The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] , so that it is completely divisible by [tex]x^{2} -3x+2[/tex] is -14 .
What are Polynomials ?
A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.
The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.
the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form as : [tex](x-1)(x-2)[/tex] ,
that means the polynomial is divisible by both x = 1 and x = 2 ;
So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;
on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;
So , the remainder is 14 .
Therefore , -14 should be added in the given polynomial .
The given question is incomplete , the complete question is
What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?
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What does 5a+10a equal to?
Answer:
15a
Step-by-step explanation:
5a + 10a = 15a
What are the properties of directed line segment?
The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.
1. It has a definite starting point and a definite ending point.
2. It has a definite length.
3. It has a definite direction.
4. It has a slope and equation.
5. It divides the plane into two parts.
6. It is symmetric about its mid-point.
7. It is two-dimensional.
A directed line segment is a line segment that has a definite starting point and a definite ending point. Its length is the distance between the two points and it has a direction, given by the vector from the starting point to the ending point. The line segment divides the plane into two parts. It is symmetric about its mid-point, which is the point halfway between the two endpoints. It has a slope and an equation. The slope is the ratio of the change in y-coordinates to the change in x-coordinates. The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.
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If Mr. Brust can bambam 8 jamjams in 12 whamwhams, the how many jamjams can he bambamin 33 whamwhams? (Yes, I know this is weird)
Answer: 22 jamjams in 33 whamwhams
Step-by-step explanation:
33 ÷ 12 = 2.75 = 12 x 2.75 = 33
2.75 x 8 = 22
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
Step-by-step explanation:
Mr. Brust can bambam 8 jamjams in 12 whamwhams.
Mr. Brust can bambam x jamjams in 33 whamwhams.
Use a proportion.
8/x = 12/33
12x = 8 × 33
x = 8 × 33/12
x = 12
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
Don’t know just need help with answer
The length AB is 15.
What is length ?
Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.
The definition of length is the measurement or extent of something from end to end. In other terms, it is the largest of the two or the highest of the three dimensions of geometrical forms or objects.
In contrast to width, which is used to gauge an object's width from side to side, length is used to gauge an object's length from one end to the other.
As it is a isosceles the two sides are equal
5x = 4x + 3
x = 3
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Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren
By probability, she will not receive a phone call from any of her grandchildren after 146 days
How does probability affect our lives?In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.
There is a [tex]\frac{2}{3}[/tex] chance that the first child won't call, a [tex]\frac{3}{4}[/tex] chance that the second child won't call, and a [tex]\frac{4}{5}[/tex] chance that the third child won't call on any given day. There is a [tex]\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}[/tex] chance that no child calls her on a randomly selected day.
When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in 144.
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4. Write an equation of the circle that has a diameter with endpoints (12, 3) and
(-18, 3). (Lesson 6-4)
x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).
What is the equation of a circle?We are aware that a circle's general equation is (x - h)2 + (y - k)2 = r2, where (h, k) is its center and r is its radius.
Therefore, to bring the constant term to the righthand side of the equation, add 21 to both sides.
So, the midpoints of the diameter are determined by the coordinates of the circle's center since the endpoints of the diameter are (x1, y1) = (12,3) and (x2, y2) = (-18,3).
The midpoints are so:
x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and
y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.
Consequently, the circle's center's coordinates are (-3, 3)
The circle's diameter:
The circle's radius is [(x1 - h)2 + (y1 - k)2], where:
(x₁, y₁) = coordinates of end of diameter = (12, 3) and
(h, k) = coordinates of center of circle = (-3, 3)
As a result, when we enter the values of the variables into r, we get:
r = √[(x₁ - h)² + (y₁ - k)²]
r = √[(12 - (-3))² + (3 - 3)²]
r = √[(12 + 3)² + 0²]
r = √[15² + 0²]
r = √15²
r = 15
The formula for the circle:
The formula for a circle with a center (h,k) is: (x - h)² + (y - k)² = r²
By changing the variables' values in the equation, we arrive at:
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - 3)² = 15²
(x + 3)² + (y - 3)² = 15²
x² + 6x + 9 + y² - 6y + 9 = 225
x² + 6x + y² - 6y + 9 + 9 - 225 = 0
x² + y² + 6x - 6y - 207 = 0
Therefore, x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).
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4 Siobhan and Ralph shared £700 in the
ratio 2:3.
Siobhan gave a quarter of her share to Karen.
Ralph gave a fifth of his share to Karen.
What fraction of the £700 did Karen receive?
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
What is a proportion?The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.
Here,
Given :
Siobhan and Ralph shared £700 in the
ratio 2:3.
Thus,
280 / 420 = 2/3
Thus,
Siobhan and Ralph has £280 and £420 respectively.
and Siobhan gave a share of quarter to karen :
So,
280/4 =70
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
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HELPPP 1. Write an equation of the ellipse with foci (0,14) and co-vertices at (±4,0).
The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].
Define ellipse.An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.
[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]
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The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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This is chemistry, but I asked two times when I picked chemistry as the subject, yet no one answered, so I am doing mathematics because this does include math.
Show ALL your WORK and make sure to LABLE all the numbers with the CORRECT UNITS; if you do, I will give you the brainliest:
A: A sample of sulfuric acid has a mass of 15.0 g. How many molecules are in this sample?
B: How many moles of sulfuric acid are present in 45 g of this sample?
C: How much would a .750 mole sample of Ammonium sulfate weigh?
D: What is the mass percent of hydrogen in this sample?
PS: Please do not spam or give the wrong answer; I will report the comment, the "answer', and your account if you do.
Rewrite in simplest rational exponent form. Show each step of your process
The final answer is 4x, which is the simplest form of expression.
What is the rational exponent?
A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.
To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:
4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)
x^(1) = x
So, the expression in simplest rational exponent form is 4x
x * 4x = 4x
Notice that 4 and x are in the same radical which means 4 is a coefficient of x.
Therefore, 4√x * √x can be written as 4x, which is in the simplest form.
hence, the final answer is 4x, which is the simplest form of expression.
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Reduce 22/154
to its lowest form.
22/154=11/77=1/7
1/7 is the lowest form
Tina's favorite shade of teal is made with 777 milliliters of blue paint for every 555 milliliters of green paint. Tyler's favorite shade of teal is made with 555 milliliters of blue paint for every 777 milliliters of green paint. How does Tina's favorite shade of teal compare to Tyler's favorite shade of teal
Comparing the volume of the paints used and analyzing the proportions, The answer is Tina's shade is more blueish and Tyler's shade is more greenish.
What do you mean by ratio?A ratio is a way to compare two or more numbers or amounts. It tells you how much bigger or smaller one number is compared to the other. It is often written as two or more numbers separated by a colon, such as "3:5" or "2:4:6". For example, if a recipe calls for 2 cups of sugar to 4 cups of flour, the ratio would be 2:4. This means for every 2 cups of sugar, there are 4 cups of flour. It's a way to express a relationship between values or quantities and it helps to understand the proportion of one value to the other values.
What do you mean by proportions?Proportion is a relationship between two or more values or quantities that compares their sizes. It's a way of saying that two or more values are equal in some way. It can be written as an equation, such as "a/b = c/d", which means that the ratio of a to b is equal to the ratio of c to d. In other words, the proportion states that two or more ratios are equal to each other. For example, if a cake recipe calls for 2 cups of sugar to 4 cups of flour, the proportion would be 2/4 = 1/2. This means that for every 2 parts of sugar, there are 4 parts of flour, which can be written as a ratio 2:4 .
Tina's ratio of blue paint to green paint = 777:555
Tyler's favorite shade has a ratio = 555:777.
The ratio for Tina's shade is greater than 1 .
while the ratio for Tyler's shade is less than 1.
So Tina's shade is more blueish and Tyler's shade is more greenish.
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If an object is propelled upward from ground level with an initial velocity of 80. 1 feet per second? It’s height h in feet t seconds later is giving by the equation h= -16ft+ 80. 1t after how many seconds does the object hit the ground
The object will hit the ground after 5.01 seconds.
When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,
h= -16t^2+ (80.1)t
When the object hit the ground, the height of the object h would be zero.
To find: time (t) when h = 0
Substitute h = 0 in given equation.
h = -16t^2+ (80.1)t
0 = -16t^2+ (80.1)t
16t^2 - (80.1)t = 0
t (16t - 80.1) = 0
t = 0 or 16t - 80.1 = 0
t = 0 OR t = (80.1)/16
t = 0 OR t = 5.01
Therefore, it will hit the ground after 5.01 seconds.
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I need to factor completely to get an answer for
r²+3r-28
I need to get factors in parenthesis like (r +/- #) (r +/- #)
I need it before tomorrow
Answer:
(r + 7)(r - 4) = 0
Step-by-step explanation:
r² + 3r - 28 = 0
(r + 7)(r - 4) = 0
r = -7, 4
Does 3 3 have a solution?
Given equation 3 = 3 is an identity, so it has infinite solutions.
Consider the given mathematical equation 3 = 3
We need to check whether the given mathematical equation has solution or not.
We know that a statement 3 = 3 's true no matter what.
We can observe that for given statement 3 = 3, there's no variable in sight.
This means, 3 = 3 must has infinite solutions.
We know that an equation which is always true, no matter what values we substituted is called as an identity.
This equation is an identity, all real numbers are solutions.
Therefore, the equation 3 = 3 have infinitely many solutions.
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a A trader opens a bank account with #250 000. In one month, she pays out two cheques for #49 000 and 34 000 and pays in one cheque for N14000. How much money does she have in her account after one month?
Answer: #181000
Step-by-step explanation:
So, to solve the problem, recall these definitions:
payout - withdrawal
pay in - deposits.
Normally, deposits add money to your balance, and withdrawals take out money.
So, there is one cheque for paying in 14,000, and two cheques for paying out 49,000 and 34,000
So, the balance is 250000 + 14000 - (49000+34000)
The balance is 181,000
Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?
Answer:
64?
Step-by-step explanation:
Basically the idea is we suppose the number she thinks of is "x"
She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:
[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]
This is my best guess, not totally sure sorry
How do you find the midpoint answer?
To find the midpoint of two points in a coordinate plane, you can use the midpoint formula.
The midpoint formula is the average of the x-coordinates and the average of the y-coordinates of the two given points.
The midpoint formula is:
((x1 + x2)/2 , (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For example, if the two points are (3, 4) and (5, 8), the midpoint would be:
((3 + 5)/2 , (4 + 8)/2) = (4, 6)
So the midpoint between (3, 4) and (5, 8) is (4, 6).
It's important to note that this formula is valid for any dimension, not just 2D, and it can be used to find the midpoint of any two points in space, whether it's in 2D, 3D, 4D and so on.
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Is maths hard or easy?
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers.
Maths is a subject that can range in difficulty depending on the level of complexity and the individual's experience and knowledge. Some people may find it easy, while others may find it difficult. In the end, it all depends on the level of understanding and the amount of effort put into learning and practicing.
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers
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Answer:
BOTH!
Step-by-step explanation:
See math can be easy or hard. It all depends on YOU. The equation itself isn't hard at all. Mybe a little more work to put in. but its your brain that tells you comething is too challenging or too hard. Now if you are a straight A students and you love math then ofcource your going to be like this is easy!
What should be done to these equations in order to solve a system of equations by elimination?
To solve the problem of a system of equations by elimination, we can start with both equations in standard form. Then we can decide which variable will be easier to eliminate.
How can we decide? We want to have the coefficients of any one of the variables be opposites so that we can put the equations together and eliminate that variable.
To solve a simultaneous equation by using the elimination method, you eliminate any one variable first.
Before you can do that, the coefficient of one of the variables in the two equations must be the same.
From the given questions, for the coefficient of one variable in the two equations to be the same, we multiply the first equation by 3.
If we can do this, the coefficient of Y in the two equations will now be 3.
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What is the value of 5 by 2?
The value of 5 divided by 2 is 2.5.
Therefore the answer is 2.5.
When dividing 5 by 2, we are trying to find out how many times 2 can fit into 5. The answer is 2 with a remainder of 1, this is why it can also be written as 2 and 1/2.
When dividing 5 by 2, we can also write the result as a fraction, in this case, it is 2 and 1/2 or 2.5 in decimal form. It is the exact same thing as 2.5, just represented in a different way.
It's important to note that, in general, dividing integers will give a decimal number. If you want the result to be a fraction, you will have to express it as such.
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What is the length of 3rd side of each triangle?
The sum of squares of two sides is equal to the square of the third side.
Finding the Third Side of a Triangle with Two Sides
Let's assume that the triangle is right-angled, as the third side of a right-angled triangle can only be found when the other two sides are known.
According to Pythagoras' Theorem, the sum of squares of two sides is equal to the square of the third side.If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)If leg b is unknown, then: b = √(c² - a²)For hypotenuse c missing, the formula is: c = √(a² + b²)A right-angle triangle is what?
This particular sort of triangle adheres to the Pythagoras theorem and may be calculated using the trigonometry tool.
We are aware that the right-angled triangle follows Pythagoras' Theorem.
According to the Pythagorean Theorem, the third side's square equals the sum of the first two sides' squares.
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The complete question should be:
What is the length of 3rd side of a triangle?
A certain library charges a late fee of $0.05 for each day that a book is
late. Last month, 158 people returned books that were 7 days late.
This month, 40 less people than last month will return books that are 7
days late. How much will the library collect in late fees this month for
returned books that are overdue by 7 days?
Answer: $41.3
Step-by-step explanation:
this month late = 158 - 40 = 118
7× $0.05 = $0.35
118 × $0.35 = $41.3
How do you check whether 7 3x is a factor of 3x3 7x?
7 + 3x is not a factor of expression 3x^3 + 7x
Consider given expression 3x^3 + 7x
Let f(x) = 3x^3 + 7x
Assume that 7 + 3x is a factor of 3x^3 + 7x
This means, 7 + 3x = 0 would be the root.
x = -7/3
If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0
We find the value of given polynomial for x = -7/3
f(x) = 3x^3 + 7x
f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)
f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)
f(-7/3) = [(-343) - 147] / 9
f(-7/3) = -490 / 9
f(-7/3) ≠ 0
Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial f(x) = 3x^3 + 7x
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How do you find the hypotenuse of a 45 45 90 triangle?
The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.
The hypotenuse of a 45 45 90 triangle is calculated as the square root of the length of the leg.
We plug the known length of the leg into our 45-45-90 theorem formula:
Hypotenuse = leg * (√2)
Properties of 45-45-90 triangles :
To point out the 45-45-90 special right triangle, check for these three identifying properties:
The polygon is an isosceles right triangle.The two side lengths are congruent, and their opposite angles are also congruent.The hypotenuse (longest side) is the length of either leg times the square root (sqrt) of two, √2.Read more about the isosceles triangle:
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Han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342. Do you agree with Han
Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.
The value of 7 here refers to the place value of 7 , in 735,208 7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .
Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.
The place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.
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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.
Properties of 9-divisible numbersA number is itself divisible by nine if the total of its digits is also nine digits.
Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine.
By utilizing the aforementioned attribute, we can
3 + A +A +1 = 9, OR 18, OR 27
4 + 2A = 9, OR 18, OR 27
using 18
2A = 18 - 4
2A = 14
A = 7
therefore we can say that the number is 3771
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What is a 69 sided shape called?
A 69 sided shape called"Hexacontakaienneagon".
Naming a polygon by its number of sides requires that we know the appropriate:
3=tri, 4=tetra, 5=penta, 6=Hexa, 7=hepta, 8=octa, 9=Nona or ennea, 10=deca,11=hendeca,12=dodeca,13=triskaideca,14=tetradeca,15=pentadeca,16=hexadeca,17=heptadeca,18=octadeca,19=enneadeca,20=icosa
For polygons with 3 through 20 sides, simply add "gon" to the prefixes at the left.
For more than 20 sides, we "construct" the name by using so-called combining prefixes:
For Tens Digit:
20=icosi,30=triaconta,40=tetraconta,50=pentaconta,60=hexaconta,70=heptaconta,80=octaconta,90=enneaconta
for One's Digit:
1=hena,2=di,3=tri,4=tetra,5=penta,6=hexa,7=hepta,8=octa,9=ennea
60 and 9
hexaconta kai ennea
As per the given information, 69 is defined as "Hexacontakaienneagon".
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please help: Can a triangle have side lengths with the given lengths? Explain. 8m, 10m, 19m
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
8+10 is 18
which is less than 19