PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!

The polynomial function y = x^3 -3x^2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!The Polynomial Function Y = X^3 -3x^2 + 16x - 48 Has

Answers

Answer 1

Answer: B

Step-by-step explanation:

  x³ - 3x²  + 16x - 48 = 0

→ x²(x - 3)   + 16(x - 3) = 0

→ (x² + 16) (x - 3) = 0

→ (x² - (-16)) (x - 3) = 0

→ (x - 4i)(x + 4i)(x - 3) = 0

→ x - 4i = 0    x + 4i = 0   x - 3 = 0

→  x = 4i          x = -4i        x = 3

2 imaginary roots         and 1 real root


Related Questions

Patrick took his parents to dinner and the bill was $70 plus 6% tax. If he left a tip of 15% of the total (food plus tax), what was the total cost of the dinner?

Answers

Answer: $85.33

Step-by-step explanation:

Bill: $70

Bill + Tax: $70 + $70(0.06)

              = $70 + $4.20

              = $74.20

Bill + Tax + Tip: $74.20 + $74.20(0.15)

                        = $74.20 + $11.13

                        = $85.33

HelllPPPP

What is the measure of ABC

Answers

Answer:

B 46

Step-by-step explanation:

Using the formula for tangents, arcs and angles

< ABC = 1/2 (CDA - CA)

<ABC = 1/2 (226-134)

<ABC = 1/2(92)

<ABC = 46

What is the distance between the points (−19, −4) and (11, 12)?

A. 30
B. 34
C. 48
D. 17

Answers

Answer:

B. 34

Step-by-step explanation:

To find the distance between two point we use the formula

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

d = sqrt((12--4)^2 + (11--19)^2)

d = sqrt((12+4)^2 + (11+19)^2)

d = sqrt((16)^2 + (30)^2)

d =sqrt(256+900)

d = sqrt(1156)

d =34

Answer:

The correct answer is 34.

Step-by-step explanation:

d(A,B)d(A,B)d(A,B)=(11−(−19))2+(12−(−4))2−−−−−−−−−−−−−−−−−−−−−−−√=900+256−−−−−−−−√=34

Cedric can buy 3 songs for $3.60 or 4 songs for $4.80. How much do you think he would pay for 5 songs?
A) $5.80
B) $6.00
C) $6.20
D) $6.40

Answers

Answer:

B) $6.00

Step-by-step explanation:

well divide 3.60 and you get 1.20

and the same for 4.80 divided by 4

so it be 1.20 times 5= he pays

Final answer:

To find out how much Cedric would pay for 5 songs, we divide the total cost by the number of songs and then multiply it by 5. Cedric would pay $6.00 for 5 songs.

Explanation:

To find out how much Cedric would pay for 5 songs, we first need to determine the cost per song. From the given information, we can see that the cost of 3 songs is $3.60 and the cost of 4 songs is $4.80. To find the cost per song, we can divide the total cost by the number of songs.

Cost per song = Total cost / Number of songsCost per song for the 3 songs = $3.60 / 3 = $1.20Cost per song for the 4 songs = $4.80 / 4 = $1.20

Since the cost per song is the same for both sets of songs, we can conclude that Cedric would pay $1.20 for each song. Therefore, for 5 songs, he would pay 5 x $1.20 = $6.00.

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I need help with #8 and #9 Please! :)
I will mark as brainliest!

Answers

Answer:

see explanation

Step-by-step explanation:

(8)

the common ratio r,  of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = ......

r = [tex]\frac{\frac{1}{32} }{\frac{1}{256} }[/tex] = [tex]\frac{\frac{1}{4} }{\frac{1}{32} }[/tex] = 8

(9)

The simplest way to evaluate the sum is to substitute k = 3, 4, 5, 6 into each term and sum them

(- 9 + 20) + (- 12 + 20) + (- 15 + 20) + (- 18 + 20)

= 11 + 8 + 5 + 2 = 26


Will mark you as brainiest
if right!! Please Please answer this question! I need it done by 4 P.M. Eastern Time


Which answers describe the end behaviors of the function modeled by the graph?



f(x)=−3^(x+2)−2


Select each correct answer.




As x increases without bound, f(x) increases without bound.



As x decreases without bound, f(x) approaches the line y=−2.



As x increases without bound, f(x) approaches the line y=−2.



As x increases without bound, f(x) decreases without bound.


This is a multiple choice question, so there might be 2 answers.

Answers

Answer:

Option B and D are correct.

Step-by-step explanation:

Given the function: [tex]y=f(x) = -3^{x+2}-2[/tex]

End behavior states that  a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.

As [tex]x \rightarrow \infty[/tex] in the given function, then [tex]f(x) \rightarrow -\infty[/tex]

and

As [tex]x \rightarrow -\infty[/tex] in the given function, then [tex]y=-2[/tex]

Therefore, as x increases without bound , f(x) decreases without bound

and as x decreases without bound , f(x) approaches the line y =-2

NEED HELP 15 POINTS!!!!1

Answers

Answer: (D) ∠2 is supplementary to ∠8

Step-by-step explanation:

∠2 is congruent to:

∠3   vertical angles∠6    corresponding angles∠7   alternate exterior angles

Therefore, it is supplementary to the remaining angles:

∠1∠4∠5∠8

The only multiple choice option that satisfies the above statements is the last one

Need help please this is overdue,confused on what im supposed todo and how

Answers

Answer:

See below.

Step-by-step explanation:

You're supposed to follow directions. That means you examine the figure to see if it contains information that will justify the offered statement. You are not to make any assumptions based on appearances.

1. AE║BC — false. There is nothing in the diagram that shows AE to be perpendicular to AB, and there are no markings indicating AE║BC.

2. AB⊥BC — true. The right-angle mark where the segments meet at point B indicates these segments are perpendicular.

3. m∠ECB=90° — false. There is nothing in the diagram that shows EC to be perpendicular to BC, and there are no markings indicating EC║AB.

4. ∠BEC is supplementary to ∠ECB — false. These are two of three interior angles of ΔBCE. There is nothing to indicate that the third angle, ∠CBE, has a measure of 0°.

5. C is the midpoint of BD — false. BC is not marked as being congruent to CD.

6. ∠BCE and ∠ECD are a linear pair — true. Point C is on line BD, so segment EC divides ∠BCD into a linear pair.

7. ∠ABE is complementary to ∠EBC — true. Together these angles form right angle ABC, so they are complementary.

The cone shown has a diameter of 18 m and a slant height of 15 m which choice is closest to the lateral surface area

Answers

Answer:

[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.

Step-by-step explanation:

The lateral surface area of cone is:

[tex]\pi\cdot r\sqrt{h^2+r^2}[/tex]

Slant height is l which is [tex]l=\sqrt{h^2+r^2}[/tex]

We have given diameter 18 m

Since, radius is half of diameter so r=18/2 =9

Slant height l =15

[tex]\pi=3.14[/tex]

On substituting the values in the formula we get:

[tex]3.14\cdot 9\cdot 15[/tex]

On simplification we get:

[tex]3.14\cdot 135[/tex]

Further simplification will give:

[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.

The period of a pendulum is the time the pendulum takes to swing back and forth. The function Upper L equals 0.81 t squared relates the length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth. A convention center has a pendulum that is 50 feet long. Find the period.

Answers

Final answer:

The period of a 50-foot pendulum can be found by plugging the given length into the provided pendulum function and solving for the time variable. This gives a final result after taking the square root of the division between the length and a constant.

Explanation:

To find the period of a pendulum using the given length, we use the given function Upper L equals 0.81 t squared where L is the length in feet and t is the time in seconds that the pendulum takes to swing back and forth. In this case, the length of the pendulum is given as 50 feet. We plug this into the equation and solve for t:

50 = 0.81 * t^2

Rearranging this equation gives us:

t^2 = 50 / 0.81

Then we calculate the square root of this to find t:

t = sqrt(50 / 0.81)

The final answer after calculations gives the period of the pendulum.

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Final answer:

The period of the pendulum at the convention center, which is the time it takes to swing back and forth, is approximately 7.862 seconds. This is calculated using the given mathematical function relating length to swing time.

Explanation:

The given function that relates the length L of the pendulum to the swinging time t is Upper L = 0.81 t squared. If the pendulum at the convention center is 50 feet long (L = 50), we can substitute that into the equation to find the time it takes to swing (t), which in other words is the period we are trying to determine.

So, 50 = 0.81 * t squared. Solving this equation for t, we divide both sides of the equation by 0.81 to isolate t squared. This will give us t squared = 50/0.81

t = sqrt(50/0.81) ≈ 7.862. This means that the period of the convention center's pendulum is approximately 7.862 seconds.

It’s important to note that the only factors that affect the period of a simple pendulum are its length and the acceleration due to gravity, and the pendulum performs simple harmonic motion.

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PLEASE HELP!! Algebra 2 Review !!

1. What is the equation, in standard form, of a parabola that models the values in the table?

x | -2 0 4
f(x) | 2.5 1.5 -60.5
(I used STAT on the calculator, and found the answer, nevermind on this one)

2. Simplify the expression.
[tex] \frac{5 + 6i}{4 + 6i} [/tex]

Answers

Answer:

[tex]\frac{28-3i}{26}[/tex]

Step-by-step explanation:

For #2, remember that [tex]i=\sqrt{-1}[/tex], so [tex]i^{2}=-1[/tex] Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=[tex]a^2-b^2[/tex]. Now, to simplify, or radicalize, a number with surds in the denominator, you have to multiply the denominator by its conjugate. If there is a complex number [tex]a+bi[/tex], where a and b are any numbers, the conjugate is always [tex]a-bi[/tex]. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:

[tex]\frac{5+6i}{4+6i}=\frac{(5+6i)(4-6i)}{(4+6i)(4-6i)}=\frac{20+24i-30i+36}{16+36}=\frac{56-6i}{52}=\frac{2(28-3i)}{2(26)}=\frac{28-3i}{26}[/tex]

Our answer is (28-3i)/(26)!

If xy= -20 -2y= -6. What's the value of x

Answers

Answer:

x = -6 2/3 or -20/3

Step-by-step explanation:

So we know:

-2y = -6

Divide -2 on both sides

y = 3

Plug that into the other equation:

3x = -20

divide 3 on both sides

x = -20/3 or -6 2/3

a skateboard rises 2ft for every 7ft, measured horizontally. what is the slope?

Answers

Multiply 7ft- 2ft
Or add 7ft twice
Answer:14

A fence builder uses boards 3 1/2 feet long for the vertical slats on the fence. How many slats can be made from a board that is 42 feet long

Answers

Answer:

12 slats can be made from a board i,e  42 feet long

Step-by-step explanation:

As per the given statement: A fence builder uses boards [tex]3\frac{1}{2}[/tex] feet long for the vertical slats on the fence.

We have to calculate how many slats can be made from a board that is 42 feet long.

Builder uses board [tex]3\frac{1}{2} = \frac{7}{2}[/tex] feet long for the vertical slats.

then;

for 42 feet long = [tex]\frac{42}{\frac{7}{2} } = 42 \times \frac{2}{7} = 6 \times 2 = 12[/tex] slats can be made.

Therefore, 12 slats can be made from a board that is 42 feet long.

PLEASE HELP!!


A sequenced is defined by an=-3/4an-1, and a3=9/16. What is the seventh term?

Answers

Answer:

[tex]a_{7}[/tex] = [tex]\frac{729}{4096}[/tex]

Step-by-step explanation:

To obtain the next term in the sequence multiply the previous term by - [tex]\frac{3}{4}[/tex]

given [tex]a_{3}[/tex] = [tex]\frac{9}{16}[/tex], then

[tex]a_{4}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{9}{16}[/tex] = - [tex]\frac{27}{64}[/tex]

[tex]a_{5}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{27}{64}[/tex] = [tex]\frac{81}{256}[/tex]

[tex]a_{6}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{81}{256}[/tex] = - [tex]\frac{243}{1024}[/tex]

[tex]a_{7}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{243}{1024}[/tex] = [tex]\frac{729}{4096}[/tex]


Answer:

D

Step-by-step explanation:

E2020

Charlie gathers apples pears and plums. The number of apples and plums are 10 partners, there are the same number of apples and pears. How many pieces of fruit could Charlie gather? On both answers given no one mentions the pears:/ and 10 partners means 5 apples and 5 plums because 5+5=10 plus 5 pears (10+5=15) 15 fruits. Does that sound right or am I missing something?

Answers

Answer:  Yes, there is something missing.


Step-by-step explanation:  Given that Charlie gathers apples pears and plums. The number of apples and plums are 10 partners, there are the same number of apples and pears.

Since there are 10 partners of apples and plums, so

number of apples = number of plums = 10.

Also, number of apples and number of pears are same, therefore, number of pears = 10.

Thus, total number of fruits = 10+10+10 = 30.

Hence, Charlie couls gather 30 fruits.

So, this was missing in the calculation.

Charlie can be made to gather more fruit by maximizing the number of

apples gathered which gives a total of 19 fruits.

Response:

The number of pieces of fruit Charlie could gather is 19

Which method is used for solving the word problem?

The question is a word problem

Number partners of 10 are numbers that add up to 10

Therefore;

The number of apples + The number of plums = 10

The number of apples = The number pears

Required:

The number of pieces of fruit Charlie could gather

Solution:

Let x represent the number of apples, gathered, we have the following equations;

The number of plums = 10 - x

The number of pears = x

Which gives;

Total number of fruit = x + 10 - x + x = 10 + x

Where;

1 ≤ x ≤ 9

The maximum number of fruit Charlie can gather is therefore, when x = 9,  which gives;

Maximum number of fruit = 10 + 9 = 19

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A power plant has 4 tons of coal. A ton of coal produces 2460 kilowatt hours of electricity. Is this enough to power 9 light bulbs for a year? Explain.

Answers

Answer:

Yes

Step-by-step explanation:

We will assume that each bulb is of 100 kW (kilowatt).

We will calculate how much energy in kilowatt-hours the light bulb will use per year in kilowatts, by the number of hours in a year.

We have,

100 kW = 0.1 kW so the energy consumed in one year is,

[tex]0.1 \times 8760=876.0\text {kWh}[/tex]

Since there are 8760 hours in one year.

It is given that there are 9 bulbs so we need to have,

[tex]876 \times 9 = 7884 \text {kWh}[/tex]

It is given that 1 ton of coal produces 2460 kWh, so 4 tons of coal will produce,

[tex]4\times 2460= 9840 \text {kWh}[/tex]

We can observe that 4 tons of coal is producing 9840 kWh which is mroe than 7884 kWh. So, yes, 4 tons of coal can produce enough power to light 9 bulbs for a year.

Final answer:

The 4 tons of coal from the power plant will produce 9840 kilowatt hours of electricity. A single 60 watt light bulb consumes around 526 kilowatt hours in a year. Thus, the energy produced by the coal would be enough to power 9 light bulbs for a year.

Explanation:

The power plant has 4 tons of coal, with each ton producing 2460 kilowatt hours of electricity, resulting in a total production of 9840 kilowatt hours (4 tons * 2460 kilowatt hours/ton).

To discover if this can power 9 light bulbs for a year, we must first understand the energy consumption of a single bulb. A typical light bulb uses around 60 watts, and there are 8760 hours in a year. Therefore, a light bulb consumes 60 watts * 8760 hours = 525,600 watt-hours or about 526 kilowatt hours in a year.

For 9 light bulbs, the total energy consumption in a year would be 9 * 526 = 4734 kilowatt hours. Therefore, the 9840 kilowatt hours produced by the coal power plant is more than enough to power 9 light bulbs for a year.

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Which number represents 2.7 billion? A) 2,700,000,000 B) 2,700,000 C) 27,000,000,000 D) 27,000,000

Answers

Answer:

A.

Billions have three groups of zeros

Ex. 1,000,000,000


What is 15 x 11? Bjnsjxjscjsnjsnjcnsjncjsncj

Answers

Answer:

165

Step-by-step explanation:


15 x 11 is 165 Bjnsjxjscjsnjsnjcnsjncjsncj

ΔABC is an equilateral triangle. m∠A = (3x - 12)°. Solve for x. A) 14 B) 19 C) 20 D) 24

Answers

Answer:

option (d)

Step-by-step explanation:

An equilateral triangle is a triangle whose all the sides are equal and all the angles are same.

There are three angles in a triangle and the according to the property of the angles of a triangle, the angle sum of a triangle is 180°.

So, in an equilateral triangle, the measure of each angle is 60°.

[tex]3x-12= 60[/tex]

3x = 60 + 12

3x = 72

x = 24

option (d)

Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?

Answers

x - number of games

22x - cost of x tickets

10 - parking cost

The equation:

[tex]y=22x+10[/tex]

Answer:

y = 22x + 10

Step-by-step explanation:

Given,

The cost of each ticket = $ 22,

Let x be the number of tickets,

Then, the cost of x tickets = x × cost of each ticket

= 22x dollars,

Now, parking cost = $ 10,

So, the total cost of attending the game ( say y ) = cost of all tickets + parking cost

y = 22x + 10

Which is the required equation.

Dina and Masha started out on a 10 km bike path at the same time. When Dina reached the end of the 10 km, Masha still had 2 km to bike. If Dina's biking speed was 5km/h, find Masha's biking speed

Answers

Answer:

4 km/h

Step-by-step explanation:

We are told that Dina and Masha started out on a 10 km bike path at the same time.

Dina's biking speed is 5 km/h.

Let us find taken by Dina to cover 10 kn distance.

[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\text{Time taken by Dina to cover 10 km}=\frac{10km}{5\frac{km}{hr}}[/tex]

[tex]\text{Time taken by Dina to cover 10 km}=\frac{10km}{5}\times \frac{hr}{km}}[/tex]

[tex]\text{Time taken by Dina to cover 10 km}=2hr[/tex]

Therefore, Dina took 2 hours to complete 10 km.

Since both started at the same time, therefore, Masha also took 2 hours to complete 2 km less than Dina.

Let us find distance covered by Masha.

[tex]\text{Distance covered by Masha}=10\text{ km}-2\text{ km}=8\text{ km}[/tex]

Now let us find Masha's biking speed.

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Masha's biking speed}=\frac{8\text{ km}}{2\text{ hour}}[/tex]

[tex]\text{Masha's biking speed}=4\frac{\text{ km}}{\text{ hour}}[/tex]

Therefore, Masha's biking speed is 4 km per hour.

You plan to put anti-theft devices on each garment in your store. You have 1,320 garments, and it takes an employee 20 seconds to tag a garment. How long will it take TWO employees to tag all the garments?

Answers

Answer:

13,200 Seconds, or 220 Minutes


Step-by-step explanation:

Since there are 2 employees working at the same time, so in 20 seconds, they will be tagging a total of 2 garments. So we can say the rate is:

rate = [tex]\frac{20 Seconds}{2 Garments}[/tex]


So how long would it take to tag 1320 garments?

We set up the ratio, cross multiply, and solve.

[tex]\frac{TimeInSeconds}{NumberOfGarments}=\frac{20}{2}=\frac{x}{1320}}\\\frac{20}{2}=\frac{x}{1320}\\20*1320=2x\\x=\frac{26400}{2}=13,200[/tex] seconds


Or in minutes, we divide by 60, so we have:

[tex]\frac{13,200}{60}=220[/tex] Minutes

Answer:

3 hours 40 minutes.

Step-by-step explanation:

We are told that we have 1320 garments and it takes an employee 20 seconds to tag a garment.

1 employee tags one garment in 20 seconds.

So garments tagged by 1 employees in 1 minute will be [tex]\frac{60}{20} =3[/tex] garments.

2 employees will tag 3*2=6 garments in 1 minute.

To find the total time it will take two employees to tag all the garments we will divide total number of garments by 6.

[tex]\text{Time taken by two employees to tag 1320 garments}=\frac{1320}{6}[/tex]

[tex]\text{Time taken by two employees to tag 1320 garments}=220[/tex]

Therefore, it will take 220 minutes or 3 hours and 40 minutes for 2 employees to tag 1320 garments.

20 large plastic bottles can be recycled to make 1 fleece jacket. How may fleeces can be made with 280 large plastic bottles?

Answers

Answer:

14 Fleece jackets could be made.


Hope this helped:)

Step-by-step explanation:

280/20=14

Answer:

14 fleece jackets

Step-by-step explanation:

Select all that apply.

Solve for x , 0 < x < 360. 1/sin^2x = 4

answer choices (choose all that apply)
30
150
210
330

Answers

Answer:

30,150, 210 ,330

Step-by-step explanation:

1/sin^2x = 4

Multiply each side by sin^2x

1 = 4 sin^2 x

Divide each side by 4

1/4 = sin^2 x

Take the square root of each side

sqrt(1/4) = sqrt(sin^2 x)

±sqrt(1/4) = sin x

±1/2 = sinx

Take the inverse sin of each side

arcsin (1/2) = arcsin (sin x)    and arcsin(-1/2) = arcsin (sin x)

30 = x                                                   -30 = x

                                                 But this is not between 0 and 360,

                                                        so we add 360

                                                        -30+360 = 330

We also have to look at the other locations where  sin x = 1/2

Taking the arcsin only gives values between -90 and 90

Since we are looking at the sin value, we take 180 - the value given

180 -30 = 150

180 --30

180+30 = 210

So our values are 30, 150,210,330

Two planes are driving toward each other with the speeds 250 mph and 420 mph respectively. If the distance between them are 1250 miles, in how many hours they will meet?

Answers

Answer:

They will meet in 1.866 hours.

Step-by-step explanation:

This is actually quite a simple question once we think about it in a different way.

Instead of thinking of two different planes that are going at two different speeds, think of it like this: the distance between the two planes is decreasing by 670mph (250mph + 420 mph).

Note: miles per hour is equivalent to miles/hour (miles divided by hours or miles over hours)

670m/h becomes our new rate. The rate the distance between the planes is decreasing.

Now, if the distance between them is 1250 miles, how long until they meet?

If we have miles and multiply it by hours/miles, the miles cancel out and you are left with hours.

We have miles (1250) and miles/hours (670). If we multiply these we get units of miles^2 / hours which is not what we want.

we need to multiply 1250 miles by something with the units of hours/miles.

It turns out that the reciprocal of miles/hours is hours/miles

That means we need to multiply 1250 miles by the reciprocal of 670 miles/hours

Note: the reciprocal of a fraction is the fraction flipped around. 1/2 becomes 2/1, reciprocal of 3/5 is 5/3, etc...

the reciprocal of 670 miles/hours = 1/670 miles/hours

Multiplying 1250 miles by 1/670 miles/hours is the SAME as

dividing the number of miles(1250m) by the rate(670m/h)

1250m / 670m/h = 1250m x 1/670 x h/m = 1.866 h = 1.866 hours (the miles cancel out)


Note: I explained it so you know why dividing 1250miles by 670mph gives you hours. Once you understand why, all you need to do in the future is divide the distance by the rate and you get time. Distance / rate = time

In two hours holden completed 3 fouths of his race how long will holden take to complete the entire race

Answers

2 hours 45 minutes is how long it will take him to finish the race.

Arjun can type 40 words per mintue.Dalia can type 55 words per mintue.If Arjun and dalia each type for 30 mintues,about how many more words will Dalia type

Answers

Answer: 450 words

Step-by-step explanation:

Arjun: [tex]\dfrac{40 words}{1minute} \times\dfrac{30minutes}{} = 1200 words[/tex]

Dalia: [tex]\dfrac{55 words}{1minute} \times\dfrac{30minutes}{} = 1650 words[/tex]

  Dalia - Arjun

= 1650 - 1200

=      450

Calculate s4 for the sequence defined by

Answers

Answer:

The correct answer option is 36.

Step-by-step explanation:

We know that,

the sum of the first n terms of an Arithmetic Sequence is given by:

[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]

where [tex]n[/tex] is the number of terms,

[tex]a_1[/tex] is the first term of the sequence; and

[tex]a_ n[/tex]is the first term of the sequence.

So for [tex]a_n=(19-4n)[/tex],

[tex]a_1=19-4(1)=15\\\\a_4=19-4(4)=3[/tex]

Putting these values in the formula to get:

[tex]S_4=\frac{4(15+3)}{2}[/tex]

[tex]S_4=\frac{72}{2} \\\\S_4=36[/tex]

Therefore, the 4th term of the given sequence is 36.

Answer:

C is the correct one so 36 :)


Six friends equally share the cost of a gift. They pay $90 and receive $42 in charge . How much does each friend pay?

Answers

Answer:

$8.00

Step-by-step explanation:

Let's set up the equation first.

What do we know:

1. We have 6 friends spliting the costs of the gifts

2. After purchasing the gifts they have $42 in change

3. They originally had $90 to spend.

Equation:

6f + $42 = $90

Next: Subtract the $42 from each side and we are left with:

6f = $48

Divide both sides by 6 and we are left with

f = $8

Since f represented the cost each friend spent our answer is $8.00

Each friend will pay $8.

What are the fundamental mathematical operations?

The Fundamental mathematical operation are Addition,Subtraction

Multiplication and  Division.

Given,

Six friends will equally share the cost.

they paid $90 and received $42 in change.

The money they will pay = $90 -$42

                                         = $48.

As they will  equally share the cost.

the individual cost will be = $48/6

                                           =$8.

Therefore, Each friend will pay $8.

To find more question related to mathematical operations click on the link below:

https://brainly.com/question/20628271

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