Which input value produces the same output value for the two functions on the graph?

x = −3
x = −2
x = −1
x = 3

Which Input Value Produces The Same Output Value For The Two Functions On The Graph?x = 3x = 2x = 1x

Answers

Answer 1
Answer:

x = -2

Explanation:

The line represents the output value (y) for a given input value (x). Where the lines cross, the output values are equal. These lines cross at x=-2.

Answer 2

Answer:x=-2

Step-by-step explanation:

got it right on edg


Related Questions

What is the value of 2xy if x = 3 and y = 2

Answers

Substitute the values.
2(3)(2)=?
2*3=6
6*2=12
Final answer: 12

Answer:

the value of 2xy if x =3 and y= 2 is 12

Step-by-step explanation:

A salesperson sold a total of $6,400.00.If her rate of commission is 6%, what is her commission?

Answers

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.

Which number produces an irrational number when added to 2/5

Answers

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:

Someone please solve this ASAP

Answers

16/7 = 12/y

84/16

84/16 = 5.25

5.25+7 = 12.25

 x = 12.25


What does the value of the LCM represent

Answers

The LCM is Least Common Multiple, it is the product of the highest order of occurring primes in the numbers prime factorization...

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

Answers

The formula of the future value of an annuity ordinary is
Fv=pmt [(1+r)^(n)-1)÷r]
Fv accumulated amount 1000000
PMT annual payment ?
R interest rate. 0.1
N time 20 years
Solve the formula for PMT
PMT=FV÷[(1+r)^(n)-1)÷r]
PMT=1,000,000÷(((1+0.1)^(20)−1)÷(0.1))
PMT=17,459.62 round your answer
PMT=17460

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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the speed limit on a highway is 70 miles per hour about how fast is this in miles per minute

Answers

Final answer:

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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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?

Answers

Given:
h = melting point of helium
j =  melting point of hydrogen
k = melting point of neon

Number of values = 3
Therefore, the average is
(Sum of values)/(Number of values) = (h+j+k)/3

Answer:
The average melting point of helium, hydrogen, and neon is
(h+j+k)/3

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

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

Answers

Final answer:

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.

Answers

[tex](n-2)\cdot180\\\\ (12-2)\cdot180=10\cdot180=1800[/tex]

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°.

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?

Answers

Tim is 13 and Melissa is 8

What is the value of x?

16
50
130
164
Please hurry !!!

Answers

c) 130 i hope this helps good luck 

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.

Prove that there does not exist integers m and n such that 2m+4n=7

Answers

[tex]2m+4n=7\iff m+2n=\dfrac72[/tex]

There is no choice of integers [tex](m,n)[/tex] such that the left hand side is a rational number.
Final answer:

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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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

Answers

i) one of the forms that we can write the equation of a line is 

y=mx+k

where m is the slope of the line.

ii)

given lines y=mx+k and y=nx+t, which are perpendicular to each other.

Then, m*n=-1


Now consider the line 0.5x−5y=9:

0.5x−5y=9

take -5y to the right side and 9 to the left side

0.5x-9=5y

switch sides

5y=0.5x-9

divide by 5

y=0.1x-9/5

so the slope of the line is m=0.1

let the slope of the line perpendicular to 0.5x−5y=9 be n, then

0.1*n=-1

n=-1/(0.1)=-10


Answer: -10

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

Answers

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

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=?

Answers

if < 1 = 89, the < 5 = 91

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]

The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?

Answers

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 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.

Answers

The length of the shadow is about 20.2( rounded to the nearest tenth), because the shadow and the building formed as a triangle, so uses the formula of Pythagorean theorem to solve this problem
if you draw the illustration of the problem, you can see that the building, the shadow, and the length of the shadow  to the tip of the building is forming a right triangle. We can use pythagoreans theorem stating that a^2 + b^2 = c^2. In this case your side b is missing its value. Therefore we can rearrange the equation then it becomes b= √(c^2-a^2 )

The circumference of a coin is 8π What is the radius? What is the diameter?

Answers

Find the radius first.
Circumference of a circle:
[tex]=2 \pi r[/tex]
[tex]8 \pi =2 \pi r[/tex][tex] \frac{8 \pi }{2 \pi } = r[/tex]
r=4

diameter = radius x 2
4x2 = 8
The constant π is defined as C/d, meaning pi is the constant when the circumference of a circle is divided by the diameter of that circle.  Anyway:

πd=C  divide both sides by π

d=C/π, if C=8π then

d=8π/π

d=8

So the diameter is 8 units.

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?

Answers

Given that Donna's Cafe has 42 customers representing 20% of the total approved occupancy by the fire department.

a.) According to the fire department's occupancy approval, the percentage of the cafe still available for customers is 100% - 20% = 80%


b.) Given that 42 customers represent 20% of the total approved occupancy by the fire department.
Let the total approved occupancy be x, then 20% of x is 42
i.e.
[tex]0.2x=42 \\ \\ x= \frac{42}{0.2} =210[/tex]
i.e. the total approved occupancy is 210.

According to the fire department, the number of seats that are still available for customers is given by
[tex]80\% \ of \ x = 0.8 \times 210 = 168[/tex]

the quadratic formula gives which roots for the equation 2x^2+7x+-2

Answers

The quadratic expression is given [tex] 2x^{2} +7x-2[/tex] where the constants are

[tex]a=2[/tex]
[tex]b=7[/tex]
[tex]c=-2[/tex]

Quadratic formula to find the roots is given as

x₁,₂ = [-b plus minus √(b)²-4ac)] ÷ 2a

Substitute a, b, and c from our expression we have

x₁,₂ = [-7 plus minus √(7)²-(4×2×-2)] ÷ 2(2)
x₁,₂ = [-7 plus minus√65] ÷ 4

from here we'll work out x₁ and x₂ separately

x₁ = (-7+√65) ÷ 4 = 0.266 (round to 3 dp)
x₂ = (-7-√65) ÷ 4 = -3.766 (round to 3 dp)



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:

Israel claims that all 45degree right triangles are similar. Is he correct? Explain.

Answers

alrity... well, a right triangle with a 45°, will also have a third angle of 45° , and thus all three angles will then be 45° , 45° and 90°, for all right-triangles, and they'd be similar by AA anyway.   So all right-triangles with a 45°, will have another 45° angle and a 90° one, and the three angles will then be the exact same value for all right-triangles with one 45°.  Thus all would then be similar by AA.

write two different pairs of decimals whose sum are 14.1

Answers

well two different pairs can be 7.0 and 7.1 or 14.0 and .1

Please hurry !!!

Which is an x-intercept of the graphed function?

A) 0,4
B)-1,0
C)4,0
D)0,-1

Answers

Well looking at the x line you see where the line falls on and looking at your options -1 is on the x line and the line falls on it so id say the answer is B

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


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?

Answers

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:

Find the circumference and the area of a circle with radius
6yd.

Answers

Circumference: 37.7 yards
Area: 113.1 yards^2

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

Answers

Polynomials in the fourth degree are called quartic equations. In solving the roots of polynomials, there are techniques available. For quadratic equations, you use the quadratic formula. For cubic equations, you use the scientific calculator. But for quartic equations and higher, it is very complex. The method is very lengthy and can get very messy because you introduce a lot variables. So, I suggest you do the easiest method to estimate the roots.

Graph the equation by plotting arbitrary points. The graph looks like that in the figure. The points at which the curve passes the x-axis are the solution which are encircled in red.In approximation, the rational roots or zero's are -3.73, -1, -0.28 and 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.

Write the point in its current fraction form dog show all your work for full credit.
0.225

Answers

[tex]\bf 0.\underline{225}\implies \cfrac{0255}{1\underline{000}}\impliedby \textit{notice, \underline{3 decimals}, thus \underline{3 zeros} and no \underline{dot}} \\\\\\ \cfrac{\frac{255}{5}}{\frac{1000}{5}}\implies \boxed{\cfrac{51}{200}}[/tex]

Given the following sequence, find the 23rd term: 10.5, 11, 11.5, 12, 12.5, . . .

Answers

10.5, 11, 11.5, 12, 12.5...this is an arithmetic sequence with a common difference of 0.5

an = a1 + (n - 1) * d
n = term to find = 23
a1 = first term = 10.5
d = common difference = 0.5

sub and solve

a(23) = 10.5 + (23 - 1) * 0.5
a(23) = 10.5 + 22 * 0.5
a(23) = 10.5 + 11
a(23) = 21.5 <===

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?

Answers

Create a Cartesian plane with the x and y axes. Then, plot the given points on the plane: (0,0), (2,0.7), (4,1.4), (6,2.1). Lastly, connect these 4 data points to form a line. The x-axis represents minutes overdue and the y-axis represents the fine. The result is shown in the picture.

This graph shows an increasing linear trend. It shows that the fine is directly proportional with time. At time 0 minutes, the college student does not have to pay a fine because he hasn't even used the laptop yet. Therefore, the origin (0,0) signifies the starting point of the observation. But when he used 2 minutes of the time, he would pay $0.7. The trend goes on until he used up 6 minutes and paid a total of $2.1

Answer:

So the answer would be No fine is paid if the laptop is returned exactly at the time at which it is due

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