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 is the other name for factorization method Mcq?
Answer:
Another name for factorization method Mcq is Doolittle's Method
Step-by-step explanation:
Hope it helps!
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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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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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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How do you get A+ in 7th grade?
In seventh grade, you received an A+:
1. Immediately after class, go through your notes.
2. Spend the most of your time studying throughout the day.
3. Read ahead rather than catching up.
4. Instruct someone else on the material.
5. Establish a study schedule from the start.
What is grading system?Grading in education is the practice of assigning standardized grades to students based on their degree of success in a course. Grades can be assigned in the form of letters, a range, a percentage, or a number out of a potential total. Grades are averaged in certain countries to get a grade point average. A 10-point grading scale is commonly used in Indian institutes (though some use a 4-point scale). Your GPA is derived by dividing the entire amount of your grades by the number of credits you took.
Here,
You get A+ in 7th grade:
1. Review your notes from class immediately after.
2. Do the bulk of your studying during the day.
3. Try to read ahead rather than play catch-up.
4. Teach the material to someone else.
5. Create a study schedule from day one.
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Solve for y
6x+8y=10
What is the golden rule of algebra?
Answer: To keep both sides of the equation balanced
Step-by-step explanation:
The Golden Rule states that what you do to one side of an equation, that side being what is on one side of the equal sign, you must do to the other side. This is very important.
Which of the relations given by the following sets of ordered pairs is a function?
A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))
C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))
D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}
Answer:
[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
Step-by-step explanation:
Given:
Which of the relations given by the following sets of ordered pairs is a function?
A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))
B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))
C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))
D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}
Solve:
Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.
Summary:
x value can't be duplicate but y can - in a working function
Hence, based on what we see in the answer choices;
[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.
[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)
[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)
[D] ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)
RevyBreeze
Willing to give 15 points for help please help me
Note that the above problems are solved using the knowledge of the sum of angles in a triangle.
10) when computed, x = 13°
11) when computed m∠S = 158°
12) when computed, ∠P = 115.625°; ∠Q = 21.125°; ∠R = 43.25°
13) when computed, angles L, J, K is 52°, 45°, 83° respectively.
14) When computed,
∠b = 108°
∠c = 36°
∠d = 36°
What is the sum of angles in a Triangle?Note that the Triangles Theorem posits that the sum of Angles in a Triangle = 180°
10) To solve for x, we know that:
the triangle is an Equilateralall the angles are equalAll the angles sum up to 180°one of the angles is given as 8x-44°Given the above, we can state:
8x-44 = 180/3
8x-44 = 60
8x = 60 +44
x = 104/8
x = 13°
Thus x = 13°
11) For this problem, the key to solving for x is to note that the triangle is isosceles.
This means that,
15x - 31 = 9x + 11
Thus, collecting like terms, we have:
15x-9x = 11+ 31
24x = 42
x = 42/24
Thus,
x = 1.75
Since we are looking for m∠S, we can arrive at this by removing (15x - 31 ) + (9x + 11) from 180° based on the rule of the Sum of Angles in a triangle.
That is:
180 - (15x - 31 ) + (9x + 11) = m∠S
To do this, we must impute the value of x in to the above equation:
⇒ m∠S = 180 - ((15 * 1.75) - 31 ) + ((9 * 1.75) + 11)
⇒ m∠S = 180 - (-4.75) + 26.75
m∠S = 180 - 22; thus
m∠S = 158°
12) <M, <P, <R, recall that the sum of the interior angles of triangle MPR will add up to 180 degrees
so <M + <P + <R = 180
We have ∠P is 14 less than five times x = 5x-15
∠Q is five less than x = x - 5
∠R is nine less than twice x =2x - 9
Recall the angle sum property of the triangle: The sum of all angles of a triangle is 180°
So, 5x -15 + x - 5 + 2x - 9 = 180°
Collect like terms to get
8x - 29 = 180
8x = 180+29
Thus,
x= 26.125
So,∠P = 5x-15
=5 (26.125) -15
∠P = 115.625°
∠Q =x-5
=26.125 - 5
∠ Q =21.125°
∠R = 2x - 9
=2(26.125)-9
Thus
∠R = 43.25°
To confirm, if the above ∠ sum up to 180°, we say
Check 43.25+21.125+115.625
⇒ 43.25+21.125+115.625 = 180° is TRUE.
13) To solve for ∠J, ∠K and ∠ L, recall that
The sum of the interior angles of triangle JKL will add up to 180 degrees
so <J + <K + <L = 180
L = measure of angle L
J = measure of angle J = L - 7
K = measure of angle K = 2L - 21
Thus, L + L-7 + 2L - 21 = 180; Collect like terms and we have
4L - 28 = 180
4L = 208
L = 52°,
If L is 52 then
J = L - 7 = 52 - 7
= 45°
K = 2L - 21 = 2(52) - 21
= 83
To check that they all sum up to 180° we say:
52+ 45+83
= 180°
14)
The sum of angle in a triangle is 180 degrees
Hence <b + <c + <d = 180
13x-35 + 5x - 19 + 2x + 14 = 180
13x+5x+2x-35-19+14 = 180
20x-40 = 180
20x = 180 + 40
20 x = 220
x = 220/20
x = 11
Get <b
<b = 13x-35
<b = 13(11) - 35
<b = 143-35
<b = 108 degrees
Get <c
c =5x-19
<c = 5(11)-19
<c = 55-19
<c = 36degrees
Get <d
<d = 2x+14
<d = 2(11) + 14
<d = 22+14
<d = 36 degrees
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Full Question for Number 14:
In ΔBCD if bc =bd angle b = 13x-35 angle c =5x-19 and angled d = 2x+14 find x and the measure of each angle
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:
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°
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
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.
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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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
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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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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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.
what is trigonometric ratios ?The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios. Trigonometric ratios can be used to calculate the lengths of one (or both) of the acute angles in a right triangle if you know the lengths of two of its sides.
given
sinθ = - 4 / 5
cosθ = 3/5
tanθ = -4/3
secθ = 5/3
cotθ = -3/4
cosecθ = - 5/4
as Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.
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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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to translate an expression from words into a mathematical expression, _______________
Answer: to sum up
Step-by-step explanation:
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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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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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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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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What is an exponential function for 0 3?
The exponential function cannot be found.
To find an exponential function, f(x)=[tex]a^{x}[/tex], containing the point, set f(x) in the function to the y value 3 of the point, and set x to the x value 0 of the point. 3 = [tex]a^{0}[/tex]
Solve the equation for a.
Let's rewrite the equation,
[tex]a^{0}[/tex] = 3
Anything with 0 in power is 1
1 = 3
As, 1 ≠ 3
There are no solution.
Since there is no real solution, the exponential function cannot be found.
Hence, the exponential function cannot be found.
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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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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?"
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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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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