The complete factor of the polynomial x² + 5x +6 is (x + 3)(x + 2).
You can factor it by using the factorization methods such as
Factor by grouping
Factor by grouping and completing the square
Factoring by using difference of squares
Factoring by using sum and difference of cubes
For example, you can factor it by using the difference of squares method:
x² + 5x +6 = (x² + 6x + 9) - (x +3)
We know x² + 6x + 9 = (x + 3)², So
x² + 5x +6 = (x + 3)² - (x + 3)
Taking (x + 3) common
x² + 5x +6 = (x + 3)(x + 3 - 1)
x² + 5x +6 = (x + 3)(x + 2)
So (x + 3)(x + 2) is complete factor.
--The question is not readable, answering to the question below--
"What is the complete factor of x² + 5x + 6?"
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Please help me asap !
Answer:
by helping some one fast
find the gcf of each pair of monomials : x3y2 and x5y
Answer: [tex]\text{x}^3\text{y}[/tex]
This is the same as writing x^3y
===================================
Explanation:
When finding the GCF, we look for the smallest exponent for each variable.
The x terms of the given expressions are x^3 and x^5. The smallest exponent here is 3, so x^3 is part of the GCF.
The y terms are y^2 and y. Think of y as y^1, which shows 1 is the smallest exponent. We'll have y as part of the GCF.
-----------
We found that...
x^3 is part of the GCFy is also part of the GCFThe overall GCF is x^3y which can be written as [tex]\text{x}^3\text{y}[/tex]
Side note: We ignore the coefficients since they are 1 for each monomial.
Answer these questions, if you get them right i will give brainlets
x-2/9=6 5/9 ??
J+1/2=3 9/14??
x-1/8=5/24??
The results for each operation are given as follows:
x-2/9=6 5/9 -> x = 61/9.
J+1/2=3 9/14 -> J = 22/7.
x-1/8=5/24 -> x = 1/3.
How to solve the expressions?The first step to solve the expressions is to transform the mixed numbers to fractions, hence:
6 5/9 = (6 x 9 + 5)/9 = 59/9.3 and 9/14 = (3 x 14 + 9)/14 = 51/14.Then the solution for the first expression is of:
x = 59/9 + 2/9
x = 61/9.
The solution for the second expression is of:
J = 51/14 - 1/2
J = 51/14 - 7/14
J = 44/14.
J = 22/7.
The solution for the third expression is of:
x = 5/24 + 1/8
x = 5/24 + 3/24
x = 8/24
x = 1/3.
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What is the additive inverse of − 7 *?.
The additive inverse of 7 is -7.
The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.
That is, Number + Additive inverse = 0
OR
The negative of a number.
Now we are given the number
7
So, the additive inverse of 7:
⇒7 + Additive inverse = 0
⇒Additive inverse = -7
Thus the additive inverse of is 7 is -7.
--The given question is incorrect; the correct question is
"What is the additive inverse of 7?"--
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A long year-end status report for work is 125 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.66 each.
Answer:
$16.47
Step-by-step explanation:
125×18=2250
these are the pages printed
2250÷500=4.5
these are the reams of paper needed
$3.66 ×4.5=$16.47
this is the money needed
The number of water bottles, y, filled in x minutes by each of two machines is given by the equations below. Use substitution to determine if there is a point at which the machines will have filled the same number of bottles. 160x + 2y = 50 y+80x = 50
The equation system contains: No Solution.
How to find equation?A mathematical statement proving the equality of two mathematical expressions is what is meant by the term equation.
When two or more components of a situation must be taken into account in order to comprehend or describe the entire situation, this is known as an equation.
The equation in a new order:60x + 2y = 50
y+80x = 50
On both sides of the equation, lessen the most prevalent factor:
80x + y =25
80x + y = 50
Remove the two equations:
80x + y - (80x + y) = 25-50
Take the parentheses out.
80x + y - 80x - y = 25 - 50
One variable is canceled: 0 = 25 - 50
Make a difference or total calculation: 0 = -25
The equation system contains: No Solution.
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the path of the goof ball is modled by h= -2t^2+14t
1. how long will the golf ball be in the air after it is hit?
2. there is a 6 meter cedar tree that the ball encounters at approximately 3 seconds after it is hit. does the ball pass over the tree or hit it?
3. what is the maximum height that is reached by the ball, and at what time does it happen
By evaluating and using the quadratic equation we will have:
1) 7 seconds.
2) Yes, it will pass.
3) 24.5 meters, after 3.5 seconds.
How long will the ball be on the air?To find this, we need to solve the quadratic equation:
h = -2t^2 + 14t = 0
Taking t as a common factor we can write:
t*(-2t + 14) = 0
-2t +14 = 0
14 = 2t
14/2 = t
7 = t
The ball will be 7 seconds on the air.
2) To check this we need to evaluate the quadratic equation on t = 3
h = -2*3^2 + 14*3 = 24
The height is of the ball is larger than the height of the tree.
3) What is the maximum height of the ball?
This happens at the vertex of the quadratic equation:
h = -2t^2 + 14t
The two roots are t = 0 and t = 7, then the vertex is at t = (7 - 0)/2 = 3.5
And the maximum height is:
h = -2*3.5^2 + 14*3.5 = 24.5
The maximum height is 24.5 meters.
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Help me please!!!!! I need to get this done before 6:00 and it’s currently 5:45!!!
Reason: It's the coefficient to the left of the input variable.
A regular polygon i uch that it interior angle exceed three time the exterior angle by 20 degree find the number of ide the polygon ha
Answer:
9
Step-by-step explanation:
exterior angle=x⁰
interior angle=3x⁰+20⁰
3x⁰+20⁰+x⁰=180⁰
4x=160⁰
x=40⁰
number of sides = 360⁰/exterior angle
360⁰/40⁰= 9sides
If Cos A = 9/41 and tan B = 28/45 angle A and B are in quadrant I find the value of Tan(A+B)
What is the degree of polynomial 2x² 5x² 7?.
The degree of the polynomial 2x² 5x² 7 is 4.
The biggest sum of all the exponents for all of variables in a term is the polynomial's degree. Any polynomial's degree is determined solely by its variables; coefficients are to be disregarded. The highest exponential power in a polynomial equation is called the polynomial's degree.
When x is the variable with the highest power n in an nth degree polynomial function with real coefficients, where n can take whole number values.
One of the key ideas in mathematics is the degree of polynomials, which establishes the maximum number of possible solutions and the frequency with which a function will cross the x-axis on a graph.
A polynomial with many variables is of a certain degree: Find the term with the highest degree by averaging the exponents of all the variables in each phrase. That will be regarded as the polynomial's degree.
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What are prime numbers of 36?.
The prime numbers of 36 are 2 and 3 and the Prime factorization expression of 36 is equals to 2 × 2 × 3 × 3.
Prime factorization is a method of representing a number as a product of prime factors. A prime factor of a number is a factor that is prime. The numbers are called factors of 36 that divide 36 evenly. In other words, if we multiply two numbers and get the result equals to 36. So, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Steps for Prime Factorization of 36 :
Step 1: In first step, divide the number i.e., 36 by its smallest prime factor. So, by divisibility rules, 2 is the smallest prime factor of 36. So, we get, 36 ÷ 2 = 18
Step 2: Here need repeatedly divide the quotient by 2 until we get a number that is no more divisible by 2. So, we divide 18 again by 2 which is 18 ÷ 2 = 9.
Step 3 : Now, 9 is not completely divisible by 2, so, we proceed with the next prime factor of 36, which is 3. That is 9 ÷ 3 = 3
Step 5: Divide the quotient by 3 again which is 3 ÷ 3 = 1. Now, we need not proceed further as we have obtained 1 as our quotient. Therefore, the prime factorization of 36 is expressed as 2 × 2 × 3 × 3 = 2² × 3²; where 2 and 3 are prime numbers and the prime factors of 36.
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A parachutist's elevation changes by -35 ft in 5 seconds. What is the change in the parachutist's elevation each second?
Answer:
7 feet per second
Step-by-step explanation:
The change in elevation of the parachutist is -35 ft in 5 seconds. To find the change in elevation per second, we can divide the total change by the number of seconds.
Change in elevation per second = -35 ft / 5 seconds = -7 ft/s
So the parachutist's elevation changes by -7 ft/s each second.
It means the elevation of the parachute is decreasing by 7 feet per second.
A shipping container will be used to transport several 120-kilogram cr country by rail. The greatest weight that can be loaded into the contair kilograms. Other shipments weighing 12400 kilograms have already b the container. Which inequality can be used to determine , the great 120-kilogram crates that can be loaded onto the shipping container?
27500 ≥ 120x + 12600 is the inequality that can be used to determine x, the great 120-kilogram crates that can be loaded onto the shipping container.
What is inequality?A relation that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. [1] Most frequently, size comparisons are made between two numbers on the number line. Different notations can be used to represent various kinds of inequalities, including:
A is smaller than b, as shown by the symbol a < b.
When the expression a > b is used, it means that a is greater than b.
The greatest weight that can be loaded into a container = 27500kg
Shipment weight already present in the container = 12400kg
Amount of weight that can be loaded = 27500 - 12400 = 15100kg
Weight of each crates = 120 kg
Let x be the maximum number of 120 kg crates that can be loaded to the container
Weight of 'x' number of 120 kg crates = 120x
Therefore, the required inequality is as follows
27500 ≥ 120x + 12600 (since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).
Thus, 27500 ≥ 120x + 12600 is the inequality that can be used to determine x, the great 120-kilogram crates that can be loaded onto the shipping container.
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The letters of the alphabet are written on cards and placed in a hat. What is the probability of drawing a constant, replacing it, and then drawing a vowel
The probability of drawing a constant, replacing it, and then drawing a vowel is given as follows:
105/676.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
In the context of this problem, we have that:
For the first hat, 21/26 probability of drawing a consonant.For the second hat, 5/26 probability of drawing a vowel.Hence the probability of drawing a constant, replacing it, and then drawing a vowel is calculated as follows:
p = 21/26 x 5/26 = 105/676.
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Help me solve this pls
9 + 8 > 20 or 2q - 5 <13
Answer:
So the final solution is q < 9 and the inequality is False.
Step-by-step explanation:
To solve the given inequality, you first need to simplify the left-hand side of the inequality:
9 + 8 = 17
so the inequality becomes:
17 > 20 or 2q - 5 < 13
Since 17 is not greater than 20, this inequality is false.
Next, we need to solve the other inequality:
2q - 5 < 13
To isolate the variable on one side of the inequality, we need to add 5 to both sides:
2q < 18
Then, we divide both sides by 2:
q < 9
So the solution is q < 9
So the final solution is q < 9 and the inequality is False.
The function h(t) = −16t2 48t 36 model the height of a ball, in feet, at t econd after being thrown into the air. What i a reaonable range for the function?
The function h(t) models the height of a ball thrown into the air, so it makes sense for the range of the function to be all non-negative values. This means that the range of the function will be all non-negative values up until the point where the ball reaches its maximum height, and then it will decrease to zero as the ball hits the ground.
To determine when the ball reaches its maximum height, we can find the vertex of the parabola. The vertex is found by taking the average of the x-coordinates of the roots of the quadratic. In this case, the roots of the quadratic are found by setting h(t) = 0 and solving for t:
-16t^2 + 48t - 36 = 0
By factoring the quadratic, we get:
(t-9)(-16t+4) = 0
So the roots of the quadratic are t = 9 and t = -0.25. The average of these two values is (9 - 0.25)/2 = 4.375. Therefore, the vertex of the parabola is at (4.375, h(4.375)).
To find the y-coordinate of the vertex, we can plug in 4.375 for t in the function h(t):
h(4.375) = -16(4.375)^2 + 48(4.375) - 36 = -16(19.140625) + 195 - 36 = -307.5 + 159 = -148.5
So the vertex of the parabola is at (4.375, -148.5). This means that the maximum height of the ball is -148.5 feet. Since the ball can't go below ground level, the range of the function h(t) is all non-negative values less than or equal to -148.5. Therefore, a reasonable range for the function is [-148.5, ∞).
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The convienience store sells a 16-ounce bottle of water for $2.40 and a 28 ounce bottle of water for $2.80. Tiana wants to compare the unit rates to find out which is a better deal. Which one is a better deal?
To compare the unit rates, we need to find the cost per ounce for each bottle of water.
For the 16-ounce bottle, the unit rate is:
$2.40 / 16 ounces = $0.15 per ounce
For the 28-ounce bottle, the unit rate is:
$2.80 / 28 ounces = $0.10 per ounce
From the unit rate we can see that the 28 ounce bottle of water is a better deal because it cost $0.10 per ounce while the 16 ounce bottle cost $0.15 per ounce.
It's important to know that as the amount of water increases the price decreases making the 28 ounce bottle cheaper than the 16 ounce bottle.
Hugo works for the Produce and Pantry grocery store as a bagger. He earns $57.50 for a 5-hour shift. How much does he earn per hour?
Answer:
Hugo earns $11.50 per hour
Step-by-step explanation:
57.50/5 = 11.50
Answer:$11.5 per hour
Step-by-step explanation: $57.50 / 5 hour shift = $11.5 per hour
What i the lowet poitive whole number that hould replace the quetion mark on the pinner o that the probability of pinning an odd number greater than 6 i 1/4
The lowest positive whole number that should replace the question mark on the pinner such that the probability of pinning an odd number greater than 6 is 1/4 is 9.
Lowest Odd NumberIt could be determined by calculating the probability of pinning an odd number greater than 6 out of the total number of possible outcomes.
If we consider the lowest positive whole number greater than 6 is 7, then we have 7,9,11,13,15,17,19,21,23,25 and so on.
Out of these numbers, 1/4 are odd numbers greater than 6. So the lowest whole number that could replace the question mark on the pinner is 9.
This is applicable for any situation where the probability of an event occurring out of a set of possible outcomes needs to be determined, and the lowest value for which that probability is a certain ratio needs to be found. In this case, the event is pinning an odd number greater than 6, and the set of possible outcomes is all positive whole numbers greater than 6. The probability being considered is 1/4, and the question is what is the lowest value that can replace the question mark on the pinner such that this probability is achieved.
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help please dont understand why this is wrong
Answer:
I also don't know good luck girly
What is the product of improper fraction?.
Improper fraction is greater than 1, their product is also greater than 1.
Now, According to the question:
A fraction is called a proper fraction if its numerator is less than its denominator. The value of a proper fraction is always less than 1. Whereas, in an improper fraction, the numerator is equal to or greater than the denominator. Its value is always one or greater than one. Consider 1/3 and 3/2. Their product is 1/3 × 3/2 = 3/6 = 1/2
Therefore, according to the definition, the product of a proper and improper fraction is less than the improper fraction.
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Graph 16x - 4y = 12
(You can only graph on the given points)
*NO IN BETWEEN*
Step-by-step explanation:
16x - 4y = 12
4x - y = 3
4x = 3+y
x= 3+y/4
for y = 1
x= 3+1/4 = 1
y = 2
x=3+2/4 = 5/4 = 1.25
y = 3
x = 3+3/4 = 6/4 = 1.5
Mark ha 15 feet of tring. He will cut the tring into equal length of 7 inche each. How much tring will be left after he cut a many piece of thee length a poible
25 equal pieces of lenth 7 inch is possible and 5 inch remains after the cutting string.
What is inequality?An inequality is a statement that compares the value of one expression to another, using one of the symbols: <, >, ≤, ≥, ≠. It shows a relationship between two expressions that are not equal. It can be represented in a graph as a boundary line, with a specific region representing the solution set of the inequality.
Convert value of foot to inches:
we know that 1 foot = 12 inches
15 feet ⇒ 15 feet × 12 inches/ft = 180 inches
now the let the number of peice be x
so 7*x<=180
=> x<=180/7
=> x<=25.71
solving the inequality we get
so there is 25 equal pieces of string of length 7 is possible.
remaining piece = 180 - 25*7
=> 180 - 175
=> 5
so 5 inch remains after cutting the string
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Please help me quick : )
We can rewrite the given linear equation to have the different numbers of solutions as:
a) 3x + 8 = 3x + 4
b) 3x + 8 = 3x + 8
c) 3x + 8 = 3x +x
What we need to add such that the equation is not true?Here we have the linear equation:
3x + 8 = 3x + ?
Notice that the first term (the one that depends of x) is equal in both sides, so the equation will not be true only if the second term is a constant and is different to 8, so for example we could write:
3x + 8 = 3x + 4
b) Infinite solutions means that we have the same thing in both sides, so here we can add 8
3x + 8 = 3x + 8
Is true for all values of x, thus, it has infinite solutions.
c) The equation will have one solution only if the coefficients of the variable x are different in both sides, then here we can add "x"
3x + 8 = 3x +x
3x + 8 = 4x
That equation has a single solution:
8 = 4x - 3x
8 = x
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What is the ratio to 15 unshaded squares to 10 shaded
The ratio of unshaded squares to shaded squares is 15:10. This means that for every 15 unshaded squares, there are 10 shaded squares. This can also be simplified to 3:2, which means that for every 3 unshaded squares, there are 2 shaded squares.
It is important to keep in mind that the ratio is not equal to the fraction, it's just a way to express the relationship between the two.
Answer:
15:10
Step-by-step explanation:
15:10 which means that for every 15 unshaded squares there are 10 shaded squares which can also be simplified to 3:2 which means pretty much the same thing, for every 3 unshaded squares there will be 2 shaded ones. A ratio is not a fraction, so i advise not treating it like one.
Please help me with these questions
The two column proof showing that ΔKLG ≅ ΔMLG is as detailed below.
How to carry out a two column proof?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons for which we know those statements to be true.
Statement 1: GL ⊥ KM
Reason 1: Given
Statement 2: KG ≅ MG
Reason 2: Given
Statement 3: ∠GLK and ∠GLM are right angles
Reason 3: Definition of right angles
Statement 4: GL ≅ GL
Reason 4: Reflexive Property
Statement 5: ΔKLG and ΔMLG are right triangles
Reason 5: definition of right triangles
Statement 6: ΔKLG ≅ ΔMLG
Reason 6: HL Congruency postulate
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HELP THIS WILL MAKE MY GRADE GO UP!!!!!!!
A sixth grade class is going on a field trip. The school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.
Identify which list below shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots if there are an equal number of each type of sack lunch and students are randomly selecting their lunch. Use this information to mark the probability on the number line.
The list below that shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots List 2
How to identify the list?the statement states that the school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.
List 1 mentions that there is "Ham, Carrots, celery". We know that students can only have either carrots or celery, but the list shows that the students have both. Therefore, list 2 is correct.
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How do you find the discriminant and nature of the roots of a quadratic equation?.
To find the discriminant and nature of the roots of a quadratic equation, you can use the quadratic formula.
Write the quadratic equation in the form of ax² + bx + c = 0, where a, b, and c are constants, and x is the variable.
Calculate the discriminant using the formula
b² - 4ac.
Use the discriminant to determine the nature of the roots:
If the discriminant is greater than 0, the roots are real and distinct.
If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).
If the discriminant is less than 0, the roots are complex and not real numbers.
To find the roots of the quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The plus-minus sign indicates that there are two possible solutions, and the square root of the discriminant is used to find them.
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A rectangular basketball court has a perimeter of 232 feet. The length of the court is 74 feet. What is the width of the basketball court?
Answer:
42 feet
Step-by-step explanation:
p = 2l + 2w
232 - 2(74) =
232 - 148 = 84
84/2 = 42
Check
232 = 2(42) + 2( 74)
232 = 84 + 148
232 = 232