The number k is equal to 60 when the top right angle at the intersection of the lines y and x is (2 k + 11) degrees and the bottom left angle is 131 degrees.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical expression is a sentence that includes numbers, variables, or both. The equal sign is never used in expressions. A mathematical statement stating the equality of two expressions is known as an equation.
Here,
Those two angles have the same measure. so you have,
2k+11=131
22k=120
k=60
The value of k where at the intersection of lines y and x, the top right angle is (2 k + 11) degrees and at the intersection of lines z and x, the bottom left angle is 131 degrees is 60.
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A rumor about canceling spring break is being spread around a school. The following equation models the number of students in the school who have heard the rumor after t days:
Equation: N (t) = 1800/1+149e^-0.625t
A.). How many people started the rumor?
B. ). How many students are in the school?
C.). To the nearest 1/10, how many days will it be before the rumor spreads to ½ the student body?
D.). The following equation represents the instantaneous rate of change in students per day of the spread of the rumor.
Another Equation: N^1 (t)=0.625N (1- N/1800)
N represents the number of students who have heard the rumor and t is time in days.
How many students have heard the rumor when the rumor is spreading the fastest?
What is the rate of change in students per day at this time ?
A) The number of people who have started the rumor is N(0)=12
B) The number of students who are in the school are 1800
C) The number of days the rumor spreads to ½ the student body are 8 days.
D) The number of students who have heard the rumor when the rumor is spreading the fastest are 900.
The rate of change in students per day at this time is 281.
What is meant by rate of change?The rate of change is a mathematical term that describes the percentage change in value over a given time period and represents the momentum of a variable.
A) Number of people who have heard the rumor after t days is given by:
N (t) = 1800/1+149e^-0.625t
At start t=0, so from the above equation at t=0, we get
N(0)=(1800)/1+149e^0
N(0)=1800/(1+149(1))
N(0)=1800/150
N(0)=12
B) At t=∞, all of the students would have heard the rumor. So putting t↔∞ in the above equation we get,
[tex]\lim_{t \to \infty}[/tex]N(t)=[tex]\lim_{t \to \infty}[/tex] 1800/1+149e^-0.625t
=1800/(1+0)
=1800
Therefore, the number of students in the school are 1800.
C) Putting N=1800/2 in the above equation, we get
1800/2= 1800/1+149e^-0.625t
1+149e^-0.625t=2
e^-0.625t=(2-1)/149
=1/149
Taking log on both sides, we get
ln(e^-0.625t)=ln(1/149)
-0.625t=-ln(149)
t=ln(149)/0.625
t=8.006≈8
D) N'(t)=0.625N(1-(N/1800)
=0.625(N-(N²/1800)
=(0.625/1800)(1800N-N²)
=(0.625/1800)(900²-900²+1800N-N²)
=(0.625/1800)(900²-(N²-1800N+900²)
N'(t)=(0.625/1800)(900²-(N-900)²)
For N to be maximum,
N=900
Thus, rumor is spreading fastest when 900 students have heard the rumor.
And rate of change in students per day is obtained by putting N=900 in expression of N'(t) as follows:
N'(t)=(0.625×900)(1-(900/800))
N'(t)=281.25≈281
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a password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits. how many different passwords are possible?
As per the concept of probability, there are 4,717,440 number of passwords are possible.
Probability:
In statistics, probability refers the favorable outcome of the particular event.
Given,
A password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits.
Here we need to find how many different passwords are possible.
Total number of characters = 6
According to this, each password would have
5 digits of 10 digits: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], and
one of 26 letters: [A to Z].
Here there is no repeats are allowed, and assuming only upper case letters are valid and the letter is the last character, then we can form 10*9*8*7*6 * 26 = 786,240 such passwords.
If the repetition is allowed then number of possible passwords is
786,240 * 6 = 4,717,440.
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Select the correct answer from each drop-down menu. Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Average rate of change plotted on coordinate plane linear graph. A solid boundary line intersects X-axis at unit minus 2.5 and Y-axis at unit 5. The Y-value for x= minus 1 is 3 and for x= minus 4 is minus 3. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
The average rate of change of f(x) over the interval [-4, -1], with coordinates, (-4, -3) and (-1, 3) is 2
How can the average rate of a function over an interval be found?The average rate of change of a function over an interval is found from the change in the output values of the function over the period indicated, divided by the change in the input values of the function over the specified interval.
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex]
The interval over which the average rate of change of the function is required = [-4, -1]
The formula for the average rate of change over the interval, [-4, -1], can be presented as follows;
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex] = [tex]\dfrac{f(-1) - f(-4)}{\left(-1 - (-4)\right)}[/tex]
The coordinates of the points of the graph of the function in the indicated range are; (-1, 3), and (-4, -3)
f(-1) = 3, f(-4) = -3, therefore;
Average rate of change = [tex]\dfrac{3 - (-3)}{-1 - (-4)}[/tex] = 2
The average rate of the function over the specified interval is 2
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An object weighing 5 pounds on Earth will weigh 2 pounds on Mercury. The Statue of Liberty weighs 225 tons. What would it weigh on Mercury? Show all work:
Answer:
90 tons
Step-by-step explanation:
given that the ration of weight from earth to mercury is 5:2, we can make an equation:
x (weight of an item on Mercury) = 0.4(weight of an item on Earth)
x=0.4(225 tons)
x=90 tons
10. The bottom of a 23-foot straight ladder is set into the ground 7 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? Show your work. Round your answer to the nearest tenth.
Answer:
4√130 or just √480
Step-by-step explanation:
You set up each number for pythagorean theorem as a squared plus b squared equals c squared. Then you solve for b squared and simplify into radical form, or...
your answer is 21.9
A swimming pool is on sale for $875.50. If the sale price is discounted 15% from the original price, what was the original price?
The original price of the swimming pool is $1030.
How to calculate the value?From the information, the swimming pool is on sale for $875.50 and the sale price is discounted 15% from the original price.
Let the original price be x.
This will be illustrated as:
(x - 15% × x) = 875.50
x - 0.15x = 875.50
0.85x = 875.50
Divide
x = 875.50 / 0.85
x = 1030
The original price is $1030.
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The odds in favor of Michael Jordan making a free throw were 21:4. Find the probability of Michael Jordan missing a free throw.
Give answer as a decimal rounded to the nearest hundredth.
The probability that Jordan misses a free throw is 0.16
How to determine the probability that he misses?From the question, we have the following parameters that can be used in our computation:
Odds in favour = 21 : 4
Represent the odds as a fraction
So, we have the following representation
Odds in favour = 21/4
To convert the odds to probability, we make use of the following equation
Probability = Numerator/(Numerator + Denominator)
Substitute the known values in the above equation, so, we have the following representation
Probability = 21/(21 +4)
Evaluate the sum
Probability = 21/25
The probability that he misses is
Misses = 1 - 21/25
Evaluate the probability
Misses = 4/25
So, we have
Misses = 0.16
Hence, the probability is 0.16
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E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022. Show how the bonds would be reported on the january 2, 2022, balance sheet if they are issued at 97. (deductions should be indicated by a minus sign. ).
The preparation of the bond that should be reported on the balance sheet is presented below:
E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022.
We need to present it on balance sheet balance sheet if they are issued at 97.
E-Tech Initiatives Limited
Partial balance sheet
As on January 2, 2019
Liabilities
Long term Liabilities
Bond Payable $500,000
Add: Premium on Bond $10,000 ($510,000 - $500,000)
Carrying value $510,000 ($500,000 * 97%)
Therefore, The preparation of the bond that should be reported on the balance sheet is presented above.
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find the slope of the line that contains the following points: (17, -12) and (7,8)
The slope of the line that contains the points (17, -12) and (7, 8), is -2.
Calculating the slope of a line with given pointsFrom the question, we are to determine the slope of the line that contains the given points.
The given points are (17, -12) and (7, 8)
Using the formula for calculating slope,
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope
Then,
The slope of the line is
m = (8 - (-12)) / (7 - 17)
m = (8 + 12) / (-10)
m = 20 / - 10
m = -2
Hence, the slope is -2
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a group of 15 people are ordering pizza each person wants 2 slices and each pizza has 15 slices how many pizzas should they buy
By conducting mathematical operations, we know that the group of friends will order 6 pizzas.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Mathematical operations include addition, subtraction, multiplication, division, and finding the root.
So, a number of pizzas the friends should buy:
We know that a group is of 15 people.
They are ordering a pizza which have also 15 slices in each.
And each person wants 2 slices: That is
Then, the number of pizzas they have to order will be:
1 pizza (15 slices) * 2 = 2 pizza (30 slices)
Therefore, by conducting mathematical operations, we know that the group of friends will order 6 pizzas.
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What are the equations to the slopes of 1/5, 3/5, and 6/5?
Answer:
1/ y= 1/5x
2/ y= 3/5x
3/ y= 6/5x
Step-by-step explanation: Our original equation is y=mx+b
Where m is the slope and b is the y-intercept. Since there is no y-intercept, so we just say it is 0 and only put in the slope to the equation.
can y’all help me w these 2 probs ! Find the square root of the number
Answer:
Step-by-step explanation:
4.) - 20
5.) 66 i
Feel free to double check with a calculator
(Hope that helps!)
Someone pleasee helppp!
Geometry A
Answer: I think it is 5
Step-by-step explanation:
10 students have volunteered for a committee. 7 of them are seniors and 3 of them are juniors. 1) how many ways are there to select a committee of 8 students? 10!/(8!2) 2) how many ways are there to select a committee with 3 seniors and 5 juniors? 7!/(3!/4!)*(3!/(5!/(2)!)) 3) suppose the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair. how many ways are there to make the selection?
(a) The number of ways of selecting a committee of 8 students = 45.
(b) The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the 8 must be selected as chair = 360 ways
What is combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given that 10 students have volunteered for a committee. 7 of them are seniors and 3 are juniors.
a) Need to find the number of ways of selecting a committee of 8 students
The number of ways of selecting a committee of 8 students = [tex]10_C_8[/tex]
[tex]10C_8= \frac{10!}{8!(10-8)!}= \frac{10!}{8!(2!)}=45[/tex]
The number of ways of selecting a committee of 8 students = 45.
(b) Need to find the number of ways to select a committee with 3 seniors and 2 juniors
The number of ways to select a committee with 3 seniors and 2 juniors
= [tex]7_C_3(3_C_2)[/tex]
[tex]7_C_3*3_C_2 = \frac{7!}{3!*4!} *\frac{3!}{2!*1!} = 35 * 3 = 105[/tex]
The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) Need to find the ways to make the select the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair.
Number of ways = [tex]10_C_8*8_C_1[/tex]
[tex]10_C_8*8_C_1 = \frac{10!}{8!*2!} *\frac{8!}{7!*1!} = 45*8 = 360[/tex]
The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the five must be selected as chair = 360 ways.
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How many solutions does this equation have? –2g + 2g = 0
The equation -2g+2g has infinitely many solutions.
Define solving an equation.The method of solving equations involves determining the value of the unknown variable while maintaining the equality of the equation on both sides. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. After separating the variable whose value has to be calculated, the solution is found. We can answer it depending on the type of equation we are dealing with. Equations come in a variety of forms, including linear, quadratic, rational, and radical equations.
Consider the given equation
-2g + 2g = 0
Solve the equation,
0 = 0
This means that the equation is valid for all values of g.
Therefore, the equation can have infinitely many solutions.
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Please Help! - Algebra
Zachary purchased a computer for $1,800 on a payment plan. Two months after he purchased the computer, his balance was $1,540. Three months after he purchased the computer, his balance was $1,410. What is an equation that models the balance y after x months?
Using an exponential decay equation, the function that models the balance is y = 1800(1 + 0.081)⁻ˣ at a rate of 8.1%
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
To solve this problem, we need to find the rate at which the payment is calculated on.
The general equation for an exponential decay is given as
A = P(1 + r)⁻ˣ
x = timer = rateSubstituting the values and solving for r
1540 = 1800(1 + r)⁻²
r = 0.081
r = 8.1%
Comparing the third month to ascertain values
1410 = 1800(1 + r)⁻³
r = 0.081
r = 8.1%
The rate which the payment is calculated is 8.1%
An exponential equation that models the balance after y months will be
y = 1800(1 + 0.081)⁻ˣ
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The square of a number added to 2 times a number is 8. Find the number.
Answer:
x = -4 or 2
Step-by-step explanation:
Let the number be x.
Given condition:x² + 2x = 8
Subtract 8 to both sides
x² + 2x - 8 = 0
Using mid-term break method
=> 4 × -2 = 8 (side-term), 4 - 2 = 2 (mid-term)
So, we can break the mid-term into 4 and -2.
x² + 4x - 2x - 8 = 0
Take common
x(x + 4) - 2(x + 4) = 0
Take (x+4) common
(x+4)(x-2) = 0
Either
x + 4 = 0 OR x - 2 = 0 (Zero's method)
x = -4 OR x = 2
[tex]\rule[225]{225}{2}[/tex]
explain how you could use a regression model to estimate the wage gender gap using the data on earnings of men and women. what are the dependent and independent variables?
A regression model could be used to estimate the wage gender gap by comparing the earnings of men and women.
Regression is a statistical technique used in the fields of finance, investing, and other areas that aims to assess the nature and strength of the relationship between one dependent variable and another. In this case, the dependent variable would be the gender gap in wages and the independent variable would be the earnings of men and women. The regression model would be used to calculate the difference between the two variables, which would indicate the wage gender gap.
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There are 1,200 bacteria in a lab dish. The population decreases 10% per day. Calculate the average rate of change in the decrease in population for days 1 to 3 with the decrease for days 4 to 6.
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The total number of bacteria in lab dish is 1200
The population decreases 10% per day
In first day:
10/100×1200=120
120 bacteria decreased in lab
1200-120=1080
In second day:
0.1×1080=108
1080-108=972
In third day
0.1×972=97.2
972-97.2=874.8
In fourth day
0.1×874.8=87.48
874.8-87.48=787.32
In fifth day
0.1×787.32=78.732
787.32-78.732
708.588
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
Hence, the population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
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Cynthia Besch wants to buy a rug for a room that is 25 ft wide and 32 ft long. She wants to leave a uniform strip
of floor around the rug. She can afford to buy 330 square feet of carpeting. What dimensions should the rug
have?
Sean tutors math students to earn extra money. Sean chargers $20 per hour. Write an equation to model Sean's earnings, y, after x hours.
Answer:
y=20x
if he charges $20 and hour multiply your hours by 20 to get the total amount of earnings
exhibit 12-2 last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. a random sample of 300 students taken from this year's student body showed the following number of students in each class. freshmen 83 sophomores 68 juniors 85 seniors 64 we are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. refer to exhibit 12-2. if the distribution is the same as the previous year, the expected number of freshmen is . a. 30 b. 10 c. 90 d. 83
Option D is the correct answer.
What is distribution?
To “distribute” means to divide something or give a share or part of something.
From the given information , 83 + 68 + 85 + 64 = 300 students.
30 % = freshmen, 24% =sophomores, 26% = juniors , 20% = seniors
Class Observed frequency Expected proportion
Freshman 83 0.30
Sophomores 68 0.64
juniors 85 0.26
seniors 64 0.20
Total 300 1
The expected number of students in freshman class can be calculated as
Expected Frequency = Total number of value x Expected Proportions
= 300 x 0.30
= 90
Therefore, the expected number of students in freshman class = 90
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What is the measure of angle o in parallelogram lmno? 35° 75° 105° 155
The measure of angle O in the given parallelogram is equal to 105°.
As given in the question,
Given parallelogram LMNO,
As shown in the attached diagram we have,
Measure of angle L = ( x + 40 )°
Measure of angle O = (3x)°
In the parallelogram LMNO,
LM is parallel to NO .
LO is the transversal.
∠MLO and ∠NOL are interior angles and are supplementary.
m ∠MLO + m ∠NOL = 180°
⇒ ( x + 40 )° + ( 3x )° = 180°
⇒ 4x° = 180° - 40°
⇒x = 140° / 4
⇒ x = 35°
Measure of ∠O = 3x°
= 3(35°)
= 105°
Therefore, the measure of ∠O in the parallelogram LMNO with the given conditions is equal to 105°.
The complete question is :
What is the measure of angle O in parallelogram LMNO?
Diagram of parallelogram LMNO is attached.
m∠O = ?
a. 35° b. 75° c. 105° d. 155°
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Answer: 105 degrees
Step-by-step explanation:
edge 2023, (Proving a Quad. is a Parallelogram)
karrie was late to work 14 times last year. if she workded 250 days last year, what percent of the days was she left
By using the concept of percentage, it can be calculated that Karrie was late to work in 5.6 % of the days.
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 9% means [tex]\frac{9}{100}[/tex]. Here 9 is expressed as a fraction of 100
Here the concept of percentage will be used
Number of days in which Karrie was late = 14
Total number of days she worked = 250
Percentage of days Karrie was late = [tex]\frac{14}{250} \times 100[/tex] = 5.6 %
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how much does each apple cost?
Apples
4 for $2
the average adult horse needs 2/5 bale of hay each day to meet dietary requirements. A horse farm has 44 bales of hay. How many horse can be fed with 44 bales of hay
The horse that can be fed with 44 bales of hay is 110 horses.
How many horses can be fed?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
Given that the average adult horse needs 2/5 bale of hay each day to meet dietary requirements and a horse farm has 44 bales of hay.
The number of horses that can be fed will be:
= Total number of hay / Fraction needed
= 44 ÷ 2/5
= 44 × 5/2
= 22 × 5
= 110
100 horses can be fed.
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write your answer as a mixed number in simplest from
3 9/10 + 4 9/10
The simplified form of the given fraction, 3 9/10 + 4 9/10 , in its simplest form is 8 4/5
Simplifying fractionsFrom the question, we are to write the given fraction as a mixed number in simplest form
The given fraction is
3 9/10 + 4 9/10
First, we will convert the fractions to improper fractions
39/10 + 49/10
Now, add the fractions
(39 + 49)/10
= 88/10
Write as a mixed fraction
8 8/10
Simplify the fraction
8 4/5
Hence, the fraction becomes 8 4/5
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Triangle A'B'C' is a reflection of triangle ABC across line l. Select all statements that must be true.
A Line l bisects segment AB.
B Line l bisects segment CC’.
C Angle ABC is 60 degrees.
D Line BB’ is perpendicular to line l.
E Angle ABC is congruent to angle A’ B’ C’.
F Triangles ABC and A’ B’ C’ are congruent.
G Segment BC is congruent to segment B’ C’.
H The distance from point A to line l is the same as the distance from point A’ to line l.
Answer:
A, B, D, E, F, G, H
Step-by-step explanation:
If triangle A'B'C' is a reflection of triangle ABC across line l, the following statements must be true:
A. Line l bisects segment AB.
B. Line l bisects segment CC’.
D. Line BB’ is perpendicular to line l.
E. Angle ABC is congruent to angle A’ B’ C’.
F. Triangles ABC and A’ B’ C’ are congruent.
G. Segment BC is congruent to segment B’ C’.
H. The distance from point A to line l is the same as the distance from point A’ to line l.
Statements C and H are not necessarily true. The angle ABC may not be 60 degrees, and the distance from point A to line l may not be the same as the distance from point A’ to line l.
PLEASE PROVIDE EXPLANATION!
In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed number and the original number is 121. Find the original number.
Step-by-step explanation:
Also, we know that , because the unit digit is three less than tens digit, or tens digit is three more units than the unit digit. Then, the sum of the reversed number and the original number is 121, this would be expressed: Therefore, the digits are 7 and 4. The number would be 74.
Answer:
The original number is 74
Step-by-step explanation:
The answer of 74 provided by brey90 is absolutely correct. I am just providing a mathematical way of determining the number
Let the number be ab
That means [tex]b[/tex] is in the units place and [tex]a[/tex] is in the tens place.
The actual value of this two digit number is [tex]10a + b[/tex]
The difference between a and b is 3:
[tex]a - b = 3[/tex] [1]
If we reverse the number we get the number [tex]ba[/tex]
The actual value of [tex]ba[/tex] is [tex]10b + a[/tex]
The sum of [tex]ab[/tex] and [tex]ba[/tex] is 121. This means the sum of their actual values must be 121
So we get
[tex]10a + b + 10b + a = 121\\\\11a + 11b = 121\\\\[/tex]
Dividing both sides by 11 yields:
[tex]a + b = 11[/tex] [2]
Add [1] and [2] to get:
[tex]2a = 14\\\\a = 7\\\\[/tex]
Sub for a in Equation [1] to get
[tex]7 - b = 3\\\\b = 4\\\\[/tex]
So the original number is 74
Check
Reversed is 47
74 + 47 = 121
E ≠ V + Ir
Solve for r
Answer:
r ≠ E – V/r
Step-by-step explanation:
E ≠ V + Ir
E – V ≠ Ir
divide both sides by I
E – V/I ≠ r
r ≠ E – V/r
i hope i helped