Find the measure of the missing arc lengt. pt. 2

The given polynomial is P(x) = x^3 + 5x^2 - 6x + 6. The given c is 3. To use the Remainder Theorem, we must divide P(x) by (x - c). The result of this division will be a quotient and a remainder. The remainder is the value of the polynomial when x = c, so in this case when x = 3, the remainder is 45.

This is because when x = 3, P(x) = 45. Therefore, according to the Remainder Theorem, the remainder when we divide P(x) by (x - 3) is 45. This means that when we divide P(x) by (x - 3), the remainder is 45. Thus, the Remainder Theorem can be used to determine the remainder when we divide a polynomial P(x) by (x - c), where c is some given constant.

Know more about Remainder Theorem here

https://brainly.com/question/13264870#

#SPJ11

i think it may be 16:36

explanation: if the 9 was multiplied by 4 which 9x4 is 36 it means that the 4 for the 4:9 will probably end up 16 hence 4x4 is 16 making the answer probably 16:36 to my own understanding

To find f(x)-g(x), we need to subtract the two given functions.

f(x) = x^(2)-6x-40

g(x) = x+4

f(x)-g(x) = (x^(2)-6x-40) - (x+4)

Next, we need to distribute the negative sign to the terms inside the parentheses:

f(x)-g(x) = x^(2)-6x-40 - x - 4

Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44

Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.

To know more about polynomial click on below link :

https://brainly.com/question/11536910#

#SPJ11

Answer: $89

Step-by-step explanation:

to find average add up all numbers and divide by how many there are

so, do

(125+110+95+80+70+54)/6

which equals 89

AB =

BC = 2x

T.P. =>

4x² = x² + 6²

3x² = 36

x² = 12

=> x = 2sqrt3

The quadratic formula multiplied by π divided by x is: π(-b ± √(b² - 4ac)) / (2ax).

The quadratic formula is used to solve quadratic equations, and is given by: x = (-b ± √(b² - 4ac)) / 2a.

Pi otherwise denoted by the symbol π in real terms is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, although its decimal representation goes on infinitely without repeating.

Since the rational objective of every mathematical expression or problem is to simplify, we  will leave Pi in it's symbolic form - π.

Thus, multiplying quadratic formula by π and dividing by x, we get:

π(-b ± √(b² - 4ac)) / (2ax)

Therefore, the quadratic formula multiplied by π divided by x is:

π(-b ± √(b² - 4ac)) / (2ax).


Learn more about quadratic formula on:
https://brainly.com/question/2615966
#SPJ1

Answer:  π(-b ± √(b² - 4ac)) / (2ax)

Step-by-step explanation:

take the standard quadratic formula and plug in pi and x and you get you answer hope this helps

The equation of the line is y = 780x + 150, r² value  is 0.186, the r value is 0.431, and the predicted population in year 12 is 9450.

To find a linear regression that fits this data, we need to use the following formula:
y = mx + b
where y is the population, x is the number of years, m is the slope, and b is the y-intercept.

We can use the data given to find the slope (m) and the y-intercept (b). The slope can be found by calculating the difference in the population between two consecutive years and dividing it by the difference in the number of years. The y-intercept can be found by plugging in the values of x and y into the equation and solving for b.

Using the data given, we can find the slope and y-intercept as follows:

m = (1950 - 1170) / (3 - 2) = 780
b = 150 - (0)(780) = 150

Therefore, the equation of the line is:
y = 780x + 150

To find the r² value, we can use the formula:
r² = 1 - (SSres / SStot)

where SSres is the sum of squares of residuals and SStot is the total sum of squares.

SSres = (150 - 150)² + (620 - 930)² + (1170 - 1710)² + (1950 - 2490)² = 2,484,400
SStot = (150 - 1222.5)² + (620 - 1222.5)² + (1170 - 1222.5)² + (1950 - 1222.5)² = 3,051,875

r² = 1 - (2,484,400 / 3,051,875) = 0.186

The r value can be found by taking the square root of the r²value:
r = √0.186 = 0.431

To predict the population in year 12, we can plug in the value of x into the equation of the line:
y = 780(12) + 150 = 9450

Therefore, the predicted population in year 12 is 9450.

Learn more about equation at https://brainly.com/question/11186716?

#SPJ11

Answer:

Step-by-step explanation:

Let x be the first term.  Let y be the common difference between each number in the sequence. x and the next three terms would be:

x, x+y,  x+2y,  and x+3y

The sum of the 4 terms is 4x + 6y and is equal to 38

4x + 6y = 38

4x  = 38 - 6y

x  = (19/2) - (3/2)y   [x is isolated here, to the left, for use in a lovely substitution coming up]

or x = 9.5 - 1.5y  [simplified]

===

The sum of the first 7 terms would be the first 4 [from above:   4x + 6y] plus the next 3 terms;

4x + 6y

 x + 4y

 x + 5y

 x + 6y

7x + 21y

7x + 21y is equal to 98

7x + 21y = 98

====

We have two equations and two unknowns, so we should be able to find an answer by substitution:

---

From above:

x  = (19/2) - (3/2)y  

7x + 21y = 98

Now use the first definition of x in the second equation:

7x + 21y = 98

7( (19/2) - (3/2)y) + 21a = 98

66.5 - 10.5y + 21y = 98

10.5y = 31.5

y = 3

Now use this value of y in either equation to find x:

7x + 21*(3) = 98

7x + 63 = 98

7x = 35

x =  5

====

Check:

Do the first 4 terms sum to 38?

5 + 8 + 11 + 14 = 38  YES

Do the first 7 terms sum to 98?

38 + 17 + 20 + 23 =   YES

Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.

On the x- axis the y- coordinate of any point is zero.

Set the factored form of the polynomial to zero and solve for x

x(x - 3)(x + 3)(x - 2) = 0

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

the x-intercepts are then x = - 3, x = 0, x = 2, x = 3

these can be confirmed from the graph of the polynomial

Answer:

a) 1024 - 14280x + 720x² - 240x³

b) 117616

Step-by-step explanation:

#CarryOnLearning

Shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

First, we graph the lines y = -x-2 and y = -5x+2 using their y-intercepts and slopes.

The line y = -x-2 has a y-intercept of -2 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.

The line y = -5x+2 has a y-intercept of 2 and a slope of -5, which means that for every increase of 1 in x, y decreases by 5.

The shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

Hence, shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

Answer: 2.1429

Step-by-step explanation:

The answer is 2.1429. This is because 7 divided by 1 is 7, and 7 divided by three thirds is the same as 7 divided by 1.5, which is equal to 4.6666. Therefore, 7 divided by 1 and three thirds is equal to 7 divided by 4.6666, which equals 2.1429.

It will take Mrs. Reed 3 hours to catch up to Mr. Reed.

First we can start by figuring out how far Mr. Reed will have traveled when Mrs. Reed starts her journey.

Distance traveled by Mr. Reed in 3 hours at a speed of 40 mph:

When Mrs. Reed starts her journey, Mr. Reed is 120 miles ahead of her.

Now, let's determine how long it will take Mrs. Reed to catch up to Mr. Reed.

We can use the formula:

time = distance / relative speed

Where "distance" is the distance Mrs. Reed needs to travel to catch up to Mr. Reed, and "relative speed" is the speed at which Mrs. Reed is gaining on Mr. Reed, which is the difference between their speeds:

relative speed = 80 mph - 40 mph

relative speed = 40 mph

So, the time it will take for Mrs. Reed to catch up to Mr. Reed can be calculated as:

Therefore, it will take Mrs. Reed 3 hours to catch up to Mr. Reed.

Learn more about distance here : brainly.com/question/4931057

#SPJ1

There are no values of x that satisfy the equation -6-(4x)/(x+2)=(8)/(x+2).

To find the values of x for the equation -6-(4x)/(x+2)=(8)/(x+2), we need to follow the following steps:

Multiply both sides of the equation by (x+2) to eliminate the fractions:
(x+2)(-6-(4x)/(x+2))=(x+2)(8)/(x+2)

Simplify the equation:
-6(x+2)-4x=8

Distribute the -6:
-6x-12-4x=8

Combine like terms:
-10x-12=8

Add 12 to both sides:
-10x=20

Divide both sides by -10:
x=-2

However, we need to check our answer to make sure it does not result in a zero denominator in the original equation. If we plug in x=-2 into the original equation, we get a zero denominator, which is not allowed. Therefore, there are no values of x that satisfy the equation.

For more information about equation, visit:

https://brainly.com/question/22688504

#SPJ11

By applying synthetic division concept, it can be concluded that if f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11, then, f(-5) = 6.

Synthetic division is a shorthand way of dividing polynomials where we can divide the coefficients of the polynomial by omitting variables and exponents. As a result, we get the coefficient of the quotient and the remainder.

Polynomial remainder theorem states that the value of p in argument b is equal to the remainder of the polynomial division p(x) / (x - b). Specifically, p(x) is divided by x - b with a remainder of zero if, and only if, b is a root of p.

We have the following polynomial:

f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11

To find f(-5) using synthetic division, we will divide the polynomial f(v) by (z + 5). The steps are as follows:

1. Put the coefficients in a row and multiply the outside coefficient by the divisor: 8(-5)= -40.

2. Add the inside coefficient to the product from the previous step: -40 + 34 = -6.

3. Multiply the result from the previous step by the divisor: -6(-5) = 30.

4. Add the next coefficient to the product from the previous step: 30 - 26 = 4.

5. Multiply the result from the previous step by the divisor: 4(-5) = -20.

6. Add the next coefficient to the product from the previous step: -20 + 21 = 1.

7. Multiply the result from the previous step by the divisor: 1(-5) = -5.

8. Add the last coefficient to the product from the previous step: -5 + 11 = 6.

The final result of the synthetic division is 6, so the answer to the question is f(-5) = 6.

To learn more about synthetic division, click here: https://brainly.com/question/27979968

#SPJ11

No function exists in this relation. No, since there isn't always a single output for every input.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.

We have to show the relation between a function.

The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.

A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively

but according to the definition of y, it should give only one value

Hence, it is not a function.

To learn more about the function

https://brainly.com/question/10439235

#SPJ1

Answer:

jimmy has 12 candy bars left

Step-by-step explanation:

28-7-9=12

Answer:

Jimmy has 12 candy bars.

Step-by-step explanation:

Subtract 28 from 7.
=21

21-9=12.
Jimmy has 12 candy bars left if he eats 7 and his mom takes 9.

The factors which would be considered while constructing a road for a steep slope are the terrain of the area, the estimated daily traffic, minimum and maximum sight distance, and the design speed.

Constructing roads on a steep slope is a challenge for every civil engineer. It is because such slopes which are possibly found in hilly areas have less access to main land from where the resources/ material for construction are to be transported and also need specific calculations to estimate maximum durability of the roads and also prevent accidents which might occur due to steep slopes.

Hence, an engineer has to keep in mind several factors which can help to reduce the accident cases, provide road safety and better connectivity with major areas.  It is essential that roadway engineers design roads that allow drivers to travel at the right speed. Topography determines the terrain, the different gradient and the construction cost. Every roadway should be built with illuminated raised pavement markings for facilitating safe travel during the night.

Learn more about constructing a road at:

brainly.com/question/29287784

#SPJ4

The unit rate for inches per mile is 0.8 inches.

The length of road B is 9.6 inches on map.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.

Road in inches = 1 1/5 = 6/5 inches

Road in miles = 1 1/2 miles =

Inches per mile = 6/5 / (3/2)

                         = 6/5 x 2/3

                         = 4/5

                         = 0.8 inches

If the road B is 12 miles long, on the map it would be;

= 0.8 x 12

= 9.6 inches

Learn more about Unit Rate here:

https://brainly.com/question/19908576

#SPJ1

∆ABC = ∆BCD because they are congruent

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

AB is parallel to CD and AB is equal to CD,

Therefore AC = BD( opposite sides of a parallelogram are equal

therefore CB is common to both triangle

We can therefore say that all the corresponding three sides of the two triangles are equal

i.e AC = BD

AB = CD

CB = CB

therefore triangle ABC and BCD are congruent

This means ;

∆ABC = ∆BCD

learn more about congruent triangles from

https://brainly.com/question/2938476

#SPJ1

Answer:

8.50667 or approximately 8.51 feet per second

Step-by-step explanation:

The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.

Answer:

23

Step-by-step explanation:

All of Four table shows the proportionality.

Proportionality refers to any relationship that always has the same ratio. For example, the amount of apples in a crop is proportionate to the number of trees in the orchard, with the proportionality ratio being the average number of apples per tree.

To the proportionality we have to find the rate change of each table

Table 1:

Rate of change

= (4-2)/ (4-0)

= 2/4

= 0.5

Again, (6-4)/ (8-4)

= 2/4

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 2:

Rate of change

= (1-0)/ (2-0)

= 1/2

= 0.5

Again, = (2-1)/ (4-2)

= 1/2

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 3:

Rate of change

= (3-1)/ 5-0)

= 2/5

= 0.4

Again, (5-3)/ (10-5)

= 2/ 5

= 0.4

As, the rate of change is constant then the table shows the proportionality.

Table 4:

Rate of change

= (7-3)/ (3-0)

= 4/3

Again, (11-7)/ (6-3)

= 4/3

As, the rate of change is constant then the table shows the proportionality.

Learn more about proportionality here:

https://brainly.com/question/29126727

#SPJ1

The three possible forms of any positive odd integer, as required.

According to the Euclid Division Lemma, for any two positive integers a and b, there exist unique integers q and r such that a = bq + r where 0 ≤ r < b.

We can use this lemma to show that any positive odd integer is of the form 6q + 1, 6q + 3, or 6q + 5 where q is some integer.

Let a be any positive odd integer and let b = 6. By the Euclid Division Lemma, we can write a = 6q + r where 0 ≤ r < 6. Since a is odd, r cannot be an even number. Therefore, r can only take on the values of 1, 3, or 5.

Thus, we can write a as:

a = 6q + 1
a = 6q + 3
a = 6q + 5

These are the three possible forms of any positive odd integer, as required.

Learn more about positive integers

brainly.com/question/18380011

#SPJ11

write the equation with both of them = 100

(3x + 50) + (2x + 15) = 100

combine like terms

5x + 65 = 100

subtract

5x = 35

x = 7

the question asks for <JTU = 2x + 15

plug in x = 7

x = 29

EDIT

Answer:

JTU = 29°

Step-by-step explanation:

I'm not sure if this is correct but I got 29°

(3x+50)° + (2x+15)° = 100°

x= 7°

(2x+15)°

((2x7)+15)° = 29°

Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.

The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the out trace.

Since T is the midpoint of both chords PQ and RS, it follows that the perpendicular bisectors of these chords pass through the centre of the circle. Let O be the centre of the circle.

Consider the perpendicular bisector of PQ passing through T. Let it intersect the circle at point A. Since TA = TP and OT is perpendicular to PQ, it follows that AO is also perpendicular to PQ, and hence PQ is the diameter of the circle.

Similarly, consider the perpendicular bisector of RS passing through T. Let it intersect the circle at point B. Since TB = TS and OT is perpendicular to RS, it follows that BO is also perpendicular to RS, and hence RS is the diameter of the circle.

Therefore, PQ and RS are both diameters of the circle.

To know more about circle follow

https://brainly.com/question/25308989

#SPJ1

Answer:

x=63

Step-by-step explanation:

------------------

For a metal ball which is 3.25m long and weighs 15kg. Mass per meter of the metal bar would be 4.61 kg/m.

Accordingly, the metal bar's mass is 15 kg, Metal bar measures 3.25 meters in length. We're looking for the metal bar's mass per square meter.

Find the sum or total value of two or more numbers by adding them together. It is possible to calculate their difference by subtracting one number from the other. Times or repeated addition are examples of multiplication. After multiplying two or more numbers, the result is a product. Splitting an amount into equal parts is the process of division. When compared to multiplication, it is exactly the opposite.

Afterwards, we can calculate,

The mass per meter of the metal bar = mass of the metal bar / length of the metal bar

⇒ 15 kg / 3.25 m

[tex]= \frac{15}{3.25}=4.61kg/m[/tex]

Hence, the mass per meter of the metal bar would be 4.61 kg/m.

Learn more about Mass at:

brainly.com/question/30321193

#SPJ4