Polynomial function of least degree with integral coefficients that has the given zeros 1/4, -5/2, 3

The equation of the line is y = x + 6

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

Read more about linear function at

https://brainly.com/question/15602982

#SPJ1

The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer: $ 875

Step-by-step explanation:

3,500-0.03(4)

3,499.97/4

= $875

Answer:

\(x = 24.75\)

Step-by-step explanation:

Required

Find x

To find x, we have:

\(\angle PQR + \angle RPQ + \angle QRP = 180\) -- angles in a triangle

Because \(\bar {PR}\) is extended to S, then:

\(\angle QRS = \angle QRP\)

So, we have:

\(2x + 6 + x - 7 + 5x -17 = 180\)

Collect like terms

\(2x + x + 5x = 180 + 17 + 7-6\)

\(8x = 198\)

Divide by 8

\(x = 24.75\)

The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²

Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

Answer:

yes

Step-by-step explanation:

becaise you can solve it

Answer:

B

Step-by-step explanation:

easy

Answer:

B. Improper fraction

Step-by-step explanation:

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).

Answer:

C. z < -19 or z > 11

Step-by-step explanation:

|z+4| > 15

z+4<-15 or z+4<15

z < -19 or z > 11

Domain: -∞ < x < ∞

Range: -1 ≤ y ≤ 1

Option A is correct

The given function is:

y = cos x

The graph of y = cos x is plotted below

The domain of a function is a set of all the valid/real inputs of that function

The range of a function is a set of all the valid/real outpouts

Note that the given cosine function (y = cos x) can take in all real values of x. This means that is domain is a set of all real numbers

cosx has a range between -1 and 1

Therefore, the domain and range of y = cos x are:

Domain: -∞ < x < ∞

Range: -1 ≤ y ≤ 1

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

y

Step-by-step explanation:

The exponential function giving the number of bacteria after x hours is given as follows:

\(y = 250(2)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

\(y = 250(2)^x\)

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Roman Rounds normally charges $18 for a large pizza.

What is the equation in one variable?

An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.

Let's use p to represent the normal price of each large pizza charged by Roman Rounds.

Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:

12(p - 2) = $192

We can simplify this equation by first distributing the 12 on the left side:

12p - 24 = $192

Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:

12p = $216

Finally, we can solve for p by dividing both sides by 12:

p = $18

Therefore, Roman Rounds normally charges $18 for a large pizza.

To learn more about the equation in one variable, visit:

https://brainly.com/question/85774

#SPJ1

Answer:

10

Step-by-step explanation:

Mean = sum of the terms / number of the terms

Let's assume that the sum of the terms is x

So it'd be: x/6 = 7  

x = 6 X 7 = 42

Since two numbers are removed, there are only 4 terms

So it'd be: x/4 = 8

x = 8 X 4 = 32

Finally work out the difference between the two averages:

42 - 32 = 10

So the sum of the 2 numbers was 10.

Hope this helps :)

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

Learn more about greatest common factor  at;

https://brainly.com/question/219464

#SPJ1

Answer:

  independent: day number; dependent: hours of daylight

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

  1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

__

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

  d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

  d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

__

c) d(41) = 10.34, so February 10 will have ...

  12.13 -10.34 = 1.79

hours less daylight.

Answer:

  220

Step-by-step explanation:

You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.

Subtracting each term from the next, we find the sequence of first differences to be ...

  5, 7, 13, 23, 37, 55

The first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.

The second differences are the differences of the sequence of first differences. They are ...

  2, 6, 10, 14, 18

The differences of the terms of the 2nd-difference sequence are constant: 4.

  4, 4, 4, 4, 4

Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.

Since we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.

  next 2nd difference = 18 +4 = 22

  next 1st difference = 55 +22 = 77

  next sequence term = 143 +77 = 220

The eighth term should be 220.

__

Additional comment

The n-th term is ...

  f(n) = 2/3n^3 -3n^2 +28/3n -4

Answer:

8:6

or

4:3

Step-by-step explanation:

Condense the logarithm on the right side:

\(3\log_b(p)-\left(2\log_b(t)+\dfrac12\log_b(r)\right)\)

\(n\log_b(m)=\log_b(m^n) \implies \log_b(p^3)-\left(\log_b(t^2)+\log_b\left(r^{\frac12}\right)\right)\)

\(\log_b(m)+\log(n)=\log_b(mn) \implies \log_b(p^3)-\log_b\left(t^2r^{\frac12}\right)\)

\(\log_b(m)-\log(n)=\log_b\left(\dfrac mn\right) \implies \log_b\left(\dfrac{p^3}{t^2r^{\frac12}}\right)\)

So,

\(x=\dfrac{p^3}{t^2r^{\frac12}}\)

and \(r^{\frac12}=\sqrt{r}\), which makes (4) the correct choice.

Enola needs to contribute $4,330.68 per month to the account.

Let's denote the monthly contribution as X.

The interest rate is 0.4% per month.

Since Enola plans to save for 3 years, the total number of months is:

= 3 * 12

= 36 months.

Using formula for compound interest: Future value = Present value * (1 + interest rate)^number of periods

We will plug values:

$5,000 = X * (1 + 0.004)^36

X = $5,000 / (1 + 0.004)^36

X = $5,000 / (1.004)^36

X = $4,330.68248

X = $4,330.68.

Answer:

63 km

Step-by-step explanation:

Given :

Solving :

Convert minutes into hours so that the units are equal, otherwise your answer will not be correct.

Calculating distance

Answer:

frist convert 315k/h into m/s

then convert 12min into sce

=12*60

=720

distance = v*t

=315*720

=226800m

The computation of the figure illustrates that 0.47 expressed as a fraction in simplest form is 43/90.

From the information given, let a = 0.47. Now 10a = 4.777 .... equation i

100a = 47.77 ..... equation ii

Subtract equation i from ii

100a - 10a = 47 - 4

90a = 43

Divide both side by 90

90a/90 = 43/90

a = 43/90

Learn more about fractions on:

https://brainly.com/question/78672

Answer:480$

Step-by-step explanation:

Hope this helps

Answer:

480

Step-by-step explanation:

Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

Answer:

not

Step-by-step explanation:

Answer:

non-equivalent

Step-by-step explanation:

the equivalend fraction of \(\frac{2}{3}\) is \(\frac{6}{9}\) not \(\frac{6}{10}\)

The situation can be represented by the equation y = 0.5x

The given parameters are

Total amount = $30

Cost of bag of popcorn = $5 each

Cost of each drink = half the cost of each bag of popcorn

Let the bag of popcorn be x and the number of drinks be y

So, we have

y = half the value of x

This gives

y = 1/2x

Evaluate

y = 0.5x

This means that the equation that represents the situation is y = 0.5x

In (a), we have

The equation that represents the situation to be

y = 0.5x

The above equation is a proportional linear equation

Proportional linear equations have only one intercept at the origin

See attachment for the sketch of the graph

Read more about proportional linear equation at

https://brainly.com/question/24802265

#SPJ1

\(f(x) = a \cos(bx + c) + d\)

Where a is the amplitude

b is used to find the period

\( \frac{2\pi}{b} \)

The phase shift can be fined by doing

\(bx + c = 0\)

then the midline is y=d.

Finding A: The amplitude is the half of the distance between the. y values of the max and the min.

\( \frac{2 - ( - 3)}{2} = 2.5\)

So a=2.5

Note: A is Positve never negative so if you get a negative a, take the absolute value.

Period:

Find the distance between x values,

\( - 1 - ( - 4) = 3\)

The distance between the x values of the max and min x values is half the distance of the period. So the period is 6.

\( \frac{2\pi}{b} = 6\)

\(b = \frac{\pi}{3} \)

Note : If b is negative, take the absolute value.

Finding the midline.

To find the midline find the midpoint of the max and min y values.

\( \frac{2 + ( - 3)}{2} \)

\( \frac{ - 1}{2} \)

So our midline is

\( - 0.5\)

So as of right now, our trig formula is

\(2.5 \cos( \frac{\pi}{3}x ) - 0.5\)

Plug in any x or y value,

\(2.5 \cos( \frac{\pi}{3} ( - 4)) - 0.5 = 2\)

\(2.5 \cos( \frac{ - 4\pi}{3} ) = 2.5\)

\( \cos( \frac{ - 4\pi}{3} ) = 1\)

This is not right so we need to shift this to the nearest value that is right

If we subtract,

\( \frac{ - 2\pi}{3} \)

We will have a cosine value of 1.

So our phase shift is

\( 2.5\cos( \frac{\pi}{3} x - \frac{2\pi}{3} ) - 0.5\)

Our phase shift would be 2 units to the right.

\(2.5 \cos( \frac{\pi}{3} (x - 2)) - 0.5\)

Answer:

\(\text{f}(x) = \dfrac{5}{2} \cos \left(\dfrac{\pi}{3}x + \dfrac{4 \pi}{3}\right) -\dfrac{1}{2}\)

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function

f(x) = A cos(B(x + C)) + D

where:

Given:

The mid-line of a cosine function is halfway between the maximum and minimum y-values.  Therefore, the mid-line of the graph is:

\(\sf y=\dfrac{-3+2}{2} =-\dfrac{1}{2}\)

Therefore, D = -¹/₂

The amplitude is the height from the mid-line to the peak.  Therefore, calculate the distance between the y-value of the maximum and the mid-line:

\(\implies \sf A=2-\left(-\dfrac{1}{2}\right)=\dfrac{5}{2}\)

The period is twice the distance between the x-values of the minimum and maximum points.

\(\sf \implies Period = \dfrac{2 \pi}{B}=2(-1-(-4))=6\)

\(\sf \implies \dfrac{2 \pi}{B}=6\)

\(\sf \implies \dfrac{2 \pi}{6}=B\)

\(\implies \sf B=\dfrac{1}{3}\pi\)

Substitute the found values of A, B and D into the standard formula:

\(\text{f}(x) = \dfrac{5}{2} \cos \left(\dfrac{1}{3}\pi(x + C)\right) -\dfrac{1}{2}\)

To find the value of C, substitute one of the given points into the formula:

\(\implies \dfrac{5}{2} \cos \left(\dfrac{1}{3}\pi(-1 + C)\right) -\dfrac{1}{2}=-3\)

\(\implies \dfrac{5}{2} \cos \left(\dfrac{1}{3}\pi(-1 + C)\right)=-\dfrac{5}{2}\)

\(\implies \cos \left(\dfrac{1}{3}\pi(-1 + C)\right) =-1\)

\(\implies \dfrac{1}{3}\pi(-1 + C)=\cos^{-1}(-1)\)

\(\implies \dfrac{1}{3}\pi(-1 + C)=\pi\)

\(\implies \pi(-1 + C)=3 \pi\)

\(\implies -1 + C=3\)

\(\implies C=4\)

Finally, substituting the found values into the formula:

\(\implies \text{f}(x) = \dfrac{5}{2} \cos \left(\dfrac{1}{3}\pi(x + 4)\right) -\dfrac{1}{2}\)

\(\implies \text{f}(x) = \dfrac{5}{2} \cos \left(\dfrac{\pi}{3}x + \dfrac{4 \pi}{3}\right) -\dfrac{1}{2}\)

Learn more about cosine graphs here:

https://brainly.com/question/27818219

The distance in miles between the two electric scooters travelling in opposite direction is 2 miles.

An equation is a formula that proves the equality of two mathematical expressions in algebra and is the most commonly used formula. For example, in the expression 3x + 5 = 14 the two terms 3x + 5 and 14 are separated by the "equals" symbol.

What is distance?

The length or width in between two objects, points, lines, etc. Distance is the condition or fact that something or someone is physically apart.

Given 4x - 4 = 2x,

so 2x = 4

x = 2

To know more about equation and distance visit to:

https://brainly.com/question/13718921

#SPJ1