for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division

Answers

Answer 1
[tex]\bf x^3-7x^2+8x+16\qquad f(10)\\\\ -------------------------------\\\\ f(10)=r\implies \begin{cases} x=10\\ remainder=r \end{cases}\\\\ -------------------------------\\\\ \textit{so, let's do the division} \\\\\\ \begin{array}{r|rrrrrrrllll} 10&&1&-7&8&16\\ &&&10&30&380\\ -&&-&--&--&--\\ &&1&3&38&\boxed{396}&\leftarrow remainder \end{array}[/tex]

Related Questions

$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.

Answers

hmm is very straight forward, how much is whatever% of anything? is just (whatever/100) * anything.

[tex]\bf \textit{4\% of 2,500}\implies \cfrac{4}{100}\cdot 2,500\implies 100 \\\\\\ \textit{the rest is 7,500 at 5\%, what's 5\% of that?}\implies \cfrac{5}{100}\cdot 7,500\implies 375[/tex]

A journal entry for the sale of $10 par common stock for $18 per share would include
a. a credit to Cash
b. a debit to common stock
c. a credit to Paid in Capital in Excess of Par-Common Stock
d. a debit to Paid in Capital n Excess of Par-Common Stock

Answers

credit to paid in capital in excess of par-common stock. the word stock in the question instantly removes a and b there is no debit so c or d but i would go with c. just cause d is missing an i in one of its 'in'

8.76× 10 6  is  times  than 8.76× 10 2 .

Answers

10^6 = 10 *10*10*10*10*10 = 1,000,000

10^2 = 10*10 = 100

1000000/100 = 10,000 times larger

a culture started with 6,000 bacteria. After 4 hours, it grew to 6,600 bacteria. Predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number.

Answers

P = 6,600  

A = 6,000  

t = 4  

k = ?  


6600 = 6000e^(4k)  

6600/6000 = e^(4k)  

1.1 = e^(4k)  


Take the natural log of both sides.  


ln 1.1 = 4k ln e (remember that ln e = 1)  

ln 1.1 = 4k  

(ln 1.1) / 4 = k  

k = 0.0238  


Bacteria after 10 hours.  

P = 6000e^(0.0238*10)  

= 6000e^0.238  

= 7612  


Therefore, the bacteria will grow to 7612 after 10 hours.

Find the value of ab

Answers

ab= a*b

(1/12)*(1/6)= (1/72)

Final answer: 1/72

What is the inverse of the function below? F(x) = x - 6

Answers

To compute the inverse function of F(x) you simply have to get how argument x depends of value F(x).
F(x)=x-6
Inverse function:
x = F(x)+6
To show that there are different mathematical objects just use e.g F(y)
F(y)=y+6 

Answer:

f(x)=x+6

Step-by-step explanation:

its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6

A bag contains 40 marbles, 4 of which are blue, 10 are red, 25 are green, and 1 is purple. Shawna takes a marble out of the bag, records the color, and returns it to the bag. How many green marbles should she expect after 400 trials? (5 points)

Answers

250.

Since she returns the marble every time, the probability of drawing a green marble remains constant, which is 25/40.

An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground? (s= 16t^2)

Answers

Given 
s=16t^2 
where
s=distance in feet travelled (downwards) since airborne with zero vertical velocity and zero air-resistance
t=time in seconds after release

Here we're given
s=144 feet
=>
s=144=16t^2 
=> 
t^2=144/16=9
so
t=3
Ans. after 3 seconds, the object hits the ground 144 ft. below.

Answer:

After 3 seconds the object hit the ground.

Step-by-step explanation:

An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.

Given that displacement, s = 16t²

To reach ground displacement should be 144 feet.

That is

            s = 16t² = 144

                      t² = 9

                       t = 3 seconds.

After 3 seconds the object hit the ground.

If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles

Answers

Because ∠A=40°, therefore ∠B + ∠C = 180.

To create two triangles, we could make a = 10 in.

From the Law of Sines,
a/sinA = b/sinB.
 
Therefore
10/sin(40) = 15/sin(B)
sin(B) = (15/10)*sin(40) = 0.9642
∠B = arcsin(0.9642) = 74.6°

Because the sine function is positive in quadrants 1 and 2, we could also have ∠B = 180 - 74.6 = 105.4°.
This means that
a/sin(105.4) = 15/sin(40°)
a = [sin(105.4)/sin(40)]*15 = 22.5 in

Answer:
We could have a = 10 in, or a = 22.5 in

a rectangle has a width of 17 ft and a lenghth of 8ft....PLEASE HELP ME SOS!!! ASAP!!!

Answers

perimeter is 17 +17 +8 + 8 = 50 feet

area = 17 x 8 = 136 square feet

cost = 136 x $3.50 = $476.00

find the volume of a sphere with a diameter of 25 cm. approximate pi as 3.14 and round your answer to the nearest hundredth

Answers

4/3[tex] \pi [/tex]r^3 is the forumla, and r = d/2, so 25/2 = 12.5 so r = 12.5 cm

4/3*[tex] \pi [/tex]*(12.5)^3 = 4/3*[tex] \pi [/tex]*1953.125 = 4/3 * 6132.8125 = 
8177.08 cm

Branliest Please!
The formula for the volume of a sphere is:

V=4/3πr³

The diameter given is 25 cm, so that means the radius is 12.5 cm.

Now you just need to plug in the numbers and you will have:

V=(4/3)(3.14)(12.5)³

After plugging that all in the calculator, you should get the answer:

V=8,177.083333 cm³, which rounds to 8,177.08 cm³

I hope this helps!

If using spss, what is the exact likelihood of obtaining a t-test value at least as extreme or as close to the one that was actually observed, assuming that the null hypothesis is true

Answers

Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.

To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.

What are the counting numbers in base 6

Answers

In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1  one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we  would need:

 

Base 6                                                                   Base 10

 

1                                                                                  1   

2                                                                                  2

3                                                                                  3

4                                                                                  4

5                                                                                  5

10  (1 six plus 0 ones)                                                 6

11  (1 six plus 1 one)                                                   7

12  (1 six plus 2 ones)                                                 8

13                                                                                9

14                                                                              10

15                                                                              11

20  (2 sixes plus 0 ones)                                           12

21  (2 sixes plus 1 one)                                             13

22                                                                              14

23                                                                              15

Final answer:

The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.

Explanation:

The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.

The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.

Text me the answer please

Answers

p(4)= 1/8

This is because there are 8 equal parts and 4 is just one of those 8 parts.
probablility=desired outcomes/total possible outcomes

so

we want to hit the 4

there are 1 of those numbers on the spinner
and 8 numbers total

1 desired outcome
8 total possible outcomes

1/8 is the probablitiy
?=8

A $28,000 car loan is used to purchase a new car. The loan is for 6 years and has a 5.75% APR. Use the amortization formula to determine the amount of the monthly payments.

Answers

[tex]\bf \qquad \qquad \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]

[tex]\bf \qquad \begin{cases} P= \begin{array}{llll} \textit{original amount}\\ \end{array}\to & \begin{array}{llll} 28,000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5.75\%\to \frac{5.75}{100}\to &0.0575\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{payments are monthly, thus} \end{array}\to &12\\ t=years\to &6 \end{cases} \\\\\\ pymt=28000\left[ \cfrac{\frac{0.0575}{12}}{1-\left( 1+ \frac{0.0575}{12}\right)^{-12\cdot 6}} \right][/tex]

Can someone please solve this ASAP?

Answers

surface area = 5ab +5bh

a = 4

b=7

h=18

5*4*7 = 140

5*7*18 = 630

630+140 = 770 square meters


G study find the exact value of each of the remaining trigonometric functions cos theta=4/5 270< theta

Answers

This will be a 4th quadrant 3,4,5 triangle.
Sin = -3/5
Tan = -3/4
Final answer:

Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.

Explanation:

The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.

This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.

Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.

Plugging in the given cosine value, we have:

sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5

However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:

sin(theta) = -3/5

For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:

tan(theta) = (-3/5) / (4/5) = -3/4

The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:

sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3

A = h/2 * (a + b ); for h

Answers

[tex]A=\dfrac{h}{2}(a+b)\\ 2A=h(a+b)\\ h=\dfrac{2A}{a+b} [/tex]
h/2 * (a + b )=A
h/2=A/(a+b)
h=2A/(a+b)

Two pairs of shoes and four pairs of socks cost $131, and three pairs of shoes and five pairs of socks cost $190. Find the cost of a pair of socks.

Answers

s = shoes
x = socks

 3( 2s + 4x = 131) ------>  6s + 12x = 393
-2( 3s + 5x = 190) ------>-6s - 10x = -380

(2x = 13)/ 2

x = 6.5

A pair of socks is equal to $6. 50

Hope this helps :)
Please give brainliest

The cost of a pair of socks would be $6.50

Ignoring color, what kind of symmetry does the pinwheel have? A. rotational symmetry B. line symmetry C. both rotational and line symmetry D. neither

Answers

the answer is a because there isn't any line of symmetry

In a circle of radius 25 inches, a central angle of 35 degrees will intersect the circle forming an arc of length ____

Answers

arc length = (central angle/360) x 2 x PI x r

= (35/360) x 2 x 3.14 x 25

=15.2638

round answer as needed, you don't say how to round it.

What is the area of a parallelogram with a base of 20 inches and an altitude of 8 inches?

Answers

140 i think think think or 160

The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.

What is a parallelogram in math?

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.

Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.

A = base * altitude

A = 20 * 8

A = 160 inches square.

learn more about the area here https://brainly.com/question/25965491

#SPJ2

If there are 400 cubic centimeters of a chemical in 1 liter of solution, how many cubic centimeters of water must be added to dilute it to a 25% solution?

Answers

keeping in mind that, in 1 liter, there are 1000 cm³, and that the concentration amount of the chemical for say 25% will be 0.25 of whatever the quantity is, so... we convert the percentage amounts to decimal formats.

[tex]\bf \begin{array}{lccclll} &\stackrel{cm^3}{amount}&\stackrel{\textit{\% of chemical}}{concentration}&\stackrel{total~amount}{concentration}\\ &------&------&------\\ solution&1000&0.4&400\\ water&x&0&0x\\ ------&------&------&------\\ mixture&y&0.25&0.25y \end{array}[/tex]

so.. whatever "x" and "y" are, we know that 1000 + x = y.

and that 400 + 0x = 0.25y.

thus then

[tex]\bf \begin{cases} 1000+x=\boxed{y}\\ 400+0x=0.25y\\ 400=0.25y\\ ----------\\ 400=0.25\left( \boxed{1000+x} \right) \end{cases} \\\\\\ 400=250+0.25x\implies 150=0.25x\implies \cfrac{150}{0.25}=x\implies 600=x[/tex]

Jim drove 204 miles in 4 hours. If he can keep the same pace how long will it take him to drive 918 miles

Answers

18 hours.

Proportions and stuff.

[tex] \frac{204}{4} [/tex] = [tex] \frac{918}{x} [/tex]

Cross multiply,

204x = 918 * 4

204x = 3672
/204      /204
x = 18

18 hours.

Raphael paid 636 for camera during a 60% off sale with the cameras regular price

Answers

Your question needs some rewording.  How does this sound?  "Raphael paid $636 for camera during a 60% off sale.  The camera's regular price is x.  Find this price."

If the price is 60% lower than usual, Raphael is paying only (100% - 60%), or 40%, for the camera.

Thus, 0.40x = $636.  Divide both sides of this eq'n by 0.40 to find the original price of the camera.

x = $636/0.40 = ?

The scatter plot below shows the relationship between the length (x) in meters and mass f(x) in kg of a marine animal
(1,0)(2,10)(3,20)(4,30)(5,40)(6,50)(7,65)(8,70)(9,80)(10,90)

Which of the following fuction is best represented by the scatter plot?
F(x)=9-10.3x
F(x)=-10.3+9x
F(x)=-9+10.3x
F(x)=10.3-9x

Answers

F(x) = -9 + 10.3x probably.
It's definitely not the first or last option as they have negative gradients (i.e. negative x-coefficient) and so represent a negative correlation. The data given tells us there is a positive gradient and so a positive correlation.
It could be the second option as the second and third are not so vastly different but I would go for the third because it appears to most closely fit the data pattern.

Answer:

F(x)=-9+10.3x

Step-by-step explanation:

Given:

(1,0)

(2,10)

(3,20)

(4,30)

(5,40)

(6,50)

(7,65)

(8,70)

(9,80)

(10,90)

F(x)=9-10.3x and F(x)=10.3-9x cannot be the function of given scatter plot since the slope in these functions are negative

So, The equation of line can be F(x)=-10.3+9x or F(x)=-9+10.3x

Refer the attached figure.

Using desmos calculator

We conclude that the function is best represented by the scatter plot is [tex]F(x)=-9+10.3x[/tex]

Peter decides to mix grades of gasoline in his truck. He puts in 11 gallons of regular and 7 gallons of premium for a total cost of $76.99. If premium gasoline costs $0.25 more per gallon than regular, what was the price of each grade of gasoline?

Answers

11r + 7p = 76.99
p = r + 0.25

11r + 7(r + 0.25) = 76.99
11r + 7r + 1.75 = 76.99
18r = 76.99 - 1.75
18r = 75.24
r = 75.24/18
r = 4.18 <=== regular : $ 4.18 per gallon

p = r + 0.25
p = 4.18 + 0.25
p = 4.43 <=== premium : $ 4.43 per gallon

Final answer:

Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.

Explanation:

We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.

Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:

11r + 7(r + $0.25) = $76.99r = regualar gasoline price per gallon

Simplifying the first equation:

11r + 7r + $1.75 = $76.99

18r + $1.75 = $76.99

18r = $76.99 - $1.75

18r = $75.24

r = $75.24 / 18

r = $4.18

So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.

A boat takes 4 hours to go 20 miles upstream.It can go 32 miles downstream in same time.Find the rate of the current and the rate of the boat in still water.

Answers

recall your d = rt, distance = rate * time.

now, if the boat has a speed of say "b", and the current has a speed of say "c", when the boat is going upstream, is not really going "b" fast, is going " b - c " fast, because the current is eroding speed from it, going upwards.

And when the boat is going downstream, is not going "b" fast either, because the current is now adding to speed to it, so is really going " b + c " fast.

The time it took one way, is the same time it took back, 4 hours each way.

thus

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ Upstream&20&b-c&4\\ Downstream&32&b+c&4 \end{array} \\\\\\ \begin{cases} 20=4(b-c)\implies \frac{20}{4}=b-c\implies 5+c=\boxed{b}\\ 32=4(b+c)\implies \frac{32}{4}=b+c\implies 8=b+c\\ --------------------\\ 8=\left(\boxed{5+c} \right)+c \end{cases} \\\\\\ 8=5+2c\implies 3=2c\implies \cfrac{3}{2}=c\implies 1\frac{1}{2}=c[/tex]

what's the speed of the boat?  well, 5 + c = b.

Which of the following is a polynomial with roots negative square root of 5, square root of 5, and −3?
x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15

Answers

If the roots are -sqrt(5), sqrt(5), and -3, then the three factors of the polynomial are: (x + sqrt(5)), (x - sqrt(5)), and (x+3) Let's multiply the first two factors together. (x + sqrt(5)) * (x - sqrt(5)) = x^2 - 5 Let's multiply this by the third factor (x+3). (x^2 - 5) * (x+3) = x^3 + 3x^2 -5x - 15 The correct answer is the last polynomial in the list of choices above.

A certain species of tree grows an average of 4.2 cm per week. write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.

Answers

Average growth rate = 4.2 cm/week.

So, common difference d = 4.2

The height of the tree a0 = 200 centimeters.

The height of the tree after end of the first  week a₁ = 200 + 4.2 = 200 + 4.2(1)

The height of the tree after end of the second  week  a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).

The height of the tree after end of the third  week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).

The height of the tree after the end of the nth week an =  200 + 4.2(n).

The equation is a_n = 200 + 4.2(n).

Other Questions
The solution to m + (-38) = 15 is 53. True False What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%? If magma or lava cools quickly, the resulting igneous rock will have ________. Which refers to the temperature to which air would have to be cooled to reach saturation? Classical drama began in _____.EgyptGreeceRome How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table The area of a circle is a function equal to the product of pi (pi) and the square of the radius (r). Which of the following shows this function? If the unit sales price is $7 and variable costs are $3, how many units have to be sold to earn a profit of $3,600 if fixed costs equal $5,000 On a cloudless day, what happens to most of the visible light headed toward earth? hints on a cloudless day, what happens to most of the visible light headed toward earth? it is reflected by earths atmosphere. it is absorbed and reemitted by gases in earths atmosphere. it is completely reflected by earths surface. it reaches earths surface, where some is reflected and some is absorbed. Excel is an electronic version of a(n) ____ Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero The pulse site located at the point where the upper leg bends is called the Which of the following statements is always true?A All integers are counting numbers.B All rational numbers are integers.C All integers are whole numbers.D All counting numbers are whole numbers. the questionnnnnnnn issssssssss Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last? The tendency of an organization to identify and capitalize successfully on opportunities to launch new ventures by entering new or established markets with new or existing goods or services is known as innovativeness. competitive aggressiveness. entrepreneurial orientation. opportunity analysis. bootlegging. Choose the answer.In the story, Negi's father intervenes so that she does not have to help her mother in the kitchen. What can you infer from this?Negi's father is mean.Negi's sisters are their father's favorites.Negi's mother is the leader of the family.Negi's father is the leader of the family. What does the number 16 on the map represent?A.Mount Everest B.Mount KangchenjungaC.Mount Godwin-AustenD.Khyber Pass Brutus and federal farmer were two pseudonyms used by the ________. what can 4 and 22 divided into equally the answer is smaller than 88 Steam Workshop Downloader