Find the quotient and remainder using synthetic division for
1³ + 31² + 8x + 14
------------------------
x + 2
The quotient is
The remainder is
Answers
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2
Explain equationA mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.
Here,
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As
x² +x+6+ [tex]\frac{2}{x+2}[/tex]
and remainder is 2
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Related Questions
solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Answers
Step-by-step explanation:
please refer to the sketch
let f(x)= 2x-9. Find the inverse and evaluate f^1 (-2).
Answers
Answer:
f(x)= 2x-9
f(-2)= 2(-2)-9
f(-2)= -4-9
=-13
The width of a rectangle measures (k+3)(k+3) centimeters, and its length measures (k-9)(k−9) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180
Step-by-step explanation:
A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:
p = 2w + 2l
We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.
We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.
Plugging these values into our equation we get:
p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.
Or in the form of a quadratic equation:
p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162
=
p = 4k^2 - 24k + 180
Hope this helps!
The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.
Explanation:The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).
Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.
Learn more about perimeter here:https://brainly.com/question/31695951
#SPJ2
a wall is 50cmx50cm how many 2cmx1cm tiles would you need to fill it
Answers
Answer: 1250
Step-by-step explanation: 50 x 50 = 2,500
2,500 divided by 2 is 1250
The composite number 50 is between what two prime numbers?
Answers
Answer:
47 and 53
Step-by-step explanation:
list of prime numbers to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
50 is between 47 and 53
What is the reciprocal of 1 4/13
Answers
Answer:
Step-by-step explanation:
PLS HELP ASAPPAPA
Type the correct answer in the box. If necessary, use / for the fraction bar.
If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the volume of the prism is
cubic centimeter.
Answers
Explanation:
Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.
(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512
This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.
Answer:
105/512
Step-by-step explanation:
hope this helps
Can someone help with these 2 questions please :) or 1 whichever one u know
1. Overall, how successful were resistors to Spanish colonial rule? What factors prevented them from being more successful?
2. What lasting impacts do you think Spanish colonial rule will have on Native American cultures and civilizations? Explain.
Answers
After conquering indigenous civilizations in Mexico and South America, Spanish Colonial Rule became wealthy thanks to the gold and silver it discovered.
What is Spanish Colonial Rule?The objectives of Spanish Colonial Rule were to take gold and silver from the Americas, to boost the Spanish economy, and to increase Spain's might. Additionally, Spain sought to evangelize Native Americans.
Further Spanish conquistadors, who were mostly poor nobility from Spain's destitute west and south, were able to conquer the vast empires of the New World with the aid of sickness (which reduced native resistance), superior military equipment, and tactical strategies such as surprise attacks and strong.
However, it was challenging to convince immigrants to colonize there due to friction with the local Indian population and the absence of significant silver or gold discoveries.
Thus these are the most leading factors that prevent to become more successful for Spanish Colonial Rule.
Learn more about Spanish Colonial Rule:
https://brainly.com/question/1375219
#SPJ1
To purchase 12,100 worth of machinery for her business, Latoya made a down payment of 1800 and took a business loan for the rest. After 3 years of paying monthly payments of 313.36, she finally paid off the loan.
A, what was the total amount latoya ended up paying for the machinery. (including down payment and monthly payments)
B. How much interest did latoya pay on the loan
Answers
The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96
The amount of interest that Latoya paid was $ 980.96
How to find the total amount paid ?The total amount paid by Latoya for the machinery can be found as :
= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )
= 1, 800 + ( 313. 36 x 12 x 3 )
= $ 13, 080 .96
The total interest paid on the loan was :
= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment
= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800
= $ 980.96
Find out more on total interest at https://brainly.com/question/14419626
#SPJ1
Trace is buying notebooks. Each notebook is $2 off the original price. He buys 8 notebooks for $28. What is the original price of a notebook?
Answers
The original price of each notebook is $5.5
How to calculate the original price of each notebook ?
Trace is purchasing some notebooks
Each notebook is $2 off the original price
He buys 8 notebooks for $28
The first step is to calculate the price of one notebook
8= 28
1= x
Cross multiply both sides
8x= 28
x= 28/8
x= 3.5
1 notebook is $3.5
$2 was removed from the initial price. Therefore the original price is
2 + 3.5
= 5.5
Hence the original price of the notebook is $5.5
Read more on original price here
https://brainly.com/question/21284703
#SPJ1
Goran wants to build a square frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
Answers
A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.
What is a square?The wood left over after making the frame and the sandbox is 10 inches.A square is a two-dimensional figure that has four sides and all four sides are equal.Definition. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.A square is a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.Square is slang for a person who is conventional and old-fashioned, similar to a Fuddy-duddy. This sense of the word "square" originated with the American jazz community in the 1940s, in reference to people out of touch with musical trends.The area of a square is given as side².
We have,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
Thus,
The remaining wood is 10 inches.
To learn more about squares refer to:
brainly.com/question/22964077
#SPJ1
Solve each equation for both variables help please 15 points
Answers
Answer:
x = -5
y = 2
Step-by-step explanation:
1) -5x-4y = 17
2) 3x-4y = -23
subtract equation 2 from equation 1:
-8x + 0 = 40
-8x = 40
x = -5
substitute x = -5 into equation 1 and solve for y:
-5(-5) - 4y = 17
-4y = -8
y = 2
test answers by substituting x and y values into eqation 2:
3(-5) - 4(2) = -23 Answers are correct!
Part A
A function f(x)=^3√x is transformed into the function g (x) = 2^3√x-4+5. Name and explain in
complete sentences the transformations that occurred to the parent cube root function.
Part B
How is the general shape of a cube root function different from the shape of a square root function? Use
complete sentences in your response.
Answers
Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.
What is function?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that,
we have to say that, How is the general shape of a cube root function different from the shape of a square root function.
Now, we get,
Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.
To learn more on function click:
brainly.com/question/21145944
#SPJ1
Please help will mark Brainly
Answers
Step-by-step explanation:
1. Simplify -6y >= 12 by dividing both sides by -6 to get y alone. This results in y<=-2, because when dividing an inequality by a negative number the sign gets switched.
2. Mark the point (0, -2) because there is no x-value. Shade everything lower and equal to -2 because y can be equal to -2 or less than it.
Answer:
Y less than
Step-by-step explanation:
Two angles are vertical angles. One angle measure is 95°. What is the measure of the
other angle?
A
85°
B
95°
C
90°
D
45°
Answers
By using the definition of vertical angles, we will see that the correct option is B, the measure of the other angle is 95°.
What is the measure of the other angle?We define by vertical angles as angles that share a vertex and are in opposite sides of the two intersecting lines that form that vertex.
Vertical angles always have the same measure, in this particular case, we know that one of the vertical angles has a measure of 95 degrees, then the other vertical angle (whose measure we want to find) will also be 95 degrees, just by definition of vertical angles.
In that way, we conclude that the correct option is B: 95°
Learn more about vertical angles by reading:
https://brainly.com/question/14362353
#SPJ1
hello i need help with question 5 please
Answers
5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.
5b) Under the lease, the customer saves $14,760.
5c) The lessee after returning the car has the following lease options:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.
6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.
6c) The monthly payment will be $567.26.
6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.
Car Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)
Learn more about Car Financing at https://brainly.com/question/24182131
#SPJ1
A family has a budget of $400 to spend on groceries each month.
Answers
19x+4 find the value of x
Answers
Answer:
x= -4/19
Step-by-step explanation:
19x+4
19x+4=0
19x= - 4
x= -4/19
Sevati's collection has 14 fewer magazines in it than Alita's collection. They have 50 magazines
collection? How many magazines are in Alita's collection?
Select the person with more magazines: Alita
Select a label for each bar. Drag the bar representing Sevati's magazines to the right to draw a model that represents the scenario.
Enter expressions to complete the model.
Alita's
magazines
Sevati's
magazines.
x-14
14
X
Enter the expression that represents the number of magazines in Alita's collection.
Enter the expression that represents the number of magazines in Sevati's collection. x-14
Enter an expression for the number of magazines they have together.
Enter the number of magazines in Sevati's collection.
How
-50
50
Answers
Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.
what is expression ?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Let's examine the writing of expressions. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
given
If x is the alita collection,
then sevati is equal to x - 14 + x = 50.
Sevati's collection of magazines is represented by the formula 2x - 14 = 50, hence the alita collection is equal to 2x = 36
x = 18
Sevati has 18 magazines in her collection. Sevati's collection of periodicals is represented by the phrase x - 7 = 25.
To know more about expression visit :-
https://brainly.com/question/14083225
#SPJ1
An online store charges $5 for shipping on all orders. They are having a sale on all t-shirts, $7 each! You and your friends are going to order some shirts. Write an expression that you could use to find the cost of the order.
Answers
Answer:
which one is correct about HRM?
The cost of the order can be expressed as 7x + 5, where x is the number of t-shirts ordered.
In this expression, "7x" represents the cost of the t-shirts, where each shirt is $7 and the number of shirts is represented by "x". The "$5" represents the flat shipping fee for the entire order, which does not change regardless of the number of shirts being ordered.
By adding the cost of the shirts and the shipping fee, we can find the total cost of the order. It's important to understand that the value of "x" must be specified to evaluate the expression.
For example, if 3 shirts are ordered, then x = 3 and the expression becomes:
7 * 3 + 5 = 26So the total cost of the order would be $26.
Learn more about math expression here: brainly.com/question/1859113
#SPJ1
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 140 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
Answers
0.65x + 0.90y = 140 * 0.80 = 112
x + y = 140
To solve this system of equations, we can first multiply the second equation by -1 and add the resulting equations:
-1 * (x + y = 140)
-x - y = -140
0.65x + 0.90y = 112
-x - y = -140
-0.35x - 0.10y = -28
Next, we can divide both sides of the second equation by -0.1 to get rid of the fractional coefficient:
-0.35x - 0.10y = -28
(-0.1/-0.1) * (-0.35x - 0.10y) = (-0.1/-0.1) * -28
-3.5x - y = -28
Finally, we can add the resulting equations to eliminate one of the variables:
-3.5x - y = -28
0.65x + 0.90y = 112
0.35x + 0.90y = 84
Dividing both sides by 0.35, we find that x = 240.
Substituting this value back into the equation x + y = 140, we find that y = -100. Since y represents the number of ounces of Solution B, this is not a valid solution. This means that there is no solution to the system of equations, and the scientist cannot obtain a mixture that is exactly 80% salt using these two solutions.
Shaikha types at a rate of 34 words per minute. How many words does she type in 2 minutes?
Answers
Answer:
68 words
Step-by-step explanation:
If 34 words are typed in a minute what about two minutes hence take 34×2
Answer:
68
Step-by-step explanation:
What is a rate?A rate can be a quantity, or frequency, measured against a different quantity or amount.
If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:
Let m = minutes, w = words per minute and t = total words
m × w = t
Simply just insert your numbers into the equation.
2 × 34 = 68
Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.
Click on a factor pair of 32
Answers
Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
⇒ Firstly find the factors of 32
How Do You Work Out Factors of 32?
Step 1: Let's start with the whole number 1 and work our way up to the factors of 32. 32 ÷ 1= 32
Step 2: Now divide 32 by two. 32 ÷ 2= 16
Step 3: Then we get. 32 ÷ 4= 8
Step 4: Similarly, we calculate all the 32 factors.
32 factors = 1, 2, 4, 8, 16, and 32.
⇒ Secondly, find factor pairs of 32
The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.
Products of 32 Factor pair of 32
1 × 32 = 32 (1, 32)
2 × 16= 32 (2 ,16)
4 × 8 = 32 (4, 8)
∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)
Read more about factor pairs here:
https://brainly.com/question/28672630
Sean baked 18 dozen chocolate cupcakes and 13 dozen vanilla cupcakes. About how many cupcakes did sean bake
Answers
Anyone know about this thanks :)
Answers
The height of the rock ledge is 20 meters and height of the tree is 59 meters.
What are heights and distances?Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.
From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.
a) Let the height of the rock ledge be x.
Now, tan12°=x/96
0.2125=x/96
x=20.4 meters
x≈20 meters
b) Let the height of the tree be y
Here, part of the tree is y-20
Now, tan22°=(y-20)/96
0.404=(y-20)/96
y-20=38.784
y=58.784
y≈59 meters
Therefore, the height of the rock ledge is 20 meters and height of the tree is 59 meters.
To learn more about the heights and distance visit:
brainly.com/question/24271007.
#SPJ1
HELP ASAP PLS THIS IS VERY IMPORTANT!!!!!!!
Please answer correctly!
Answers
Answers to ratios are first one is option B, second one is option A and third one is option C.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
1. Ratio of smoothie size to mangos used for Kim = 8 : 1
Ratio of smoothie size to mangos used for Bri = 24 : 3
= 8 × 3 : 1 × 3
= 8 : 1
Ratio of smoothie size to mangos used for Angela = 32 : 4
= 8 × 4 : 1 × 4
= 8 : 1
So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
So the answer is option B.
2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3
Ratio of width to length of smaller canvas = 2 : 3
So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.
So the answer is option A.
3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19
Total students = 12 + 19 = 31
Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.
So the answer is option C.
Hence the answers on ratios are done.
Learn more about Ratios here :
https://brainly.com/question/1504221
#SPJ1
A builder buys a 21.5 acres of land to develop a new community of homes and parks.The builder plans to use 0.75 of the land for a park.How many acres will he use for the park?
Answers
He will use 9.375 acres of the land for the park
How to determine how many acres he will use for the park?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
Since the land is 21.5 acres and 0.75 of the land was used for a park. we can write:
acres used for the park = 0.75 × 12.5 = 9.375 acres
Thus, he will use 9.375 acres for the park
Learn more about fractions on:
brainly.com/question/11562149
#SPJ1
APQR is dilated from the origin at a scale factor of to create APQ'R'.
2
Select the option that completes the statement:
The triangles are
because their corresponding sides are
O congruent, similar, proportional
O congruent, proportional; similar
O similar, congruent; proportional
Osimilar, proportional; congruent
and their corresponding angles are
Answers
Find the difference between Mary's weight when she was 10 year's old and when she was born
Answers
The difference between Mary's weight when she was 10 year's old and when she was born will be;
⇒ 72 pounds
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
When Mary was born, she weighed 8 pounds.
And, When she was 10 years old, she weighed 10 times as much.
Now,
Since, When she was 10 years old, she weighed 10 times as much.
Hence, When she was 10 years old, she weighed = 10 × 8 pounds
= 80 pounds
And, When Mary was born, she weighed 8 pounds.
Thus, The difference between Mary's weight when she was 10 year's old and when she was born is,
⇒ 80 - 8 pounds
⇒ 72 pounds
So, The difference between Mary's weight when she was 10 year's old and when she was born is 72 pounds.
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ1
The complete question is this,
When Mary was born, she weighed 8 pounds. When she was 10 years old, she weighed 10 times as much. How much more did Mary weigh when she was 10 years old than she was born?
how many inscribed circle can exist inside a triangle ?
Answers
Answer:
1 circle
Step-by-step explanation:
Angle bisectors will meet at one specific point. Radius taken from centre to one side of triangle is the radius of the incircle. There can be no other configuration to form an incircle so only one incircle can be inscribed in a triangle.