The values of m and n are -29/3 and 40/3 respectively
Factor and remainder theoremA polynomial is a function that has a leading degree of 2 and greater. Given the polynomial
P(x) = 2x^3 + mx^2 + nx – 2
If it is divided by x – 3, the remainder is 4 and divided by x – 2, the remainder is 2, hence;
4 = 2(3)^3 + 9m + 3n - 2
4 = 54 + 9m + 3n - 3
9m + 3n = -47
Similarly
2 = 2(2)^3 + 4m + 2n - 2
4m + 2n = -12
Solve simultaneously
9m + 3n = -47 * 2
4m + 2n = -12 * 3
______________
18m + 6n = -94
12m + 6n = -36
Subtract
6m = -58
m = -58/6 = -29/3
For the value of n
4m + 2n = -12
2m + n = -6
2(-29/3) + n = -6
n = -6 + 58/3
n = 40/3
Hence the values of m and n are -29/3 and 40/3 respectively
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What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) -4 = 0 as a quadratic equation?
Ou= (x + 5)
Ou= (x-5)
u = (x + 5)²
O u =(x-5)²
The substitution that should be used to rewrite the equation is u = x+5, the correct option is A.
What is a Quadratic Equation?The polynomials of the 2nd degree are called Quadratic Equations.
It has a general form as ax² +bx+c=0
To rewrite the expression as a quadratic equation
6(x+5)² + 5(x+5)-4 = 0
=6(x+5)(x+5)+5(x+5)-4
=6(x² + 5x + 5x + 25)+5(x+5)-4
=6(x²+10x+25) + 5(x+5) - 4 = 0
=6x² + 60x + 5x + 150 + 25 - 4 = 0
=6x² + 65x + 171 = 0
This is the quadratic equation of the form ax² +bx+c=0
but if directly it has to be written in this ax² +bx+c=0 form , it can be written by substituting u = (x + 5)
6(x+5)² + 5(x+5)-4 = 0
6u²+5u-4 = 0
Therefore, the substitution that should be used to rewrite the equation is u = x+5, the correct option is A.
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a customer buys 3 cappuccinos that costs $2.54 each and a bottle of water that costs $0.76 she gives the shop assistant $20 how much change should she receive
Answer:
$11.62
Step-by-step explanation:
2.54×3=$7.62
0.76+7.62=8.38
20-8.38=$11.62
Answer:
Step-by-step explanation:
Discussion
3 cappuccinos at 2.54 each 2.54 * 3 = 7.62
1 bottle of water at 0.76 0.76*1 = .76 Add
Total 8.38
Change = 20 - 8.38 = 11.62
Answer
She should receive 11.62 in change.
A population of squirrels is growing in a Louisiana forest with a monthly growth constant of 55 percent. If the initial count is 100100 squirrels, how many are there in a year? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.
The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
The final value of any quantity growing constantly at a particular rate is given as [tex]V = V_{0}e^{rt}[/tex] ,
where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.
The current population of squirrels (V₀) = 100.
The growth rate (r) = 5% per month.
The time period (t) = 1 year = 12 months.
Hence, the final population of squirrels (V), is given as:
[tex]V = V_{0}e^{rt}[/tex] ,
or, [tex]V = 100e^{(0.05*12)}[/tex] ,
or, [tex]V = 100e^{0.60}[/tex] ,
or, V = 100*1.822119,
or, V = 182.2119 ≈ 182.
Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
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Change 9% to fraction?
9/100
Step-by-step explanation:
[tex]9\% = \frac{9}{100} [/tex]
9% as a Fraction is 9/100
☆...hope this helps...☆
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What is the volume of the solid?
Answer: C. 3052,08 cm³.
Step-by-step explanation:
D=18 cm V=?
[tex]R=\frac{D}{2} =\frac{18\ cm}{2} =9\ cm.\\\boxed {V=\frac{4}{3}*\pi *R^3 }\\V=\frac{4}{3}*\pi *9^3 \\V=4*\pi *3*9^2\\V=12*81*3,14 \\V=3052,08\ (cm^3).[/tex]
use the distrubutive property to simply -8(6x+3)
A principal amount of $3000 is invested for 3 years at 4% compounded semi-annually. Use the compound interest formula to determine how much interest was earned on the investment.
The $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
Here,
P = $3000
r = 4% = 0.04
n = 2
t = 3 years
After plugging all the values in the formula:
[tex]\rm A = 3000(1+\dfrac{0.04}{2})^{2\times 3}[/tex]
After solving:
A = $3,378.49
I = A - P = 3,378.49 - 3000 = $378.49
Thus, the $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.
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Sharon drops a rubber ball from 160 feet every bounce sends the ball half as high as it was before. What is the total distance the ball has traveled from the moment it is dropped until it hits the floor for the fourth time
The total distance the ball has traveled from the moment it is dropped until it hits the floor for the fourth time is: 300 feet.
Total distanceFirst bounce
160 feet
Second bounce
= 1/2×160 = 80 feet
Third bounce
= 1/2×80 = 40 feet
Fourth bounce
= 1/2×40 = 20 feet
Hence:
Total distance= (160 feet+ 80 feet + 40 feet+20 feet
Total distance= 300 feet
Therefore the total distance traveled by the ball is 300 feet.
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HELPPPP ASAP !!
Write a compound inequality that represents the given graph
Answer:
x <= -2 or x >= 3
Step-by-step explanation:
Shaded circles represent <= or >=, and the first arrow points left from -2, and the second arrow points right from 3. Therefore x <= -2 or x >= 3 would represent the graph.
A plane has a maximum fuel capacity of 5,300 gallons. The airline requires that the pilot fly no more than 400 minutes before refueling. A one-way flight to a certain destination requires 2,000 gallons of fuel and 190 minutes of flight time. How many round trips can the pilot make before having to refuel?
A) 1
B) 2
C) 3
D) 4
Answer:
it is B
Step-by-step explanation:
that is because j3jejejdudduiwjsj
The requried pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1
To determine how many round trips the pilot can make before having to refuel, we need to consider both the fuel capacity and the flight time limit.
Given:
Maximum fuel capacity = 5,300 gallons
Flight time limit before refueling = 400 minutes
Fuel required for one-way flight = 2,000 gallons
Flight time for one-way flight = 190 minutes
First, let's calculate the maximum number of one-way trips the pilot can make based on the fuel capacity:
Max one-way trips based on fuel capacity = Maximum fuel capacity / Fuel required for one-way trip
Max one-way trips = 5,300 gallons / 2,000 gallons = 2.65 trips
Since we cannot have a fraction of a trip, we need to consider the flight time limit.
The total flight time for a round trip is twice the one-way flight time: 2 * 190 minutes = 380 minutes.
The pilot can fly a round trip as long as the flight time for the round trip is within the flight time limit. In this case, the round-trip flight time of 380 minutes is less than the flight time limit of 400 minutes.
Therefore, the pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1
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Jamaal washes 25 dishes per hour and works for 3 hours. Daniel can wash 22 dishes every two hours. Who can wash more dishes in 3 hours? And by how many?
Answer:
1. Jamaal
2. 42 more dishes
Step-by-step explanation:
1. Jamaal: 25 dishes per hour and works for 3 hours
25(3) = 75 dishes
Daniel: Daniel can wash 22 dishes every two hours.
22 = 2x
11 = x
11(3) = 33 dishes
2. 75 - 33 = 42
Jamaal can wash 42 more dishes than Daniel.
Jamaal washes 25 dishes per hour and works for 3 hours. Daniel can wash 22 dishes every two hours. Jamaal washed 42 more dishes than Daniel in 3 hours.
Let's calculate the number of dishes washed by each person in 3 hours and then compare the results.
Jamaal:
Jamaal washes 25 dishes per hour and works for 3 hours.
Number of dishes washed by Jamaal in 3 hours = 25 dishes/hour * 3 hours = 75 dishes
Daniel:
Daniel washes 22 dishes every two hours.
To find the number of dishes washed by Daniel in 3 hours, we need to find how many times he washes dishes in 3 hours.
Number of times Daniel washes dishes in 3 hours = 3 hours / 2 hours (time for 1 cycle) = 1.5 cycles
Now, multiply the number of cycles by the number of dishes washed per cycle:
Number of dishes washed by Daniel in 3 hours = 1.5 cycles * 22 dishes/cycle = 33 dishes
Comparison:
Jamaal washed 75 dishes in 3 hours.
Daniel washed 33 dishes in 3 hours.
Now, let's find the difference in the number of dishes washed by each person:
Difference = Jamaal's dishes - Daniel's dishes
Difference = 75 dishes - 33 dishes = 42 dishes
Therefore, Jamaal washed 42 more dishes than Daniel in 3 hours.
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Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the right of f of x. .
Explanation:
Refer to the graph below. It should be similar to what your teacher gave you, based off the description.
Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.
As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.
In terms of notation, we can write [tex]\displaystyle \lim_{x\to3^{+}}f(x) = 3[/tex]
The portion [tex]x \to 3^{+}[/tex] means we're approaching 3 from the positive side, aka the right hand side on the number line.
Graph the function.
f(x)=5\cdot\left(\dfrac{4}{5}\right)^xf(x)=5⋅(
5
4
)
x
f, left parenthesis, x, right parenthesis, equals, 5, dot, left parenthesis, start fraction, 4, divided by, 5, end fraction, right parenthesis, start superscript, x, end superscript
Answer:
Please review my interpretation of the written expression.
Step-by-step explanation:
f(x) = 5*(4/5)^x : Is this correct?
If so, see attached graph.
One can calculate several points and then draw the graph, or use an online, and free, graphing app (DESMOS in this case).
Since the exponent is the variable, I'll pick a few vaules that are easy (for me) to calculate:
f(0) = 5*(4/5)^0
Anything raised to the 0th power is equal to 1, so we get 5*1 or 5 to make the point (1,5).
When x = 1, the fraction (4/5) remains (4/5) and when multiplied by 5, reduces to simply 4. The second point is (1,4)
For the last point, I chose x to be 10. 5(4/5)^10 becomes 0.5. The third point is (10,0.5)
We can see the line approaches 0 as x increases.
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?
The probability that they do not use the swimming pool will be 0.2.
How to calculate the probability?From the information given, there are 135 people in a sport centre and 31 people use the gym and the track while 4 people use all three facilities.
Based on the information given, the people who use the gym and the track only will be:
= 31 - 4
= 27
The probability that they do not use the swimming pool will be:
= 27/135
= 0.2
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The names of the months are each written on a slip of paper. if a slip of paper is randomly drawn, which scenario depicts mutually exclusive events? begins with a j and contains a u ends with an r and has five or fewer letters has thirty-one days and ends with a y contains an e and has thirty or fewer days
Answer:
Ends with r and has five or fewer letters
Step-by-step explanation:
Answer:
The answer is : B
Step-by-step explanation:
trust me I did it on edge 2022
pls helpppp!!!!!!
What kind of compound inequality is….>>>>>look at pic
Answer:
(d) intersection
Step-by-step explanation:
When given two inequalities, you must determine whether the solution set must satisfy both, or must satisfy either. The key is found in the conjunction associated with the inequalities.
ConjunctionHere, the conjunction is "and," which means the solution must satisfy both inequalities. It also means, the solution set will be the intersection of the solution sets of the different inequalities.
The attached number line shows the first solution set in red, the second solution set in blue, and the "and" (intersection) of those in purple.
The conjunction "or" will signify the solution set is the union of those of the separate inequalities.
help me help me ………….
Answer:
not similar
Step-by-step explanation:
not similar--it doesn't work out for the angles to be similar
if we find the angle x of the right-hand triangle, we can tell it would be 41 degrees
meaning that these triangles are not similar
Find the length of JH help pls
Answer:
c) 19
Step-by-step explanation:
To find the length of JH, subtract the length of HM from JM.
Length of JH = JM - HM
= 40 - 21
= 19
Answer:
JH = 19
Step-by-step explanation:
from the diagram
JH + HM = JM , that is
JH + 21 = 40 ( subtract 21 from both sides )
JH = 19
Can someone help? ASAP Find each missing length, give all answers in simplest radical form
Volume=
What is the volume?
Please help thank you
Answer:
288π
Step-by-step explanation:
The volume of a sphere can be evaluated by using the following formula:
[tex]A=\frac{4}{3}\pi r^{3}[/tex]
We are given that the radius is 6, so we can plug into the formula to solve:
[tex]A=\frac{4}{3}\pi*6^{3} =\frac{4}{3}*216*\pi =288\pi[/tex] (216/3 is 72, and 72*4 is 288)
Therefore, the volume is exactly 288π. The approximate answer, if you let π be 3.14 and evaluate it out, is around 904.78
i have no clue what to do
Answer:
4x + 3y = 12
Step-by-step explanation:
Answer:
4x + 3y = 12
Step-by-step explanation:
At x-intercept, y = 0.
∴ When we substitute y = 0 into the equation, x should equal 3.
• 1st equation: 3x + 4(0) = 12 ⇒ x = 4 ❌
• 2nd equation: 4x + 3(0) = 7 ⇒ x = 7/4 ❌
• 3rd equation: 3x + 4(0) = 7 ⇒ x = 7/3 ❌
• 4th equation: 4x + 3(0) = 12 ⇒ x = 3 ✅
This means the 4th option is the correct one.
To check, we can replace x = 0 into the 4th equation to see if the y-intercept value comes out to be 4:
4(0) + 3y = 12 ⇒ y = 4 ✅
simplify 4(x+7)-7-x+2
Answer: 3x + 23
it should be right!
Answer:
3x + 23
Step-by-step explanation:
To simplify this expression, the first thing we have to do is distribute the 4 outside the parentheses. This gives us 4x + 28 - 7 - x + 2. Now, we can combine like terms (those that have variables and those that don't) to get 3x + 23
Simplify
1) 9/7+1/6
2) 1 1/6- 2 1/5
3) 4/7x8/4
4) 4/7* 8/4
you answer fast and correct I will mark you as a brainliest
Answer:
1 19/42
- 1 1/30
3&4 are both 1 1/7
Step-by-step explanation:
the measures of the sides of a triangle are 2x+3, 8x-4 and x^2. Write an expression that describes the perimeter of the triangle
Answer:
[tex]\textsf{Perimeter}=x^2+10x-1[/tex]
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given sides of a triangle:
[tex]2x + 3[/tex][tex]8x - 4[/tex][tex]x^2[/tex]Therefore, to find the perimeter of the triangle, sum the given sides:
[tex]\begin{aligned}\sf Perimeter & = (2x+3)+(8x-4)+x^2\\& = 2x+3+8x-4+x^2\\& = x^2 + 2x+8x+3-4\\& = x^2+10x-1\end{aligned}[/tex]
Perimeter=
Sum of sidesx²+2x+3+8x-4x²+2x+8x+3-4x²+10x-1A machine that is programmed to package 1.50 pounds of cereal is being tested for its accuracy in a sample of 56 cereal boxes, the sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the mean.
The 95% confidence interval for the mean is (1.535, 1.504).
It is given that a machine produces 1.50 pounds of cereal. The sample is 56 cereal boxes. The sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds.
Mean = 1.50 pounds
x = 1.52 pounds
Standard deviation = SD = 0.06 pounds
n = 56
We need to find the 95% confidence interval for the mean.
So, z = 1.96
So, the confidence interval would be
[tex]x[/tex]±[tex]z\frac{mean}{\sqrt{n} }[/tex]
[tex]1.52[/tex]±[tex]1.96*\frac{0.06}{\sqrt{56} }[/tex]
= [tex]1.52[/tex]±[tex]1.96*0.00801[/tex]
= [tex](1.52 + 0.0156996),(1.52 - 0.0156996)[/tex]
= [tex](1.535, 1.504)[/tex]
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Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
Answer:
noStep-by-step explanation:
Can 10 people be divided into two groups with a ratio of 1 : 2?
Explain.
10 : 3 = 3.33
or 10 : 3 = 9 remaining 1
since it is not possible to divide a person into three parts, your answer is no
1. Try It #1
If f(x) is a linear function, and (2,3) and (0,4) are points on the line, find the slope. Is this function increasing or decreasing?
Answer:
The slope of the line representing the linear function f(x) is determined as [tex]$-\frac{1}{2}$[/tex]. The function f(x) is decreasing because the slope is less than zero, i.e., m<0.
Step-by-step explanation:
A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).
It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.
Step 1 of 1
Determine the slope of the line.
The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
So, substitute [tex]$4 \& 3$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$0 \& 2$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,[tex]$m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$[/tex]
The slope of the line is obtained as [tex]$-\frac{1}{2}$[/tex]. Now, as [tex]$-\frac{1}{2} < 0$[/tex], so the function f(x) is decreasing.
How many ways can the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled
The number of ways is 497420
The ways can the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled is [tex]22_{C_9}[/tex]
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
22C9 = 22! /(9!*13!) = 497420
Thus, In 497420 ways the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled.
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How many solutions exist for the given equation? 0.75(x 40) = 0.35(x 20) 0.35(x 20)
The equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is having only one solution.
Given equation 0.75(x+40)=0.35(x+20)+0.35(x-20)
We have to find the number of solutions.
To find the number of solutions we have to solve the equation for the value of variable x. Equation is often solved to find the value of variables.
Equation : 0.75(x+40)=0.35(x+20)+0.35(x-20)
Opening the brackets and multiply the numbers outside by the numbers in the bracket.
0.75x+30=0.35x+7+0.35x-7
Take all the numbers having same variables at one end of equal to.
0.75x-0.35x-0.35x=7-7-30
0.75x-0.7x=-30
0.05x=-30
x=-30/0.05
x=-600
Which is the only value of x.
Hence the number of solutions of the equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is one.
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sk...
What is as for the geometric sequence 6, 561; -2, 187; 729; -243;....
A. 1
B. -3
C. -9
D. -1
Option B is the answer. The term for the geometric sequence that we have here is -3.
How to solve for the geometric sequenceWe have u1, u2, u3 = a, ar, ar², ar³
From here we have to find the common ratio that is used to divide the sets of numbers
6,561 divided by −2,187 = -3
Hence when we go further each of the value when divided by -3 gives the next value.
Hence the value for the geometric sequence is -3.
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