The zeroes of the polynomial f(x) are 7, 6 and -1. The solution is obtained by the method of polynomial long division.
What is polynomial long division?
A long division polynomial is a formula for dividing one polynomial by another of the same degree or lower. The divisor, quotient, dividend, and remainder are all components of the long division of polynomials, just like they are for long division of numbers.
We are given f(7) = 0.
This means that (x-7) is one factor of f(x).
Using Polynomial Long Division,
Dividing : x^3 -12x^2 + 29x + 42 ("Dividend")
By : x-7 ("Divisor")
Dividend x^3 - 12x^2 + 29x + 42
- divisor * x2 x^3 - 7x^2
Remainder - 5x^2 + 29x + 42
- divisor * 5x - 5x^2 + 35x
Remainder - 6x + 42
- divisor * (-6) - 6x + 42
Remainder 0
Quotient : x^2-5x-6
Remainder: 0
Now, factoring x^2-5x-6 , we get
⇒x^2-6x+x-6
⇒x(x-6)+1(x-6)
⇒(x+1)(x-6)
Thus, the factors are (x+1), (x-6) and (x-7).
Hence, the zeroes of the polynomial f(x) are 7, 6 and -1.
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Sam ued to be 175cm tall. He i now 7% taller. To the nearet centimeter,how tall i Sam now
Sam is now 187cm tall. When we say that Sam is now 7% taller, it means that his new height is 7% greater than his original height.
To find out how much taller he is, we can calculate 7% of his original height using the percentage formula:
percentage of original value = (part / whole) * 100
In this case, the part is the increase in height, and the whole is the original height. To find the part, we can rearrange the formula to:
part = (percentage / 100) * whole
So, to find the increase in height, we can substitute the values we know:
increase in height = (7 / 100) * 175 cm
This simplifies to:
increase in height = 12.25 cm
Now that we know how much taller Sam is, we can add this increase to his original height to find his new height:
new height = original height + increase in height
new height = 175 cm + 12.25 cm = 187.25 cm
So, Sam is now 187.25 cm tall. This number is rounded to the nearest centimeter, so his new height is 187cm tall.
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Tiffany went shopping at Forever 21 and The Gap. She spent a total sum of $450 at the two stores. If the amount she spent at Forever 21 was four times as much as the amount she spent at The Gap, how much did she spend at each of the two stores?
According to the algebraic expression she spend at each of the two stores:
= 90 in the gap
= 360 in the Forever 21
What are expressions in algebra?Any mathematical statement with variables, numbers, as well as an arithmetic operation in between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated either by arithmetic sign +.
According to the given information:Tiffany went shopping at Forever 21 and The Gap.
She spent a total sum of $450 at the two stores.
the amount she spent at Forever 21 was four times as much as the amount she spent at The Gap.
SO,
The amount she spent in Forever 21 = y
The amount she spent in Gap = 4x
4x + y = 450
5x + y = 450
= 450/5
= 90
She spent in the gap.
= 450- 90
= 360
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What is the perfect square trinomial of 36?.
A perfect square trinomial is a polynomial of the form (x + b)^2 = x^2 + 2bx + b^2. It is called a "perfect square" because when it is multiplied out, the resulting polynomial is a square of a binomial.
To find the perfect square trinomial of 36, we need to find two numbers that when added, give us b and when multiplied give us b^2=36.
Those two numbers are 6 and -6, since 6*-6 = -36 = 36.
So, the perfect square trinomial of 36 is (x + 6)(x - 6) = x^2 - 36
Another way to find the perfect square trinomial is to take the square root of the constant term (36) and then add and subtract that value to the variable.
√36 = 6
then x^2 + 6x - 6x + 36 = x^2 - 36
So, the perfect square trinomial of 36 is x^2 - 36.
[tex]36[/tex] is the square of [tex]6[/tex]. The square of a binomial is called a perfect square trinomial. [tex]X^2+12x+36[/tex] is a perfect square trinomial.
A rental car company charges $24 per day to rent a car and $0.10 for every mile
driven. Xin wants to rent a car, knowing that:
• She plans to drive 200 miles.
.
. She has at most $140 to spend.
Write and solve an inequality which can be used to determine d, the number of days
Xin can afford to rent while staying within her budget.
Inequality:
Answer:
24 a b c d
Step-by-step explanation:
whyats the answert
Answer:[tex]d\leq 5[/tex]
[tex]24d+20\leq 140[/tex]
Step-by-step explanation: First You do 200x0.10 which equals 20. then you put the cost per day first so 24 per day + the cost of all miles which is 20 at most means she can also spend less then 380 so we use the greater than equal symbol.
Omar went to the college traveling 8 mph and returned home traveling 24 mph. If the total trip took 8
hours, how long did Omar travel at each speed?
hours at 8 mph
hours at 24 mph
The distance that light travels in 12.3 nanoseconds is 37.9 meters.
What is speed?
Speed is the rate of change of an object's position relative to a given frame of reference. It is a scalar quantity, meaning it has both magnitude and direction. Speed is usually measured in meters per second (m/s) or kilometers per hour (km/h). Speed is an important factor in many activities, including travel, sports, and transportation.
This can be calculated by multiplying the speed of light (3.0 x 108 m/s) by the time (12.3 nanoseconds), which yields a result of 37.9 meters. This answer is rounded to the correct number of significant figures, which is two.
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A cell phone company charge 50$ for a phone plu 25$ per month. You get a gift card for 100$. When doe the total pent on your phone ervice exeed the amount on you gift card?
The money spent on a phone plan can be represented by the inequality:
50 + 25x > 100 and the total money spent on the phone service exceeds the amount of the gift card after the 2nd month.
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.
The first part of the inequality, 50$, represents the initial cost of the phone.
The second part, 25x, represents the monthly cost of the service, 25$ per month.
So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.
50 + 25x > 100
It states that the total cost (50 + 25x) of the phone plan is greater than 100$.
It's the total cost you have to pay for the phone and the service.
It's used to know when the total cost exceeds 100$, which is the gift card's value.
To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.
50 + 25x > 100
x > (100-50)/25
x > 2
So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.
Therefore, The money spent on a phone plan can be represented by the inequality : 50 + 25x > 100 and the total money spent on the phone service exceeds the amount of the gift card after the 2nd month.
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Find the distance between the points C(0, 0) and D(8, 3).
8.3
011
√73
√55
Answer: Number 3, which is √73
Step-by-step explanation:
Use the distance formula:
Distance (d)
= √(8 - 0)2 + (3 - 0)2
= √(8)2 + (3)2
= √73
= Number 3 :>
HELP ME ASAP!!! PLS!!
The Chu family can hike 3 miles per hour. How long will it take them to hike 15 miles?
A- 3.75 hours
B- 4 hours
C- 4.5 hours
D- 5 hours
Answer:
D- 5hrs
Step-by-step explanation:
If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.
Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours
Answer:
D. 5 hours
Step-by-step explanation:
3 miles per 1 hour so 3/1
15 miles per x hours so 15/x
3/1 = 15/x or 3 = 15/x
get x by itself so
3 divided by 3 and 15 divided by 3
x = 5 hours
Where would the intensity of an earthquake be higher?.
The intensity of an earthquake generally higher near the epicenter.
Intensity is based on observed effects of ground motion on people, buildings and natural features. This varies from site to site within the fault region, depending on the observer's position relative to the earthquake epicenter. The seismic intensity of an earthquake decreases as the distance from the epicenter increases, and decreases as the distance from the epicenter increases. An epicenter is a point on the surface of the Earth directly above where an earthquake begins. Earthquakes with a moment magnitude of approximately 6.5 or less occur in a concentrated area directly below the epicenter. Therefore, apart from the effects of different rock types and different soil types, the greatest shaking occurs at the epicenter. Earthquakes with a moment magnitude greater than 6.5 cause faults at some distance from the epicenter. At these large sizes, it is common for fractures to reach the surface. In such cases, the maximum shaking may or may not occur at the epicenter..
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What is the mirror image of 4 46?.
The mirror image is (4, 46) is (4, -46)
The term mirror image is defined as it is like a reflection of it either because it is exactly the same or because it is the same but reversed.
Here we have given the point (4, 46) and here need to mirror image of the points.
The rule Mirror image of (x , y ) in the x - axis is written as ( x , -y)
Here we have the value of x as 4 and the value of y as 46.
Here we also know that it is defined as a reflected duplication of the number that appears almost identical but is reversed in the direction perpendicular to the mirror surface.
When we apply the values on the formula then we get the mirror image as (4, -46).
Complete Question:
What is the mirror image of the coordinate (4, 46)?
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Which graph shows the solution to the system of linear equations?
y = 3x
y = x + 1
a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma 3 and another line that passes through the points 0 comma 1 and 1 comma 2
a coordinate grid with one line that passes through the points 0 comma 1 and 1 comma 2 and another line that passes through the points 0 comma 1 and 1 comma 4
a coordinate grid with one line that passes through the points 0 comma 1 and 1 comma 2 and another line that passes through the points 0 comma 3 and 1 comma 4
a coordinate grid with one line that passes through the points 0 comma 1 and 1 comma 3 and another line that passes through the points 0 comma 3 and 1 comma 4
The graph of the system of equations can be seen in the image at the end, and the solution is (0.5, 1.5)
Which graph shows the solution of the system of equations?Here we want to show which graph shows the system of equations below:
y = 3x
y = x + 1
So the graph will have two linear equations, the first one:
y = 3x
Passes through the points (0, 0) and (1, 3) (check that by evaluating)
And the equation:
y = x + 1
Passes through (0, 1) and (1, 2)
Then the correct option is the first one, and the graph of the gis the one below.
There we can see that the solution is (0.5, 1.5)
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You buy a 1:1000 cale model of the Statue of Liberty during a trip to New York City. The height of the model i 9. 3 centimeter. Find the actual height x (in meter) of the Statue of Liberty
The actual height of the Statue of Liberty in meter is 93 m
What is proportionality?It is a constant relationship between different measurable quantities.
Data of the problem:
Scale 1:1000Height model = 9.3 cmWe calculate the proportion of the model scale:
1/1000 = 9.3/x
We clear the variable, noticing the rules of clearing:
What is multiplying goes to the other side of the equality dividing.What is dividing goes to the other side of the equality by multiplying.Clearing the variable we have:
1/1000 = 9.3/x
x* (1/1000) = 9.3
x = (9.3*1000) / 1
x = 9300 cm
Converting the centimeter to meters we have:
9300 cm * (1 m /100 cm) = 93 m
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a circle have a diameter of 12 units and a center that lies on the y-axis, we need to find its equation,
We know that, the standard form of the equation of a circle is expressed as;
(x-a)² + (y-b)² = b=r²
where;
(a, b) is the center of the circle
r is the radius of the circle
We have,
diameter = 12 units
radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)² + (y-3)² = 6²
x²+ (y-3)² = 36
Hence, the equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
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State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement.
Thank you!
Answer: Similar by SAS, and ABC ~ AVU
Step-by-step explanation:
AV = 77 - 66 = 11
AU = 42 - 36 = 6
6/36 = 1/6
11/66 = 1/6
Therefore, these two triangles ABC and AVU are similar by SAS similarity.
ABC ~AVU :>
What is the y value of the solution to the system of equations 3x 5y 17x 4y − 13?.
So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.
To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.
The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:
4(3x + 5y) = 4(17)
12x + 20y = 68
-3(4x + 4y) = -3(-13)
-12x - 12y = 39
then we can add these two equations:
12x + 20y = 68
-12x - 12y = 39
0 = 29
This is an impossible equation, which means that the system has no solution.
Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.
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the local kennel needs to buy dog food. which dog food will save the kennel the most money? 1st 150 pounds for $53.50 2nd 75 pounds for $336.75
Answer:
The First food will save the most money
Step-by-step explanation:
150lb- $53
75lb- $336.75
The first one saves them quite a bit of money.
to solve the equation below you need to divide by what number 2X = 8
What is the degree of polynomial 5x2 4x2 7x?.
The degree of the polynomial 5x2 + 4x2 - 7x is 3.
5x2 and x2 are the same power value is 4 and 7x contain the power value 1 so the difference of the degree of polynomial we find is 3. When they don't already, unite all the different phrases in the expression to make it simpler.
The phrases that are not associated with a variable, like 3 or 5, are referred to as constant terms. The terms associated with the variable are known as coefficients. Either intentionally disregard these terms or check them off the list while looking for the degree of a polynomial.
The polynomial is represented in standard form in this manner. First should be the phrase with the highest exponent, and last should be the word with the lowest exponent. This will enable you to determine which term's exponent has the highest value.
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What is the limit of sum formula?.
The limit of sum formula is Sn=a(1−rn)1−r,for r≠1.
Consider a curve that lies above the x-axis. This graph's function is a continuous function with all of its values being non-negative, defined on the closed interval [a, b]. The definite integral ab f(x) dx of any such continuous function "f" is the region bound between the curve, the points "x = a" and "x = b," and the x-axis.
On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as,
[tex]\int\limits^b_a {f(x)} \, dx = F(b)-F(a)[/tex]
∫ = Integration symbol
a = Lower limit
b = Upper limit
f(x) = Integrand
dx = Integrating agent
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
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given g(x)=-x^2+10x-3 find the following,
g(9)
g(-1)
Step-by-step explanation:
g(x) = - x² + 10x - 3
To get the g(9) substitute X in the equation for 9
g(9) = - 9² + 10(9) -3
g(9) = 81 + 90 - 3
g(9) = 171 - 3
g(9) = 168
Similarly to get g(-1)
g(-1) = - (-1)² + 10(-1) - 3
g(-1) = - 1 - 10 - 3
g(-1) = - 14
The measure of an interior angle of a regular polygon is 108°. Find the number of sides in the polygon?
The internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.
What is a regular polygon?An -sided polygon with regular sides that are all the same length and symmetrically arranged around a common center is known as a regular polygon (i.e., the polygon is both equiangular and equilateral).
Only a few regular polygons are "constructible" with the compass and straightedge of classical Greece.
A regular polygon's interior angle measures 108°.
The pentagon is a 5-sided polygon.
A two-dimensional closed figure with three or more straight sides is called a polygon.
A polygon is any shape with straight edges, such as a triangle or rectangle.
Figures with open sides or any curved sides are not considered to be polygons.
Therefore, the internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.
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Which diagram represents the net of a square pyramid? Choose all that apply.
Answer:
D is the answer
match each table to an equation that represents the relationship.
table a Equation 1 400 + x = y
table b Equation 2 x - 400 = y
table c Equation 3 x + y = 400
table d Equation 4 400 X x = y
The equation y = 400x represents the relationship as shown in the table.
The correct option is table d.
What is the proportional relationship?
A proportional relationship is a relationship between two expressions, where changes in one expression mean some constant change in another expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A table is shown in the attached image.
To find the relationship:
We will find the common ratio,
y/x = k, where k is the proportionality constant,
400/1 =400
800/2 = 400
1200/3 = 400.
That means, the equation is,
y = 400x
Therefore, y = 400x is the equation.
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The complete question is given in the attached image.
factorise
12x*2 + 15xy-9x
Answer:
see picture
Step-by-step explanation:
Factorise for 12[tex]x^{2}[/tex]+15xy-9x is 3x (4x+5y−3)
Solution steps:
The first step is to factor out 3.
So,
3 (4[tex]x^{2}[/tex]+5xy-3x)
The second step is to consider 4[tex]x^{2}[/tex]+5xy−3x. Factor out x.
So,
x (4x+5y−3)
The third step is to rewrite the complete factored expression.
3x (4x+5y−3)
Evaluate:
3x (4x+5y−3)
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When the magnitude level of an earthquake is between 3. 0 3. 9 then the category is?.
When the magnitude level of an earthquake is between 3. 0 3. 9 then the category is known as minor category.
The scale goes from "minor" for earthquakes with a magnitude between 3.0 and 3.9, when people typically start to feel them, to "great" for earthquakes with a magnitude more than 8.0, when major damage is anticipated.
A single earthquake frequently has many somewhat different magnitudes published for it. This occurs because there is a complex relationship between seismic readings and magnitude, and several methods frequently produce slightly different magnitudes for the same earthquake.
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What is the first step for solving the system using substitution results in an equation?.
The first step for solving the system using substitution results in an equation is solve one equation for either x or y.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.
We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
If we take an example ,
Equation 1: 3x + 2y = 11
Equation 2: -x + y = 3
Substituting y = 3+x in equation 1 is the first step in the equation.
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For 5-8, use the diagram to complete each sentence.
(diagram attached)
5. An exterior angle of the triangle is ________.
6. The remote interior angles of the triangle to the exterior angle 1 are ________ and ________.
7. The sum of the measure of angles 2 and 3 is equal to the measure of ________.
8. The sum of the measure of angles 1 and 4 is _______.
By using the diagram, each of the sentence should be completed as follows;
An exterior angle of the triangle is ∠1.The remote interior angles of the triangle to the exterior angle 1 are ∠2 and ∠3.The sum of the measure of angles 2 and 3 is equal to the measure of ∠1.The sum of the measure of angles 1 and 4 is 180°.What is the exterior angle theorem?In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of both angle 2 and angle 3 in the given triangle is equal to the measure of angle 1 (∠1);
∠2 + ∠3 = ∠1
By applying the Linear Pair Postulate to the two angles formed at a point, we have the following:
∠1 + ∠4 = 180°
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What are the two properties of irrational numbers?.
Properties of irrational number:
The addition of an irrational number and a rational number gives an irrational number. Multiplication of any irrational number with any nonzero rational number results in an irrational number.Here, The definition of irrational number:
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
The following are the properties of irrational numbers:
The addition of an irrational number and a rational number gives an irrational number. Multiplication of any irrational number with any nonzero rational number results in an irrational number.Learn more about Irrational Number at:
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In the expression 5 x y over 7 what value of y would make a product greater than 5 ?
Answer:
y > 7x
Step-by-step explanation:
(5xy)/7 [5 x y over 7]
["what value of y would make a product greater than 5 ?"] can be written as:
(5xy)/7 > 5
Rearrange to find y:
(5xy)/7 > 5
(5xy) > 35
y > 35/5x
y > 7x
The triangle with coordinates (2,-3),(2,1),(-4,2) is reflected
across the y-axis and then translated by vector
(3,-2).
Part A
Find the new coordinates
Part B
What is the composition of functions for the
given sequence of transformations?
(x, y) → (
The new coordinates after reflection will be (4,2) (-2,1) (-1,-3).
A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.
The general guidelines for the reflection over x-axis equation are as follows: The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). In other words, the function is just multiplied by 1, which results in a curve that crosses the x-axis.
The new coordinates after reflection will be -
(4,2) (-2,1) (-1,-3)
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