What is the quotient (x2 − 9x + 20) ÷ (x − 4)? (1 point) x − 5 x − 4 x + 4 x + 5

Sam's average score based on the six quizzes is 78%.

The average is the mean, a central tendency value.

We compute the mean by summing the values of a data set and dividing by the number of items in the collection.

In this situation, the average of 5 quizzes multiplied by 5 gives the total score in the 5 quizzes, which resulted in the average score.

This total is added to the score in the sixth quiz to get the total score for the six examinations before dividing the sum by 6, giving the overall average.

The average score in 5 quizzes = 74%

Total score in the 5 quizzes = 370% (74 x 5)

The score on the sixth quiz = 99%

Total score in six quizzes = 469% (370 + 99)

The average score in the 6 quizzes = 78.167% (469/6)

= 78%

Thus, Sam scored an average of 78% on the six tests.

Learn more about averages at https://brainly.com/question/20118982

#SPJ1

The largest change in momentum will happen when the velocity and mass of the object are doubled( option A)

The momentum of a body is the product of the mass of the body and it's velocity. Momentum is measured in kg/ms^-1. It is a vector quantity. it is represented by p

Momentum of a body is expressed as p= m× v

where m is the mass of the body and v is it's velocity. This means that the higher the mass and velocity of the body the higher it's momentum.

The initial momentum of the body of mass 850kg and velocity 10ms^-1 = 850kgms^-1

When the velocity and mass are doubled , then the new momentum will be 1700× 20= 34000kgms^-1

Therefore the largest change in momentum will be obtained when both mass and velocity are doubled.

learn more about momentum from

https://brainly.com/question/1042017

#SPJ1

The vertex is at (8, -2).The point (10, -22) is also on the parabola.

Step-by-step explanation:

Here is the graph of the function:

The vertex is at (8, -2).

To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.

For example, if we choose x = 10, then we have:

f(x)   = -5(x - 8)² - 2

f(10) = -5(10 - 8)² - 2

f(10) = -5(2)² - 2

f(10) = -5(4) - 2

f(10) = -20 - 2

f(10) = -22

So, the point (10, -22) is also on the parabola.

To know more about parabola check the below link:

https://brainly.com/question/4061870

#SPJ13

The distance between points  (-3,-4) and (2,8) is 13.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.

The horizontal distance = 5

And the vertical distance = 12

The vertical and horizontal lines make a right angle when they meet,

To find distance between points, use Pythagoreans theorem,

(D)² = (5)²+(12)²

(D)² = 25 + 144

(D)² = 169

D = 13

The distance between points  (-3,-4) and (2,8) is 13.

To know more about Triangle on :

https://brainly.com/question/2773823

#SPJ1

Student B has raised the least amount of money after walking for 7 miles.

A unit rate means a rate for one of something.

Given that, three students are participating in a walkathon,

Student A's money is represented by the equation y = 13x, where y is money raised for walking x miles.

Student B raised $36 money for 3 miles and Student C has raised  $52 and $65 money for 4 and 5 miles respectively.

Money raised by each of them for a mile =

Student A = $13

Student B = $12

Student C = $13

Money raised by them by walking 7 miles =

Student A = $13*7 = $91

Student B = $12*7 = $84

Student C = $13*7 = $91

Hence, Student B has raised the least amount of money after walking for 7 miles.

For more references on unit rate, click;

https://brainly.com/question/11258929

#SPJ1

When the circumference of a circle is 19π cm the area of the circle is

28.27 square centimeters

Information given in the question include

The circumference of a circle is 19π cm

Area of a circle is given by

π r^2

where r = radius

π = constant = 3.124

circumference of a circle is given by 2πr

2πr = 19

πr = 9.5

r = 3.024

r = 3 cm

The area is solved as

= π * 3^2

= 28 .27square centimeters

Learn more about circle at:

https://brainly.com/question/29324404

#SPJ1

The variance of the number of packages that will be filled before the process is stopped will be 600 when the probability of falling outside the specification is 0.04.

Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in relation to the mean the more dispersed the data. In statistics, the variance is used to assess how accurately the mean summarizes all of the data. For instance, more range exists within the set the higher the variance. 

P(fail)=0.04

P(pass)=0.96

variance=(1-P)/P²

=(1-0.04)/0.0016

=0.96/0.0016

variance=600

When the likelihood of falling outside the specification is 0.04, the range of packages that will be filled before the process is stopped is 600.

To know more about variance,

https://brainly.com/question/16269880?referrer=searchResults

#SPJ4

Answer:

9/2

Step-by-step explanation:

X/2+1=5x

(X+2)/2=5x

x+2=10x

2=9x

X=9/2

The rules for the rotation and translation for the rectangle RSTU is:

Rotation: (x,y) ↔ (-y,x)

Translation : (x,y) ↔ (x+k , y)

Given,

we have rectangle R'S'T'U' which is the image of the rectangle RSTU under a rotation 90° counterclockwise about the origin followed by a translation.

we are asked to determine the rule of rotation and translation.

Rotation :

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x).

so the rule is:

Rotation: (x,y) ↔ (-y,x)

Translation:

When the shape is moved towards the right by k units, then replace x with x + k.

let's check:

R(-6,3) ↔ 90° counterclockwise rotation ↔ (-3,-6) ↔ translation↔R'(-3+9,-6) → R'(6,-6)

S(-4,7) ↔ 90° counterclockwise rotation ↔ (-7,-4) ↔ translation↔S'(-7+9,-4) → R'(2,-4)

Hence we get the required rules for sequences of congruence transformations.

Learn more about Transformations here:

brainly.com/question/2387958

#SPJ9

This relationship is not a function because more than one amount of plant food remains each day.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.

Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a  function between the two, as there are more than one plant food remaining each day for the plant.

Hence, This relationship is not a function because more than one amount of plant food remains each day.

For more references on Functions, click;

https://brainly.com/question/21145944

#SPJ1

Answer: show us the graph

Step-by-step explanation:

The length, breadth and height will be 78 cm, 78cm, 78cm each.

let consider the length = l

breadth = b

height = h

we are provided that

l + b + h = 234cm .......(1)

Also we have to maximize the volume , provided length is equal to breadth

∴ eqn (1) becomes

2b + h = 234

h = 234 - 2b

also ,

volume(v) = lbh

v = b²(234 - 2b)

v = b²234 - 2b³

now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )

i.e. d( v)/db = 0

∴  468b - 6b² = 0

 6b² - 468b = 0

6b( b - 78 ) = 0

∴  b = 78 cm

now as length = breadth

l = b = 78 cm

also putting this value in eqn (1)

h = 234 - 2b

h =  78 cm

So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .

learn more about lagrange method here :

https://brainly.com/question/24208980

#SPJ4

The equation of the linear function represented by the table would be y = 4x - 1.

What is the slope-intercept form of the line?

When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula

                               y = mx + c.

The y value of the y-intercept point is represented by c in the formula.

By using the given table,

for x = 0 , y = -1

so by using the slope-intercept form of the line, we can write

              y = mx + c

              -1 = m(0) + c

               c = -1 ----------(I)

Then for x = 1, y = 3

again by using the slope-intercept form of the line, we can write

                  y = mx + c

                 3 = m(1) + (-1)  -----from (I)

                  3 = m - 1

             ⇒ m = 3 + 1

             ⇒ m = 4 -----------(II)

Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line

                     y = 4x - 1

Hence, the equation of the linear function represented by the table would be y = 4x - 1.

To learn more about the slope-intercept form of the line, visit:

https://brainly.com/question/24907633

#SPJ1

Answer:

600ml

Step-by-step explanation:

Answer:

Slope = -2

Step-by-step explanation:

Slope of Line passes through two Points [tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex]

is given by [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

So by Substitution

[tex]m=\frac{-6- 2 }{-1 - (-5)}=\frac{-8}{4} =-2[/tex]

The slopes 0/3 and 9/0 are not perpendicular .

In the question  ,

the two slopes are given ,

the value of slope 1 (m₁) = 0/3

the value of slope2 (m₂) = 9/0 .

We know that the two slopes m₁ and m₂ are perpendicular is

m₁ × m₂ = -1 .

So , for the given values ,

On substituting the values of m₁ and m₂ ,

we get ,

= (0/3) × (9/0) ≠ -1

Since the product of the two given slope is not equal to -1 .

the slopes are not perpendicular .

Therefore , The slopes 0/3 and 9/0 are not perpendicular .

Learn more about Slopes here

https://brainly.com/question/10431875

#SPJ1

Answer:

y = [tex]\frac{1}{5}[/tex] x - 5

Step-by-step explanation:

y = mx +b  You have to find the slope and the y intercept

slope:

I used the two points on the graph (0,-5) and (5,-4)  The slope is the change in y over the change in x.  An ordered pair is given in the form (x,y)

[tex]\frac{- 4 - - 5}{5-0}[/tex] = [tex]\frac{-4 + 5}5}[/tex] = [tex]\frac{1}{5}[/tex]

or you could just look at the two points.  If you start at (0,-5) and go straight up one and the then go right 5 spaces, you will be at the point (5,-4) [tex]\frac{1}{5}[/tex]

The y intercept for the b is where the line crosses the x axis.  It crosses at the point (0,-5)  The -5 is the b part.

With the help of equations we can say that function has a f(x) = x,straight line.

What is an equation?

acc to our question-

f(x) = Ixl

f(x) = x

f(x)=x²

Hence, function f(x) = x is a line.

learn more about equations click here:

brainly.com/question/2972832

#SPJ13

(5) All snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.

What is snow geese?

Despite having a reputation for having white feathers, many snow geese are actually blue geese, which are darker, gray-brown birds. These birds were formerly believed to be two distinct species, however it has recently been discovered that they are actually just two color variants of the same bird. The variation in color is controlled by a single gene.

9 snow geese are housed in the research and rescue center.

Each geese consumed 16 ounces of seeds, therefore that's how much.

Therefore, the amount of seeds consumed by 9 snow geese is equal to (16*9) ounces.

144 ounces of seeds were consumed by 9 snow geese.

There are currently 1,656 ounces of seeds.

Thus, the number of days before the center runs out of food is equal to the sum of the ounces of seeds eaten by the nine snow geese divided by the total ounces of seeds.

Days till the food center runs out of supplies = 1656/144

11.5 days are required until the center runs out of food.

Hence, all snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.

To know more about the snow geese, click on the link

https://brainly.com/question/28888262

#SPJ1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

X2+Y2 =53

= 53 + (50-1)(-4)

= 53-196

= -143

To learn more about Equation refer to:

https://brainly.com/question/2972832

#SPJ13

The window width in the blueprint is 1.5 in.

As per the given question-

A window in the room measures 2. 5 feet in width.

The given scale is-

Blue print (inches) : original (feet)

3 in : 5 ft

Divide both side by 2

1.5 in : 2.5 ft

Window's width in Blue print (inches) = 1.5 in.

As a result, the window width in the blueprint is 1.5 in.

To know more about the scale factor, here

https://brainly.com/question/25722260

#SPJ4

An equation relating x and y is given by y = 3x/4 - 11/2.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For the slope of this line using point AB, we have:

Slope of AB = (2 - (-1))/10 - 6)

Slope of AB = (2 + 1)/4

Slope of AB = 3/4

Since point AB and points (2, -4), (x, y) all lie on the same straight line, they would all of the same slope. Therefore, an equation relating x and y can be calculated as follows:

3/4 = (y + 4)/(x - 2)

3(x - 2) = 4(y + 4)

3x - 6 = 4y + 16

4y = 3x - 6 - 16

4y = 3x - 22

y = 3x/4 - 22/4

y = 3x/4 - 11/2

Read more on slope here: brainly.com/question/3493733

#SPJ1

Addition of the given is (a) [tex]9x^{3} +x^{2}-6x+5[/tex]

Equation given,

Eq 1 = [tex]7x^{3} - 2x^{2}-5x+6[/tex]

Eq 2 = [tex]2x^{3}+ 3x^{2}-x-1[/tex]

Adding Eq 1 + Eq 2,

[tex](7x^{3} - 2x^{2}-5x+6) + (2x^{3}+ 3x^{2}-x-1)[/tex]

[tex](7x^{3} + 2x^{3}) + (- 2x^{2}+ 3x^{2})+(-5x-x)+(6-1)[/tex]

[tex]9x^{3}+ x^{2}-6x+5[/tex]

Hence, the answer.

To learn more about Addition here:

https://brainly.com/question/29053821

#SPJ1

Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

According to the question,

We have the following information:

Amount to be invested = $15200

Interest earned 1% a year and 4% a year

Total amount interest to be earned at the end of first year = $548

Now, let's take the amount to be invested in 1% interest a year's mutual fund to be $x.

Then, we have the amount to be invested in mutual fund that earns 4% a year:

$(15200-x)

So, we have the following expression by removing percentage sign:

x/100 + (15200-x)4/100 = 548

Taking 100 as the least common factor and using the cross multiplication method:

x+60800-4x = 548*100

-3x = 54800-60800

-3x = -6000

x = 6000/3

x = $2000

Now, the amount invested in second mutual fund:

15200-2000

$13200

Hence, Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

To know more about interest here

https://brainly.com/question/13655754

#SPJ1

The Excel formula that Bill would use is PMT.

From Bill's situation, he has the following information:

time = NPER = number of periods = 18 years

RATE of the bank

FV = future value = cost of tuition

PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."

In conclusion, the correct option is PMT.

Learn more about Excel on:

https://brainly.com/question/25879801

#SPJ1

Complete question

Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.

Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle [tex]C = \pi d[/tex].

Perimeter of circle [tex]= 2 \pi r[/tex]

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.

So it was proved.

Learn more about Circle click on this:

https://brainly.com/question/24375372

#SPJ13

Answer:  30 in.

Step-by-step explanation:

So when you look at the right triangle closely, you can see that the c is the same length as the 30 in. That's why I think it is 30 in. (May be wrong)

The amount of wire that can be bought from 21 cents is 7 inches.

It is given in the question that 12 inches of wire costs 36 cents.

We have to find the amount of wire that can be bought from 21 cents.

We will use the unitary method to solve this question.

Amount of wire that can be bought from 1 cent = 12/36 = 1/3 inches

Hence, according to the data given in the question, we can write,

The amount of wire that can be bought from 21 cents = (1/3)*21 = 7 inches.

Unitary method

The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result.

To learn more about unitary method, here:-

https://brainly.com/question/22056199

#SPJ1