Find an equation of a polynomial function of least degree having the given complex zeros, intercepts, and graph. \(\mathrm{f}\) has a complex zero \(5i\). \(f(x)=?\).

Recent
Algebra
Arithmetic
Calculus
Finance
General
Geometry
Precalculus
Probability
Statistics
Trigonometry

Q:

Find an equation of a polynomial function of least degree having the given complex zeros, intercepts, and graph. \(\mathrm{f}\) has a complex zero \(5i\). \(f(x)=?\).

Q:

Consider matrix \(\mathrm{A}\).

\(A=\begin{bmatrix}-3&5&2\\8&-1&3\end{bmatrix}\)

What matrix results from the elementary row operations represented by \(-3R_2+4R_1\)?

Q:

Find the sum of the following series, Round to the nearest hundredth if necessary.

4+12+36+...+234196

Sum of a finite geometric series:

\(S_n=\frac{a_1-a_1r^n}{1-r}\)

Q:

The perimeter of a rectangle is 44 meters and the length is 10 meters more than twice the width. Find the dimensions.

Q:

Two cyclists start at the same point and travel in opposite directions. One cyclist travels \(3\mathrm{km/h}\) faster than the other. If the two cyclists are \(135\) kilometers apart after \(3\) hours, what is the the rate of each cyclist?

Q:

Find the values of the A, B, C and D so that the difference below is equal to \(3x^4-x^3-6x+16\)

\((\mathrm{A}x^3+7+11x^4)-(\mathrm{B}x^4-2x^3+\mathrm{C}+\mathrm{D}x)\)

Q:

Three sisters are saving for a special vacation. The ratio of Jenna's savings to Ellie's saving is 6:4, and the ratio of Ellies saving to Jasmine's savings is 4:2. Together, all three girls have saved 48 dollars. How much has each girl saved?

Q:

Find the GCF of the following literal terms:

\(\mathrm{m}^7\mathrm{n}^4\mathrm{p}^3\) and \(\mathrm{m}\mathrm{n}^{12}\mathrm{p}^5\)

Q:

The ordered pairs shown below represent a relation R,

R={(-2, 2), (2, -2), (-4, 4), (4, -4)}

Is the relation R a function? Explain why or why not.

Q:

After spending 3/5 of his money on a tennis racket, Sean had $14 left. How much did the tennis racket cost?

Q:

Find the 7th term of the geometric sequence show below

\(-9x^7,-27x^{10},-81x^{13},\ldots\)

Q:

Mrs Tan cycles daily to work every day. The distance between his workplace and his home is 35 km. He cycles at a speed of \(x\) km/h while going to work and increases his speed by 3 km/h when returning from work.

(a) Find the time he takes to travel to work in terms of \(x\).

(b) Find the time he takes to return from work in terms of \(x\).

(c) Given that he takes 20 minutes less while returning from work, show that his journey can be expressed by \(x^2+3x-315=0\)

(d) Solve \(x^2+3x-315=0\)

(e) Hence, find the speed when he is going to work.

Q:

Given the function \(f(x)=x^2-x\), then what is \(f(-x)\) as a simplified polynomial?

Q:

Wilbur left the hardware store and traveled toward the recycling plant at an average speed of \(33\text{ km/h}\). Mary left two hours later and traveled in the same direction but with an average speed of \(55\text{ km/h}\). How long did Wilbur travel before Mary caught up?

Q:

Wilbur left the hardware store and traveled toward the recycling plant at an average speed of 33 km/h. Mary left two hours later and traveled in the same direction but with an average speed of 55 km/h. How long did Wilbur travel before Mary caught up?

Q:

Aaron's parents want to buy an area rug for their 4 m×4 m living room. They want space around the rug. The rug itself cannot take up more than 90% of the living room.What is the maximum size of rug they can buy? Show your work.

Q:

At a certain lab, the average mass of one ant is measured to be 2.9 times 10\(^{-6} \) kilograms. Use scientific notation to express the mass of 130 ants.

Q:

The members of the Business club conducted a sale for the survivors of a typhoon. If the cost of the items is five pesos or below,they sell it for ₱8.00.If the coat of the items is greater than five,the markup is 20% of the cost. Write the function that expresses selling price as a function of cost.

Q:

Isabelle has \(\$3496\) in her retirement account, and Felipe has \(\$3524\) in his. Isabelle is adding \(\$19\) per day,whereas Felipe is contributing \(\$12 \) per day.Eventually,the two accounts will contain the same amount,How long will that take?What balance will each account have?

Q:

Christine noticed that her snacks allowance every grade level increases. When she was in grade 1 her allowance was Php10.00, in grade 2 was PhpP12,00, and grade 3 was Php16.00. Now that she is in Grade 4, her allowance is Php22.00. What will be her allowance when she goes to Grade 6?

Q:

Write the function f as a piecewise-defined function f(x)=|2x-8|

Q:

When solving equations algebraically,Meghan and Meredith each got a different solution.Who is correct?Why did the other person not get the correct answer?

Q:

Identify whether the equation is a direct variation,inverse variation,or neither.

9y=x

A.direct

B. inverse

C.neither

Q:

Andre has read 5 books, 12 magazines, and 20 newspaper articles this year so far. Based on this data, what is the probability that the next reading material he chooses is a newspaper article?

Q:

Find the 14th term of the geometric sequence 10, 20,40, ...

Q:

To make a quilt, Darla first cut 3\(\frac{2}{5} \) yards of white fabric.Then she cut 1\(\frac{1}{2} \) yards of pink fabric. What is the total amount of fabric Darla cut to make the quilt?

Q:

write an equation in the form y=mx+b that represents the function defined by this table of values

(-5,12),(-3,6),(-1,0),(1,-6)

Q:

Please finish this as soon as possible

Q:

Tish and Emma are knitting scarves. Tish's scarf is17.75 inches long, and she knits 2\(\frac{3}{8} \) inches per minute.Emma's scarf is 4 inches long, and she knits 3\(\frac{3}{4} \) inchd per minute.After how many minutes will Emma's scarf be longer than Tish's scarf?

Q:

Mr. Tortola wants to put a new coat of stain on his back patio. The following diagram shows the design of the patio, with all dimensions represented as polynomials. The main patio is a rectangle, with a smaller rectangle on the end, a hot tub (blue), and \(2\) congruent flower boxes (grey).

a) Create a simplified polynomial to represent the area of the patio that needs to be stained. Assume that the areas covered by the hot tub and the flower boxes will not be stained.

b) If the actual value of \(x=1\mathrm{m}\), what is the area of the patio to be stained?

c) If a can of stain covers \(35\mathrm{m}^2\) and costs \(\$50\), how much will it cost Mr. Tortola to stain the patio with \(1\) coat of stain?

Q:

Fargo's population in \(2015\) was about \(57,600\), and was growing by about \(2.3\%\) each year. If this continues, what will Fargo's population be in \(2025\)?

Q:

Micah has a roll of cloth that is \(52.5\) feet long. She uses the cloth to make scarf that are each \(3.75\) feet long. How many scarves can Micah make?

\(1\) scarf

\(14\) scarves

\(28\) scarves

\(140\) scarves

Q:

The expression \(12a+ 8s\) can be used to calculate the cost for adults and students to go to the Science Museum in Miami, where a is the number of adults and s is the number of students. How much will it cost for \(3\) adults and \(22\) students to go to the museum?*

Q:

Mr James travelled from east to west. He travelled \(3/5\) of the journey in the first hour, \(1/3\) of the journey in the next half hour and the rest of the journey in another one hour. The average speed in the first \(1~1/2\) hour journey is \(70\) km/h. Find the distance travelled during the last part of the journey.

Q:

Madison needs six and one fourth cups of oatmeal for a recipe. She has two and three fourths cups of oatmeal. How many more cups does she need?

Q:

Jeanne Louise Calment of France lived to be the oldest human on record. Mitoyo Kawate of Japan lived \(8\) years less than Calment. If the sum of their ages is \(236\) years , how old was Calment when she died?

Q:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

A charitable organization in Hampton is hosting a black tie benefit. Yesterday, the organization sold \(25\) regular tickets and 100 VIP tickets, raising \(\$15,175\). Today, \(85\) regular tickets and \(100\) VIP tickets were sold, bringing in a total of \(\$18,715\). How much do the different ticket types cost?

A regular ticket costs \(\$\fbox{\phantom{?????}}\), and a VIP ticket costs \(\$\fbox{\phantom{?????}}\)

Q:

List values in order \(\mathrm{A}\), \(\mathrm{B}\), \(\mathrm{C}\). Use commas between values and do not use spaces. Find values for \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{C}\) so that \((5n+\mathrm{A})(\mathrm{B}n+2)\) is equal to \(15n^2+\mathrm{C}n-2\).

Q:

Ashlyn visits \(14\) houses every day in her neighborhood to conduct a survey. If there are \(126\) houses in her neighborhood, how many days will it take her to complete the survey?

Q:

A party rental company has chairs and tables for rent.The total cost to rent \(3\) chairs and \(5\) tables is \(\$52\).The tatal cost to rent \(9\) hairs and \(7\) tables is \(\$86\).What is the cost to rent each chair and each table?

Q:

Web music store offers two versions of a popular song. The size of the standard version is \(2.9\) megabytes (MB). The size of the high-quality version is \(4.1\) MB.Yesterday, there were \(740\) downloads of the song, for a total download size of \(2458\) MB. How many downloads of the high-quality version were there?

Q:

A food store makes a \(7\)-lb mixture of walnuts, cashews, and dates. The cost of walnuts is \(\$1.50\) per pound, cashews cost \(\$1.00\) per pound, and dates cost \(\$2.00\) per pound. The mixture calls for twice as many walnuts as cashews. The total cost of the mixture is \(\$12.00\) . How much of each ingredient did the store use?

Q:

Find the 11th term of the geometric sequence show below.

\(7x,~-35x^5,175x^9,~...\)

Q:

Rosa bought \(1\) pound of cashews and \(2\) pounds of peanuts for \(\$10\). At the same store, Sabrina brought \(2\) pounds of cashews and \(1\) pounds of peanuts for \(\$11\). Find the cost per pound for cashews and peanuts. Make sure to define all variables.

Q:

Amos, Bryan and Carol are given a total of \(\$2400\). Bryan's share is twice the total amount of money that Amos and Carol receive. The ratio of Amos's share to Carol's share is \(2:3\). How much does each of them receive?

Q:

Bacteria are growing in a culture, and their number is increasing at the rate of \(5\%\) an hour. Initially, \(400\) bacteria are present. How many bacteria are present in four hours?

Q:

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function \(h(t)=-16t^2+16t+480\), where t is the time in seconds and h is the height in feet.

a) How long did it take for Jason to reach his maximum height?

b) What was the highest point that Jason reached?

Q:

Which expression is equivalent to: \(42t+28y\)

A. \(6(7t+4y)\)

B. \(7(6t+4)\)

C. \(7(6t+4y)\)

D. \(6(7t+4y)\)

Q:

What is the slope of the line?

Q:

Point \(\mathrm{M}\) is the midpoint of \(\mathrm{PQ}\). If \(\mathrm{PM}=25\), and \(\mathrm{MQ}=5x+5\), determine the value of \(x\).

Q:

A school administrator who was concerned about grade inflation looked over the number of straight-A students from year to year. According to the table, what was the rate of change between \(2013\) and \(2017\)?

Q:

Billy's car gets \(25\) miles per gallon of gas. If Wilmington, DE is \(150\) miles away, how many gallons of gas is he going to need to get to Wilmington and come back home?

Q:

Use the properties of logarithms to write the logarithm in terms of \(\log_3(5)\) and \(\log_3(7)\).

\(\log_3(35)\)

Q:

Is the system inconsistent?

\(\begin{cases}3x+y=3\\5x+5y=5\end{cases}\)