The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?
Answer:
(x +5)
Step-by-step explanation:
The problem statement is telling you that one factor of (x⁴ +5x³ -3x -15) is (x³ -3). It is asking for the other factor. Clearly, you can find the other factor by dividing the polynomial by the given factor.
That is ...
(x⁴ +5x³ -3x -15) / (x³ -3) = (x +5)
so ...
(x⁴ +5x³ -3x -15) / (x +5) = (x³ -3)
The divisor of interest is (x +5).
Answer:
(x+5)
The answer is c.
A salesperson sold a total of $6,400.00.If her rate of commission is 6%, what is her commission?
multiply 6400 x 6%
6% = 0.06
6400 x 0.06 = 384
her commission was $384
Answer:
The commission amount of the salesperson is $384.
Step-by-step explanation:
A salesperson sold a total of $6,400.00.
The rate of commission is 6% or 0.06. Commissions are based on sales. These are some percentage of the sales amount.
So, here the amount will be = [tex]0.06\times6400=384[/tex] dollars
So, the commission amount of the salesperson is $384.
A 31-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37 m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.
The circumference of a coin is 8π What is the radius? What is the diameter?
What is the slope of a line that is perpendicular to the line whose equation is 0.5x−5y=9 0.5 x − 5 y = 9
Someone please solve this ASAP
16/7 = 12/y
84/16
84/16 = 5.25
5.25+7 = 12.25
x = 12.25
Write the point in its current fraction form dog show all your work for full credit.
0.225
which statements describe the function f(x)=2(x-4)^4
A) The left end of the graph of the function goes up, and the right end goes down
B) It has 3 zeros and at most 4 relative maximums or minimums
C) It has 4 zeros and at most 3 relative maximums or minimums
D) It is a translation of the parent function 4 units to the right
E) It is a translation of the parent function 4 units to the left
F) Both ends of the graph of the function go up
There was 3 answers.
Answer one is It has 4 zeros and at most 3 relative maximums or minimums.
Answer two is It is a translation of the percent function 4 units to the right.
Answer three is Both ends of the graph of the function go up.
:)
it is a transition of the parent function 4 units to the right, it has 4 zeros and at most 3 relative maximums and minimums, both ends of the graph of the function go up this is for apex
1) On average, Donna's Cafe has 42 customers, which represents 20% of the total approved occupancy by the fire department.
a) According to the fire department's occupancy approval, what percentage of the cafe is still available for customers?
b)According to the fire department's occupancy approval, how many seats are still available for customers?
Given the following sequence, find the 23rd term: 10.5, 11, 11.5, 12, 12.5, . . .
The graph below shows the fine that a college student pays to the library based on the number of minutes a loaner laptop is overdue:
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8. The values on the y axis are 0, 0.70, 1.40, 2.10, 2.80. Points are shown on ordered pairs 0, 0 and 2, 0.70 and 4, 1.40 and 6, 2.10. These points are joined by a line. The label on the x axis is Minutes Overdue. The title on the y axis is Fine.
Which statement best describes the point (0, 0) on the graph?
Answer:
So the answer would be No fine is paid if the laptop is returned exactly at the time at which it is due
What does the value of the LCM represent
A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?
Answer:
Step-by-step explanation:
Given that A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same
Whatever position cone is placed, the space remaining will have volume as
volume of the cylinder - volume of the cone
Let radius of cylinder be r and height be h
Then volume of cylinder = [tex]\pi r^2 h[/tex]
The cone has height as h and radius as r/2
So volume of cone = [tex]\frac{1}{3} \pi (\frac{r}{2} )^2h\\=(\pi r^2 h)\frac{1}{24}[/tex]
the volume of the space remaining in the cylinder after the cone is placed inside it
=[tex]\pi r^2 h (1-\frac{1}{24} )\\=\frac{23 \pi r^2 h}{24}[/tex]
Answer:
11/12 pie r^2 h
Step-by-step explanation:
Israel claims that all 45degree right triangles are similar. Is he correct? Explain.
the quadratic formula gives which roots for the equation 2x^2+7x+-2
The roots for the equation [tex]\(2x^2 + 7x = -2\)[/tex] are [tex]\(x = \frac{{-7 \pm \sqrt{65}}}{{4}}\).[/tex] So, option D is correct.
To find the roots of the quadratic equation [tex]\(2x^2 + 7x = -2\),[/tex] we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Here, [tex]\(a = 2\), \(b = 7\), and \(c = -2\).[/tex]
Substituting these values into the formula:
[tex]\[x = \frac{{-7 \pm \sqrt{{7^2 - 4 \cdot 2 \cdot (-2)}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-7 \pm \sqrt{{49 + 16}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-7 \pm \sqrt{{65}}}}{{4}}\][/tex]
So, the correct answer is option D:
[tex]\[x = \frac{{-7 \pm \sqrt{{65}}}}{{4}}\][/tex]
Complete Question:
Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 - 5x2 - 9x - 2
The rational zero -1 is a root of f(x). Synthetic division yields [tex]\(x^3 + 2x^2 - 7x - 2\)[/tex]. Further factorization or testing other rational roots finds the remaining zeros.
To find a rational zero of the polynomial function [tex]\(f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2\)[/tex], we can use the Rational Root Theorem. According to this theorem, any rational zero of the polynomial function must be of the form ±p/q, where p is a factor of the constant term (-2 in this case) and q is a factor of the leading coefficient (1 in this case).
The factors of -2 are ±1, ±2, and the factors of 1 are ±1. Therefore, the possible rational zeros are:
±1, ±2
We can try these values to see if they are roots of the polynomial.
Let's start by trying x = 1:
[tex]\[f(1) = (1)^4 + 3(1)^3 - 5(1)^2 - 9(1) - 2\]\[= 1 + 3 - 5 - 9 - 2\]\[= -12\][/tex]
So, x = 1 is not a root.
Next, let's try x = -1:
[tex]\[f(-1) = (-1)^4 + 3(-1)^3 - 5(-1)^2 - 9(-1) - 2\]\[= 1 - 3 - 5 + 9 - 2\]\[= 0\][/tex]
Therefore, x = -1 is a root of the polynomial.
To find the other zeros, we can perform polynomial division or synthetic division by dividing f(x) by (x + 1). Let's use synthetic division:
-1 1 3 -5 -9 -2
1 2 -7 -2 ↓
The result is [tex]\(x^3 + 2x^2 - 7x - 2\)[/tex]. Now, we can factor this cubic polynomial or continue using the Rational Root Theorem to find additional roots. Let's try x = 1 again:
[tex]\[f(1) = (1)^3 + 2(1)^2 - 7(1) - 2\]\[= 1 + 2 - 7 - 2\]\[= -6\][/tex]
x = 1 is not a root, so we continue to try the other possible rational zeros. However, to save time, let's check if any of the values of [tex]\(x = \pm 2\)[/tex] are roots using synthetic division:
For x = 2:
2 1 2 -7 -2
1 4 1 ↓
For \(x = -2\):
-2 1 2 -7 -2
1 0 -7 ↓
Since none of these values result in a remainder of 0, [tex]\(x = \pm 2\)[/tex] are not roots.
Therefore, the zeros of the polynomial function [tex]\(f(x) = x^4 + 3x^3 - 5x^2 - 9x - 2\) are \(x = -1\),[/tex] and the other zeros can be found by further factoring the reduced cubic polynomial.
Which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?
Final answer:
The algebraic expression for finding the average melting points of helium, hydrogen, and neon, using variables h, j, and k as their respective melting points, is (h + j + k) / 3.
Explanation:
The question asks for the algebraic expression that represents the average melting points of helium, hydrogen, and neon. The variables h, j, and k denote the individual melting points of these elements, respectively. To calculate the average melting point, you would add the melting points of each element and divide by the number of elements.
The algebraic expression for the average melting point is:
(h + j + k) / 3
What is the value of x?
16
50
130
164
Please hurry !!!
Answer:
x = 16.
Step-by-step explanation:
Given : Transverse line b and parallel line e and f.
To find : What is the value of x.
Solution : We have given Transverse line b and parallel line e and f.
Corresponding angles : When two lines are crossed by another line the angles in matching corners are called corresponding angles.
corresponding angles are always equal.
2x + 18 = 4x - 14.
On subtracting both sides by 4x
2x -4x + 18 = -14.
- 2x + 18 = - 14 .
On subtracting both sides by 18
- 2x = - 14 -18 .
- 2x = - 32 .
On dividing both sides by -2 .
x = 16.
Therefore, x = 16.
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function
C (x) = 0.8x ^ 2 - 256x +25,939 . How many machines must be made to minimize the unit cost? Do not round your answer.
Number of copy machines:
To minimize unit cost, 160 machines must be made.
Step-by-step explanation:
Find the first derivative of the cost function: C'(x) = 1.6x - 256.
Set the derivative equal to 0 and solve for x to find the critical point: 1.6x - 256 = 0. x = 160.
Check the nature of the critical point using the second derivative test to confirm that x = 160 gives the minimum cost.
Therefore, the number of machines that must be made to minimize the unit cost is 160 machines.
The number of machines that must be made to minimize the unit cost is 160.
To find the number of machines that must be made to minimize the unit cost, we need to find the minimum point of the function [tex]\(C(x) = 0.8x^2 - 256x + 25,939\).[/tex]
The function \(C(x)\) represents a quadratic equation, and the vertex of a quadratic equation represents its minimum or maximum point. The x-coordinate of the vertex of a quadratic function in the form [tex]\(ax^2 + bx + c\) is given by \(-\frac{b}{2a}\).[/tex]
[tex]For the function \(C(x) = 0.8x^2 - 256x + 25,939\), we have \(a = 0.8\) and \(b = -256\).Now, let's calculate the x-coordinate of the vertex:\[ x_{\text{vertex}} = -\frac{b}{2a} = -\frac{-256}{2 \times 0.8} = -\frac{-256}{1.6} = 160 \][/tex]
So, the number of machines that must be made to minimize the unit cost is 160.
Prove that there does not exist integers m and n such that 2m+4n=7
To prove that there are no integers m and n that satisfy 2m + 4n = 7, we can assume the opposite and show that it leads to a contradiction. We can rearrange the equation and analyze the parity of the terms to prove there are no integer solutions.
Explanation:To prove that there does not exist integers m and n such that 2m + 4n = 7, we can start by assuming that such integers do exist. Let's suppose m and n are integers that satisfy the equation.
Rearranging the equation, we have 2m = 7 - 4n. This means that 2m is an even number and 7 - 4n is an odd number. However, there is no way for an even number and an odd number to be equal. Therefore, our assumption was incorrect, and there are no integers m and n that satisfy the equation 2m + 4n = 7.
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Lines A and b are parallel and lines e and f are parallel. If m<1=89, what is the measure of <5?
M<5=?
Answer:
Given the statement:
Lines a and b are parallel and lines e and f are parallel.
if [tex]m \angle 1 = 89^{\circ}[/tex]
By supplementary angles:
[tex]m\angle 1+ m\angle 2 = 180^{\circ}[/tex]
⇒[tex]89^{\circ}+ m\angle 2 = 180^{\circ}[/tex]
Subtract 89 degree from both sides we have;
[tex]m \angle 2 = 91^{\circ}[/tex]
Since,
m∠4 = m∠5 [Vertically Opposite angles] .....[1]
m∠4 = m∠3 [Alternate Interior angle] .....[2]
By [1] and [2] we have;
m∠5 =m∠3 ....[3]
Also;
m∠2 = m∠3 [Alternate interior angle] ....[4]
by [3] and [4] we have;
m∠5 = m∠2
Substitute the given values we have;
[tex]m \angle 5 = 91^{\circ}[/tex]
Therefore, the measure of [tex]m \angle 5[/tex] is, [tex]91^{\circ}[/tex]
write two different pairs of decimals whose sum are 14.1
Find the circumference and the area of a circle with radius
6yd.
David wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years. if david can earn 10 percent on his investments, how much must he deposit at the end of each year? $50,000 $17,460 $14,900 $117,453
David must deposit approximately $16,150.01 at the end of each year to accumulate $1 million by the end of 20 years at a 10 percent interest rate.
To calculate the equal annual end-of-year deposits that David must make to accumulate $1 million in 20 years at a 10 percent interest rate, we can use the formula for the future value of an ordinary annuity.
The formula for the future value of an ordinary annuity is given by:
[tex]FV = P * ((1 + r)^n - 1) / r[/tex]
where:
FV is the future value of the annuity (the desired $1 million in this case)
P is the annual deposit (what we need to find)
r is the annual interest rate (10% or 0.10 as a decimal)
n is the number of years (20 years in this case)
Substituting the known values:
[tex]$1,000,000 = P * ((1 + 0.10)^{20} - 1) / 0.10[/tex]
Now, we can solve for P:
$1,000,000 = P * (6.1917364224) / 0.10
$1,000,000 = P * 61.917364224
P = $1,000,000 / 61.917364224
P ≈ $16,150.01
So, David must deposit approximately $16,150.01 at the end of each year to accumulate $1 million by the end of 20 years at a 10 percent interest rate.
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Tim is 5 years older than Melissa. The sum of their ages is 21. This system is represented by the equations: t = 5 + m t + m = 21 What is the solution if you represent Tim's age on the y-axis and Melissa's age on the x-axis?
Please hurry !!!
Which is an x-intercept of the graphed function?
A) 0,4
B)-1,0
C)4,0
D)0,-1
we know that
The x-intercept is the value of the coordinate x when the value of the function is equal to zero
so
In this problem we have that the x-intercepts of the graphs are the points
[tex](-2,0)\\(-1,0)\\(1,0)\\(2,0)[/tex]
therefore
the answer is the option
B)-1,0
Which number produces an irrational number when added to 2/5
The correct answer to this is that:
Any irrational number when added to 2 / 5 still produces an irrational number.
For example, if we use π to add to 2/5 or 0.4. As far as we know the decimal digits for π just go on forever and do not have a repeating cycle hence making it an irrational number. Adding a rational number such as 0.4 to the value of π does not really greatly change the value of π. The decimal digits (hundredths place and so on) of the resulting number will still go on forever without a continual repeat.
So 0.4 + π is still irrational.
Answer:
5
Step-by-step explanation:
the speed limit on a highway is 70 miles per hour about how fast is this in miles per minute
The speed of 70 miles per hour is approximately equivalent to 1.17 miles per minute. This conversion is done by dividing the speed in miles per hour by 60, the number of minutes in an hour.
Explanation:To calculate the conversion from miles per hour to miles per minute, you divide the speed in mph by 60, as there are 60 minutes in an hour. So if we are given a speed limit of 70 miles per hour, that would convert to approximately 1.17 miles per minute.
This is calculated as 70 miles per hour ÷ 60 minutes per hour = 1.17 miles per minute
It's important to remember to use the correct conversion factor related to time, in this case that there are 60 minutes in an hour, to ensure the accuracy of the conversion.
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 195, x = 162; 95% confidence
To construct a 95% confidence interval for the population proportion, calculate the sample proportion p' and its complement q', determine the Z-score for 95% confidence, calculate the margin of error using the formula E = Z*sqrt((p'q')/n), and add/subtract E from p' to get the lower and upper bounds.
Explanation:To construct a 95 percent confidence interval for the population proportion p using the given sample data, we must first calculate the sample proportion (p') and its complement, the estimated proportion of failures (q'). Using the formula p' = x/n, we find that p' = 162/195. Next, we determine q' by calculating q' = 1 - p'.
With the sample proportion and its complement, we can use the standard formula for a confidence interval for a population proportion: p' ± Z*sqrt((p'q')/n), where Z* is the Z-score corresponding to the given degree of confidence. For a 95% confidence level, the Z-score is approximately 1.96.
By substituting the values of p', q', n, and the Z-score into the formula, we calculate the margin of error (E) and then the lower and upper bounds of the 95 percent confidence interval.
Suppose p' is 0.83 and q' is 0.17 for n = 195 and the Z-score for a 95% confidence interval is 1.96. The margin of error (E) would then be 1.96 * sqrt((0.83*0.17)/195), and the confidence interval would be p' ± E, resulting in a specific numerical range which would constitute our 95% confidence interval for the true population proportion.
The 95% confidence interval for the population proportion [tex]\( p \)[/tex] is [tex]\( (0.7783, 0.8833) \)[/tex].
To construct a confidence interval for the population proportion [tex]\( p \),[/tex] we will use the given information: sample size [tex]\( n = 195 \)[/tex], number of successes [tex]\( x = 162 \),[/tex] and a confidence level of 95%.
The formula for the confidence interval for a population proportion [tex]\( p \)[/tex] is:
[tex]\[ \hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]
where:
- [tex]\( \hat{p} \)[/tex] is the sample proportion [tex](\( \frac{x}{n} \)),[/tex]
- [tex]\( z^* \)[/tex] is the critical value from the standard normal distribution corresponding to the desired confidence level.
Calculate the sample proportion [tex]\( \hat{p} \):[/tex]
[tex]\[ \hat{p} = \frac{x}{n} = \frac{162}{195} \][/tex]
[tex]\[ \hat{p} \approx 0.8308 \][/tex]
For a 95% confidence level, the critical value [tex]\( z^* \)[/tex] can be found using the standard normal distribution table or a calculator. It corresponds to the middle 95% of the distribution, which leaves 2.5% in each tail.
The critical value [tex]\( z^* \)[/tex] for a 95% confidence level is approximately 1.96.
Calculate the standard error [tex]\( SE \):[/tex]
[tex]\[ SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ SE = \sqrt{\frac{0.8308 \cdot (1-0.8308)}{195}} \\ SE \approx \sqrt{\frac{0.8308 \cdot 0.1692}{195}} \\ SE \approx \sqrt{\frac{0.1405}{195}} \\ SE \approx \sqrt{0.0007205} \\ SE \approx 0.0268 \][/tex]
Now, we can construct the 95% confidence interval for [tex]\( p \):[/tex]
[tex]\[ \hat{p} \pm z^* \cdot SE \][/tex]
[tex]\[ 0.8308 \pm 1.96 \cdot 0.0268 \][/tex]
Calculate the margin of error:
[tex]\[ 1.96 \cdot 0.0268 \approx 0.0525 \][/tex]
So, the confidence interval is:
[tex]\[ 0.8308 \pm 0.0525 \][/tex]
Finalize the interval: [tex]\[ (0.7783, 0.8833) \][/tex]
The 95% confidence interval for the population proportion [tex]\( p \)[/tex] is approximately [tex]\( (0.7783, 0.8833) \)[/tex]. This means we are 95% confident that the true population proportion [tex]\( p \)[/tex] lies between 0.7783 and 0.8833.
A polygon has 12 sides. Find the sum of its interior angles.
Answer: 1800°
Step-by-step explanation: In this problem, we're given that a polygon has 12 sides and we're asked find the sum of the measures of its interior angles.
The formula for finding the sum of the measures of the interior angles of a polygon is 180 (n - 2) where n represents the number of sides.
So here, since our polygon has 12 sides, we can plug a 12 in for the n in our formula and we have 180 (12 - 2) which is our equation.
Simplifying inside the parentheses first, 12 - 2 is 10 so we have 180 (10) which is 1800.
So if a polygon has 12 sides, then the sum of the measures of its interior angles is 1800°.