A- The scale factor from Polygon A to Polygon B is 2.
B- The missing length of each side marked with ? in Polygon B is 3, 5
C- The measure of each angle marked with ? in Polygon A is 53°, 82°
Given that,
A- scale factor = side A/ side B = 5 / 2.5 = 2
B- Length of each missing sides= 1.5*2 = 3 and 2.5* 2 = 5
C- Since the scale factor does not change the measure of the angles, the missing angles remain the same that is 53° and 82°
Thus,
The scale factor from Polygon A to Polygon B is 2.
The missing length of each side marked with ? in Polygon B is 3, 5
The measure of each angle marked with ? in Polygon A is 53°, 82°
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The y-intercept of function h(z) = −3(z+13)² - 28 is _____The domain is ________
and the range is______
The domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.
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.
The given functions are h(z)=-3(z+13)²-28.
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): None
y-intercept(s): (0,-535)
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞),{x|x∈R}
Range: (-∞,-28],{y|y≤-28}
Therefore, the domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.
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find the value of the variable
Answer: 25
Step-by-step explanation:
The sum of all exterior angles = 360
Using this, we can get the equation
2x+20+x+40+3x+6x=360
12x+60=360
12x=300
Simplify, and you get
x = 25
What are the 5 types of inequality math?
The four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.
What is meant by inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.
A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.
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y less than or equal to 5
The equation should be rearranged such that "y" is on the left and everything else is on the right.
What does less than or equal to mean in math?Plot the "y=" line, using a solid line for y or y and a dashed line for y or y>. For "more than" or "less than" indications, shade above the line (y> or y), or below the line variable (y or y).
The symbols for less than and less than or equal to are "" and "," respectively. In contrast to less than or equal to, which requires that the variable or quantity be either equal to or less than the specified limit, less than means that the variable or quantity must have a value lower than the specified limit. There must be a difference between a and b's values.
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The complete question is " How do you graph the inequality y≥−5?"
You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.
a. Write an exponential equation to determine when the balance of the account will be $1500
b. Solve the equation.
Answer:
a. 1500 = 1000 × 1.05^x
b. 1500 = 1000 × 1.05^x
Divide both sides by 1000
1500/1000 = 1.05^x
Take the natural log of both sides
ln(1500/1000) = ln(1.05^x)
ln(1.5) = x ln(1.05)
x = ln(1.5) / ln(1.05)
x = 5.12 years
14. Select all the expressions that are
equivalent to 28c-56
A. 7(4c-8)
B. 28(c-2)
C. -2(14c-28)
D. - 7(4c + 8)
E. - 7(8-4c)
The equivalent expressions are 7(4c - 8), 28(c - 2), - 7(8-4c). Options A, B, E
What are algebraic expressions?
Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.
They are also composed of mathematical operations, such as;
SubtractionMultiplicationDivisionFloor divisionAdditionBracket, etcEquivalent expressions are those with the same solution but different arrangement of values, we have the expression;
28c-56
Let's factor the terms, we get;
7(4c - 8)
Also,
28(c - 2)
Hence, the expressions are 7(4c - 8), 28(c - 2), - 7(8-4c)
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Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.Sketch a line showing Lin's original plan on the axes. Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph. What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
No. of pages read on day of planning are represented by vertical intercept.
The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.
What is slope-intercept form of line?The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:
y = mx + c.
Given,
No. of pages Lin read on day of planning = 30
No. of pages she plans to read everyday = 40
If total pages are y for x days then,
y = 40x + 30
which is the original plan of Lin.
comparing it with slope-intercept form of line
y = mx + c
slope m = 40
vertical intercept of original plan c = 30 unit
slope m represents the no. of pages read everyday.
vertical intercept represents the no. of pages read on day of planning.
vertical intercept c' of line drawn by Lin = 40 unit
Comparing intercept of original plan to line drawn by Lin
= |c - c'|
= |30 - 40|
= 10 unit
Hence, the vertical intercept represents the no. of pages read on day of planning.
There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.
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Write a function rule to represent the situation. the total cost C for p pounds of lithium each pound costs $3.89 Write a function rule using C and p as variables. enter your response here (Type an equation.)
Answer: C = P$3.89
Step-by-step explanation:
how will the interval compare to the interval calculated for the same percentage if a normal distribution is assumed and the Empirical Rule is used?
The 68-95-99.7 rule, also known as the empirical rule, is a shorthand for remembering the percentage of values in a normal distribution that lie within an interval estimate: 68%, 95%, and 99.7% of values lie within one, two, and three standard deviations of the mean, respectively.
What is empirical rule?The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule stating that for a normal distribution, nearly all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
The Empirical Rule states that 99.7% of data from a normal distribution is within 3 standard deviations of the mean.
68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations, according to this rule.
Three-sigma limits that follow the empirical rule are used to define the upper and lower control limits in statistical quality control charts and risk analysis such as VaR.
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A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 403 gram setting. Is there sufficient evidence at the 0.01 level that the bags are underfilled? Assume the population is normally distributed.
State the null and alternative hypotheses for the above scenario.
The null hypothesis is H0: p = 403
The alternative hypothesis is given as: H1: p < 403
What is the alternative hypothesis and the null hypothesis?The null hypothesis is a statement that there is no significant difference or relationship between two groups or variables. It represents the status quo or the default assumption that there is no effect.
The alternative hypothesis is the statement that there is a significant difference or relationship between the groups or variables. It is the opposite of the null hypothesis and represents the research hypothesis or the claim that you are trying to test.
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Choose one item of interest to you in the Historical Pricing Chart on the next page.
2. Calculate the percent of change of the item's price each decade, and use your results to determine the average rate of change from 1980-2020.
3. Comment on the trend in your item's percent of increases.
4. Go shopping! Find the average current price of your item online, in the newspaper, or locally by looking at the price when you go to the store in the next day or two. Does the current price match the trend from 1980-2020 that you identified? Explain your thinking.
5. Create a line graph or other visual model to show the pricing trend. Be sure to include the current price in your model.
6. Predict the item's price at a future date. Use your calculations and visual model to justify your prediction.
7. Organize your analysis, prediction, explanations, and visual model in a brief news article. Your completed article will be submitted as your portfolio assessment.
I decided to use Gallon Of Gas
The rate of change is 19.8 cents annually.
The average cost of a gallon of gas is $3.744 this year (2021).
Does It Match The Trend ?
Gas prices increased significantly in 2021, almost by $2 in some states, due to disease.
Gas prices forecast for the coming year!
Capital price at the average rate of change and economic fixtures: $4 per gallon (Real-Life Problems)
Detailed explanation:
Determine the average rate of change from 1960 to 2000 by computing the percentage change in the item's price for each decade.
A simple reveals the anticipated rise in petrol prices over the coming ten years.
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I made the decision to utilise a gallon of gas. The annual change is 19.8 cents. This year, a gallon of gasoline costs on average $3.744. (2021).
What is the percent of change of the item's price each decade?Disease caused a substantial rise in gas prices in 2021, almost by $2 in some places. Future gas prices, the average rate of change in capital prices, and economic indicators: At $4 per gallon (Real-Life Problems). By calculating the price change percentage for each decade, you can calculate the overall rate of change between 1960 and 2000.
A quick calculation shows how much gasoline prices are expected to climb over the next ten years. Subtract the original price from the new price to determine the percent change, then divide the result by the original price and multiply by 100. We must now calculate the percentage change when 25 is raised to 45. To determine the percentage change, we can easily use the formula.
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Lia i currently taking phyic a one of her elective in chool. Her grade at the end of the year i determined by the average of four exam, each worth 100 point. On her firt tet he got an 84, on her econd he got a 92, and on her third an 80. What mut he core on her fourth exam to get exactly 80% in the coure?
a. 60
b. 64
c. 84
d. 85
64 marks must he score on her fourth exam to get exactly 80% in the course.
From the question, we are informed that Lisa is currently taking physics as one of her electives in school and that her grade at the end of the year is determined by the average of four exams, each worth 100 points.
First test = 84,
Second test = 92
Third test = 80
Forth test = y
And,
The fourth test is denoted by y.
Since we are told that she must get exactly 80% in the course and she took 4 exams, that means her total score will be: = 80 × 4 = 320
Therefore,
⇒ 84 + 92 + 80 + y = 320
⇒ 256 + y = 320
⇒ y = 320 - 256
⇒ y = 64
The fourth exam's score is 64.
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What are the 10 types of equation?
The 10 types of equation used in the mathematics are explained.
What are the 10 different types of equations?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.
For instance, the equation 3x 5 = 14 consists of the two expressions 3x 5 and 14, which are separated by the 'equal' sign.A linear equation is an algebraic equation. Each term in a linear equation is either a constant or the result of a constant plus one variable.In the case of a linear equation with two variables, the graph is a straight line.Equation with one variableEquation with two variablesMonomial EquationsBinomial EquationTrinomial EquationQuadratic equationTrigonometric equationRadical equationExponential equationRational equationThus, the 10 types of equation are mentioned.
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Match the notation on the left with the term that best describes it.
1. AB
2.
3.
4.
5.
6.
7.
AB
OC
AC
CD
Point C
Point O
a.
b.
C.
d.
e.
f.
center
chord
diameter
radius
point of tangency
tangent
secant
D
B
You Try
A
Answer: AB : secant
OC : radius
AC : tangent
CD : chord
Point C : center
Point O : Point of tangency
D B You Try A : Not enough information provided to match the notation.
Step-by-step explanation:
The slope of the line segment A-D is the same as the slope of the line segment A-F. What are the two line segments that make this proportion equal?
What is the change of base property?
The change of base property is a formula that makes it possible to express a logarithm in terms of logs expressed in a different base.
It is possible to express a logarithm in terms of logs stated in a different base using the change of base property formula. This is especially useful when evaluating a log to a base other than 10 or e using a calculator. X, a, and b are all taken to be positive. The base change property can be used to simplify equations with different bases for the logarithmic terms. All the logarithmic terms of an equation with logarithmic functions should have the same base in order to be solved.
Examples given below:
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PLS HELP FAST! Calculate the average rate of change on the interval
The average rate of change for the quadratic function in the graph is 1
What is average rate of change of quadratic function?The proportion of change along the y-axis to change along the x-axis represents the average rate of change between the two points.
Since the graph of a quadratic function is curved and lacks a constant rate of change between any two distinct locations, it is referred to as the average rate of change rather than the slope.
The average rate of change between points (2, 0) and (3, 1) is
= (0 - 1) / (2 - 3)
=-1 / -1
= 1
The average rate of change within the interval 1 to 3 is 1
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Which of the following is a solution of equation 3x² 13x 14 0?
The solution of the given equation 3x² + 13x + 14 = 0 is given by :
option b . x = -2.
As given in the question,
Given equation is equal to :
3x² + 13x + 14 = 0
Solve the given equation by method of splitting middle term we get,
3x² + 13x + 14 = 0
⇒ 3x² + 6x + 7x + 14 = 0
⇒ 3x ( x + 2 ) + 7 ( x + 2 ) = 0
⇒ ( 3x + 7 ) ( x + 2 ) = 0
⇒ ( 3x + 7 ) = 0 or ( x + 2 ) = 0
⇒ x = -7/3 or x = -2
From the given options:
Option b . x = -2 is the solution of the equation 3x² + 13x + 14 = 0.
Therefore, the solution of the given equation 3x² + 13x + 14 = 0 is equal to : option b. x = -2.
The above question is incomplete, the complete question is:
Which of the following is one of the solution of equation 3x² + 13x + 14 = 0?
a. x = 2 b. x = -2 c. x = 3 d. x = -3
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3. Andre and Elena are saving money. Andre starts with $50 in his savings account and adds $5 per week. Elena starts with $5 in her savings account and adds $10 each week. a. After four weeks, who has more money in their savings account? Explain how you
In given word problem Andre has more money than Elena after four weeks.
What is word problem?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Here,
Initial investment of Andre= $50
She add $5 per week for next 4 weeks , then
=> 4×5 = $20
Then total savings of Andre = $50+$20=$70.
Now Initial investment of Elena = $5
She adds $10 for each 4 weeks then
=> 10×4=$40.
Now total savings of Elena = $40+$5=$45.
Here $70>$45.
Hence after 4 weeks Andre has more money than Elena.
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1. Which of the following would be in the solution set to the system of inequalities given below?
y>4x+7
8x-2y> 10
a No solution
b (-4,1)
c Both (-4,1) and (6,2) are solutions
d (6,2)
Option A will be the solution set of given linear inequalities.
What exactly are linear inequalities?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol ((≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.
Hence,
For given inequalities
y>4x+7
8x-2y>10
there will be no solution as the graph of these inequalities does not coincide anywhere.
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(-4,0) is the solution of the set to the system of inequalities
What is Inequality?
A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given two inequalities are
y<-3x-6 and 4x-2y<-8
Let us check for (-4, 0)
0<-3(-4)-6
0<6
4x-2y<-8
4(-4)-2(0)<-8
-16<-8
So (-4, 0) is the solution of the inequalities.
Now let us check for (0, 2)
replace y value as 2 and x as 0.
2<-3(0)-6
2<-6
Which is not true.
Hence, (-4,0) is the solution of the set to the system of inequalities.
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consider a square based straight pyramid. suppose that the base is a square with sides 22 in long, and all other edges are 61 in long. find an approximate.value if the angle.found between the base and a triangular face
The approximate angle between the base and a triangular face is; 79.43°
How to use pythagorean theorem?The dimensions of the pyramid are;
Side Length; a = 22 inches
Edge length; b = 61 inches
Using Pythagoras theorem:
h = height of pyramid
h = √(b² - 1/2a²)
h = √(61² - 22²/2)
h = √(3479)
h = 58.98
Slant height :
L = √(58.983² + 22²/4)
L =√(3479 + 121)
L = 60
Sinα = h/L
α = sin⁻¹(58.983/60)
α = 79.43°
That is the approximate angle found.
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wbat is the y- intercept of this graph?
Answer:
Step-by-step explanation:
To find the y-intercept on a graph, you must look at where the line intercepts through the y-axis.
For this problem it would be 16
An Isosceles triangle has two congruent sides. the first side is expressed by x+2 and the second side is expressed by 2x-25 what is the value of X
The value of x is 27
How to determine the value
From the information given, we have that the triangle is an isosceles triangle.
The properties of an isosceles triangle are;
It has two equal sidesTwo equal anglesIt has three edges and three verticesSum of internal angles is 180We have that;
First side = x + 2
Second side = 2x - 25
Equate the two sides, we get;
x+ 2 = 2x - 25
collect like terms
x - 2x = - 25 - 2
subtract like terms
-x= -27
make 'x' the subject
x = 27
Hence, the value is 27
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Can 8 7 and 15 form a triangle?
It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 8 and 7
8 + 7 = 15
15 = 15
Now we add 8 and 15
8 + 15 > 7
23 > 7
Now we add 7 and 15
7 + 15 > 8
22 > 8
It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).
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What is called XYZ in algebra?
Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.
A coordinate plane is defined.The phrase "coordinate plane" describes a two-dimensional area made up of two rational numbers. It appears at the point where the X and Y axes connect, called the origin. A coordinate grid's numbers can be used to find points.
Here,
The x, y, and z axes of the Cartesian coordinate system,
which is used to represent three-dimensional space, are three axes that are mutually perpendicular to one another.
The origin is the location where the three axes converge.
Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.
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Drives Co. sells portable hard drives. They can sell 905 drives when the price is $66/drive, and they can sell 800 drives when the price is $87/drive. If x represents the number of drives sold, determine the following. a. Drive Co.'s revenue function: R(X) = b. The price per drive when revenue is maximized: $ c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250: $
a. Drive Co.'s revenue function R(X) = (-x^2/5)-247x.
b. The price per drive when revenue is maximized is $370.6.
c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250 is $6030.
What is a function?
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
Drive Co. sells portable 905 hard drives when the price is $66/drive and can sell 800 hard drives when the price is $87/drive.
Let p be the price of hard drive and x be the number of hard drives.
When x = 905, then p = 66.
So, (x1,p1) = (905,66)
Similarly, when x = 800, then p = 87.
So, (x2,p2) = (800,87)
So, the equation of line between x and p is given as -
p-p1=[(p2-p1)/(x2-x1)}(x-x1)
Plugging in the values -
p-66=[(87-66)/(800-905)](x-905)
p-66=(21/-105)(x-905)
-105p+6930=21x-19005
-105p-21x=-19005-6930
-105p-21x=-25935
p=(-21x/105)-247
p=(-x/5)-247
So, the price function p(x) = (-x/5)-247.
Now, derive the revenue function -
Revenue = Number of drives × price per drive
Revenue = x · p(x)
Revenue = x · (-x/5)-247
Revenue = (-x^2/5)-247x
Therefore, the revenue function R(x) = (-x^2/5)-247x.
For maximum revenue -
dR/dx = R'(x) = 0 and R''(x)<0
dR/dx = -2x/5-247 = 0
-2x/5 = 247
x = -1235/2
x = -617.5
Therefore, the number of drives at maximum revenue is 618 drives.
The price per drive is -
p(618) = {-618/5}-247
p(618) = -370.6
Therefore, the price per drive is $370.6.
Now, the profit S(x) = Revenue R(x) - Total Cost C(x)
C(x) = fixed cost + variable cost
Variable cost = number of drives × price per drive
C(x) = 250 + 179x
Substituting the values -
S(x) = [(-x^2/5)-247x] - [250+179x]
S(x) = (-x^2/5)-68x-250
In order to get maximum profit differentiate the equation and equate it to 0.
dS/dx = 0
dS/dx = -2x/5-68 = 0
-2x/5 = 68
x = 340/-2
x = -170
d^2S/dx^2 = -2/5<0
So, maximum profit will be at x = 170.
S max = S(170) = [(170)^2 /5] - 68 (170) - 250
= 5780 - 11560 - 250
= -6030
Therefore, the maximum profit earned is $6030.
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One side of a right-angled triangle is f. The other two sides are 2 times bigger than f and 7 smaller than f. Write an expression for the perimeter of the triangle in its simplest form.
Answer:
4f-7
Step-by-step explanation:
You want the perimeter of a triangle whose side lengths are f, 2f, and f-7.
PerimeterThe perimeter is the sum of the side lengths:
P = f +2f +(f -7)
P = 4f -7
The perimeter of the triangle is 4f-7.
__
Additional comment
No such triangle can exist. The sum of the two shortest sides is f+(f-7) = 2f-7, which is not greater than the longest side, 2f. The triangle inequality is not satisfied.
solve................... 5(x+3)<60
x<9
5(x+3)<60
5(x+3)/5<60/5 .................... Dividing by 5 into both the sidesx+3< 12
x+3 - 3< 12-3 ......... Subtracting 3 from both sidesx<9
Which simply means x will always be less than 9 in this case.
These are the Simple inequation in one variable which can be simply solved by operating the same operations on both sides to get a simplified answer.
We follow the same algorithm even for equations where the left side and right sides are equal so we simply transfer the left digits to the right side simply by changing their operational signs like + will be -, * will be /.
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What is the slope of y =- 3x 10?
Answer:
The Slope would be 3
What is m/M?
Enter your answer in the box.
Answer: ∠M = 98°
Step-by-step explanation:
Given:∠M = (3x-16)°
∠N = x°
∠O = (x+6)°
Sum of all angles in a triangle is 180°
Therefore, 180° = ∠M +∠N +∠O, substitute the given values
180° = (3x-16)° + x° + (x+6)° (add/combine like terms)
180° = (3x+x+x)° + (-16+6)°
180° = (5x)° + (-10°)
180° + 10° = (5x)° ( divide both sides by 5)
190°/5 = (5x)°/5
38° = x°
IF ∠M = (3x-16)°, substitute x°=38°,
Therefore, ∠M = 3(38)-16
∠M = 114 - 16 = 98°