The factors of 2x² - 7x - 15 are (2x + 3) and (x - 5).
What are the factors of 2x² - 7x - 15?By splitting the middle term and factoring the polynomial,
2x² - 7x - 15
= 2x² - 10x + 3x - 15
= 2x(x - 5) + 3(x - 5)
= (2x + 3)(x - 5)
The factors of 2x² - 7x - 15 are (2x + 3) and (x - 5).
What is factoring?By searching for factors, factoring is the process of attempting to make a mathematical expression resemble a multiplication problem.In essence, factoring is the multiplication process in reverse. It is possible to factor both numerical and algebraic expressions using a specific technique.Finding two integers to multiply to obtain another number can be as simple as factoring. You might also seek out a number's prime factorization when factoring.Of course, numerical expressions are the easiest to factor.A number or other mathematical object is factored when it is written as the product of numerous factors, typically smaller or simpler counterparts of the same kind.To learn more about polynomial, refer:
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Denominations matter in digital money true or false
Hi! I really need help with this problem
Amelie is shopping for children’s books and puzzle books. she wants to purchase at least 2 more children’s books than puzzle books, but she can afford no more than 15 items total. if x represents the number of children’s books and y represents the number of puzzle books amelie purchases, which point lies in the solution set?
a. (4,12)
b. (6,8)
c. (12,4)
d. (9,5)
The point lies in the solution set if x represents the number of children's books and y represents the number of puzzle books Amelie buys (9,5).
To find the point that lies in the solution set, you need to consider the constraints given in the problem. Amelie wants to purchase at least 2 more children's books than puzzle books, which means that the number of children's books should be greater than or equal to the number of puzzle books plus 2. She can afford no more than 15 items total, which means that the total number of children's books and puzzle books should be less than or equal to 15.
Based on these constraints, the point that lies in the solution set is (9,5). This point satisfies both constraints, because the number of children's books (9) is greater than the number of puzzle books (5) plus 2, and the total number of children's books and puzzle books (14) is less than or equal to 15. Therefore, the correct answer is (d) (9,5).
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How do you find volume with base and area?
We constantly gauge a prism's height perpendicular to the plane of its base. That holds true even when a prism is tilted or turned on its side.
Volume of a prism is equal to base area into height.
A prism's total surface area is equal to the sum of its two bases' surfaces and lateral surface area.
Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.
Dimensions of a prism. the separation between a prism's two bases. The technically smallest line segment between the bases . The term "altitude" also relates to how long this part is.
Any prism's volume is equal to V = BH, where B is its base's area and H is its height.
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help me out on this please
The value of other Zeroes are -1/2,2
How to find all the other zeros of the polynomial p(x)=2x³ +3x ² −11x−6?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable)
Algebraic expressions known as polynomials can have exponents that are multiplied, divided, or added. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively. A monomial is a polynomial with only one term. A polynomial having two dissimilar terms is called a binomial.
Given ,
p(x)=2x ³ +3x² −11x−6
Since x=−3 is a zero of p(x)
So, by factor theorem x+3 is a factor of p(x)
Now, if we divide 2x³+3x²−11x−6 by x+3, quotient is 2x² −3x−2 and remainder is 0.
Therefore,
2x³+3x² −11x=(x+3)(2x² −3x−2)
=(x+3)(2x+1)(x−2)
for other zeroes of p(x)
2x+1=0,x−2=0
Hence the other zeroes are − 1/2,2
The complete question is : Find all the other zeros of the polynomial p(x)=2x³ +3x ² −11x−6 if one of its zero is −3.
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The polynomial p(x)=x^3-7x-6p(x)=x
3
−7x−6p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 7, x, minus, 6 has a known factor of (x+1)(x+1)left parenthesis, x, plus, 1, right parenthesis.
Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors.
p(x)=p(x)=
The polynomial p(x) is x³ - 7x - 6 that is (x+1) (x+2)(x - 3)
How to calculate the polynomial function ?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Given that polynomial:
p(x) = x³ - 7x - 6
Known factor: (x+1)
polynomial equation expressed as the sum of linear components.
The degree of polynomial is 3, and when we divide it by a linear equation, the result will be a quadratic. That quadratic will have 2 solutions.
We can solve the quadratic in two linear factors and as a result we will have the answer.
First of all, we need to divide the polynomial p(x)with the given factor (x+1) to find the other factors.
x³ - 7x - 6/x+1 = x² - x -6
Solving the quadratic:
x²- x - 6 = x² -3x +2x - 6
x(x-3)+2(x-3)
(x+2)(x-3)
Therefore the polynomial will be p(x) = x³ - 7x - 6 = (x+1) (x+2)(x - 3)
The complete question is : The polynomial p ( x ) = x 3 − 7 x − 6 p(x)=x 3 −7x−6p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 7, x, minus, 6 has a known factor of ( x + 1 ) (x+1)left parenthesis, x, plus, 1, right parenthesis. Rewrite p ( x ) p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p ( x ) = p(x)=p, left parenthesis, x, right parenthesis, equals
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What is square root of 1 called?
Answer:
1
Step-by-step explanation:
The square root of 1 is called 1.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.
The square root of 1 is 1, because 1 x 1 = 1. Therefore, the square root of 1 is simply called 1.
Solve for x:
2/x+2+1/5=6/x+5?
A wood stove burns 24 same sized logs in 5 hours. How many can I burn in 8 hours?
Answer: 38
Step-by-step explanation:
24 divided by 5 = 4.8 per hour
4.8 times 8 = 38.4 or 38 in 8 hours
It can burn 38 in 8 hours
You are a coach Who coache to team, a high chool team and a team for 7 and 8 year old. You are ordering occer ball for your team. Soccer ball are ized baed on age group, ranging from ize 2 to 5. The 7-8 team ue a ize 3 ball, and each ball cot $15. The 14 team ue a ize 5 ball, and each ball cot $20. You accidentally lot the bill, but you know that you purchaed a total of 12 occer ball for $220. How many of each ize did you order? math word problem
So, we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.
To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x be the number of size 3 balls purchased for the 7-8 year old team, and let y be the number of size 5 balls purchased for the 14 year old team.
The first equation will represent the cost of the size 3 balls: 15x = $220.
The second equation will represent the cost of the size 5 balls: 20y = $220.
The third equation will represent the total number of balls purchased: x + y = 12.
Now that we have set up the system of equations, we can solve for x and y using the method of substitution.
First, we can solve the first equation for x: x = $220 / 15 = 12/3 = 4.
Then, we can substitute this value for x in the second equation: 20y = $220 -> y = $220 / 20 = 11.
Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which does not equal 12. This means that our solution is incorrect.
To find the correct solution, we can go back and try solving the second equation for y instead: y = $220 / 20 = 11.
Then, we can substitute this value for y in the first equation: 15x = $220 -> x = $220 / 15 = 12/3 = 4.
Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which equals 12. This means that our solution is correct: we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.
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The first equation will represent the cost of the size 3 balls: 15x = $220.
The second equation will represent the cost of the size 5 balls: 20y = $220.
The third equation will represent the total number of balls purchased: x + y = 12.
Now that we have set up the system of equations, we can solve for x and y using the method of substitution.
First, we can solve the first equation for x: x = $220 / 15 = 12/3 = 4.
Then, we can substitute this value for x in the second equation: 20y = $220 -> y = $220 / 20 = 11.
Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which does not equal 12. This means that our solution is incorrect.
To find the correct solution, we can go back and try solving the second equation for y instead: y = $220 / 20 = 11.
Then, we can substitute this value for y in the first equation: 15x = $220 -> x = $220 / 15 = 12/3 = 4.
Finally, we can check our solution by substituting these values for x and y in the third equation: 4 + 11 = 15, which equals 12. This means that our solution is correct: we ordered 4 size 3 balls for the 7-8 year old team and 11 size 5 balls for the 14 year old team.
How do you describe the end behavior of the graph if the degree is even and the leading coefficient is negative?
The end behavior of the graph would be that it would approach negative infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.
When the degree of a polynomial is even and the leading coefficient is negative, the end behavior of the graph is that it will approach negative infinity as x increases or decreases without bound in either direction. This is because the degree of the polynomial is even and the coefficient is negative, meaning that the leading term will always be negative. Since the leading term is always negative, the graph will approach negative infinity as x increases or decreases without bound in either direction. This is the general behavior of a polynomial with even degree and a negative leading coefficient.
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Can anyone help me find this answer fast.
Answer:
8cm
Step-by-step explanation:
We can figure out what the side length of this would be by squaring the area.
[tex]\sqrt{64}[/tex] = 8
To check our work, we can multiply the length by the height. (8 and 8)
8 × 8 = 64
Nado's chessboard side length would be 8cm.
Determine whether the statement is true or false:
4 sin x cos x dx = -cos 2x + C
Answer:
False
Step-by-step explanation:
[tex]2\sin x \cos x =\sin 2x \implies 4 \sin x \cos x=2\sin 2x \\ \\ \therefore \int 4\sin x \cos x dx=2\int \sin 2x dx \\ \\ 2\int \sin 2x dx=\frac{2}{2}(-\cos 2x)+C=-\cos 2x+C[/tex]
Mrs. Dyson works at a music camp. She has $90 to spend on guitar strings for her students. A pack of bronze strings costs $6.00. A pack of nickel strings costs $4.50. The following equation represents her situation.
6x + 4.5y = 90
How can you use the equation to find the total number of packs Mrs. Dyson can buy if she only buys nickel strings?
A. Substitute 0 for X and solve for Y. C. Substitute Y for X and solve for Y.
B. Substitute 0 for Y and solve for X. D. Substitute X for Y and solve for X.
Answer:
The answer is A but I must put very much more characters in order to fulfill the character limit
If EF=10x+20,FG=36 , And EG=156 , Find The Value Of X
The value of x is 10.
What is expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The structure of an expression is:
Expression is (Number/variable, Math Operator, Number/variable)
According to the given question:
EF = 10x+20
FG=36
EG=156
The following expression is true for the given data.
EF+FG = EG
Substitute the given data into the expression
(10x + 20) + (36) = 156
Solve for the unknown value of x
10x + 56 = 156
10x = 100
x = 10
Hence the value of x is 10.
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How many terms are there in the expression 2y +10x+ 5 *?
the residual plot below suggests which violation(s) of regression assumptions? a. autocorrelation b. multicollinearity c. heteroscedasticity d. nonnormality
the residual plot below suggests that this violation is Heteroscedasticity
The residual is the discrepancy between the actual value and the model's estimated value. The fundamental premise of regression or time series analysis is that the residual variance or quantity should be constant. As a result, there shouldn't be any patterns visible in the residual scatter plot.
The residuals scatter plot reveals a pattern. The dispersion of residuals is growing at higher values of Docs. As a result, residual variance is not constant.
Heteroscedasticity is present when the residual variance is non-constant. Regression makes the supposition that the residual variance should be constant (Homosceasticity). Consequently, the scatter plot of residuals violates the heteroscedasticity condition.
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Enter the surface area of the net of the triangular prism in the space provided, in centimeters squared.
The surface area of the net of the triangular prism in the space provided,
2400cm².
What is prism?Prism is a polyhedron with two identical ends in three dimensions.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)
= (S₁ + S₂+ S₃)l + bh
where, b is the bottom edge of the base triangle, h is the height of the base triangle, l is the length of the prism and S₁, S₂, and S₃ are the three edges (sides) of the base triangle (bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bh.
The side of the triangle is S₁ = 8, S₂= 15, and S₃= 17.
The rectangular's base = 20 and height = 8
Substituting all the values in the formula:
Surface area
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
= [ ( 15 +17+8) x 20] + (20 x 80)
= 800 + 1600
= 2400 cm²
Therefore, the surface area of the prism is 2400 cm².
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How do you identify greater than and less than?
To identify whether a mathematical expression represents a "greater than" or "less than" relationship, you can use the following symbols:
Greater than: >
Less than: <
For example, the expression "3 > 2" represents a "greater than" relationship because it means that 3 is greater than 2. Similarly, the expression "5 < 7" represents a "less than" relationship because it means that 5 is less than 7.
You can also use the symbols "greater than or equal to" and "less than or equal to" by using the following symbols:
Greater than or equal to: >=
Less than or equal to: <=
For example, the expression "3 >= 2" represents a "greater than or equal to" relationship because it means that 3 is greater than or equal to 2. Similarly, the expression "5 <= 7" represents a "less than or equal to" relationship because it means that 5 is less than or equal to 7.
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5/3X + 1/3X = 13 1/3+8/3X
The value of x in the equation 5/3x + 1/3x = 13⅓ + 8/3x is calculated as: x = -20.
How to Solve an Equation?To solve an equation is to find the value of the variable by isolating it in such a way that it is moved to one side of the equation.
Given the equation, 5/3x + 1/3x = 13⅓ + 8/3x, to solve this equation, we need to find the value of x by isolating the variable x to one side.
Follow the steps below:
5/3x + 1/3x = 40/3 + 8/3x
2x = 40/3 + 8/3x
Substract both sides by 8/3x:
2x - 8/3x = 40/3 + 8/3x - 8/3x
-2/3x = 40/3
Multiply both sides by -3/2:
-2/3x × -3/2 = 40/3 × -3/2
x = -120/6
x = -20
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Prove the following statement using the given pieces of information.
Given: Line AB is parellel to Line DC and Line AD is parellel to Line BC.
Prove: Triangle ABC is congrent to Triangle CDA.
Triangle ABC is congruent to Triangle CDA using the SSS rule.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
SSS rule states that,
If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
To prove:
ΔABC ≅ ΔCDA.
AB = DC ( given)
AD = BC (given)
AC = AC (common to both the triangles)
ΔABC ≅ ΔCDA ( By SSS rule )
Thus,
ΔABC ≅ ΔCDA by SSS rule.
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Find the area of the segment enclosed by
chord [BC] and the subtended arc with
radius 4 cm and central angle 55⁰.
The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]
What is an area of Segment?Segment and area of a circle segment:
A segment is essentially the area of a circle between the chord and the arc. A circle is a path that a point equidistant from a single point on the plane can follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle formed inside the sector from the sector where the segment is located, one can calculate the area of a circular segment.
Calculation:Given radius and angle subtended by arc on circle is 4 cm and 55° respectively.
So the length of chord [BC] is [tex]\frac{55}{180}[/tex]×π = 3.84 cm.
Required area of segment enclosed = Area of segment subtended by arc [BC] - area of ΔABC
>semi-perimeter of ΔABC is [tex]\frac{(4+4+3.84)}{2} = 5.92[/tex]
>Area of ΔABC is [tex]\sqrt{5.92*(5.92-4)*(5.92-4)*(5.92-3.84)} = 6.74 cm^{2}[/tex]
>Area of segment subtended by arc {BC} = θ/360° × π[tex]r^{2}[/tex]
=[tex]\frac{55}{180}[/tex]×16π
= 7.68[tex]cm^{2}[/tex]
∴The area of segment enclosed by chord [BC] is [tex]7.68-6.74 = 0.94 cm^{2}[/tex]
The area of segment enclosed by chord [BC] is 0.94 [tex]cm^{2}[/tex]
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Is divisible by 3 yes or no?
No, using divisibility test we find that 3194 is not divisible by 3.
What is divisibility test of 3?According to the rule of three, if a whole number's digit sum is a multiple of three, the original number is also divisible by three. It is simple to determine if a lower number is divisible by 3 or not using the three-digit multiplication table or skip counting by three (beginning at 0 and adding 3). Without actually dividing larger numbers, we can determine if they are entirely divisible by three or not.
If a whole number's digit sum is a multiple of three or precisely divisible by three, it is said to be divisible by three.
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this question is incomplete, the complete question is
3194 is divisible by 3 yes or no?
What number is 10 more than 40?
The number that is 10 more than 40 is 50, using addition.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Here, what we can do is use addition to find the number that is 10 more than 40.
We can do 10 + 40 = 50.
Hence, the number that is 10 more than 40 = 50.
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Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Here, what we can do is use addition to find the number that is 10 more than 40.
We can do 10 + 40 = 50.
Hence, the number that is 10 more than 40 = 50.
What is the slope of the function 4x 2y =- 10?
The slope of the given function 4x + 2y = -10 is equal to -2.
As given in the question,
Given function is equal to 4x + 2y = -10
Standard form of the equation in slope intercept form is given by :
y = mx + c
'm' is the slope of the function
'c' is the value of y-intercept.
Now simplify the given function in standard form we have,
4x + 2y = -10
⇒2y = -4x -10
⇒ y = (-4x -10 ) / 2
⇒ y = -2x - 5
Compare with the standard form we get,
Slope of the function m = -2.
Therefore, the slope of the given function 4x + 2y = -10 is given by m = -2.
The given question is incomplete , the complete question is:
What is the slope of the function 4x + 2y =- 10?
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How do you factor x³?
Factoring x³ is a relatively straightforward process.
What is factor?Factory is a quantity or an expression that is multiplied to another quantity or expression to obtain a product. Factor are used in mathematics to solve problems involving multiplication division and equation factor can also be used in financial analysis to calculate interest, payments loan repayments, and another financial transaction factor can also be used to analyze supply and demand market trends and other economic indicators.
The most common way to factor x³ is to use the factorization method. This involves writing x³ as a product of three linear factors, which can be done in the following way:
x³ = x × x × x
Alternatively, you can use the method of grouping to factor x³. This involves writing x³ as a product of two binomials, which can be done in the following way:
x³ = (x × x) × x
You can also use the method of synthetic division to factor x³. This involves dividing the coefficient of x³ by the coefficient of x and then dividing the resulting coefficients by the coefficient of x. This can be done in the following way:
x³ = x² + 0 × x + 0
Once you have factored x³, you can use the factors to solve equations or to find other information related to the equation. In addition, you can use the factored form of x³ to simplify certain expressions.
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What is slope in graph example?
The level of a line's slope indicates its steepness.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates.Example -
This line goes through the points (0,0) and (4,4).
Now, slope = (y₂ - y₁) / (x₂ - x₁)
slope = (4 - 0) / (4 - 0)
slope = 4 / 4
slope = 1
So, from the above calculation it is shown that, the slope of the line is 1.
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Estimate the height of the tree 50 years after it was planted. How did you
make your prediction?
Estimate the height of the tree 50 years after it was planted is 15.92 feet
How to Find the height of the tree?DBH (inches) × π = Estimated Age of Tree (years)
Let us Consider inches is X
X *3.14=50
X=50/3.14
X=15.92
sheet of paper :There is no need for math or other instruments!Shadows: Needs a tape measure, a level surface, discernible shadows, and simple mathematics.Pencil: A quick, rough estimate made with a pal and a pencil.The most precise tools are the clinometer or instruments. You can create your own clinometer using common classroom items. If you don't know when a tree was planted, it might be quite difficult to determine its age. However, an approximate estimation method based on the trunk's circumference can be used to determine the age of the tree.The International Society of Arboriculture (ISA) first presented this method, which is based on a straightforward calculation that use the tree's diameter at breast height (DBH), which is the tree's circumference.To learn more about to find height of the tree refer to:
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How do you know if FX and GX are inverses?
First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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How do you find the measure of an isosceles triangle?
The measure of the missing angle in the given isosceles triangle ABC is 70° .
The Isosceles Triangle is defined as a type of triangle in which the measure of the angle of two sides of the triangle are equal in measure .
In the figure given below , we can see that ,
In triangle ABC , the triangle is an isosceles triangle ,
So , measure of angle B is = x° ;
the measure of angle C is = x° ;
So , By Angle Sum Property Of Triangle ;
∠B + ∠C + ∠A = 180°
x° + x° + 40° = 180° ;
2x + 40 = 180
2x = 180 - 40 ;
2x = 140 ;
x = 140/2 ;
x = 70° .
Therefore , the measure of the missing angle is 70° .
The given question is incomplete , the complete question is
How do you find the measure of the missing angle of the given isosceles triangle ?
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