PLEASE HELP ME!!! and if you could give me an explanation that would be good but if you can’t at least give me the answer please :(
Answers
Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C
=============================
Explanation:
Given roots: -2, 4, 4, 3
Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)
x = -2 leads to x+2 = 0, so (x+2) is one factor
x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor
x = 3 leads to x-3 = 0 so (x-3) is the last factor
Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)
Use the distributive property to expand everything out
g(x) = (x+2)(x-4)(x-4)(x-3)
g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )
g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )
g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )
g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96
g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96
which shows how I got choice C as the answer
Related Questions
An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly on 5 hours?
Answers
Greetings!
Answer:
2370 miles can be travelled
Step-by-step explanation:
If 474 miles can be travelled in 1 hour, this means that to find the total amount in 5 hours we can simply multiply this value by 474:
474 * 5 = 2370
So it can travel 2370 miles!
Hope this helps!
Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)
Answers
Answer:
(–6, –4)
Step-by-step explanation:
After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.
Using the substitution method, make y the subject in the first equation
y = 5x + 26
substitute into the second equation
2x -7(5x + 26) = 16
-33x - 182 = 16
-33x = 16 + 182
-33x = 198
x = 198/-33
x = -6
since y = 5x + 26
y = 5(-6) + 26
= -30 + 26
= -4
hence (x,y) = (-6,-4)
1950, the U.S. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. Find an exponential function to model this data
Answers
Let's do the usual thing and make t the years since 1950. We'll just abbreviate a billion B.
f(1950-1950)=39.4 B
f(2000-1950) =2025.2 B
Our exponential form for f will be
[tex]f = a e^{kt}[/tex]
[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]
[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]
Dividing
[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]
[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]
[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]
Our function is
[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]
Since [tex]e^{0.0787932} \approx 1.08198[/tex]
[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]
around 8.2 % annualized growth.
Final answer:
An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]
Explanation:
We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.
From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:
f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.
f(50) = 2025.2 = 39.4 × b^50.
To find the value of 'b', we solve the second equation:
2025.2 = 39.4 × [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]
Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:
[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]
Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.
For the following functions, (a) describe the domain and range, and (b) sketch the graph.
f(x)=(1/2)^x(-3)
Answers
(a)Domain:(-∞,∞)
Range:(0,∞)
Can someone help me with 1-3
Answers
2. Is A since 3^2=9 and -3^2=9 And 9-9=0. Im pretty sure A. For number 3. Just because the two x-values are 3 and -3. I’m sorry if I’m wrong on #3.
A total of 17,100 seats are still available for the next hockey game. If 62% of the tickets are sold, how many seats are in the arena? A. 7,100 seats B. 7,900 seats C. 45,000 seats D. 27,900 seats
Answers
Answer:
We have
seats x ( 62 / 100 ) = (seats - 17,100);
seats x 62 = 100 x (seats - 17,100);
seats x 62 = seats x 100 - 1710000;
1,710,000 = seats x 38;
seats = 1,710,000 ÷ 38;
seats = 45,000;
The correct answer is c. 45,000 seats;
Step-by-step explanation:
45, 000 A for plato users
Step-by-step explanation:
Trust me im Master chief
The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon with two sides of length 3.
Answers
The first hexagon: 2, 2, 3, 4, 6, 7
The second hexagon: 3, 3, a, b, c, d
The hexagons are similar. Therefore the sides are in proportion.
[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex] multiply both sides by 3
[tex]a=\dfrac{3}{2}=4.5[/tex]
[tex]\dfrac{b}{4}=\dfrac{3}{2}[/tex] multiply both sides by 4
[tex]b=\dfrac{3}{2}\cdot4=6[/tex]
[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex] multiply both sides by 6
[tex]c=\dfrac{3}{2}\cdot6=9[/tex]
[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex] multiply both sides by 7
[tex]d=\dfrac{21}{2}=10.5[/tex]
The perimeter:
[tex]P=4.5+6+9+10.5=30[/tex]
Answer:
36
Step-by-step explanation:
The previous answerer forgot to add the two 3's to the sum so the correct answer it 36
What is the value of x?
Answers
Answer:
x = 22 tan 31
x is approximately equal to 13.22
Step-by-step explanation:
We know from trigonometric functions that
tan A = opposite side/ adjacent side
tan 31 = x / 22
Multiply each side by 22
22 tan 31 = x
13.2189332
x is approximately equal to 13.22
solve f(x)=x²+7x+12/-x²-3x+4
Answers
[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1[/tex]
In a basketball game,Carolyn made 14 out of 20 shots. Anna made 16 out of 24 shots. Explain how you can tell if the two players made a proportional number of shots.
Answers
Answer:
You will want to set up the ratio for each and set them equal to each other. Then you can cross multiply to verify if you get the same answer. Another strategy is to set up each ratio and then reduce to lowest terms to see if you get the same fraction.
Step-by-step explanation:
Brooke has to set up 70 chairs in equal rows for the clas talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Answers
70 chairs 35 per row is 2 rows
70 chairs 14 per row is 5 rows
70 chairs 7 per row is 10 rows
70 chairs 10 per row is 7 rows
70 chairs 5 per row is 14 rows
Someone help plz (20 points)
Answers
Answer:
The answer is C)
Step-by-step explanation:
In order to fully solve a system of equations, you need both variables, x And y. Therefore he has to go back and solve for x
Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. After how many weeks will Gina have exactly $700 in her account, excluding interest?
Answers
Answer:
After 33 weeks.
Step-by-step explanation:
Let w be number of weeks.
We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.
To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.
[tex]20w+40=700[/tex]
Let us subtract 40 from both sides of equation.
[tex]20w+40-40=700-40[/tex]
[tex]20w=660[/tex]
Upon Dividing both sides of our equation by 20 we will get,
[tex]\frac{20w}{20}=\frac{660}{20}[/tex]
[tex]w=\frac{660}{20}[/tex]
[tex]w=33[/tex]
Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.
Light travels at a speed of 1.17 × 107 miles per minute. Pluto's average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Enter your answer in scientific notation, and, if necessary, round your multiplier to the nearest hundredth.
Answers
Speed is the rate of change of distance over time.
It will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
The given parameters are:
[tex]\mathbf{Speed = 1.17 \times 10^7 miles/mins}[/tex]
[tex]\mathbf{Distance = 3670000000 miles}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]
Make Time the subject
[tex]\mathbf{Time = \frac{Distance}{Speed}}[/tex]
Substitute values for Speed and Distance
[tex]\mathbf{Time = \frac{3670000000\ miles}{1.17 \times 10^7 miles/mins}}[/tex]
[tex]\mathbf{Time = \frac{3670000000\ mins}{1.17 \times 10^7 }}[/tex]
Rewrite as:
[tex]\mathbf{Time = \frac{3.67\times 10^9\ mins}{1.17 \times 10^7 }}[/tex]
Apply law of indices
[tex]\mathbf{Time = \frac{3.67\times 10^{9 - 7}\ mins}{1.17}}[/tex]
Divide
[tex]\mathbf{Time = 2.20 \times 10^{2}\ mins}[/tex]
Hence, it will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
Read more about speed and rates at:
https://brainly.com/question/359790
[15 POINTS] A rectangle has a width w and a length that is two more than its width. what is the perimeter of the rectangle? Write and simplify an expression.
Answers
Answer: P = 4w + 4
Step-by-step explanation:
width (w) = w
length (L) = w + 2 (2 more than its width)
Perimeter (P) = 2L + 2w
P = 2L + 2w
= 2(w + 2) + 2(w)
= 2w + 4 + 2w
= 4w + 4
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Simplify.
Answers
Answer:
(B): (x - 2)/(x + 1)
Step-by-step explanation:
The numerator is x^2 + 5x - 14. That is equal to (x - 2)(x + 7).
The denominator is x^2 + 8x + 7. That is equal to (x + 1)(x + 7).
You can then eliminate (x+7) to get (x - 2)/(x + 1).
Answer: B
Step-by-step explanation:
[tex]\dfrac{x^{2}+5x-14}{x^{2}+8x+7}[/tex]
[tex]=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}[/tex]
[tex]=\dfrac{(x-2)}{(x+1)}[/tex]
Find the exact values of the six trigonometric functions for angle in standard position if a point with the coordinates (-6, 6) lies on its terminal side.
Answers
Answer:
sin = √2/2, cos = -√2/2, tan = cot = -1
csc = √2, sec = -√2
Step-by-step explanation:
Angle runs around unit circle (where x^2+y^2=1)
from (1,0) to (-√2/2,√2/2)
Which of the options represents the resulting equation after an equivalent expression for y is substituted into the second equation?
1 THROUGH 4 ARE THE ANSWERS
Answers
Answer:
Correct choice is D
Step-by-step explanation:
Given the system of two equations:
[tex]\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..[/tex]
Fro mthe first equation
[tex]y=8-4x.[/tex]
Substitute into the second equation [tex]8-4x[/tex] instead of y:
[tex]6x-9(8-4x)=12.[/tex]
Note that [tex]8-4x=-4x+8,[/tex] then the second equation will take look
[tex]6x-9(-4x+8)=12.[/tex]
1. What is the radical form of the expression 4 2/3?
2. What function equation is represented by th graph?
Answers
Answer:
1. [tex]\sqrt[3]{4^2}[/tex]
2. Answer A
Step-by-step explanation:
1. A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.
[tex]4^{\frac{2}{3} }[/tex]
[tex]\sqrt[3]{4^2}[/tex]
2. An exponential always crosses at (0,1) This function crosses at (0.6) meaning it has shifted up 5 units or +5. These means only answer options A and D are possible solutions. Also, since the graph starts high and ends low and leveling out, this means the base is less than 1. Only 3/4 is less than 1. Answer A is the solution.
Indicate the method you would use
Answers
Answer:
SSS can be used to prove that the given triangles are congruent.
Step-by-step explanation:
In the given two triangles ΔADC and ΔABC,
AD = AB = 7 units,CD = BC = 8 units,AC is common to both triangles,Hence, ΔADC ≅ ΔABC by Side-Side-Side (SSS) congruence.
SSS congruence-
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
A 20-foot piece of string is cut into two pieces so that the longer piece is 5 feet than twice the shorter piece
Answers
Hector went shopping for a computer. At RST store, a computer originally prices at $955 had a price reduction of 40%. What was the sale price?
Answers
Answer:
$573
Step-by-step explanation:
955* 0.60=573
or
10% of 955= 95.5
50% of 955=477.5
477.5=95.5=573
The sale price of the computer is given by the equation A = $ 573
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the sale price of the computer after the price reduction be A
Now , the equation will be
The initial sale price of the computer = $ 955
The price reduction percentage on computer = 40 %
So , the sale price after reduction A = initial sale price of the computer - ( price reduction percentage x initial sale price of the computer )
Substituting the values in the equation , we get
The sale price after reduction A = 955 - ( 40/100 ) x 955
On simplifying the equation , we get
The sale price after reduction A = 955 - 382
The sale price after reduction A = $ 573
Therefore , the value of A is $ 573
Hence , the price of the computer is $ 573
To learn more about equations click :
https://brainly.com/question/19297665
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line A and line B are parallel. If line A is 2x + 3y =10, what is the equation for line B if it passes through the point (-6,8)
Answers
Let us Represent the Line A in the Standard form : y = mx + c
where : m is the Slope of the Line and c is the y-intercept
Given : Equation of Line A is 2x + 3y = 10
[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]
Comparing with the Standard form, We can notice that :
Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]
We know that : Parallel lines have Same Slope
Given : Line A and Line B are Parallel
⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]
Given : Line B passes through the Point (-6 , 8)
We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)
Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]
Equation of Line B is :
[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]
⇒ 3y - 24 = -2x - 12
⇒ 2x + 3y = 12
Which is equivalent to 80 1/4 ?
Answers
Hey there!
"Which is equivalent to [tex]80\frac{1}{4}[/tex]?"
In order for you to solve this particular equation, you multiply the front number from the denominator, then whatever that outcome is, add to the nominator
So,
[tex]80\frac{1}{4}[/tex]
[tex]80(4) = 320[/tex]
[tex]320 +1 = 321[/tex]
[tex]4[/tex] stays the same
[tex]\boxed{Answer: \frac{321}{4}}[/tex]
If you want the decimal form, simplify the the mixed to a improper then you should get a outcome of: [tex]80.25[/tex]
For percentage do the fraction out of [tex]100[/tex] then solve it from there ([tex]0.8025[/tex]) would be the percentage form
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
[tex]80\frac{1}{4}[/tex] is equivalent to the decimal number 80.25, which can also be expressed as the improper fraction 321/4.
The question asks for an equivalent of the number [tex]80\frac{1}{4}[/tex]. To find this, we can convert the mixed number to an improper fraction or decimal. Since 1/4 is a standard fraction that is equivalent to 25 percent, we can express 1/4 as 0.25. Adding this to 80, we get an equivalent decimal number of 80.25. Another way to express 80 1/4 would be as an improper fraction, which would be [tex]\frac{321}{4}[/tex] because 80 times 4 equals 320, plus the numerator 1 equals 321.
You have 10 batteries sitting on your desk, three of which are dead. You choose 2 batteries are random for you calculator. What is the expected number of good batteries that you get?
A) 0
B) 1
C) 1.4
D) 2
Answers
Answer:
C) 1.4
Step-by-step explanation:
The probability of choosing 2 good ones is 7/10·6/9 = 42/90.
The probability of choosing 1 good one is 7/10·3/9 +3/10·7/9 = 42/90.
The probability of choosing 0 good ones is 3/10·2/9 = 6/90
The expected value is the sum of the product of number of good ones and their probability:
... 2·42/90 +1·42/90 +0·6/90 = (2+1)·42/90 = 42/30 = 1.4
Dana can jump a rope 264 times in 4 minutes. How many jumps can Dana make in one minute?
A) 55 jumps
B) 60 jumps
C) 66 jumps
D) 72 jumps
Whoever can answer it right, gets brainliest too!
Answers
Answer:
66
Step-by-step explanation:
divide 264/4=66
Answer:
C) 66 jumps
Step-by-step explanation:
Dana can jump 264 times in 4 minutes
Divide 364 by 4 to see how many times she can jump in one minute
264/4 = 66
Which Expression are equivalent to -12(2-3x)-5x
Answers
Answer:
-24-36x-5x
-24-41x
or -41x-24
Step-by-step explanation:
Evaluate the infinite sum
Answers
Answer:
It does not converge.
Step-by-step explanation:
Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.
The series ∑a·rⁿ converges if we have |r| < 1.
And the series ∑a·rⁿ diverges if we have |r| > 1.
But we can easily check that |r| = 7/6 > 1.
It means the given series diverges, i.e. does not converge.
Hence, option D is correct answer, i.e. It does not converge.
Answer:
D. it does not converge
What is the perimeter of a triangle with the given side lengths? s1 = x + 4 cm s2 = 3x + 1 cm s3 = 7x + 3 cm P = x + cm
Answers
Answer:
11x+8 cm = Perimeter
Step-by-step explanation:
A triangle has 3 sides. We add up all three sides to get the perimeter.
s1+s2+s3 = Perimeter
(x+4) +( 3x+1) + (7x+3) = Perimeter
Combine like terms
11x+8 = Perimeter
Answer:
P = 11x + 8 cm
Step-by-step explanation:
The perimeter of a triangle is the sum of the lengths of the three sides.
... P = s1 + s2 + s3
... P = (x +4 cm) +(3x +1 cm) +(7x +3 cm) . . . . substitute for s1, s2, s3
... P = x(1 +3 +7) + cm(4 + 1 + 3) . . . . . . collect terms
... P = 11x + 8 cm
Help please !Algebra Two!!
Answers
Answer:
a. -1, odd; 2, even
b. [tex](x+1)(x-2)^2[/tex]
c. odd likely 3
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -1,2
We can write them in intercept or factored form as (x+1) and (x-2).
Because the graph crosses the x-axis at -1, it's multiplicity is odd likely 1. However, the graph does not cross at 2 and has an even multiplicity likely 2.
The graph is ends up and is a sideways s so is positive with an odd degree.
This means the function has a degree of 3 or higher with the degree being odd.