefficient 5 means the length is 5 times the width.

What is the output value for the following function if the input value is 3.2?

y = 2x - 1

1
2
4.2
5.4

Answers

the answer to this is 5.4

The given function is y = 2x -1 which is of the form of a straight line with the form y = mx + c

now, we have been given that the value of x is 3.2 as it says input value is 3.2

we plug in x =3.2 in the equation

y = 2x -1

y = 2*3.2 -1

y = 6.4 -1

y = 5.4

So the value of y we get is 5.4

Answer = 5.4 (option D)

Which of the following sequences is not arithmetic?

a.1, 2, 3, 4, ...
b.2, 4, 6, 8, ...
c.0, -2, -4, -6, ...
d.1, 4, 9, 16, ...

Answers

Answer: Choice D

===========================

A is arithmetic since we add 1 each time. The common difference is d = 1
B is arithmetic because the common difference is d = 2
C is arithmetic because d = -2 is the common difference
D is not arithmetic. The jump from 1 to 4 is +3 while the jump from 4 to 9 is +5

Answer:

1, 4, 9, 16, ...

Step-by-step explanation:

Cindy's job is to check computer printers for defects. Out of 420 printers she has to check, only 3 of the first 84 have been defective. What is the best prediction of the total numbers of printers in this group that will be defective?

Answers

46% printers are defective = 106 printers defective

I need help on these problems

Answers

Hope this helps and hope you can read it, if not let me know :)

what equation results from completing the square and then factoring.

Answers

The answer is D (x+11)^2=152

helppppppppppppppppppppppppp

Answers

Set the two expressions equal to each other.

7x + 3 = 9x

Simplify, isolate the x, subtract 7x from both sides

7x (-7x) + 3 = 9x (-7x)
3 = 2x

Set the equation = 0, subtract 3 from both sides

3 (-3) = 2x (-3)

0 = 2x - 3

2x - 3, or D, should be your answer

hope this helps

can somebody help me please this is my last question i need to submit this!! help!!

Answers

Both the vertical and horizontal cross-section would be a square.  The cross-sections are the same because all of a cube's dimensions are the same.  A cube is made up of 6 congruent square faces.

What is the coefficient of y in the expression 3 ⋅ 6 + 4y?

Answers

4 is the answer
Hope this helps:)

Answer:

Sorry I'm late, but I think the answer is D.

Step-by-step explanation:

according to the graph what is the value of the constant in the equation below rewritten in

Answers

B. 80 My work is shown in the picture above.

Answer:

The answer to this is B. 80

the initial number of bacteria in a culture is 12,000. the xulture doubles each day write an exponential functin to model the population Y of bacteria after X days

Answers

The equation would be y=12000(2)ˣ.

This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by.  In this problem, a = 12000 and b=2, since it doubles each time.

Answer:

[tex]Y = 12,000 \cdot (2)^X[/tex]

Step-by-step explanation:

The exponential function is given by:

[tex]y =a \cdot b^x[/tex]

where,

a is the initial values and b is the growth factor.

As per the statement:

The initial number of bacteria in a culture is 12,000.

⇒Number of bacteria initially(a) = 12,000

It is also given that the culture doubles each day.

⇒ growth factor [tex]b= 2[/tex]

We have to find the exponential function to model the population Y of bacteria after X days.

By definition of exponential function:

[tex]Y = 12,000 \cdot (2)^X[/tex]

where, x represents the days and Y is the population after X days.

Therefore,  an exponential function to model the population is,

[tex]Y = 12,000 \cdot (2)^X[/tex]

Solve the Systems of equations algebraically

4x+5y=15
-4x+6y+7

Answers
A- (5/4, 2)
B- (2, 5/4)
C- (4/5,2)
D (2, 4/5)

Answers

STEP 1:
4x + 5y= 15
-4x + 6y= 7
add the two above equations; the x term cancels out; solve for y

11y= 22
divide both sides by 11

y= 2


STEP 2:
substitute the y value in step 1 into either original equation

4x + 5y= 15
4x + 5(2)= 15

4x + 10= 15
subtract 10 from both sides

4x= 5
divide both sides by 4

x= 5/4


ANSWER: (A) x= 5/4, y= 2 or (5/4, 2)

Hope this helps! :)

Find the difference. express your answer in simplest form. (2s/s^2-4s+4) - (4/s^2-4s+4)

Answers

To find the difference, we are going to destroy the parenthesis first, and then, we are going to perform the operations. Remember that to destroy a parenthesis preceded by a negative sign (-), you should change the signs of the factors inside the parenthesis:
[tex] \frac{2s}{s^2-4s+4} -( \frac{4}{s^2-4s+4} )[/tex]
[tex]\frac{2s}{s^2-4s+4} -\frac{4}{s^2-4s+4}= \frac{2s-4}{s^2-4s+4} [/tex]

Now we can factor both numerator and denominator and simplify:
[tex]\frac{2s-4}{s^2-4s+4} = \frac{2(s-2)}{(s-2)^2} = \frac{2}{s-2} [/tex]

We can conclude that the difference in simplest form is: [tex] \frac{2}{s-2} [/tex]
To get started, combine -4s+4 with 4s - 4.  Result:  0.  That leaves

 2s        4          2(s+2)
------ - ------- = ------------
s^2      s^2           s^2

Part 1: Solve the system by graphing. Draw the graphs on paper and indicate their intersection point. Type the ordered pair solution here as your answer to Part 1.
Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.

2x+3y=6

x-2y=10

Answers

Part (1):
The graph is shown in the attached image.
As we can note from the graph, the solution of the system of equations is indicated by the point of intersection between the two lines which is (6,-2)

Part (2):
The equations given are as follows:
2x + 3y = 6 ...........> equation I
x - 2y = 10
which can be rewritten as:
x = 2y + 10 ...........> equation II

Substitute with equation II in equation I and solve for y as follows:
2x + 3y = 6
2(2y+10) + 3y = 6
4y + 20 + 3y = 6
7y = 6 - 20
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x = 10 + 2y 
x = 10 + 2(-2)
x = 10 - 4
x = 6

The solution is (6,-2)

Part (3):
The equations given are:
2x + 3y = 6 .............> equation I
x - 2y = 10 ...........> equation II

Multiply equation II by -2, this will give:
-2x + 4y = -20 ............> equation III

Add equation I and equation III as follows:
                                       2x + 3y = 6
                                +    -2x + 4y = -20
                           .........................................
                                       0x + 7y = -14
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x - 2y = 10
x - 2(-2) = 10
x + 4 = 10
x = 10 - 4
x = 6

The solution is (6,-2)

Hope this helps :)


what's the answer to this?

Answers

The measure of the side length of the right triangle is 20.

What is the measure of the missing side length?

A tangent makes an angle of 90 degrees with the radius of a circle.

Therefore, the triangle formed is a right triangle.

From the diagram:

Leg 1 = 12

Leg 2 = 16

Hypotenuse =?

To find the hypotenuse, we use the Pythagoras theorem:

(Hypotenuse)² = ( Leg 1 )² + ( Leg 2 )²

(Hypotenuse)² = ( 12 )² + ( 16 )²

(Hypotenuse)² = 144 + 256

(Hypotenuse)² = 400

Take the square roots of both sides:

Hypotenuse = √400

Hypotenuse = 20

Therefore, the side length measures 20 units.

Option C) 20 is the correct answer.

The complete question is:

Find the missing line segment in the diagram.

Learn more about Pythagorean theorem here: brainly.com/question/343682

#SPJ1

four times the sum of a number and 2/3 is 16/3. find the number. express your answer as a fraction in simplest form

Answers

times= multiply
sum= addition
is= equal sign

x= a number

4 times x plus 2/3 equals 16/3.


4x + 2/3= 16/3
subtract 2/3 from both sides

4x= 14/3
divide both sides by 4

x= 14/3 ÷ 4
to divide fractions, multiply by reciprocal/inverse of 4

x= 14/3 * 1/4
multiply numerators (top); multiply denominators (bottom)

x= (14*1)/(3*4)
x= 14/12
simplify by 2

x= 7/6


ANSWER: The number in simplest form is 7/6.

Hope this helps! :)

I need help with the first three please!!!

Answers

Number 1is nine days for the rest do you have formulas

What is the solution of x+8/5x-1>0 ?

Answers

x + [tex] \frac{8}{5} [/tex]x - 1 > 0

First combine like-terms (x + [tex] \frac{8}{5} [/tex]x).
2.6x - 1 > 0

Add 1 to both sides.
2.6x > 1

Divide both sides by 2.6 to isolate x.
x > 0.38

Answer:

Step-by-step explanation:

Eli, Freda and Geoff were given £800 to share in the ratio of their ages.
Eli is 9 years old,Feda is 13 years old and Geoff is 18 years old.
How much should they each get?
Eli-
Freda-
Geoff-

Answers

First, we are going to find the sum of their age. To do that we are going to add the age of Eli, the age Freda, and the age of Geoff:
[tex]9+13+18=40[/tex]
The combined age of Eli, Freda, and Geoff is 40, so the denominator of each ratio will be 40.

Next, we are going to multiply the ratio between the age of the person and their combined age by £800:
For Eli: [tex] \frac{9}{40} *800=180[/tex]
For Freda: [tex] \frac{13}{40} *800=260[/tex]
For Geoff: [tex]\frac{18}{40} *800=360[/tex]

We can conclude that Eli will get £180, Freda will get £260, and Geoff will get £360.

Final answer:

Calculate how £800 should be divided among Eli, Freda, and Geoff based on their ages.

Explanation:

Ratio of ages: 9:13:18 = 9/40 : 13/40 : 18/40

Total amount: £800

Eli: £200

Freda: £290

Geoff: £410

A spinner is spun 300 times and stops on C 95 times. Calculate the experimental probability of the spinner stopping on C.

Answers

it would be 32% or 32/100

Answer:

19/60

Step-by-step explanation:

Suppose you have $16,000 to invest in three stocks, A, B, and C. Stock A is a low-risk stock that has expected returns of 4%. Stock B is a medium-risk stock that has expected returns of 5%. Stock C is a high-risk stock that has expected returns of 6%. You want to invest at least $1,000 in each stock. To balance the risks, you decide to invest no more than $7,000 in stock C and to limit the amount invested in C to less than 4 times the amount invested in stock A. You also decide to invest less than twice as much in stock B as in stock A. How much should you invest in each stock to maximize your expected profit? Complete the constraints.

Answers

Answer:

Stock A: 1

Stock B: 1 and y=2

Stock C: 1, 7, 4

Final answer:

To maximize expected profit, you need to determine the amount to invest in stocks A, B, and C while considering the given constraints.

Explanation:

To invest in each stock to maximize expected profit, we need to determine the amount to invest in stocks A, B, and C while considering the given constraints.

Let's denote the amount invested in stock A as x, in stock B as y, and in stock C as z.

The constraints are as follows:

At least $1,000 should be invested in each stock: x > $1,000, y > $1,000, z > $1,000No more than $7,000 should be invested in stock C: z < $7,000The amount invested in C should be less than 4 times the amount invested in A: z < 4xThe amount invested in B should be less than twice the amount invested in A: y < 2x

To maximize expected profit, we need to maximize the sum of the expected returns from each stock:

Expected profit = 0.04x + 0.05y + 0.06z

By solving the constraints and optimizing the expected profit function, we can find the optimal values for x, y, and z.

which recursive formula can be used to reresent the sequence 2,6,10,14,18

1. a = 0
1
a = a + 4
n n-1


2. a = 2
1
a = a +4
n-1 n

3. a = 2
1
a = a -4
n n-1

4. a = 2
1
a = a +4
n n-1

Answers

Answer:

[tex] 4.\\\left\{\begin{array}{ccc}a_1=2\\a_n=a_{n-1}+4\end{array}\right\\\\check\\\\a_2=a_1+4\to a_2=2+4=6\\\\a_3=a_2+4\to a_3=6+4=10\\\\a_4=a_3+4\to a_4=10+4=14\\\\a_5=a_4+4\to a_5=14+4=18 [/tex]

Help with all of them please

Answers

Your answers are:
1. B
2. A
3. 1.5
4. D
Tell me if you want to see the work.

I need help ASAP

The figure of a rocket launched for space exploration is shown below.
Find the volume of the rocket to the nearest hundredth.

A) 90.36 cubic meters

B) 98.91 cubic meters

C) 80.07 cubic meters

Answers

It would be B.) 98.91 cubic meters

PLEASE HELP AND FAST, 15 POINTS! In the coordinate plane shown, how far apart are points B and D? Explain how you can use the Pythagorean theorem to determine this.

Answers

5 to the power of 2 = 25
9 to the power of 2 = 81
25 + 81 = 106
Square root of 106 = 10.29563
If you round it to the nearest hundredth, it will become 10.30
If you round it to the nearest tenth, it will become 10.3

help me? Answers por favor ?

Answers

6. complementary is they add to 90 degrees, a right angle.
4x+50=90.
90-50=4x
40=4x
x=10

7. theyre suplementary, they add to 180 degress, a straight line.
 42+6x=180
6x=180-42
6x=138
x=23

8-10, Do i state them all or just some. (Im going to name just 1 or 2)

8. angle AKB and BKG, angle CGD and CGJ
9.CGK and KGJ
10. DGE and KGJ

Help with question 12 please

Answers

I really don’t know I’m so sorry hope someone will help
Daniel's Train: 1:45 + 12 min = 1:57
Teri's Train: 2:35 - 20 min = 2:15
Time between 1:57 and 2:15 is 13 minutes
Other Questions
_____ is any condition of unusual deposits of black pigment in body tissues or organs.a. melanosisb. ileumc. iliumd. leukocyte PLEASE HELP: Question above WILL MARK BRAINLIEST!!!Which action would be prevented by the underlined portion of the First Amendment? A)Newspapers cannot criticize the President. B)Citizens cannot attend a rally against war. C)Methodism is declared the national religion. D)People are prevented from worshiping on Saturday. Jen makes necklaces by stringing different color beads each necklace is 18 in Long Jen has an 86 inch length of beaded string how many necklaces can she make How has the history and understanding of african art been influenced by colonialism? Select the equations that are equivalent to the equation y 2 = 3(x + 6). Select all that apply.y = 3x + 20y = 3x + 62x - y = -33x - y = -20 *98 POINTS*The Fall of the House of UsherBy Edgar Allan PoeNoticing these things, I rode over a short causeway to the house. A servant in waiting took my horse, and I entered the Gothic archway of the hall. A valet, of stealthy step, thence conducted me, in silence, through many dark and intricate passages in my progress to the studio of his master. Much that I encountered on the way contributed, I know not how, to heighten the vague sentiments of which I have already spoken. While the objects around mewhile the carvings of the ceilings, the sombre tapestries of the walls, the ebon blackness of the floors, and the phantasmagoric armorial trophies which rattled as I strode, were but matters to which, or to such as which, I had been accustomed from my infancywhile I hesitated not to acknowledge how familiar was all thisI still wondered to find how unfamiliar were the fancies which ordinary images were stirring up. On one of the staircases, I met the physician of the family. His countenance, I thought, wore a mingled expression of low cunning and perplexity. He accosted me with trepidation and passed on. The valet now threw open a door and ushered me into the presence of his master.Roderick Usher's poemBy Edgar Allan PoeIn the greenest of our valleys,By good angels tenanted,Once a fair and stately palaceRadiant palacereared its head.In the monarch Thought's dominionIt stood there!Never seraph spread a pinionOver fabric half so fair.Banners yellow, glorious, golden,On its roof did float and flow;(Thisall thiswas in the oldenTime long ago);And every gentle air that dallied,In that sweet day,Along the ramparts plumed and pallid,A winged odor went away. ...And, round about his home, the gloryThat blushed and bloomedIs but a dim-remembered storyOf the old time entombed.And travellers now within that valley,Through the red-litten windows seeVast forms that move fantasticallyTo a discordant melody;While, like a rapid ghastly river,Through the pale door,A hideous throng rush out forever,And laughbut smile no more.Which theme is represented in both the paragraph and the poem? Change is for the better. Change is for the worse. Love is always everlasting. Health and happiness always win out. Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?3 hrs.4 hrs.6 hrs. Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.What would Phil's total earnings be over the term of the contract?Enter your answer, rounded to two decimal places, in the box. 1.a verb form ending in -ing used as an adjective participle 2.a verb form used as another part of speech gerund 3.a verb form ending in -ing used as a noun adverb phrase 4.group of words without a subject or verb used as single part of speech infinitive 5.verb form preceded by to, used as a noun, an adjective, or an adverb verb phrase 6.phrase beginning with a preposition adjective phrase 7.prepositional phrase modifying a noun or pronoun verbal 8.participle with complements and modifiers coordinating conjunction 9.verb ending in -ing used with a helping verb participial phrase 10.prepositional phrase modifying a verb, adjective, or adverb prepositional phrase 11.A conjunction that joins words or groups of words of equal rank. restrictive clause 12.An adjective clause that is essential to the meaning of the sentence. phrase 13.A verbal form ending in -ing with its object and modifiers used as a noun. gerund phrase how do u simplify this?4r-3+6s-8r-(4s-6) You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.) In a study administered by alyssa zucker and her colleagues to college-educated women, it was found that _________ was higher in the 40s than in the 20s. The recursive rule for a sequence is shown. an=an1+7 a1=17 what is the explicit rule for this sequence? After the industrial revolution, dark-colored moths outnumbered light-colored moths in certain regions of england. within the past 40 years, factories in these regions have added scrubbers and air purifiers to their smokestacks, and the relative number of light-colored moths has increased. the probable reason for this increase is that What are non examples of Asexual reproduction What is one role of reasons in an argumentative research essay? An animal emits a response in the presence of a certain tone. if a slightly higher pitched tone elicits the same response, then stimulus _______ has taken place he walks 200m west and 125m north how far away is he from his starting point How was Arlo Guthries song Alices Restaurant a commentary on the draft?