50 Points! Multiple choice algebra question. One factor of x^3+4x^2-11x-30=0 is x+2. Find the remaining factors. Photo attached. Thank you!
Answers
The solution to the above algebra question is (b) x-3, x+5.
What is the explanation for the above response?To find the remaining factors of the polynomial x^3+4x^2-11x-30=0, we can use polynomial long division or synthetic division. However, since we are given that x+2 is a factor of the polynomial, we can use synthetic division to simplify the process.
We set up the synthetic division table as follows, using -2 as the divisor:
-2 | 1 4 -11 -30
|____-2__-4___30
| 1 2 -15 0
The bottom row of the table represents the coefficients of the quadratic polynomial obtained by dividing x^3+4x^2-11x-30 by x+2. The last term of the quadratic is 0, which indicates that x+2 is a factor of the polynomial. The remaining quadratic polynomial can be factored as:
x^2 + 2x - 15 = (x - 3)(x + 5)
Therefore, the remaining factors of the polynomial x^3+4x^2-11x-30=0 are x+2, x-3, and x+5.
The correct answer is (b) x-3, x+5.
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Related Questions
For questions 16, write the negation of each conditional statement.
16. If you don’t look both ways before crossing the street, then you will get hit by a car.
Answers
Answer:
The symbols used to represent the negation of a statement are “~” or “¬”. For example, the given sentence is “If you don’t look both ways before crossing the street, then you will get hit by a car." Then, the negation of the given statement is “that u won't get hit”. Thus, if the given statement is true, then the negation of the given statement is false.
A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
Answers
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
Answers
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
if a square has length of its side is 8cm then find length of its diagonal
Answers
Answer:
8√2 cm
Step-by-step explanation:
In a square, the diagonal is the hypotenuse of a right triangle whose legs are the two sides of the square. Since all sides of a square are equal, we can label the length of one side of the square as "a". Therefore, the length of the diagonal "d" can be found as:
d = √(a^2 + a^2) (using Pythagorean theorem)
Substituting the value of "a" as 8 cm, we get:
d = √(8^2 + 8^2)
d = √(64 + 64)
d = √128
d = 8√2 cm (rounded to two decimal places)
Therefore, the length of the diagonal of a square whose side length is 8 cm is approximately 11.31 cm (rounded to two decimal places).
differentiate with respect to x the implicit function sin(y)+x^2y^3-cos(x)=2y
Answers
Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Identify the interquartile range from the box and whisker plot above
Answers
Answer:
interquartile range = 6
Step-by-step explanation:
the interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁
Q₃ is the value at the right side of the box, that is 86
Q₁ is the value at the left side of the box, that is 80
interquartile range = Q₃ - Q₁ = 86 - 80 = 6
Nora bought 100 shares of a technology stock and 200 shares of a mutual fund for $3600. Her sister, Erin, bought 300 shares of
the technology stock and 50 shares of the same mutual fund for $5300. Find the cost per share of the technology stock, and the
cost per share of the mutual fund.
Answers
The cost per share of the technology stock is $14.
What is a variable?
In mathematics, a variable is a symbol or letter that represents a value or a quantity that can change or vary in a given context or problem. Variables are used to express mathematical relationships and to formulate equations and functions.
Let's use variables to represent the cost per share of the technology stock and the mutual fund. We can call the cost per share of the technology stock "T" and the cost per share of the mutual fund "M".
From the problem, we know:
Nora bought 100 shares of the technology stock and 200 shares of the mutual fund for a total of $3600:
100T + 200M = 3600
Erin bought 300 shares of the technology stock and 50 shares of the mutual fund for a total of $5300:
300T + 50M = 5300
We now have a system of two equations with two variables. We can solve for T and M by using elimination or substitution. Here, we will use the substitution method:
From the first equation, we can isolate T by subtracting 200M from both sides:
100T = 3600 - 200M
Divide both sides by 100 to get:
T = 36 - 2M
Now substitute this expression for T into the second equation:
300(36 - 2M) + 50M = 5300
Expand and simplify:
10M = 1100
Divide both sides by 10 to get:
M = 110
So the cost per share of the mutual fund is $110.
To find the cost per share of the technology stock, we can substitute M = 110 into either of the original equations. Let's use the first equation:
100T + 200(110) = 3600
Simplify:
100T = 1400
Divide both sides by 100 to get:
T = 14
So the cost per share of the technology stock is $14.
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Which is more, 19 ounces or 1 pound?
Answers
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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Hazel is playing hide-and-seek with Audrey and Jamal. Audrey is hiding 6 meters south of Hazel, and Jamal is hiding 8 meters east of Audrey. How far apart are Hazel and Jamal?
Answers
Answer:
=10 m
Step-by-step explanation:
PYTHAGOREAN THEOREM
8^2+6^2=64+36=100
=√100m
=10 m
Use L’hospital if it applies
Lim x—> infinity
(lnx)^3/x^2
Answers
The calculated value of the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
Calculating the limits of the derivativesTo apply L'Hopital's rule, we need to take the derivative of the numerator and denominator separately with respect to x.
We can apply this rule repeatedly until we get a determinate form.
lim x → ∞ [(ln x)^3 / x^2]
Taking the derivative of the numerator:
= 3(ln x)^2 (1/x)
Taking the derivative of the denominator:
= 2x
Applying L'Hopital's rule again by taking the derivative of the numerator and denominator:
= lim x → ∞ [6(ln x) / x]
Taking the derivative of the numerator:
= 6/x
Taking the derivative of the denominator:
= 1
Applying L'Hopital's rule one last time:
= lim x → ∞ 6 / x^2
= 0
Therefore, the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
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5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
Answers
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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I believe I missed the lesson on how to solve for x and y from this photo. Any help would be appreciated!
Answers
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
Explain about the Pythagorean theorem:The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the
a² + b² = c².
For the larger triangle, applying Pythagorean theorem:
4² + (4√3)² = x²
x² = 16 + 16*3
x² = 16 + 48
x² = 64
x = 8
Then, x - 6 = 8 - 6 = 2
Now applying Pythagorean theorem for smaller triangle:
y² + (x - 6)² = 4²
y² = 4² - 2²
y² = 16 - 4
y² = 12
y² = √12
y = 2√3
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
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One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other. 4
Golf, 7
Soccer, 11.
Baseball, 14
Football,39
Basketball, 22
Answers
The percentage of adults who preferred soccer or basketball is 25%.
What is circle graph?The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.
From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.
Thus,
11% + 14% = 25%
Hence, the percentage of adults who preferred soccer or basketball is 25%.
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What am i supposed to do?
Answers
The histogram that displays the data in the table correctly is C. Histogram C.
How to find the histogram ?Look at the data in the table and look for the number of photocopies that are located between 800 and 899. There are 3 of these.
The number located between 900 and 999 are 5 in number including 915, 919, 923, 950, and 989. The number located between 1,000 and 1, 099 is 8 photocopies.
The histogram that shows this is Histogram C.
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You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
Answers
With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.
What is Compound interest?
Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.
Now,
Using the given formula:
N = (-log(1 - i * A / P)) / (log(1 + i))
where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250
N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))
N = (-log(1 - 175)) / (log(1.0025))
N = (-log(0.9883)) / (0.0025)
N = 376.48
Rounding up to the nearest whole number, it will take 377 months to pay off the loan.
Therefore, it will take approximately 31 years and 5 months to pay off the loan.
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Determine the number of solutions to the system of linear equations shown on the graph.
No solution
Infinitely many solutions
One solution at (−3, 2)
One solution at (2, −3)
Answers
Answer:
explanation:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
a red car travels 20km in one hour .
a blue car travels 130km in the sAME TIME
which car thas greater average speed???
Answers
Answer:
The answer is the Blue car
Step-by-step explanation:
let Red car be x
let blue car be y
x=120km---->1hr
y=130km----->1hr
Average speed =distance(km)/time(hr)=km/hr
let A be average speed
A(x)=120/1=120km/hr
A(y)=130/1=130km/hr
therefore,
the blue car has the greatest average speed
Consider two points A(0,0) and B(1, 1) on a Cartesian plane. The equation of the axis of the segment AB is: A. y = 1 2 − B. y = 2 − C. y = 1 − 2 D. y = 1 − E. y = 1 − 2
Answers
So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
The slope of the line passing through points A and B can be calculated as follows:
slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1
The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
To find the y-intercept, we can use point A (0,0) and substitute the slope value.
y = mx + b
0 = 1(0) + b
b = 0
Therefore, the equation of the line passing through points A and B is:
y = 1x + 0
Simplifying, we get:
y = x
So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:
y - 0 = 1(x - 0)
y = x
This confirms our earlier answer.
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Consider a triangle ABC.
Answers
.............................
Which statement about population parameters and point estimates is false? O A. o is the population standard deviation. It is usually unknown. B. p is the sample mean. It is used to estimate the population mean. C. sis the sample standard deviation. It is the square root of the variance. O D. nis the sample size. It is used to calculate the sample mean. SUBMIT
Answers
Answer: B
Step-by-step explanation:
Mr. Wang and Mrs. Wang have 3 sons. Every son has 1 wife, 1 son, 1 sister. How many people in this family?
Answers
If Mr. Wang and Mrs. Wang have 3 sons and every son has 1 wife, 1 son, and 1 sister, the total number of people in the family, based on mathematical operations, is 14.
How is the total number determined?The total number of people in the family can be determined using the mathematical operations of multiplication and addition.
Multiplication and addition are two of the four basic mathematical operations.
Multiplication involves the multiplicand, the multiplier, and the product, while addition involves two or more addends added to get the sum.
The number of parents = 2
The number of sons = 3
The number of additional family members for each son = 3
The total number of additional family members = 9 (3 x 3)
The total number of persons in the family = 14 (9 + 3 + 2)
Thus, there are 14 people in the family of Mr. Wang and Mrs. Wang.
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Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answers
Answer:
Step-by-step explanation:
Leah said on her birthday: “Today I am exactly three times as old as I was four years ago.“ And that was true. In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“?
Answers
in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
How to determine In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“Let's start by setting up an equation based on the given information.
Let Leah's current age be represented by "x". Then, we know that:
x = 3(x-4)
Expanding the right side of the equation:
x = 3x - 12
Bringing the "x" term to the left side and simplifying:
2x = 12
x = 6
So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:
6 + y = 2(6 - 4 + y)
Simplifying:
6 + y = 2(2 + y)
6 + y = 4 + 2y
2 = y
So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
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Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Answers
= 173.903t
Step-by-step Explanation:
The given equation is: f(t) = 227e^(b*t)
To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.
Let's start by taking the natural logarithm (ln) of both sides:
ln(f(t)) = ln(227e^(b*t))
Using the properties of logarithms, we can simplify this to:
ln(f(t)) = ln(227) + ln(e^(b*t))
ln(f(t)) = ln(227) + b*t
Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:
ln(f(t)) = ln(a) + k*t
where a = 227 and k = -0.09
Taking the exponential of both sides, we get:
f(t) = e^(ln(a) + k*t)
f(t) = e^(ln(a)) * e^(k*t)
f(t) = a * e^(k*t)
Substituting the values of a and k, we get:
f(t) = 227 * e^(-0.09*t)
Therefore, the equation f(t) = ab is:
f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)
Shandra is giving a snack bag to each of her
4 friends. She puts 4 pear slices in each bag.
How many pear slices are there in all?
Answers
In a case whereby Shandra is giving a snack bag to each of her 4 friends. She puts 4 pear slices in each bag the number of pear slices that are there in all is 16 pear slices.
How can the slice be calculated?The calculation can be done in a simple way, If Shandra puts 4 pear slices in each of the 4 snack bags, then the total number of pear slices will be:
4 friends x 4 pear slices per bag = 16 pear slices
Therefore, there are 16 pear slices in all.
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Can you please help me with this.
Answers
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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4. Greta's neighborhood is having a picnic to celebrate the end of the school year. She has been
asked to prepare potato salad. Greta actually has to work at 2pm when the picnic is scheduled, so
she asks Lynn, the neighbor coordinating food, if she can drop off the potato salad at the park
when she goes into work at 10am. Lynn is not sure this will work. Describe why Lynn is hesitant
and what might happen if Greta's potato salad sits out in the sun until the picnic begins at 2pm.
Then offer at least one suggestion to solve Greta and Lynn's problem.
Answers
Lynn is hesitant to allow Greta to drop off the potato salad at 10am .
How to solve Greta and Lynn's problem?Greta could make the potato salad the night before and keep it in the refrigerator to solve the problem she and Lynn were having. She could then transport the potato salad at a safe temperature in a cooler filled with ice packs on the day of the picnic.
She could ask Lynn to store the potato salad in a cooler or refrigerator until the picnic starts when she gets to the park. Along these lines, the potato salad will be protected to eat and won't represent a gamble of food contamination.
The mayonnaise in Greta's potato salad will spoil, leading to the growth of bacteria that could result in foodborne illness, if it is left outside in the sun until the picnic begins at 2 p.m. The potato salad may cause nausea, vomiting, diarrhea, and stomach cramps in those who consume it.
Because food safety guidelines state that perishable foods, like potato salad, should not be kept at room temperature for more than two hours, Lynn is hesitant to let Greta drop off the potato salad at 10 a.m.
If the potato salad is left out in the sun from 10 a.m. to 2 p.m., bacteria can grow on it, and eating it could make you sick.
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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 60.1% of their carbon-14. How old were the bones at the time they were discovered?
please help me with this problem.....
Answers
Answer: To solve the problem, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t/T)
where:
N(t) is the amount of the radioactive element at time t
N0 is the initial amount of the radioactive element
t is the time that has elapsed
T is the half-life of the radioactive element
Let's assume that the initial amount of carbon-14 in the bones was N0. After the bones were discovered, they had lost 60.1% of their carbon-14, which means that only 39.9% of the original carbon-14 remained. Therefore, we can write:
N(t) = 0.399 * N0
We want to find the time t that has elapsed since the mastodon died. We can rearrange the formula for exponential decay to solve for t:
t = T * log( N(t) / N0 ) / log(1/2)
Substituting the given values, we get:
t = 5750 * log( 0.399 ) / log(1/2)
Using a calculator, we find that t is approximately 16060 years. Therefore, the bones were approximately 16060 years old at the time they were discovered.
Step-by-step explanation:
Which measurement is equivalent to 47 mL?
Answers
47 mL is equivalent to 0.047 L (liters).
What is measurement refers to?Measurement refers to the process of quantifying or determining the amount, size, or degree of something using a standard unit of measurement. It is a way of expressing the quantity or magnitude of a physical property, such as length, mass, volume, time, temperature, etc.
Define the term equivalent?Equivalent means having the same value, function, or meaning as something else. In mathematics, two values are said to be equivalent if they have the same numerical value or satisfy the same equation or inequality. In chemistry, equivalent refers to the amount of a substance that can react with or replace a given amount of another substance in a chemical reaction. In general, equivalent is used to indicate that two things are equal in some way or have the same effect or significance.
1L =1000mL
1mL=1/1000L
Therefore 47 mL=.047 L
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A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answers
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.