The quotient is (6x + 1) and the remainder is (-7x + 1).
What is a factor of a polynomial?
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.
So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).
= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.
The same applies to the division of polynomials.
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Jamie has 18/5 cups of frosting she uses 2/5 cups of frosting for each cupcake how many cupcakes will Savannah be able to frost
Answer:
9
Step-by-step explanation:
18/5 ÷ 2/5 = 18/5 x 5/2 = 9
Rick claims that the equation
×2 + 5x + 9 = 0 has no solution. Jenny claims that there are two solutions. Explain how Rick could be correct, and explain how Jenny could be correct.
Answer: Both Rick and Jenny could be correct because we do not know what "x" is.
Step-by-step explanation:
The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.
I hope this helps :)
There are 90 new houses being built in a neighborhood last month 2/5
of them were sold this month 1/3 of the remaining houses were sold.How many houses are left to be sold?
The number of houses left to be sold is 12
How to calculate the number of houses left to be sold?There are 90 new houses built in the neighbourhood
2/5 were sold last month
2/5 × 90
= 18 × 2
= 36
1/3 of the remaining were sold this month
1/3 × 36
=12
Hence there are 12 houses left to be sold
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So i am trying to help out my son with his homework and i do not remember this at all if anyone could help me it would greatly be appreciated
Answer:51x900/100
Step-by-step explanation:
So you’ll do 51 x 900
And then at the denominator when there is no number it is automatically 1 so the denominator will be 100.
Helpp!! I’m stuck on this!!
the quotient of x divided by 5 is greater than or equal to 6. Write an inequality and graph its solution
Find f(g(x)) f(x)= 2x^2-4x-6. G(x)= 2x+7
if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
What is a function?A relation is a function if it has only One y-value for each x-value.
Given functions are f(x)= 2x²-4x-6
g(x)=2x+7
We need to find expression of f(g(x))
f(g(x))=f(2x+7)
Now replace x with 2x+7 in f(x)
f(2x+7)=2(2x+7)²-4(2x+7)-6
=2(4x²+49+28x)-8x-28-6
Apply distributive property
=8x²+98+56x-8x-28-6
Add the like terms
=8x²+48x+64
f(g(x))=8(x+2)(x+4)
Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
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For polynomial function f, if f(3)=5 and f(5)=-2, what do we know about any roots of f(x)?
Answer:
There is a root between x=3 and x=5.
Step-by-step explanation:
Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.
5 pizzas cost £35.00. How much do 3 pizzas cost?
Answer:£21.00
Step-by-step explanation:
One pizza: (£35/5) =£7
Three pizza's: (£7x3)=£21
Prove limit of function by using definition (delta-epsilon)
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].
For part f:
Plug in the value of the limit, 2,
[tex](2)^{2} =4[/tex]
Thus we proved the limit.
For part g:
Plug in the value of the limit, -1,
[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]
Thus we proved the limit.
For part h:
Plug in the value of the limit, 1,
[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]
Thus we proved the limit.
Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars. At the counter, he received a discount. If he only paid 22 dollars total, how many dollars was the discount?
There was 4 dollar of discount on the total amount.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.
At the counter, he received a discount. If he only paid 22 dollars total, then
Total cost 11 + 15 = 26
But 26 - 22 = 4
Therefore, the discount was 4 dollar.
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Fill in the missing values to make the equations true. (a) log 5 + log 3 = log₁ 5 (b) log, log, 7 = log, 7 - (c) log, 4 = log, 2
Step-by-step explanation:
try this option:
[tex]a) \ log_{15}5+log_{15}3=log_{15}15;\\b) \ log_{1/2}log_{49}7=log_77;\\c) \ log_44=log_22.[/tex]
4. Find the sum of the first 21 terms in a series where a = 20 and t21= 400.
5. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
6. Find the sum of the first 50 terms in a series where a = 4 and t50= 196.
7. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
8. Find the sum of the first 10 terms in an arithmetic series where t7= 7 and t10= 13.
9. Find the sum of the first 10 terms in an arithmetic series where t5= 15 and t10= 45.
10. Find the sum of the first 30 positive multiples of 5.
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
what is arithmetic progression ?An arithmetic progression is when the difference between each phrase that follows another in a sequence is always the same. For instance, the sequence 5, 7, 9, 11, 13, and 15 is an example of an arithmetic progression with a 2 tolerance. A progression having a set tolerance between any two consecutive numbers is known as a "arithmetic progression" (A.P.). Two alternative types of mathematical progression exist: finite-length mathematical series A series that has a limited number of terms is a finite geometric progression. One may calculate the early, late, tolerance, and number of terms in a series using the terms in the series.
given
1) n6 = 6 where a = 5 and d = 5 = 105
2)n6 =6 where a = 9 and d = 12 = 234
3) n5= 5 where a = 5.7 and d = 1.4 = 42.5
4) a = 20 and t₂₁ = 400 ,
= 380
Therefore, Sum of 21 terms = 4410
5) In series a = 0 and t₁₀₀ = 99 = 4950
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
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Convert:
25 decimeters
=
Round to the tenths.
meters
Answer:
2.5
Step-by-step explanation:
Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.
write each percent as a fraction and
as a decimal.
7/100%
I NEED THIS BY 2:30PM
7/100% can be written as a fraction as 7/100, and as a decimal as 0.07.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{100}\%}[/tex]
[tex]\mathsf{= \dfrac{7}{100} \div 100}[/tex]
[tex]\mathsf{= \dfrac{7}{100}\times \dfrac{1}{100}}[/tex]
[tex]\mathsf{= \dfrac{7(1)}{100(100)}}[/tex]
[tex]\mathsf{= \dfrac{7}{1,000}}[/tex]
[tex]\mathsf{= 0.0007}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{7}{1,000} \ \& \ 0.0007}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the quotient and remainder using synthetic division for
1³ + 31² + 8x + 14
------------------------
x + 2
The quotient is
The remainder is
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.
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In triangle JKL, angles J and L each measure 51° and JK = 18. Triangle PQR is similar to triangle JKL, where J corresponds to P, K corresponds to Q, and QR = 36. Which expression represents the length of segment PR?
Answer:
Step-by-step explanation:
Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:
(PR)/(JK) = (PQ)/(JL) = (36)/(18)
Cross multiplying and solving for PR, we find:
PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36
A movie studio keeps 240 dresses in its wardrobe for historical films. Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era. A. What percent of the dresses are for films set in the 1700s? B. What percent of the dresses are for films not set in the 1700s? Explain how you found your answer. C. What percent of the dresses are for films set in the 1700s or during the civil war era? Explain how you found your answer. D. What percent of the dresses are not for films set during the civil war era? Explain how you found your answer.
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
What is a percentage?
The percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". It is used to express a proportion of a number out of 100. It is useful in many applications such as finance, statistics, and other fields.
A. Three-fifths of the dresses can be used for movies that take place in the 1700s, which is 3/5 * 100 = 60%.
B. The percent of the dresses that are not for films set in the 1700s is 100% - 60% = 40%. This is found by subtracting the percentage of dresses that are used for 1700s movies from 100%.
C. The percent of the dresses that can be used for films set in the 1700s or during the civil war era is 60% + 15% = 75%. This is found by adding the percentage of dresses that can be used for 1700s movies and the percentage of dresses that can be used for civil war era movies.
D. The percent of the dresses that are not for films set during the civil war era is 100% - 15% = 85%. This is found by subtracting the percentage of dresses that are used for civil war era movies from 100%.
Hence,
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
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Solve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
The value of x = -7 and y = 9 from the system of equations .
What is System of Equation ?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
The equations are :
-x - y = -2 (i)
and
5x + 7y = 28 (ii)
multipling eqation (i) with 5 and then adding both equations we get,
-5x - 5y +5x + 7y = -10 + 28
⇒ 2y = 18
⇒ y = 9
Again, -x -9 = -2
or, x = -7
The value of x = -7 and y = 9 from the system of equations
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The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answer:
Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.
Recall:
Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.
The ratio of any of their corresponding side length = scale factor
Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:
A side length of Figure A = 10
Corresponding side length of Figure B = 4
Scale factor of Figure A to Figure B = 10/4 = 5/2
Step-by-step explanation:
A condominium owner pays property taxes of $2,000 per year. If taxes are figured
at a rate of $1.25 for every $100 in value, what is the value of his condominium?
Step-by-step explanation:
the tax rate gives us a ratio of tax amount to value.
this ratio (in our case 1.25/100) is constant for any value.
therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.
in other words, we multiply
1.25/100 × f/f
so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.
f = 2000 / 1.25 = 1600
so, we get
1.25/100 × 1600/1600 = 2000 / 160000
so, the value of the condominium is
value = $160,000
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
8 jars
10 jars
Answer:
(c) 8 jars
Step-by-step explanation:
You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.
JarsThe number of jars can be found from ...
(2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars
Lorraine can fill 8 jars from the 2.5 gallon pot.
<95141404393>
A triangular side panel for a roof has the dimensions shown.
26 ft
30°
What is the approximate area, in square feet, of the side panel?
OA.
О в.
O C.
O D.
239
146.4
119.5
60°
292.7
Answer:
d
Step-by-step explanation:
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
Itzel purchased 18 pounds of oranges.
How many ounces of oranges did she
purchase?
Answer:
288
Step-by-step explanation:
1 pound is equal to 16 ounces
if Itzel purchases 18 pounds, to convert to ounces simply multiply 18 by 16.
Answer:
288
I wish you luck in your assignments.
(I just noticed someone got here in before me and answered WAY better. So I edited this to tell you to give them brainliest.)
What is the common denominator of y + StartFraction y minus 3 Over 3 EndFraction in the complex fraction y + StartFraction y minus 3 Over 3 EndFraction divided by five-ninths + StartFraction 2 Over 3 y EndFraction?
The common denominator of the given expression is 5y+6.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
Given expression,
(y+(y-3)/3)/(5/9+2/3y)
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
=3y(4y-3)/5y+6
Hence the common denominator of the above expression is given by 5y+6
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1. The sum of two angles is 85°, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.
On solving the provided question, we can say that - by equation angles will be, x + 5x = 85 => 6x = 85 => x = 14.1666666667
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
let one angle be = x
other angle be 5x
then, x + 5x = 85
6x = 85
x = 14.1666666667
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1. This week Tony practiced basketball 2 hours on Tuesday, 1 hours Wednesday, and 2 hours on Friday. Next
week Tony will practice basketball for the same number of hours Tuesday, Wednesday, and Friday. What is
the total number of hours Tony will practice basketball over the 2 weeks?
For 2 weeks tony will spent time for practice basketball is 10 hours.
How do you find time in math problems?The equation for calculating time is [Time = Distance Speed]. The distance may be calculated using the time formula [Distance = Speed Time].Work completed equals Time x Rate of Work. Work Rate is equal to One/Time. Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x.The Greenwich hour angle, abbreviated GHA, is used to define the Equation of Time as E = GHA (apparent Sun) - GHA (mean Sun) (1). E = right ascension of the fictional mean Sun - right ascension of the apparent (real) Sun is a different formula that is frequently used in textbooks.Given data :
1st week
= Tuesday = 2 hours
= Wednesday = 1 hour
= Friday = 2 hours
same for 2nd week
so total hours = 1st week + 2nd week
= 2 + 1 + 2 + 2 + 1 + 2
= 10 hours
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What is the length x of a diagonal support, to the nearest tenth of a foot?
CORRECT ANSWER
PROVIDE EXPLANATION
The length of x of a diagonal support is 13.8 feet.
What is the hypotenuse of a triangle.The hypotenuse of a triangle is the length of the longest side of the triangle. So that it is always opposite to the measure of the largest angle of a triangle.
In the question given, divide the length of the footbridge into 2 parts.
So that,
Half of the footbridge = 25/ 2
= 12.5 ft
So that applying the appropriate trigonometric function to determine the value of x using any of the congruent triangles. We have;
Sin θ = opposite/ hypotenuse
Sin 65 = 12.5/ x
x = 12.5/ Sin 65
= 12.5/ 0.90631
x = 13.792 feet
The length x of a diagonal support is 13.8 feet.
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how to horizontally stretch a cubic fucnction
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
1 Chinese yuan= $0.14567. How many Chinese yuan can u buy for a dollar
The Chinese yuan you can buy for a dollar is 6.86483 Chinese yuan
How to determine how many Chinese yuan you can buy for a dollarFrom the question, we have the following parameters that can be used in our computation:
1 Chinese yuan= $0.14567
Divide both sides of the equation by 0.14567
So, we have the following representation
1/0.14567 Chinese yuan= $0.14567/0.14567
Evaluate the quotient
1/0.14567 Chinese yuan= $1
Evaluate the other quotient
6.86483 Chinese yuan= $1
This means that
$1 = 6.86483 Chinese yuan
Hence, you can buy 6.86483 Chinese yuan for $1
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