The distributive property is often used to simplify algebraic expressions.
What is algebra?Algebra refers to the involving of unknown quantities into the block relationship between variables.
In this example, the expression 2(-3x + 5) can be simplified using the distributive property. The distributive property states that for any two numbers a and b, and a third number c, a(b + c) = ab + ac. Applying this property to our expression, 2(-3x + 5) = 2(-3x) + 2(5).
By expanding the expression, we see that 2(-3x + 5) = -6x + 10. This simplified expression is much easier to work with than the original expression. The distributive property can be applied to any expression in order to simplify it, making it easier to solve.
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Which equation represents a function?
Responses
A y = ±2x + 3y = ±2x + 3
B x2
+ y2
= 16x 2 + y 2 = 16
C y = ±3x+8−−−−−√
y = ± 3 x + 8
D y2
= -5x - 8y 2 = -5x - 8
E x = 4y + 7
Option C is correct : y = ±3x + 8, represents a function because it satisfies the vertical line test.
"y = ±3x + 8" represents a function. A function is a mathematical relationship between a set of inputs (in this case, x) and a set of outputs (in this case, y). In this equation, for each value of x there is exactly one corresponding value of y, which means that it represents a function.
"y = ±2x + 3" is not a function because for each value x, there are two possible values y (one positive and one negative). This is not the definition of a function, as a function must have exactly one output value for each input value.
Options B, D, and E do not represent functions because they do not have an equal sign between the x and y variables, which is the defining characteristic of a mathematical function.
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tay practices piano for x hours. Omar practices for 2/5 less than that
Answer: Let x be the number of hours Tay practices the piano. Then, Omar practices for 2/5 less than that, or x - 2/5x = 3/5x hours.
Step-by-step explanation:
5x + 3y = 12
x - 4y= 7
Answer:
x = 3
y = -1
Step-by-step explanation:
5x + 3y = 12
x - 4y= 7
Times the second equation by -5
5x + 3y = 12
-5x + 20y = -35
23y = -23
y = -1
Now put -1 back in for y and solve for x
x - 4(-1) = 7
x + 4 = 7
x = 3
Let's check
3 - 4(-1)= 7
3 + 4 = 7
7 = 7
So, x = 3 and y = -1 is the correct answer.
How do you tell the possible rational roots of a polynomial function? How do you test one of the possible rational roots to see if it is indeed a zero?
Step-by-step explanation:
To find the possible rational roots of a polynomial function, you can use the Rational Root Theorem. According to this theorem, if a rational number "p/q" is a root of a polynomial function, where p and q are integers, and q ≠ 0, then p must div ide the constant term of the polynomial and q must divide the leading coefficient of the polynomial.
To test if one of the possible rational roots is indeed a root (zero) of the polynomial, you can use the Synthetic Division method. In this method, you divide the polynomial by the linear factor (x - p/q) corresponding to the test root, and check if the remainder is zero. If the remainder is zero, then the test root is a zero (root) of the polynomial.
The coordinate grid shows triangle STU.
Triangle STU is rotated 270* about the origin to create triangle S'T'U'. Which rule describes this transformation?
(x, y) → (x, -y)
(x, y) → (y, -x)
(x, y) (x + 3, y + 5)
(x, y) → (-x, y)
The transformation rule (x, y) → (-y, x) describes a 270* rotation about the origin for a triangle on the coordinate grid.
A transformation in mathematics is a process of mapping or changing one figure into another while preserving its shape, size and orientation. The coordinate grid is a tool used to plot points and study transformations in a two-dimensional plane.
The transformation rule that describes this rotation is (x, y) → (-y, x). This rule means that for every point (x, y) in the triangle STU, the new point (x', y') in the triangle S'T'U' is obtained by swapping the x and y coordinates and negating the y-coordinate. In other words, the x-coordinate remains unchanged, while the y-coordinate is negated.
For example, if the point (3, 4) is in the triangle STU, the new point (x', y') in the triangle S'T'U' would be (4, -3).
This rule applies to all points in the triangle, and the result is a rotation of the original triangle by 270* in a counterclockwise direction about the origin.
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Find the volume of the composed figure
Enter the correct number in the box
The required volume of the composite figure is given as 18,300 cm³.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The volume of the composed figure is given as,
Split the figure into two,
So,
Volume = Volume of 1 + Volume of 2
Volume = 15 × 15 × 30 + 35 × 22 × 15
Volume = 6750 + 11550
Volume = 18,300 cm³
Thus, the required volume of the composite figure is given as 18,300 cm³.
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Which of the following are roots of the polynomial function below?
Check all that apply.
F(x)=x²-3x²+2
A. 3-√17
4
B. 2+√/12
C. 1
D. 3+√17
4
□ E. 2-12
SUBMIT
Answer:
[tex]\textsf{B.} \quad \dfrac{2 +\sqrt{12}}{2}[/tex]
[tex]\textsf{C.} \quad 1[/tex]
[tex]\textsf{E.} \quad \dfrac{2-\sqrt{12}}{2}[/tex]
Step-by-step explanation:
Factor TheoremIf f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=x^3-3x^2+2[/tex]
Sum the coefficients:
[tex]\implies 1-3+2=0[/tex]
As the sum of the coefficients equals one, (x - 1) is a factor the polynomial.
Find the other factor by dividing the polynomial by (x - 1):
[tex]\large \begin{array}{r}x^2-2x-2\phantom{)}\\x-1{\overline{\smash{\big)}\,x^3-3x^2+2\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-x^2)\phantom{-)..)}}\\-2x^2+2\phantom{)}\\-~\phantom{()}\underline{(-2x^2+2x)\phantom{}}\\-2x+2\phantom{)}\\\phantom{)}-~\phantom{()}(-2x+2)\\\end{array}[/tex]
Therefore, the factored form of the polynomial is:
[tex]f(x)=(x-1)(x^2-2x-2)[/tex]
To find the roots, set the function to zero and solve for x.
Set the first factor to zero and solve for x:
[tex]\implies (x-1)=0 \implies x=1[/tex]
Set the second factor to zero and solve for x using the quadratic formula:
[tex]\implies x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x=\dfrac{-(-2) \pm \sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{2 \pm \sqrt{12}}{2}[/tex]
1 mile divided by 2 laps = mi/lap
the value of 1 mile divided by 2 laps is 0.5 mi/lap.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, 1 mile divided by 2 lap
Simplifying the equation in numerical form
=> 1 mile divided by 2 lap
=> 1/ 2 mil/ laps
=> 0.5 mil/lap
Therefore, the value of 1 mile divided by 2 laps is 0.5 mi/lap.
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Solve 2*x2+3xy if x=6 and y=5
The solution to the given algebraic expression is 162.
Solving algebraic expressions.The process of solving algebraic expressions can sometimes be the process whereby numbers are used as a substitute or to replace a variable(s) in order to get a desired solution.
In the given question, we have 2x² + 3xy, where x = 6 and y = 5. It means that we are going to replace the value of x with 6 where ever we see x in the expression and y with 5.
Thus, 2x² + 3xy becomes:
= 2(6)² + 3(6)(5)
= 2(36) + 3(30)
= 72 + 90
= 162
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What percent of 125 is 32?
if 5 sina =3 then find tana/cosa=5/13
Answer:
15/16
Step-by-step explanation:
Help……………………………………..
−n+(−3)+3n+5 ????????
Answer:
2n+2
Step-by-step explanation:
the polygon exterior angle-sum theorem states that the exterior angles of any polygon add up to 360 degrees. *write a formula that can help you find the measure of each individual exterior angle in any polygon. use n for the number of sides.
The formula to calculate the measure of each individual exterior angle in any polygon is: Exterior angle measure = 360°/n.
To find the measure of each individual exterior angle in any polygon, first, you must understand the Polygon Exterior Angle-Sum Theorem, which states that the exterior angles of any polygon add up to 360 degrees.
With this information, the formula for the measure of an individual exterior angle is simple: Exterior angle measure = 360°/n, where n is the number of sides in the polygon.
By dividing the total sum of the exterior angles (360°) by the number of sides (n) in the polygon, you can determine the measure of each individual exterior angle.
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when does a simple correlation between two variables justify concluding that a definitely causes b? question 9 options: when the correlation is statistically significant. when there is no obvious third variable that could be causing changes in both a
A simple correlation between two variables when there is no obvious third variable that could be causing changes in both a and b.
A measure of the degree to which two variables vary together or the strength of the link between two variables is simple linear correlation. Correlation is frequently misused. You must provide evidence that one variable is really having an impact on another. and when we compare r to the relevant crucial value in the table, the association is statistically significant. The correlation coefficient is significant if it is greater than zero and does not fall between the positive and negative critical values.
the possibility that a reported correlation between two variables may not actually reflect any underlying relationship (in a causal sense) between the two variables, but rather the shared correlation between each of the variables and a third variable.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
1/2
3
1/3
Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1), the scale factor used is: D. 1/3.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Scale factor = -1/-3
Scale factor = 1/3.
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Answer: D = 1/3
Step-by-step explanation: Took the test and got it right :>
Priya’s Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. This is represented by the inequalities x+y≤20
and x≤8
. Represent the number of cats and dogs that can be at the store on a graph. Solve the system of inequalities by graphing.
Need help graphing it and finding where the two inequalities meet.
The common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.
What is an inequality? What are algebraic expressions?An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > cIn mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Priya’s Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. This is represented by the inequalities x + y ≤ 20 and x ≤ 8.
The number of cats and dogs that can be at the store on a graph can be represented by the common region in the graph of both the inequalities.
Therefore, the common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.
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The function V(x) = 4/3πx^3 represents the volume (in cubic inches) of the sphere. The function W(x) = V(27x) represents the volume (in cubic inches) of the sphere when x is measured in feet. Write a rule for W. Find W(6) in terms of π.
W(x) = ?
W(6) = ? cubic inches.
The value of the function W(x) for x=6 is 17,799,730.56 cubic inches.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, the function V(x)=4/3 πx³ represents the volume (in cubic inches) of the sphere.
The function W(x) = V(27x) represents the volume (in cubic inches) of the sphere when x is measured in feet.
W(x) = 4/3 π(27x)³
W(x) = 4/3 π(27x)³
= 4/3 π×19683×x³
= 4π×6561×x³
W(x)= 26244πx³
W(6)= 26244×3.14×(6)³
= 17,799,730.56 cubic inches
Therefore, the value of the function W(x) for x=6 is 17,799,730.56 cubic inches.
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PLEASE HELP SUPER EASY
Answer: isosceles, because each side is accurate
Answer:
Scalene, right.
Step-by-step explanation:
Its scalene because all the sides are not equal.
It is a right angled triangle.
Hope this helps!
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Can anyone help............................................
Answer:
Last option:
x ≤ 217
Step-by-step explanation:
Mean time = Total Time/Number of observations
Mean time = (192 + 206 + 194 + 191 + x)/5 = (783 + x)/5
We want this mean time to be no greater than 200 seconds.
In other words we want mean time ≤ 200 s
We therefore get the inequality:
(783 + x)/5 ≤ 200
Multiplying both sides by 5
=> (783 + x) · 5 ≤ 200 · 5
=> 783 + x ≤ 1000
=> x ≤ 1000 - 783
=> x ≤ 217
If T.S.A of a cylinder is 231m^2 and C.S.A is 154m^2, find it's volume.
The volume of the cylinder is 538.9 m³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
The T.S.A. is equal to 231m² and C.S.A. is equal to 154m².
We know that,
T.S.A - C.S.A = 2πr².
231 - 154 = 2πr².
77 = 2πr².
πr² = 77/2.
πr² = 38.5.
r² = 12.26.
r = 3.5.
2πrh = C.S.A
2πrh = 154.
h = 154/(πr).
h = 14.01
Therefore, The volume is equal to,
π×(3.5)²×14.01.
= 538.9 m³.
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The expression -210+ 12m represents a submarine that began at a depth of 210 feet below sea level and ascended at a rate of 12 feet per minute. What was the depth of the submarine after 9 minutes?
-108 is the depth of the submarine after 9 minutes.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is -210+ 12m
This expression represents a submarine that began at a depth of 210 feet below sea level and ascended at a rate of 12 feet per minute.
We need to find the depth of the submarine after 9 minutes
m=9
Now put m value in the expression
-210+12(9)
-210+108
-108
Hence, -108 is the depth of the submarine after 9 minutes.
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divide the amount 300 in the ratio 1;5 in the correct ratio
Answer:
$50, and $250
Step-by-step explanation:
Can someone answers these fast I need them rn
Step-by-step explanation:
3.
30 + 60+ x=l 180°( being sum of angle of triangle is 180°)
90+ x= 180°
x= 180 - 90
=90
(HELP!!!) 1. 20 % of the total number of pupils in a class is 6, How many pupild are there in the class altogether? (with explanation pls)
Answer:
30
Step-by-step explanation:
this is the explanation
6÷20% = 30
The difference of a number and 7 times 11
Therefore , the solution of the given problem of expression comes out to be x - 77.
What exactly is a expression?Arithmetic, algebra, and subdivision are required in math. When united, they produce the following: A mathematical function, some data, and an equation A statement of fact contains values, parameters, and mathematical operations like additions, addition and subtraction, matrix multiplication, and divisions. It is possible to analyse and assess various phrases and terms.
Here,
If we let "a number" be represented by the variable x, then the expression "the difference of a number and 7 times 11" can be written as:
x - 7 * 11
Simplifying this expression gives:
x - 77
Therefore , the solution of the given problem of expression comes out to be x - 77.
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One side of a rectangle is 16 inches and the other side is x inches. What values of x will make the
perimeter more than 50 inches?
Any real value of x which is greater than 9 inches will make the perimeter of rectangle more than 50 inches
Let us assume that the length of the rectangle is represented by l and the width is represented by w.
Assuing l = 16 inches and width = x inches
Let P represents the perimeter of the rectangle.
We know that the formula for the perimeter of the rectangle is:
P = 2(l + w)
The perimeter should be more than 50.
So, we get an inequality,
P > 50
2(l + w) > 50
l + w > 25
16 + x > 25
16 + x - 16 > 25 - 16
x > 9
Thi means, that for any x > 9 will make the perimeter greater than 50 in.
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what is coefficient?
Answer:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
Answer:
A coefficient is a numerical or constant quantity placed before and multiplying variable.
Step-by-step explanation:
For example, 4x+8=12. 4 is the coefficient.
Describe the possible lengths of the third side of the triangle if the lengths of the other two sides are 6 meters and 9 meters.
The triangle third side may be 6 or 9 metres long, or it may be between 9 and 15 metres long.
Depending on the lengths of the other two sides, the triangle's third side can have a variety of lengths. The third side's length could range from 9 to 15 metres if the first two sides are 6 and 9 metres, respectively. The reason for this is that the length of any two sides of a triangle must always be greater than the length of the third side; in this instance, the sum of the two sides is 15 metres, or 6 and 9 metres. As a result, the triangle's third side must be either less than or equal to 15 metres. A triangle can also have two equal sides, so the third side could also be equal to 6 or 9 metres. In conclusion, the third side of the triangle may be anywhere between 9 and 15 metres long, or it could be 6 or 9 metres long.
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The length of an altitude of an equilateral triangle is √3/2 feet. Find the length of one side of the triangle
Answer: Let's call the length of one side of the equilateral triangle x.
Then, the height of the triangle can be represented as √3/2.
By the Pythagorean theorem, we have:
(x/2)^2 + (√3/2)^2 = (x/2)^2 + 3/4 = x^2/4 + 3/4 = x^2/4 + 3/4 = x^2/4
So:
x^2 = 4 * (x^2/4 + 3/4) = 4x^2/4 + 4 * 3/4 = 4x^2/4 + 3
Solving for x:
3x^2/4 = 3
x^2 = 4
x = 2
So the length of one side of the equilateral triangle is 2 feet.
Step-by-step explanation: