P is a polynomial defined by P(x) = 4x³ - 11x² - 6x + 9. Two factors are (x - 3) and
(x + 1). Rewrite the expression for P as the product of linear factors. Here is a blank
diagram to use to organize your thinking, if needed.
Answers
linear equations are defined as y=mx+b so we know the 2 given factors are linear, and our leftover (4x-3) is linear as well. Meaning we can no longer factor out anything further and the final answer is P(x)=(x-3)(x+1)(4x-3) but depending on how your teacher wants the answer you could write it P(x)=(x-3)(x+1)(x-3/4)
Related Questions
The graph of F(x), shown below, has the same shape as the graph ofG(x) = x - x? Which of the following is the equation of F(x)?F(x) = ?
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The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.
Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.
[tex]F(x)=x^4-x^2+4[/tex]C Dorothy drew a rectangle with length of 14.3 centimeters and width of 13.9 centimeters. Find its area (nearest tenth).
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Area of rectangle = Length x Width
. = 14.3 x 13.9
. = (13.9+ 0.4) x 13.9
. = 13.9^2 + 5.56
. = 13•14 +( 1.4)•8 + 5.56
. =198.77 cm2
Which of the following identities is used to expand the polynomial (3x - 4y)2?
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Recall that to expand a binomial we can use the following formula:
[tex](a+b)^2=a^2+2ab+b^2.[/tex]The above is known as the square of the binomial.
Answer:
Square of binomial.
−|a+b|/2−c when a=1 2/3 , b=−1 , and c=−3
ENTER YOUR ANSWER AS A SIMPLIFIED FRACTION IN THE BOX.
Answers
The value of the expression −|a + b|/2 − c when a =1 2/3 , b=−1 , and c=−3 is 8/3
How to evaluate the expression?From the question, the expression is given as
−|a + b|/2 − c
Also, we have the values of the variables to be
a =1 2/3 , b=−1 , and c=−3
Rewrite a as
a = 5/3
So, we substitute a = 5/3 b=−1 , and c=−3 in −|a + b|/2 − c
This gives
−|a + b|/2 − c = −|5/3 - 1|/2 + 3
Evaluate the difference in the expression
−|a + b|/2 − c = −|2/3|/2 + 3
Divide
−|a + b|/2 − c = −|1/3| + 3
Remove the absolute bracket and solve
−|a + b|/2 − c = 8/3
Hence, the solution is −|a + b|/2 − c = 8/3
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The required simplified value of the given expression is 8/3.
As per the given data, an expression −|a+b|/2−c is given when a=1 2/3, b=−1, and c=−3 the value of the expression is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the solution be x,
x = −|a+b|/2−c
Substitute value in the above equation,
x = - |1 + 2 / 3 - 1|/2 - (-3)
x = -1/3 + 3
x = -1+9 / 3
x = 8/3
Thus, the required simplified value of the given expression is 8/3.
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Given g(x) = -2√x², find g(8 + x).
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Answer:
g(8 + x) = - 2(8 + x)
Step-by-step explanation:
substitute x = 8 + x into g(x)
g(8 + x) = - 2[tex]\sqrt{(8+x)^2}[/tex] = - 2(8 + x)
Simplify the expression √112x10y13. Show your work. pls help
Answers
Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]
Step-by-step explanation:
1) Separate the radicals
sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)
2) For sqrt(112), rewrite it as the product of a perfect square and some other number.
sqrt(112) = sqrt(16) * sqrt(7)
= 4*sqrt(7)
3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
n = 2, so x^(10/2), and when simplified you have x^5
4) For sqrt(y^13), do the same thing.
y^(13/2) = sqrt(y)*(y^6)
5)Combine everything
4x^5y^6sqrt(7y)
At a sale a sofa is being sold for 67% of the regular price. The sale price is $469. What is the regular price?
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We have the following information:
• At a sale, a sofa is being sold for ,67% of the regular price
,• The sale price is $469
And we need to determine the regular price.
To find it, we can proceed as follows:
1. Let x be the regular price. Then we have:
[tex]\begin{gathered} 67\%=\frac{67}{100} \\ \\ 67\%(x)=\frac{67}{100}x \\ \\ \text{ Then we know:} \\ \\ \frac{67}{100}x=\$469 \end{gathered}[/tex]2. Now, we have to solve for x as follows:
[tex]\begin{gathered} \text{ Multiply both sides by }\frac{100}{67}: \\ \\ \frac{67}{100}*\frac{100}{67}x=\frac{100}{67}*\$469 \\ \\ x=\frac{100*\$469}{67}=\$700 \\ \\ x=\$700 \end{gathered}[/tex]Therefore, in summary, the regular price is $700.
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a/maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.This task build on important concepts you've learned in this unit and allows you to apply those concepts to a variety ofsituations. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.
Answers
Given:
Salesman A earn = 65 per sale.
Salesman B earn = 40 per sales and 300weekly salary.
Salesman C earn = 900 weekly salary
Let "x" represent the number of sales each man
Salesman A earn is:
[tex]y=65x[/tex]Salesman B earn is:
[tex]y=40x+300[/tex][tex]\begin{gathered} 65x=40x+300 \\ 65x-40x=300 \\ 25x=300 \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]So total sales is 12 then.
S=0 For Zero week
[tex]\begin{gathered} \text{Salesman A} \\ y=65x \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} \text{Salesman B} \\ y=40x+300 \\ y=40(0)+300 \\ y=300 \end{gathered}[/tex][tex]\begin{gathered} \text{ Salesman C} \\ y=900 \end{gathered}[/tex]For S=1
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(1) \\ y=65 \\ \text{Salesman B}\colon \\ y=40x+300 \\ y=40(1)+300 \\ y=340 \\ \text{Salesman C:} \\ y=900 \end{gathered}[/tex]For s=10
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(10) \\ y=650 \\ \text{Salesman B:} \\ y=40x+300 \\ y=40(10)+300 \\ y=700 \\ \text{Salesman c:} \\ y=900 \end{gathered}[/tex]NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown.
Answers
Answers:
Domain as an inequality: [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty , \infty)}[/tex]
Range as an inequality: [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]
Range in interval notation: [-3, 3]
=================================================
Explanation:
The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.
As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.
That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]
Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.
----------------------
Now onto the range.
Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.
In this case, the smallest y can get is y = -3
The largest it can get is y = 3
The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".
That inequality condenses to the interval notation [-3, 3]
We use square brackets to include the endpoints as part of the range.
Answer:
[tex]\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty[/tex]
[tex]\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3[/tex]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.Inequality notation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".From inspection of the given graph, the function is continuous and so the domain is not restricted.
Therefore, the domain of the function is:
Interval notation: (-∞, ∞)Inequality notation: -∞ < x < ∞From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3. Both values are included in the range.
Therefore, the range of the function is:
Interval notation: [-3, 3]Inequality notation: -3 ≤ y ≤ 33.50 : 1.50 ratio as a fraction
Answers
Answer:
7/3
Step-by-step explanation:
You want the ratio 3.50 : 1.50 written as a fraction.
RatioA ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:
3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50
Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:
3.50/1.50 = (2·3.50)/(2·1.50) = 7/3
The ratio 3.50:1.50 is equivalent to the fraction 7/3.
A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 361?
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The probability of selecting the integer 361 from the random generator is 0.
What is probability?It should be noted that probability simply has to do with the likelihood that a particular thing will take place.
In this case, a random number generator is used to select an integer from 1 to 50 .
The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.
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A police car traveling south toward Sioux Falls, Iowa, at 160km/h pursues a truck east away from Sioux Falls at 140 km/h. At time t=0, the police car is 60km north and the truck is 50km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing at t=10 minutes, (Use decimal notation. Give your answer to three decimal places)
Answers
The rate of change of the distance between the police car and the truck after 10 minutes is approximately 193.66 m/s
What is a rate of change of a function?The rate of change of a function is the rate at which the output of the function is changing with regards to the input.
The velocity of the police car = 160 km/h south
The velocity of the truck = 140 km/h east
Distance of the police car from Sioux Falls = 60 km north
Distance of the truck from Sioux Falls = 50 km east
Required;
The rate at which the distance between the vehicles is changing at t = 10 minutes
Solution;
Let d represent the distance between the vehicles, we have;
d² = x² + y²
Where;
x = The distance of the truck from Sioux falls
y = The distance of the police car from Sioux Falls
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d^2= \frac{d}{dt}(x^{2}) +\frac{d}{dt} (y^{2}) }[/tex]
Which gives;
[tex] \displaystyle{ 2 \cdot d \cdot \frac{d}{dt} d=2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }[/tex]
After 10 minutes, we have;
y = 60 - (10/60)×160 = 100/3
x = 50 + (10/60)×140 = 220/3
d = √((100/3)² + (220/3)²) = 20•(√146)/3
[tex] \displaystyle{ \frac{d}{dt} d=\frac{2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }{2 \cdot d }}[/tex]
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d= \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}}[/tex]
[tex] \displaystyle{ \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}\approx 193.66}[/tex]
Therefore;
[tex] \displaystyle{ \frac{d}{dt} d \approx 193.66}[/tex]
The rate of change of the distance between the vehicles with time, [tex] \displaystyle{ \frac{d}{dt} d}[/tex] after 10 minutes is approximately 193.660 m/sLearn more about rate of change of a function here:
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Given the diagram, classify the bolded line as a perpendicular bisector, angle bisector, median or alritude. I chose angle bisector. Am I right?
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we have that
the answer is the option First
perpendicular bisector
because, is perpendicular to the segment at its midpoint
evaluate the expression 2(8-4)^2-10÷2
option 1 11
option 2 27
option 3 56
option 4 59
please help quick
I have a time limit
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[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]
THE ANSWER IS OPTION 2. 27
HOPE THIS HELPS
Answer:
Answer is 27
♬
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Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon. What was the price before the 15% increase?
Answers
The price of gasoline before the 15% increase is $4.75/gallon.
What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.
How can we calculate the price before the 15% increase?
Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.
15÷100+x = $4.90/gallon
0.15+x = $4.90/gallon
Therefore, x = $4.90/ gallon - 15÷100
x = $4.90/gallon - 0.15
x = $4.75/gallon.
Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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Domain and range of the quadratic function F(x)=-4(x+6)^2-9
Answers
Answer:
Domain: (-∞, ∞)
Range: (-∞, -9]
Step-by-step explanation:
Is-7+9 = -9 + 7 true, false, or open?
Answers
-9+7=-2
so the answer is false
Derive the formular to find the area of the moon and state the assumption taken clearly, physically and mathematically, without defying Keplars laws
Answers
Answer:
Area = 4πr²
Step-by-step explanation:
- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;
Assume the moon is a perfect and regular sphere
[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]
- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;
[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]
- So, from our formular;
[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]
r is radius of the moon[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]
Eva counts up. by 3s, while Jin counts up by 5s. What is the least
number that they both say?
Answers
Explanation:
This is the LCM (lowest common multiple) of 3 and 5
3*5 = 15
Eva: 3, 6, 9, 12, 15, 18, 21, ...
Jin: 5, 10, 15, 20, 25, ...
A water tank initially contained 56 liters of water. It is being drained at a constant rate of 2.5 liters per minute. How many liters of water are in the tank after 9 minutes?
Answers
i want to ask a question
Answers
We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:
[tex]\begin{gathered} AC^2=CD\cdot BC \\ 20^2=CD\cdot BC \end{gathered}[/tex]Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,
[tex]\begin{gathered} 20^2=CD\cdot BC=(OC-OA)\cdot(OA+OC)=OC^2-OA^2=OC^2-8^2 \\ 20^2=OC^2-8^2 \\ OC^2=20^2+8^2=464 \\ OC=\sqrt[]{464}=21.54\approx22\operatorname{cm} \end{gathered}[/tex]22. After an article is discounted at 25%, it sells for $112.50. The original price of the article was:
A. $28.12
B. $84.37
C. $150.00
D. $152.00
Answers
Answer:
the answer is C
Step-by-step explanation:
25% of 150 is 37.5 so 150-37.5 is 112.5
help me with my work please
Answers
In the first one, the word increase means you will be add something
+42000
In the second one, the word withdrew means you will subtract something
-40
Aldo will take the 11:49 train to San Diego. The train is estimated to arrive in 4 hours and 32 minutes. What is the estimated arrival time?
Answers
Kevonta, this is the solution:
Time of departure : 11:49
Time of travel : 4:32
In consequence, the estimated arrival time if the train departs in the morning is:
11 + 4 = 15 hours
49 + 32 = 81 minutes
81 minutes = 1 hour + 21 minutes
4:21 pm
If the train departs at night, the estimated time of arrival is:
4:21 am
Use the appropriate form of the percentages formula. What percent of 10 is 2?
Answers
To determine a percentage we can use the following formula:
[tex]\frac{part}{whole}\cdot100\%[/tex]In this case the part is equal to two, the whole is equal to 10, then we have:
[tex]\frac{2}{10}*100\%=20\%[/tex]Therefore, 2 is 20% of 10
Trisha is using the recipe show to make a fruit salad. She wants to use 20 diced strawberries in her fruit salad. How many bananas, apples, and pears show Trisha use in her fruit salad? Fruit Salad Recipe 4 bananas 3 apples 6 pears 10 strawberries bananas apples pears
Answers
The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given
Bananas
4x2=8 bananas
Apples
3x2=6 apples
Pears
6x2=12 pears
An initial investment of $200 is appreciated for 20 years in an account that earns 6% interest, compounded continuously. Find the amount of money in the account at the end of the period.
Answers
To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
9. Rosie's Bakery just purchased an oven for $1,970. The owner expects the oven to last for 10years with a constant depreciation each year. It can then be sold as scrap for an estimatedsalvage value of $270 after 10 years. (20 points)a) Find a linear equation modeling the value of the oven, y, after x years of use.b) Find the value of the oven after 2.5 years.c) Find the y-intercept. Explain the meaning of the y-intercept in the context of this problem.d) Graph the equation of the line. Be sure to label the axes.
Answers
a)
The oven devaluated from $1970 to $270 in 10 years.
Since each year it looses the same value, divide the change in the price over the time interval to find the rate of change of the value with respect to time.
To find the change in price, substract the initial price from the final price:
[tex]270-1970=-1700[/tex]The change in price was -$1700.
Divide -1700 over 10 to find the change in the price per year:
[tex]-\frac{1700}{10}=-170[/tex]The initial value of the oven was $1970, and each year it looses a value of $170.
Then, after x years, the value will be equal to 1970-170x.
Then, the linear equation that models the value of the oven, y, after x years of use, is:
[tex]y=-170x+1970[/tex]b)
To find the value of the oven after 2.5 years, substitute x=2.5:
[tex]\begin{gathered} y_{2.5}=-170(2.5)+1970 \\ =-425+1970 \\ =1545 \end{gathered}[/tex]Then, the value of the oven after 2.5 years is $1545.
c)
To find the y-intercept, substitute x=0:
[tex]\begin{gathered} y_0=-170(0)+1970 \\ =1970 \end{gathered}[/tex]The y-intercept is the initial value of the oven when 0 years have passed.
d)
A solution must be 14% Insecticide. To make 5 gallons of this solution how much insecticide must you use? A) 0.028 gallon B) .36 gallon C) .7 gallon D) 2.8 gallons
Answers
Insecticides = 14/100 x 5 = 0.7
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤6
Answers
STEP - BY - STEP EXPLANATION
What to find?
Rate of change of the given function.
Given:
Step 1
State the formula for rate of change.
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]Step 2
Choose any two point within the given interval.
(3, 59) and (6, 44)
⇒a=3 f(a) =59
b= 6 f(b)=44
Step 3
Substitute the values into the formula and simplify.
[tex]Rate\text{ of change=}\frac{44-59}{6-3}[/tex][tex]=\frac{-15}{3}[/tex][tex]=-5[/tex]ANSWER
Rate of change = -5