As a little tip that's helped me personally when I was taking algebra, making equations for word problems feels a lot easier when you "translate" equations you make into words to make sure that you're using the right equation.
Let's boil down what the question tells us. 5/6 of the price tag of a bike from Store B is the price of a bike from Store A, which is $150.60. Let's use the variable 'b' to represent the price of Store B's bike.
[tex]\frac{5}{6}[/tex] * b = 150.60
Try "translating" the equation above. "5/6 of the price of a Store B bike is equal to 150.60." That seems about right, doesn't it? Let's isolate 'b' so we can get an official answer.
Multiply both sides by 6 to get rid of the denominator:
[tex]\frac{5b}{6}[/tex] * 6 = 150.60 * 6
5b = 903.6
Divide both sides by 5 to get rid of b's coefficient:
[tex]\frac{5b}{5}[/tex] = [tex]\frac{903.6}{5}[/tex]
b = 180.72
The price of a bike from Store B is $180.72
If you need any help on anything I just did here, don't be afraid to ask. Good luck on your Algebra endeavors!
- breezyツ
using the standard From of the quadratic Function y=-3x²-12x-9
The standard From of the quadratic Function is (−2,3).
What is the standard From?y=-3x²-12x-9
Find the given parabola's characteristics.
To continue, tap...
Opens down in the direction of ( 2, 3), with
( -2, 35 /12) as the focus.
x = 2 is the symmetry axis.
The directrix is y = 37 /12
By entering a few x values into the equation, you may get the associated y values. You should choose the x values close to the vertex.
To continue, tap...
x y − 4 − 9 − 3 0 − 2 3 − 1 0 0 − 9
Using the chosen points and the parabola's attributes, draw the curve.
Opens downward in direction
Focus: ( 2, 35 12) Vertex: ( 2, 3)
x = 2 is the symmetry axis.
The following directrix: y = 37 12 x y 4 9 3 0 2 3 1 0 0 9.
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How do you solve two parallel lines crossed by a transversal?
When two lines are crossed by a transversal, a number of angle pairs are formed. The sum of the measures of these angle pairs can be used to solve for unknown angles in the diagram.
Here are some of the angle pair relationships that hold for two lines crossed by a transversal:
Alternate Interior Angles: Alternate interior angles are pairs of angles on opposite sides of the transversal, but inside the two lines. These angles are congruent (have the same measure).Alternate Exterior Angles: Alternate exterior angles are pairs of angles on opposite sides of the transversal, but outside the two lines. These angles are congruent.Corresponding Angles: Corresponding angles are pairs of angles on the same side of the transversal, but on opposite sides of the two lines. These angles are congruent.Using these relationships, you can set up equations to solve for unknown angles in the diagram. For example, if you are trying to find the measure of angle A, you might use the fact that corresponding angles are congruent to set up the equation "m<A = m<D". Then, you can use other angle pairs to find the measures of the other angles, and solve the system of equations to find the measure of angle A.
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I need help describing this, I forgot how to find all of it
The (a) Hole in the expression is x, (b) The vertical assumption is -10 and (c) the horizontal assumption is that the denominator is greater than the numerator.
How to find Hole, vertical and horizontal assumptions?You should know that a hole occurs if there is a common term between the the numeration and the denominator when factorized, For vertical assumption, the denominator must be equal to zero and horizontal assumption, numerator will be equal to denominator
The given expression is:
[tex]\frac{x^{2}-2x }{x^{3}-9x^{2} -10x }[/tex]
The Hole is
Factorize the numerator= x²-2x
x is common in the expression
x(x-2)
Factorize the denominator= x³-9x²-10x
x(x²-9x-10)
= [x²-10x+x-10]
x[(x²-10x)+(x-10)]
Simplify further to get
x[x(x-10)+1(x-10)]
=x[(x+1)(x-10)]
Combine numerator and denominator to see the hole
[tex]\frac{x(x-2)}{x(x+1)(x-10)}[/tex]
From the expression the hole is x
b. vertical assumption
The denominator =0
x³+9x²-10x=0
Differentiate to have
dy/dx= 3x²-18x-10
2nd order derivative is
d2y/d2x=6x-18
Applying limit as x approaches 0
6x-10
Therefore x=-10
c. horizontal assumption the numerator is less than the denominator
x²-2x<x³-9x²-10x
In conclusion, the Hole in the expression is x, The vertical assumption is -10 and the horizontal assumption is that the denominator is greater than the numerator.
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(b)
(i) Factorise 1000x³-y³ completely.
(ii) Hence, without using a calculator, show that 124 is a factor of 992.
Answer:
i. (10-y)(100x^2 +10xy + y^2)
ii. See the explanation
Step-by-step explanation:
i. 1000x³-y³ =
10³x³ - y³ =
(10x)³ - y³ = ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)
(10-y)((10x)^2 +10xy + y^2) =
(10-y)(10^2 * x^2 +10xy + y^2) = ==> simplify
(10-y)(100x^2 +10xy + y^2)
ii. 992/124=
(992-192)/(124-24)=
800/100 = 8
As a result, 8*124=992.
Hence, 124 (and 8) is a factor of 992
which rule must be used to find the number of strings of four decimal digits that have exactly three digits that are 9s?
The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.
What is product rule ?
The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.
To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,
In first digit 1 possible way between 0 to 9
In second digit 1 possible way between 0 to 9
In third digit 1 possible way between 0 to 9
In fourth digit 9 possible ways between 0 to 9
That's mean 1 * 1* 1* 9* 4 = 36
Thus 36 possible ways.
The product rule must be used to find the number of strings of four decimal digits.
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What is a slope grade 11?
In grade 11 math, the slope is a concept that is typically introduced in the study of linear equations and graphing.
The slope of a line serves as a gauge for its steepness. It is defined as the change in y (the vertical distance) divided by the change in x (the horizontal distance) between two points on the line.
A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope rises as it goes from left to right, while a line with a negative slope falls as it goes from left to right. A line with a slope of zero is horizontal, while a line with an undefined slope is vertical.
The slope is often represented by the letter m in the equation of a line, which is written in the form y = mx + b. The slope of the line is the coefficient of the x term (the m in the equation).
For example, the slope of the line represented by the equation y = 3x + 4 is 3, while the slope of the line represented by the equation y = -2x + 1 is -2.
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Create a formula without a function that adds 14 days to the date the client was last contacted.
The Excel formula to enter in cell H4 is = (G4 + 14)
Excel formulas are expressions used to perform computation.
To determine the formula:
From the question,
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Excel formulas begin with the equality (=) sign
So, we have:
= (G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
Complete question:
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
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Excel formulas are expressions used to perform computation.
The date the client was last contacted is in cell G4
14 days is to be added to the content of cell G4
So, the formula is:
G4 + 14
Add bracket
(G4 + 14)
Hence, the formula to enter the cell H4 is = (G4 + 14)
In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4
The ratio in the table for ditance covered in meter to time taken in hour i contant. Let d = ditance covered in 15 hr. Let t = time taken to cover 8 m. Which table how the correct value for t and d? A. B. C. D
The table that shows the correct t and d values is
Distance Covered (m) Time Taken (hr)
8 6
32 15
How to determine the correct values for t and d
The table of values is given as:
Distance Covered (m) Time Taken (hr)
8 6
16 12
32 15
48 18
The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours
When these values are extracted, we have:
Distance Covered (m) Time Taken (hr)
8 6
32 15
The above represents the table that shows the correct t and d values
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Find the values of X and y in the diagram.
What is the 4 type of polynomial?
Answer:
Binomial,Trinomial,Monomal,Linear equation
Step-by-step explanation:
For what value of A is x 5 a factor of x³ 3x² ax 10?
The value of a is ( x - 5 ) factor of f (x) = x ³ - 3x² + ax -10 is found to be 8 .
What is a factor of an equation ?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.
Let f (x) = x ³ - 3x² + ax -10 be the given polynomial.
By factor theorem, ( x - 5 ) is the factor of f (x) , if f ( 5 ) = 0
Therefore,
f ( 5 ) = 3 ( 5 )² + a ( 5 ) - 10 = 0
125 - 75 + 5a - 10 = 0
5a = -40
a = -8
Hence, a = -8
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What form is used to inform the SSS of your illness or injury?
A sickness Notification Form is used to inform the SSS loan of your illness or injury.
The sickness benefit, according to SSS President and Chief Executive Officer Aurora C. Ignacio, is a daily cash payment made for each day a member is unable to work as a result of illness or accident.
In order to be eligible for the program, a member must have made at least three monthly contributions in the twelve months prior to the semester of illness or injury, be confined for at least four days in a hospital or at home, have used all of their current company sick days for the current year, and have informed their employer of their illness or injury.
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keegan bought 5 T-shirts and 2 pairs of shoets for $49.50. Each pair of shorts, s, cost twice as much as each T-shirt, t.
Part A
Which system ot equations can vevused to find the price of the shorts and t-shirts?
(use attachment)
Part B
how much did keegan pay for each t-shirt and each pair of shorts?
Part A
Adding the costs, [tex]2s+5t=49.50[/tex].
Since a pair of shorts costs twice as much as a T-shirt, [tex]s=2t[/tex].
The correct answer is option 3.
Part B
[tex]2(2t)+5t=49.50 \\ \\ 9t=49.50 \\ \\ \boxed{t=5.50} \imploes \boxed{s=11}[/tex]
What is 2.66666666667 as a fraction?
The fraction 2.666666666667 equals [tex]\frac{8}{3}[/tex] .
A fraction is used to represent a portion/part of something larger. It symbolises the equal parts of the whole. A fraction is comprised of two components the numerator and the denominator. The top number is referred to as that of the numerator, and the bottom number is known as the denominator. The denominator specifies the total number of equal parts in a whole, whereas the numerator describes the number of equal parts taken.
2.666667 to fraction conversion:1. Assume that x = 2.666667 (1)
2. Six is the repeating digit.
To the left of the decimal point, put the repeating digit.
In this instance, multiply the decimal point by 10 to move it one place to the right.
Thus,
(x = 2.666667) * 10
Equation 10x = 26.66667 (2)
4. Take Eq. (1) away from Eq (2)
10x - x = 26.66667 - 2.666667
9x = 24
9 divided by both sides
x = [tex]\frac{24}{9}[/tex] or [tex]\frac{8}{3}[/tex]
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Is AAA a similarity theorem?
It is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.
What is the AAA similarity theorem?According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.
Theorem: Two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.
It can also be rephrased as the AAA (angle-angle-angle) similarity theorem.
A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.
Therefore, it is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.
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How to find the height of a pyramid using Pythagorean Theorem?
The Pythagorean Theorem states that because a pyramid's height, slant height, and apothem form a right triangle with slant height as its longest side: (apothem)² + (height)² = (slant height)².
Define the term pyramid?A pyramid is a three shape having a base that is a polygon and triangular sides that come together at the apex, which is located directly just above center of the base.
The distance here between center of the base as well as the apex of a pyramid is its height. The distance between the apex and one of the base's sides is its slant height. The distance between both the center of the base and one of the base's sides is its apothem.Let's start by taking a look at a pyramid with both the height, slant height, the apothem shown in order to demonstrate how to use the Pythagorean Theorem to get a pyramid's height.
a² + b² = c².
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The graph below represents the number of miles, y, that the satellite Space Explorer
flies in a hours. Find the rate of change.
Miles
90,000
85,000
80,000
75,000
70,000
65,000
60,000
55,000
50,000
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
Answer:
0
Space Explorer
Seve
(10,10000)
(5.5000)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Hours
miles per hour
Submit Answer
Answer:
1000
Step-by-step explanation:
answer is 1000 miles per hour
shawna reads a study about exercise that includes the following scatterplot. which answer choice correctly indicates the explanatory variable and the response variable? a.) explanatory variable: exercise response variable: calories burned per minute b.) explanatory variable: weight response variable: exercise c.) explanatory variable: weight response variable: calories burned per minute d.) explanatory variable: calories burned per minute response variable: weight
Shawna finds The correct answer as "explanatory variable: weight response variable: calories burned per minute."
In this scatterplot, the explanatory variable is the weight of the individuals and the response variable is the number of calories burned per minute. The explanatory variable is the variable that is being manipulated or tested in the study, while the response variable is the variable that is being measured or observed.
In this case, the study is examining the relationship between weight and calories burned per minute, with weight being the explanatory variable and calories burned per minute being the response variable. The other answer choices do not correctly identify the explanatory and response variables in the scatterplot.
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How do I solve this?
Given h(x)=3x-5,find h(3)
Answer:
4 is correct
Step-by-step explanation:
The formula for the area of a trapezoid is A = ½h(b₁ + b₂), where h is the height
and b₁ and b2 are the two bases. Rewrite the formula to solve for h in terms of A, b₁
and b₂.
Step-by-step explanation:
that means that we need to transform the equation so that we get a form
h = ...
A = ½h(b1 + b2) | multiply both sides by 2
2A = h(b1 + b2) | divide both sides by (b1 + b2)
2A/(b1 + b2) = h
that's it.
Remember, jed's height is within 3 inches of pablo's height. Describe the solutions in words. Jed can be 67 inches or shorter. At least 67 inches, but at most 73 inches. 73 inches or taller. 67 inches or shorter, or 73 inches or taller.
at least 67 inches, but at most 73 inches if Jed can be 67 inches or
shorter
The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
67 ≤ x ≤ 73 are the solutions to the absolute value inequality |x − 70| ≤ 3
the complete question is
What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3.
Answer: 67 ≤ x ≤ 73
Remember, Jed's height is within 3 inches of Pablo's height.
Describe the solutions in words.
Jed can be
67 inches or shorter.
at least 67 inches, but at most 73 inches.
73 inches or taller.
67 inches or shorter, or 73 inches or taller.
Just found out it's the 2nd choice.
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Answer:
B: at least 67 inches, but at most 73 inches.
Step-by-step explanation:
What is a function example equation?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Example of Function is f(x) = 2x + 5.
What is a function ?A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable).
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Based on Elements
One One FunctionMany One FunctionOnto FunctionOne One and Onto FunctionInto FunctionConstant FunctionBased on Equation
Identity FunctionLinear FunctionQuadratic FunctionCubic FunctionPolynomial FunctionsBased on the Range
Modulus FunctionRational FunctionSignum FunctionEven and Odd FunctionsPeriodic FunctionsGreatest Integer FunctionInverse FunctionComposite FunctionsBased on the Domain
Algebraic FunctionsTrigonometric FunctionsLogarithmic FunctionsExample of Function is f(x) = 2x + 5.
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What kind of sequence is 6 12 24?
As there is a common ratio between each term so this is a geometric sequence.
How geometric sequence is applied in real life?The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.
What is the important property of geometric sequence?In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.
Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.
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• Question 2
In the graph of an inequality, the region below the dashed horizor
What inequality does the graph represent?
The linear inequality represented by the graph is given as follows:
y < 1/4x + 2.
How to define the inequality?The dashed line is a linear function, hence the slope-intercept format of the inequality is given as follows:
y < mx + b.
(the sign is < because the line is dashed and not solid).
In which the coefficients are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value of y when the graph of the linear function crosses the y-axis.The line crosses the y-axis at y = 2, hence the intercept b is given as follows:
b = 2.
When x = -8, y = 0, thus when x increases by 8, y increases by 2, meaning that the slope is given as follows:
m = 2/8
m = 1/4.
Thus the inequality is given as follows:
y < 1/4x + 2.
Missing InformationThe graph of the linear inequality is given by the image shown at the end of the answer.
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Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the result of that transformation into the box under it.
Answer:
g(x) = f(x) + 4 → Graph #5
h(x) = f(x + 4) → Graph #6
k(x) = f(x) - 4 → Graph #4
m(x) = f(x - 4) → Graph #3
Step-by-step explanation:
g(x) = f(x) + 4 → Graph #5
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.
⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).
h(x) = f(x + 4) → Graph #6
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.
⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).
k(x) = f(x) - 4 → Graph #4
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.
⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)
m(x) = f(x - 4) → Graph #3
⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.
⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).
does someone mind helping me with this? Thank you!
Answer:
[tex]y = 2x - 3[/tex]
Step-by-step explanation:
❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
⭐What does "opposite reciprocal" mean?
Opposite reciprocal: the slope of the perpendicular line is the reciprocal of the slope of the line it is perpendicular to and it has the opposite sign of the slope of the line it is perpendicular to.⭐What is slope-intercept form?
One way to write the equation of a line[tex]y = mx + b[/tex]m = the slopeb = the y-interceptWe can find the equation of the perpendicular line by:
Substituting the slope of the perpendicular line into the point-slope form equation using the opposite reciprocalSubstituting the given coordinate into the point-slope form equation to solve for b1. Substituting the slope into the point-slope form equation:
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
The slope of the line the perpendicular like is perpendicular to is [tex]\frac{-1}{2}[/tex].
Therefore, the slope of the perpendicular line is [tex]2[/tex]
Substitute the slope into the point-slope form equation.
[tex]y = 2x + b[/tex]
Now, all we have to do is solve for b.
2. Substituting the given coordinate into the point-slope form equation:
We are given the coordinate (6,9).
[tex]y = 2x + b[/tex]
[tex]9 = 2(6) + b[/tex]
[tex]9 = 12 + b[/tex][tex]-3 = b[/tex]
Substitute "b" into the point-slope form equation.
[tex]y = 2x + 3[/tex]
Someone please help!! (screenshot attached)
The number of CDs that can be bought are { 5, 4, 3, 2, 1 }.
What is an inequality ?
A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality emerges from an imbalance.
Given, No. of CDs = x
A CD costs $11 and He has total $60.
So, According to the question,
No. of CDs × Cost of each CD ≤ 60
x × 11 ≤ 60
11x ≤ 60
x ≤ 60/11
Since the number of CDs can't be in fraction and The maximum CDs can be bought is 5.
So, The possible No. of CDs that can be purchased are { 5, 4, 3, 2, 1 }
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Identify the number fo zeros for each function. Show your work.
1. P(x)=x³+2x²-12x+1
2.P(x)=2x⁵-5x+10
3.P(x)=3x⁴+2x
The number of zeros for each function is given as follows:
1. Three zeros.
2. One zero.
3. Two zeros.
How to obtain the number of zeros for each function?The number of zeros for each function is obtained looking at the graph of the function, counting the number of times that the function either touches or crosses the x-axis, which is the horizontal axis.
Thus the graph for each function is plotted, using a graphing calculator, as shown by the image at the end of the answer, and the number of zeros for each of the functions is given by the number of times that the function touches or crosses the x-axis.
The colors of each function are given as follows:
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What does congruent mean square?
Answer:
All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.
hope this helps
mark me brainliest
Step-by-step explanation:
Write two inequalities to compare a and b how do you know?
To compare two numbers, a, and b, we can write two inequalities:
a < b when a is less than b
a > b when a is greater than b.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We may write two inequalities to compare two numbers, a and b:
a < b
a > b
If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.
We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.
For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.
On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.
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