Two angle and an include side are congruent, hence by the ASA postulate triangle AEB congruent to triangle CED.
ASA similarity theorem: Two triangles are similar if two corresponding angles of one triangle are congruent to the two corresponding angles of another triangle. Also, the corresponding sides are proportional. ASA similarity is mostly known as the AA similarity theorem.
Statement: Line segments AE and EC are equal.
Reason: Given
Statement: angle A is congruent to angle B.
Reason: Given
Statement: Angles AEB & CED are equal.
Reason: vertically opposite angles are equal.
Hence, two angle an include side are congruent.
Triangles AOB & CED are congruent.
Reason: ASA Postulate.
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3. label the following points on the ppc: a. a point indicating inefficiency/unemployed resources, labeled as m b. a point indicating efficiency, labeled as n c. an unattainable point, labeled as p 4. calculate the opportunity cost of a movement between each of the following points:
PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.
The PPF is a boundary between the attainable and unattainable combinations of pizza and pasta.
Points inside the PPF and on the PPF are attainable and points outside the PPF are unattainable.
Unattainable points are outside the PPF.
Because the PPF shows the limits to production, it separates attainable combinations from unattainable ones.
PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.
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What is the reference angle for the given angle measure drawn in standard position?
The reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6What is a radian?The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics
Given are the angles as shown in the figure.
We can write the reference angles as -
{ 1 } -- 34π/3 → -34 x π/3 → π/3
- 34π/3 → π/3
{ 2 } -- 5π/12 → -5x π/12 → π/12
- 5π/12 → π/12
{ 3 } -17π/6 → 17 x π/6 → π/6
17π/6 → π/6
Therefore, the reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6To solve more questions on reference angles, visit the link below -
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6x + 4y = 7Kx + 8y = 7What is the value of K?
The value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
What are equations?Two things are equal, according to an equation.
It will be written with the equals sign "=" as in x+2=6.
What is on the left (x + 2) is equal to what is on the right ((6)), according to that equation.
A remark like "this equals that" can be compared to an equation.
So, we have the equations:
6x + 4y = 7
Kx + 8y = 7
Now, we know that both equations are equal to 7. so, we can write it as:
6x + 4y = Kx + 8y
Solve with subject K as follows:
6x + 4y = Kx + 8y
Kx - 6x = 4y - 8y
(K-6)x = -4y
k-6 = -4y/x
k = (-4y/x) + 6
Therefore, the value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
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how many total atoms of each element are present in the following formulas?
3 CaCl₂
Tap in the fields to enter the answers directly OR
tap on the Number Pad icon to use our built-in Number Pad.
To ascertain an element's molar mass, use the periodic table. Calculate the quantity of moles by dividing the supplied mass in grammes by the molar mass.
How many types of atoms are in an element?One type of atom makes up each individual element. Protons, neutrons, and electrons, three additional subatomic particles, make up atoms. Chemical reactions allow elements to interact with one another to create molecules.The number of atoms can be calculated by multiplying the number of moles by Avogadro's number. An atom's atomic number is equal to the quantity of protons in its nucleus or the quantity of electrons in an electrically neutral atom.CaCl2 contains 3 atoms. We can determine the number of atoms in a compound by counting the subscripts after each ingredient. Counting moles is the initial step in calculating the number of atoms.To learn more about element's refer to:
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on monday the sun was out for 3 3/10 hours. on tuesday the sun was out for 6 1/5 hours. how much longer was the sun out on tuesday than monday
Using Subtraction, The Sun was out for 7 1/30 hours more than Monday.
To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
Finding the difference between two numbers is what it entails. The icon is as follows: (minus). We take a number and divide it by a smaller number in this operation.
On monday the sun was out for 3 3/10 hours.
On tuesday the sun was out for 6 1/5 hours.
the sun out on tuesday than monday =
Using Subtraction,
⇒ 31/ 3 - 33/10
⇒ 310 - 99/30
⇒ 211/30
⇒ 7 1/30 hours
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You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers union) and mail a questionnaire to 2,500 teachers chosen at random from this list. In all 1,347 teachers return the questionnaire. In this situation, the sample is: a. the 1,347 teachers who mailed back the questionnaire b. the 2,500 teachers to whom you mailed the questionnaire. call members of the National Education Association. d. all American school teachers. e. all American school students.
You want to know the opinions of American school teachers about establishing a national test for high school graduation then correct option is D) all American school teachers.
In statistics, A population is a very large set of individuals or values that belong to a specified group established by researcher.
A sample is a subset of population that represents the entire population in research.
Given : We want to know the opinions of American school teachers about establishing a national test for high school graduation.
Clearly , by the above definition
Population = all American school teachers.
You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list.
sample = 2500 teachers chosen at random from this list.
Hence, the intended population is all American school teachers.
Thus , the correct answer is D) all American school teachers.
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A three-column table is given.
Part 8 B D
Part 10 15 45
Whole A C 72
What is the value of C in the table?
18
24
27
71
The value of C in the table will be 24.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, a table of proportional data below,
Part 8 B D
Part 10 15 45
Whole A C 72
Since the two-part will be proportional to the whole.
thus,
=> c /72 = 15/45
=> C = 72/3
=> C = 24
Therefore, the value of C in the given table will be 24 as pe the proportionality.
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Type the expression that results from the following series of steps: Start with x , subtract 4, divide by 5, then add 9.
Answer:
Step-by-step explanation:
x-4/5+9
The following shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and area of the shaded part. Give your answer as a completely simplified exact value in terms of pi. (no approximations) FIRST PERSON TO ANSWER GETS 100 POINTS
Answer:
Perimeter = 8π cm
Area = (32π - 64) cm²
Step-by-step explanation:
ABCD is a square.
Therefore:
AB = BC = CD = DA = 8 cmArea = 8 × 8 = 64 cm²PerimeterThe perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.
The arcs AC are quarter circles of a circle with radius 8 cm.
Therefore the perimeter of the shaded area is:
[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]
AreaTo find the area of the shaded area, subtract the two unshaded areas from the area of the square.
As the two unshaded areas are congruent we only need to find the area of one unshaded area.
The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).
[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]
Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:
[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]
For which of the following functions is the chain rule an appropriate method to find the derivative with respect to x ?y=sin(3x2)y=extanxy=18x4−2x
The chain rule tells us where to search the derivative of a composite function.
d/dx[f(g(x))] =f'[f[g(x)g'(x).
A function is composite if you can write it as f(g(x)) In other words, it is a function within a function, or a function of a function.
Following steps should be followed to find chain rule:
1: Recognize the chain rule: The function needs to be a composite function, which implies one function is nested over the other one.
2: Know the inner function and the outer function respectively.
3: Determine the derivative of the outer function, dropping the inner function
4: Obtain the derivative of the inner function Step
5: Multiply the outcomes from step 4 and step 5 respectively.
6: Simplify the obtained chain rule derivative.
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?The function is decreasing on the interval (0, [infinity]).The function is decreasing on the interval (–[infinity], 0).The function is increasing on the interval (0, [infinity]).The function is increasing on the interval (–[infinity], 0).
The function is decreasing on the interval (0, [infinity])
The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.
The derivative of h(x) is -2/sqrt(x).
For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.
For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.
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In addition to therapy, anti-depressant drugs are used in the treatment of depression. The data Type numbers in
below are from a study comparing two anti-depressant drugs. A baseline measurement for symptomatic behavior for depression is taken. After treatment with medication, another measurement taken. The data given in the table is for improvement which is for the reduction
in symptomatic behavior.
Drug A 2.30 2.39 4.03 2.90 3.45 3.29 3.82 3.27 4.08 1.83 4.07 5.06
Drug B 9.31 7.37 4.50 6.00 7.22 4.21 5.25 5.99 8.37 3.82 3.69 3.40
The primitive data type number has the entry 1, or 1, in the database dictionary.
What is a number data type?The database dictionary's entry for the number data type, which is a primitive data type, is 1, or 1. It is possible for a number to be a whole number, a positive or negative number, or a floating point number, and it can also denote an amount.
Numbers are stored as numeric data types in database columns. Exact numeric kinds, values where the precision and scale need to be retained, are normally the categories into which these data types are grouped. There are six distinct sorts of numbers: INTEGER, BIGINT, DECIMAL, NUMERIC, NUMBER, and MONEY.
Integral, Floating Point, Character, Character String, and Composite types are the five fundamental categories of data types recognized by the majority of current computer languages. Within each of these broad categories, numerous particular subtypes are established.
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Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept
f(x) = (x + 1)(x - 5)(x - 1)^2
The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.
What is polynomial function?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5. A polynomial is a function that has the formula f(x) = anxn + anxn + anxn+1 +... + a2x2 + a1x + a0. The highest power of x in the formulation of a polynomial is its degree. Constant (non-zero) polynomials, linear polynomials, quadratics, cubic, and quartics, respectively, are polynomials of degree 0, 1, 2, 3, and 4.Given
f(x) = x²(x+2)
To find the x-intercepts ⇒ f(x) = 0
∴ x²(x+2) = 0
∴ x² = 0 OR x+ 2 = 0
∴ x = 0 or x = -2
So, the x-intercepts will be at x = 0 , -2
We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)
The attached figure represents the graph of f(x)
As shown in the figure:
1) The graph crosses the x-axis at x = -2
2) The graph touches the x-axis and turns around at x = 0
The complete question is,
Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
f(x) = x2(x + 2)
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which correctly explains the number of solutions of the following system of linear equations -2x+2y=10
y=x+5
For the system of equations, there are infinitely many solutions exist.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equations are,
⇒ - 2x + 2y = 10 .. (i)
⇒ y = x + 5 .. (ii)
Here, From (i) equation,
⇒ - 2x + 2y = 10
Take 2 as common,
⇒ 2 (- x + y) = 10
⇒ - x + y = 5
⇒ y = x + 5
Which is same as equation (ii).
Hence, There are infinitely many solutions exist.
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B is the set of integers greater than or equal to -3 and less than or equal to 0
Integers higher than or equal to -3 and less than or equal to 0 make up the set of numbers (-3 , -2 , -1, 0)
Explain about the set of integers?The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
The formal definition of the set Z of integers is as follows: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Unknown or unidentified integers are denoted in mathematical equations by lowercase, italicised letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.
The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0.
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Please help, thank you in advance! 15 POINTS!!!
The value of the probability of event C is 0.30.
How to determine the probabilityThe law of total probability states that
P(A U B U C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C).
Substitute the known values in the above equation, so, we have the following representation
P(A U B U C) = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02.
Also are given:
P(A U B U C)' = 0.33,
This implies that
P(A U B U C) = 1 - 0.33 = 0.67.
Substituting the values, we get:
0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02
0.67 = 0.24 + 0.26 + P(C) - 0.15 + 0.02
0.67 = 0.50 + P(C) - 0.13
0.80 = 0.50 + P(C)
P(C) = 0.80 - 0.50 = 0.30.
Hence, the probability is 0.30
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What is the equation of the line that passes through the point (4, -1) and has a
slope of -2?
Answer:
y = - 2x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )
7 = c
y = - 2x + 7 ← equation of line
Is parallelogram TUVW a rectangle?
It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.
Is a parallelogram ever a rectangle?No, a parallelogram is not always a rectangle. In a rectangle, all angles must be equal to 90°. But for a parallelogram, no angles need to be equal to 90°. In a rectangle the diagonals are equal but in a parallelogram, diagonals are not equal.
Parallelogram has opposite sides equal and parallel. Rectangle also has opposite sides equal and parallel. The difference between the two is that sides of rectangles form 90 degree while that of parallelogram don't.
A square is a parallelogram. This is always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides.
It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.
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ILL GIVE BRAINLIEST
Answer: y =1x-5
Step-by-step explanation:
The question asks for the slope form y =mx+b, where m is the slope and b is the y-intercept. The y-intercept is the y value when x = 0, also known as when the line intercepts the verticle origin line. On your graph, this point is (0, -5). So, b = -5. Now, we need to pick two points to find the slope using the equation (y2-y1)/(x2-x1). Any two points on the line will work, so even if you do not pick the same points as me, you should still get the same answer.
point one: (0,-5)
point two: (4,-1)
m = (-1 - -5) / (4 - 0) = (-1+5)/(4) = 4/4 = 1
hope this helps!
Drag and drop the numbers to order them from least to greatest. 2.045 2 5/9 -2 2/3 -2.43
Answer:
-2.43, -2, 5/9, 2/3, 2, 2.045
Step-by-step explanation:
Negative numbers are less than positive numbers, and we can go in numerical order from 1, 2, 3 to find which number is greater than the other
y = (x^2/2) + x + 2; [-5, 3]
For each problem, approximate the area under the curve over the given interval using 4 left endpoint rectangles
The area under the curve over the given interval [-5, 3] can be approximated using 4 left endpoint rectangles.
The formula for this is A = ∑f(xi)∆x. Where A is the area, f(x) is the function, xi is the left rectangles. of the interval, and ∆x is the width of the interval. For this problem, the function is f(x) = (x^2/2) + x + 2 and the given interval is [-5, 3]. So, the left endpoints of the intervals are x1 = -5, x2 = -1, x3 = 3, and x4 = 7 and the width of each interval is ∆x = 4. Plugging these values into the formula, A = (f(-5)∆x) + (f(-1)∆x) + (f(3)∆x) + (f(7)∆x). Simplifying, A = (9*4) + (6*4) + (12*4) + (26*4). Thus, the area under the curve over the given interval is A = 360.
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What is the maximum rate of change of f(x,y,z)=x+y/z at the point (5,−3,5) and the direction in which it occurs.
The maximum rate of change of f(x,y,z)=x+y/z at the point (5,-3,5) can be found using the directional derivative.
The directional derivative of f(x,y,z) in the direction (u,v,w) is given by:
Df(x,y,z) = u∂f/∂x + v∂f/∂y + w∂f/∂z
Since f(x,y,z)=x+y/z, the partial derivatives of f(x,y,z) are ∂f/∂x=1, ∂f/∂y=1/z and ∂f/∂z=-y/z^2. Substituting these values into the above directional derivative equation, we get:
Df(x,y,z) = u + v/z - wy/z^2
At the point (5,-3,5), we get Df(5,-3,5) = u + (-3/5) - (5w)(-3/25)
Simplifying this expression gives us Df(5,-3,5) = u + 0.6w
Therefore, the maximum rate of change of f(x,y,z) at the point (5,-3,5) occurs in the direction (u,0,w) and has a value of 0.6w.
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Based on the results, after trying for a while, you expect your weight to decrease by at least 10% of your current weight in the next two months. If you currently weigh 70Kg. Determine the amount of weight (in Kg) that you expect to lose?
A firm’s current profits are $900,000. These profits are expected to grow indefinitely at a constant annual rate of 2 percent. If the firm’s opportunity cost of funds is 4 percent, determine the value of the firm: a.The instant before it pays out current profits as dividends. b.The instant after it pays out current profits as dividends
Answer: a. The value of the firm the instant before it pays out current profits as dividends can be calculated using the Gordon Growth Model, which is given by the formula:
Value = Dividends / (Cost of Equity - Growth Rate)
Where Dividends = Current Profits, Cost of Equity = Opportunity Cost of Funds, and Growth Rate = Constant Annual Growth Rate.
Substituting the given values into the formula, we get:
Value = 900,000 / (0.04 - 0.02) = 900,000 / 0.02 = 45,000,000
b. The instant after it pays out current profits as dividends, the firm's value will be reduced by the amount of the dividends paid out. So, the value of the firm after paying out the dividends will be:
Value = 45,000,000 - 900,000 = 44,100,000
Step-by-step explanation:
Chris buys 1.6 pounds of almonds and 2.8 pounds of cashews. Emily buys 0.7 pound of almonds and 1.5 pounds of cashews.
The total cost of the nuts that Chris and Emily buy can be found using the expression: (1.6a) + (2.8c) + (0.7a) + (1.5c) You can also use the expression (10.6a) + (2.8c) for the total cost of nuts that Chris buy.
What is pounds?pound, unit of avoirdupois weight, equal to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The Roman ancestor of the modern pound, the libra, is the source of the abbreviation lb. In medieval England several derivations of the libra vied for general acceptance.
Among the earliest of these, the Tower pound, so called because its standard was kept in the Royal Mint in the Tower of London, was applied to precious metals and drugs and contained 5,400 grains, or 0.350 kg, whereas the mercantile pound contained 6,750 grains, or 0.437 kg. The troy pound, believed to have originated in Troyes, France, superseded the lighter Tower pound in 1527 as the gold and silver standard. Increased trade with France led also to the adoption of the 16-ounce avoirdupois pound in the 16th century to replace the mercantile pound.
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In each of the following situations, data are obtained by conducting a statistical study. Classify each statistical study as experimental or correlational. Statistics students collect data on the shower length and gender of the person taking the shower for a random sample of showers. The manager of a tuna canning factory is interested in finding out which set of machine settings results in a smaller variance of the fill weight of the tuna cans. She uses one set of machine settings for the day shift and a second set of settings for the night shift. The next day she uses the second set of settings for the day shift and the first set of settings for the night shift. Data are collected on the fill weights of the tuna cans. For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn.
An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled.
What are experimental or correlational statistical study?An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled. Variables are measured in a correlational design without any of them being changed. Without influencing or modifying any of the variables, a correlational study design examines associations between two (or more) variables. This particular quantitative research method is non-experimental. These determine the three categories of correlational research: Archival research, survey research, and observational study conducted naturally.Experimental research is an investigation carried out using two sets of variables and a scientific methodology. You use the first set as a standard against which to compare the differences in the second set. For instance, experimental techniques are used in quantitative research.We would learn them all and associate each song with a certain pizza truck if there were several different pizza trucks in the region, each with its own distinctive melody. In this case, "jingle" and "distance of the truck" are the two variables that are established as having a relationship by correlational study.To learn more about correlational statistical study refer to:
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Use De Morgan’s Law to find the indicated set
Answer:
C' U (A U B')
Step-by-step explanation:
Using DeMorgan's laws
(C ∪ A' ∩ B)' = C' U (A' ∩ B)'
(A' ∩ B)' = (A')' U B' = A U B'
So (C ∪ A' ∩ B)' = C' U (A U B')
How do you solve this please
The number of students in the population would be:
Wear glasses - 165 students Wear contact lenses - 60 students No vision problem diagnosed - 525 students How to find the population ?The sample is directly related to the population of students so parts of the students can be found using the sample.
Students in population who wear glasses :
= Sample who wear glasses / Total sample x Total population
= 11 / 50 x 750
= 165 students
Students who wear contacts:
= 4 / 50 x 750
= 60 students
Students with no vision problems :
= 35 / 50 x 750
= 525 students
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use the method of mathematical Induction to Prove that 4+9+14+19+_ _ + (5n-1) = n/₂ (3+5n) for all natural numbers n
Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
To prove mathematical induction?Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).
First, establish that P1 is accurate when n equals 1.
LHS= 4
RHS
= 1/2(5 + 3)
= 1/2(8)
= 4
= LHS
Is P1 true.
2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)
3) Establish Pn+1 as true in the induction stage.
Replace (n+1) on both sides of n to obtain Pn+1.
Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=
Establish the RHS and LHS's parity.
LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]
Bold expression in (2) should be replaced with the value of Pn:
.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
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Two friends, Caleb and Hassan, took summer jobs. The equation y=21.5xy=21.5x represents Hassan's earnings in dollars and cents, yy, for working xx hours. Caleb earned $819.40 in 34 hours.
Use the dropdown menu and answer-blank below to form a true statement.
Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Two friends, Caleb and Hassan, took summer jobs. The equation y = 21.5x represents Hassan's earnings in dollars and cents, y, for working x hours. Caleb earned $819.40 in 34 hours.
The rate of Caleb is given as,
Celeb's rate = $21.5 per hour
The rate of Hassan is given as,
Hassan's rate = $819.40 / 34
Hassan's rate = $24.1 per hour
The difference is given as,
⇒ $24.1 - $21.5
⇒ $2.6
Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.
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