Using the greatest common factor, it is found that the greatest number of cards that she can place in a row is of 14.
How to find the greatest number of cards that she can place in a row?The number of cards for each family is given as follows:
April's family: 154.Groom's family: 140.We want to find a way to distribute them having the same number of cards in each row, hence this is possible finding the greatest common factor (GCF) of the numbers of 154 and 140.
The GCF is found factoring both numbers 154 and 140 simultaneously by prime factors, as follows:
154 - 140|2 (both 154 and 140 are divisible by 2).
77 - 70|7 (both 77 and 70 are divisible by 11).
11 - 7
There are no numbers for which both 11 and 7 are divisible by, hence the greatest number of cards that she can place in a row is:
gcf(154, 140) = 2 x 7 = 14.
Missing information
The complete problem is:
April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?
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How do you solve this?
a= 4
b= - 42
How the given expression is solved ?
[tex]2-\frac{x+2}{x-3} -\frac{x-6}{x+3} \\\\=\frac{2(x^{2} -9)-[(x+2)(x+3)]-[(x-6)(x-3)]}{x^{2} -9} \\\\=\frac{2x^{2} -18-x^{2} -5x-6-x^{2} +3x+6x-18}{x^{2} -9} \\\\=\frac{4x-42}{x^{2} -9}\\\\\text{This is of the form}, \frac{ax+b}{x^{2} -9}[/tex]
Thus, the value of integers a and b are :
a = 4 ; b =- 42
What are integers?
The number zero , a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The lowest group and ring of the natural numbers are formed by the integers. To distinguish them from the more generic algebraic integers, the integers in algebraic number theory are occasionally designated as rational integers. In actuality, rational integers are rational numbers that are also algebraic integers.To learn more about integers, refer:
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please help me
solve for x. if needed, round your answer to 1 decimal place.
Check the picture below.
[tex]sin(31^o )=\cfrac{\stackrel{opposite}{11}}{\underset{hypotenuse}{x}}\implies x=\cfrac{11}{sin(31^o)}\implies {\Large \begin{array}{llll} x\approx 21.4 \end{array}}[/tex]
Make sure your calculator is in Degree mode.
What is the value of n?
n–2=10n+42
[tex]n-2=10n+42\\n-10n=42+2\\-9n=44\\\frac{-9n}{-9} =\frac{44}{-9} \\n=-\frac{44}{9}[/tex]
Hope this helps.
A machine factory makes two and one 4th pounds of nails in one and a half hours at what rate in
pounds per hour does the machine make nails
The machine make nails at a rate of 8th pounds per hour
How to determine the rate of making machine?From the question, the given parameters are:
Amount of pounds of nails = 4th poundsNumber of time = half an hourThe rate in pounds per hour the machine make nails is then calculated as
Rate of making nails = Amount of pounds of nail/Number of time
Substitute the known values in the above equation
So, we have
Rate of making nails = 4th pounds/0.5 hour
Evaluate
Rate of making nails = 8th pounds per hour
Hence, the rate of making nails is 8th pounds per hour
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¿Cual es el 15% de 400?
Answer:
15/100×400=60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
son 60 porque
400/10=40 entonces 40=10% entonces 5% es 20
40+20=60
Math please its in the picture and show solution please
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Explain about the simplify?No, to simplify is to reduce anything to its most basic form without figuring out what the letter 'x' or other letters are. Finding the meaning of the 'x' or other letters is known as solving.
Overview. Making something simpler refers to making it simpler to do or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. We accomplish this by dividing the denominator and numerator by the highest possible number.
It has the same precise meaning. The phrase "expand the brackets" means the same thing as "multiply out the brackets," with the added indication that when we do so, we are multiplying everything inside by everything outside the brackets.
The answer for a is x
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Type the correct answer in each box.What values of a and b make this equation true?(4 + v=49) – 2(/(-4)2 + v=324) = a + bia =b =ReseNext
Problem
Solution
For this case we can do the following:
[tex](4+\sqrt[]{-49})-2(\sqrt[]{(-4)^2}+\sqrt[]{-324})\text{ }[/tex]We also know that :
[tex]\sqrt[]{-1}=i[/tex]Using this property we got:
[tex](4+7i)-2(4+18i)[/tex]Now we can distirbute the terms and we got:
4+7i -8 -36 i
And distributing the terms we got:
(7-36)i +(4-8)
-29 i -4
And then our solution would be:
a= -29
b= -4
The assets and liabilities of a landscaping business are listed below.
What is the net worth of the landscaping company?
$126.790
$187.205
$282.799
$470.004
The net worth of the landscaping company is given by:
$187.205.
How to calculate the net worth?The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.
In the context of this problem, the assets, and it's values, of the company are given as follows:
Owned Inventory: $48,760.Cash: $126,790.Savings account: $32,436.Owned equipment: $20,700.Accounts receivable: $15,640.Property value: $225,678.Hence the sum of the assets is given by:
Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.
The debts of the company, with it's values, are given as follows:
Small Business Loan: $76,400.Building Mortgage: $189,429.Other debt: $16,970.Hence the sum of the debts is given by:
Debts = 76400 + 189429 + 16970 = $282,799.
Then the net worth of the company is:
Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.
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the probability that a person will die when he or she contracts a virus infection is 0.001. (a) of the next 4000 people infected, what is the mean number who will die? please define the random variable x considered here. what is the probability distribution function of x? (b) of the next 1 million people infected, what is the probability of more than 2000 people die? compute the probability using two different probability distribution functions.
Answer:
6.3
Step-by-step explanation:
Given f(x)=x^2+1 and g(x)=2x−1, find (f−g)(x)
x2−2x−1
x squared minus 2 x minus 1
x2+2x
x squared plus 2 x
x2−2x+1
x squared minus 2 x plus 1
x2−2x+2
The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.
The given functions are f(x)=x²+1 and g(x)=2x-1.
What is 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.
We need to find the value of (f-g)(x).
Now, f(x)-g(x)= (f-g)(x)
=x²+1 -(2x-1)
=x²+1-2x+1
=x²-2x+2
The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.
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Adam left Julia's house and traveled toward the capital at an average speed of 65 km/h. Eugene left at the same time and traveled in the opposite direction with an
average speed of 80 km/h. How long does Eugene need to travel before they are 290
km apart?
HELP ASAP!!!!
2 hours Eugene needs to travel before they are 290 km apart.
How to find the time taken?Given,
Average speed of Adam = 65 km/h
The average speed of Eugene = 80 km/h
Both travel in the opposite direction
Solution:
Let x be hours taken.
S = d/t
65 x+ 80 x = 290
145x = 290
x = 2 hr
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Name the set(s) of numbers to which the number belongs.−32/95
The number -32/95 belongs to the set of rational numbers.
Rational numbers may be defined as set of numbers which can be expressed in the form of p/q where q cannot be equal to zero. Irrational numbers may be defined as set of numbers which cannot be expressed in the form of p/q. Rational numbers can be of three types. Positive rational numbers are those in which either both the numerator and denominator are positive, or both are negative. Negative rational numbers are those in which either of numerator or denominator is negative. Zero is also a rational number which can be expressed in the form of p/q. Now, the number -32/95 is expressed in the form of p/q and the numerator is negative, so it is a negative rational number.
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please help me complete the blank spots in the sentence!
The full sentence relating to the function in the tabulated data is;
"The x-intercept shows that if Ronald buys only apples, he can buy 12 pounds (lb). The y-intercept shows that if Ronald buys only eaches, he can buy 10 pounds (lbs). Hence the complete sentence."
What is a math function?It is to be noted that in mathematics, a function is an expression, rule, or law that describes the connection between one variable (the independent variable) and another variable (the dependent variable).
Tabular data has the following characteristics: They are made up of rows and columns. A table contains rows and columns and is used to organize everything tabular. Typically, sports statistics are provided in a tabular manner. A table is a type of graphic that arranges data into rows and columns. Tabular data is presented in a table format.
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David, Eva and Farooq share a sum of money.
David gets 1/6 of the money and Eva gets 1/4 of the money. David gets £2.50
Farooq gets the rest of the money.
Work out how much money Farooq gets
David gets £2.50 Farooq gets the rest of the money. Let the total sum of the money be x is £8.75.
What is Algebra?All mathematical applications require a basic understanding of algebra since it deals with manipulating variables as though they were numbers. To analyze algebraic structures like groups, rings, and fields, one uses the term "abstract algebra." Modern geometry presentations use linear algebra, a subject that works with linear equations and linear mappings, and it has a wide range of practical uses. Many mathematical disciplines fall under the umbrella of algebra, some of which have the word "algebra" in their name, such commutative algebra, and that do not, like Galois theory. It is also used to name specific types of algebraic structures, such as an algebra over a field, which is frequently referred to as an algebra. The word algebra is used to name both a mathematical field and some of its subfields.Therefore,
Let the total sum of the money be x,
David gets 1/6 of x = x/6 = £2.50
⇒ x/6 = £2.50
⇒ x = £2.50 x 6
⇒ x = £15
The total sum of the money = £15
Eva gets 1/4 of x = 1/4 x 15 = £3.75
Farooq gets the rest of the money = x - £3.75 - £2.50
= £15 - £3.75 - £2.50 = £8.75
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A number decreased by 8 is 27.
Answer: 35 = a number
Step-by-step explanation: okay so since the number is being decreased wd know that that is subtraction. so what minus 8=27? well how about we add those two numbers to get the whole? so whats 8+27? 35. Hope this helped
Answer:
Step-by-step explanation:
35
Answer the questions based upon the table:
1- What is the independent variable? (hint- it is the input),
2- What is the dependent variable? (hint- it is the output)
3-
Is the relation a linear function? (hint- if it has a consistent difference between the
consecutive output values, then YES)
4- What is the slope of the function?
5- What is the domain?
6- What is the range?
7- What is the y-intercept? (hint- x = 0 at the y-intercept)
8- What is the x-intercept? (hint-y = 0 at the x-intercept)
The features of the relation are given as follows:
1. Independent variable: number of weeks.
2. Dependent variable: money saved.
3. Yes, the relationship is linear.
4. The slope is of 40.
5. The domain is: {0, 1, 2, 3, 4, 5, 6, 7}.
6. The range is: {50, 90, 130, 170, 210, 250, 290, 330}.
7. The y-intercept is of $50.
8. The table has no x-intercept.
Dependent and independent variablesThe output variable is a function of the input, hence the output is the dependent variable and the input is the independent variable.
The input and the output in this problem are given as follows:
Input: number of weeks -> Independent variable.Output: money saved -> Dependent variable.Linear relationIn a linear relation, the rate of change of the output relative to the input is constant, and is called slope.
In the context of this problem, the money saved has a constant increase of $40 each week, hence:
The relation is linear.The slope is of $40.Domain and rangeThe domain is the set containing the input values of the function, hence the number of weeks, as follows:
{0, 1, 2, 3, 4, 5, 6, 7}.
The range is the set containing the output values of the function, hence the money saved, as follows:
{50, 90, 130, 170, 210, 250, 290, 330}.
InterceptsThe y-intercept is the value of y when x = 0, hence, from the table, it is of:
y = 50.
The x-intercept is the value of x when y = 0. From the given table, y never assumes a value of 0, hence the function has no x-intercept.
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Find x if DRS m = x + 143, QRS m = 167°, and QRD m = x + 30
The value of x is -3.
Given,
[tex]m \angle{DRS}= x+143 \\m \angle{QRS}= 167\\m \angle{QRD}= x+30[/tex]
[tex]m \angle{DRS} +m \angle{QRD} = m\angle{QRS}[/tex]
x+143+x+30 = 167
2x = 167-173
2x = -6
x = -3
We add the two angles in it to find the value of x.
What are angles?
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Angles' Components
Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.
Arms: The angle's two sides are linked at a single end. The arms of an angle are OA and OB.
Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.
The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.
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May you guys/girls please help me I have to submit this befoer mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Answer down below!
Step-by-step explanation:
Lets find a point on the graph that we can easily point out to start this problem
We can use the point (0,-3)
From there, we use rise/run to find our answer!
We go up 1 and over 1
Thus, our slope is 1!
Answer:
1
Step-by-step explanation:
slope = rise/run
choose any two points in the graph and count the left/right and up/down to get to that point it's hard to explain u can watch a yt video to completely understand
Please help me with this question !!!
Answer:
composition about loyalty
If Jackson kicked a soccer ball 12 times and made the shots into the goal 77% of the time, how many shots did he make?
BRAINLY IF CORRECT!!
In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘
In △ D E F , D E = 7 , E F = 12 , and m ∠ D E F = ( 2 x − 6 ) ∘
A C > D F.
What is the range of possible values for x?
(a) 44 < x < 180
(b) 3 < x < 44
(c) 0 < x < 44
d) none of these
(e) x > 44
(f) 44 < x < 93
(g) x < 44
The possible range of angle x is x < 44
How to solve for angle xgiven data
In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘
In △ D E F , D E = 7 , E F = 12 and m ∠ D E F = ( 2 x − 6 ) ∘
A C > D F
Solution for angle x is gotten from the clue in A C > D F
This means that angle included by m ∠ A B C = 82 ∘ is greater than the angle included by m ∠ D E F = ( 2 x − 6 ) ∘
We therefore say that
82 ∘ > ( 2 x − 6 ) ∘
82 + 6 > 2 x
88 > 2 x
divide both sides by 2
88 / 2 > 2 x / 2
44 > x
x < 44 degrees
Hence option g is the correct answer
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Represent each expression as a power of a (a does not equal 0)
The expansion of the given expressions of exponents are:
22. (b) a²· (a⁰)³ ÷ a¹¹ = a⁻⁹
22. (f) {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴} = a⁻²⁷
What are product rule, quotient rule, power rule for exponents?Product rule for exponents state that product of two numbers with same base is given by adding their powers.
That is aⁿ × a ˣ = aⁿ⁺ˣ
Quotient rule for exponents state that the quotient of two numbers with same base is given by subtracting the exponent of denominator from numerator.
That is aⁿ ÷ a ˣ = aⁿ⁻ˣ
Power rule : (aⁿ)ˣ = aⁿˣ
22. (b) a²· (a⁰)³ ÷ a¹¹
⇒a²· (a⁰)³ ÷ a¹¹ = a².a⁰ ÷ a¹¹ (using power rule (a⁰)³ = a⁰)
⇒a²· (a⁰)³ ÷ a¹¹ = a²⁺⁰ ÷ a¹¹ ( using product rule a².a⁰= a²⁺⁰ )
⇒a²· (a⁰)³ ÷ a¹¹ = a²÷ a¹¹ = a²⁻¹¹ ( using quotient rule a²÷ a¹¹ = a²⁻¹¹)
⇒a²· (a⁰)³ ÷ a¹¹ = a⁻⁹
Therefore, expression a²· (a⁰)³ ÷ a¹¹ is a⁻⁹
- 22 .(f) {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴}
= {(a³⁺⁴)÷ a⁻³} /{a·((a²⁺¹)³)⁴} ( using product rule, a³a⁴ = a³⁺⁴ and
a²a = a²⁺¹)
={a⁷÷ a⁻³} /{a·((a³)³)⁴}
= {(a⁷⁻⁽⁻³⁾} /{a·(a³⁽³⁾)⁴} ( using quotient rule a⁷÷ a⁻³ = a⁷⁻⁽⁻³⁾ and
using power rule (a³)³ = a³⁽³⁾)
= {a¹⁰} /{a·(a⁹)⁴}
= {a¹⁰} /{a·a³⁶} ( using power rule (a⁹)⁴ = a⁹⁽⁴⁾ =a³⁶)
= {a¹⁰} / {a¹⁺³⁶} ( using product rule a·a³⁶ = a¹⁺³⁶)
= { a¹⁰} / {a³⁷}
= a¹⁰ ⁻ ³⁷ ( using quotient rule a¹⁰ ÷ a³⁷ = a¹⁰ ⁻ ³⁷ = a⁻²⁷)
= a⁻²⁷
Therefore, expression {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴} is a⁻²⁷.
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Answer:
the answer is a^-27
Step-by-step explanation:
You and a friend are riding your bikes to a restaurant that you think is east and that your friend thinks is north. You both leave from the same starting point, with you riding 16 miles per hour east and your friend riding 12 miles per hour north. After you travel 3 miles, at what rate is the distance between you changing?
The distance between you and your friend is changing at the rate of 28 miles per hour after you travel 3 miles.
According to situation,
You are going in east direction with a rate of 16miles per hour and your friend is going towards 12 miles per hour at the rate of 12 miles per hours.
Let us say you cover L distance in east direction and your friend covers B distance in north direction,
Time taken by you to cover 3miles,
Time = Distance L/speed
time = 3/16 hours.
Distance B covered by friend in 3/16 hours,
distance B = speed x time
Distance B = 3/16 x 12
Distance B = 9/4 miles.
As both are going perpendicular to each other,
The distance between you and your friend X can be calculated by the Pythagoras theorem,
X² = L² + B²
Differentiating with respect to time t,
2dX/dt = 2(L)dL/dt + 2(B)dB/dt
As we know,
dL/dt = 16 miles/hour and,
dB/dt = 12 miles/hour,
L = 3 miles,
B = 9/4 miles.
Putting all the values,
2dX/dt = 2(3)(16) + 2(9/4)(12)
dX/dt = 48 + 27
dX/dt = 75 miles per hour.
The distance between you and your friend will change at the rate of 75 miles/hour.
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A dance school offers classes in ballet folklórico. There is a one-time registration fee and a fee
for each class. The total cost of classes, y, is a linear function of the number of classes,
Three classes cost $36. Seven classes cost $68.
What is the rate of change and what does it represent?
The most appropriate choice for equation of line in slope intercept form will be given by-
Rate of change is 8 and rate of change represents slope of the line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is written as y = mx +c
m is the slope of the line and c is the y intercept of the line.
The distance between the origin and the point where the line cuts the x axis is the x intercept
The distance between the origin and the point where the line cuts the y axis is the y intercept
Here,
Let the number of classes be x
Total cost of classes = y
Let the equation of line be y = mx + c
Three classes cost $36
Putting x = 3, y = 36
36 = 3x + c .............. (1)
Seven classes cost $68
Putting x = 7, y = 68
68 = 7x + c ............... (2)
Subtracting equation (2) from (1),
4x = 32
[tex]x = \frac{32}{4}[/tex]
x = 8
Putting the value of x in (1)
[tex]3 \times 8 + c = 36\\24 + c = 36\\c = 36 - 24\\c = 12[/tex]
Equation of line is y = 8x + 12
Now coefficient of x in y = mx + c is the slope of the line and that is the rate of change
so, rate of change is 8 and rate of change represents slope of the line.
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Answer:
$8 per classthe cost of each classStep-by-step explanation:
Given school costs of $36 for 3 classes and $68 for 7 classes, you want to know the rate of change and its meaning.
Rate of changeThe "rate of change" in this context is the change in cost for one additional class. It can be found by ...
rate of change = (change in classes) / (change in cost)
rate of change = ($68 -$36)/(7 classes -3 classes) = $32/(4 classes)
rate of change = $8/class
Interpretation
This "rate of change" is the additional cost for the addition of one class. It is the cost per class.
the drama club is printing t-shirts for the members. the printing company charges a certain amount for each shirt plus a setup fee of 40$ there is 21 students in the drama club.
a. if there are 21 students in the club and the t-shirt order costs a total of $187, how much money dose each t-shirt cost? show your reasoning
Considering the definition of an equation and the way to solve it, if there are 21 students in the club and the T-shirt order costs a total of $187, each T-shirt cost $7.
Definition of equationAn equation in mathematics is defined as an equality established between two expressions in which known elements and unknowns or unknown values appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the cost of each T-shirt, and knowing that:
The printing company charges a certain amount for each shirt plus a setup fee of 40$ There is 21 students in the drama club.The t-shirt order costs a total of $187.the equation in this case is:
21x + 40= 187
Solving:
21x= 187 - 40
21x= 147
x= 147 ÷ 21
x=7
Finally, each T-shirt has a cost of $7.
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If The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,Then each t shirt cost 7.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that, The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,
We need to find how much money dose each t-shirt cost.
Let x be the money for each t shirt.
By given data let us form a equation.
21x + 40= 187
Subtract 40 from both sides
21x=187-40
21x=147
Divide both sides by 21
x=7
Hence the cost each t shirt is 7.
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What mass of titanium displaces 125.0 cm3, if the density of titanium is 4.51 g/cm3?
The titanium has a mass value of 563.75 grams
How to determine the mass of the titanium?From the question, the given parameters are
Density of titanium = 4.51 g/cm^3
Volume of benzene = 125.0 cm^3
The mass of the titanium is then calculated using
Density = Mass/Volume
Make Mass the subject of the formula
So, we have
Mass = Volume x Density
Substitute the known values in the above equation
So, we have the following equation
Mass =125.0 x 4.51
Evaluate the product in the equation
Mass = 563.75
Hence, the mass of the titanium is 563.75 grams
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WILL GIVE BRAINLIEST
Find the value of each variable
The slope of the line through (x, 4) and (20, -2) is -1/4
PLS HELP!!!!!!
-4 is the numerical value of x which forms part of the coordinates of the points with a slope of -1/4.
What is the numerical value of x?Slope is simply expressed as change in y over the change in x.
It is expressed as;
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( x, 4 )
x₁ = xy₁ = 4Point 2( 20, -2 )
x₂ = 20y₂ = -2Slope m = -1/4To determine the value of x, plug the slope m, x and y values into the slope formula.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
-1/4 = ( -2 - 4 )/( 20 - x )
-1/4 = ( -6 )/( 20 - x )
Cross multiply
-1( 20 - x ) = 4( -6 )
-20 + x = -24
x = -24 + 20
x = -4
Therefore, the numerical value of x is -4.
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Joel digs a hole at a rate of 35 feet every 10 minutes. After digging for 30 minutes, Joel places a bush in the hole that fills exactly 12 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
The elevation of the hole after placing the bush in the hole is 93 feet
This is a problem from the unitary method. We can easily solve this problem by following a few steps.
Joel digs a hole at a rate of 35 feet every 10 minutes. So, we have to calculate the rate at 1 min.
Joel digs a hole at a rate of 35 feet every 10 minutes
Joel digs a hole at a rate of 35/10 feet every 1 minute
[ Work done for unit minute = Total work done / total time period ]
Now we have to calculate the total work done for 30 minutes.
For a unit minute work done is 35/10, then for 30 minutes the total work done is, (35/10 × 30 ) feet = 105 feet.
Joel places a bush in the hole that fills exactly 12 feet of the hole.
Therefore, the actual elevation is ( 105 feet - 12 feet ) = 93 feet.
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a police car is located 40 feet to the side of a straight road. a red car is driving along the road in the direction of the police car and is 200 feet up the road from the location of the police car. the police radar reads that the distance between the police car and the red car is decreasing at a rate of 80 feet per second. how fast is the red car actually traveling along the road? the actual speed (along the road) of the red car is feet per second
The actual speed (along the road) of the red car is 81.6 feet per second
What is Pythagoras' theorem?
The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem.
Refer to the figure attached.
[tex]z^2=y^2+40^2[/tex]
[tex]z^2=y^2+1600[/tex]
Differentiate with respect to time 't'
[tex]D(z^2)=D(y^2)+D(1600)[/tex]
[tex]2zD(z)=2yD(y)+0[/tex]
[tex]zD(z)=yD(y)[/tex]
Now, y=200, [tex]z^2=200^2+40^2[/tex] , [tex]z^2=41600[/tex], [tex]z=203.96[/tex]
D(z)=80.
Substitute the known values into the equation below:
[tex]zD(z)=yD(y)[/tex]
(203.96)(80)=200 D(y)
On simplifying, D(y)=81.6 feet per second
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The actual speed (along the road) of the red car is 81.6 feet per second
What is Pythagoras' theorem?
The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem.
Refer to the figure attached.
[tex]z^2=y^2+40^2[/tex]
[tex]z^2=y^2+1600[/tex]
Differentiate with respect to time 't'
[tex]D(z^2)=D(y^2)+D(1600)[/tex]
[tex]2zD(z)=2yD(y)+0[/tex]
[tex]zD(z)=yD(y)[/tex]
Now, y=200, [tex]z^2=200^2+40^2, z^2=41600,z=203.96[/tex]
D(z)=80.
Substitute the known values into the equation below:
zD(z)=yD(y)
(203.96)(80)=200 D(y)
On simplifying, D(y)=81.6 feet per second
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Answer:
Step-by-step explanation:
Answer:
1. x = -4, y = -5
Chosen strategy was to substitute for y in the second equation since the first equation gives y in terms of x. This gives an equation in x which can be solved for x, then y can be found by substituting for x in the first equation
2. x = -2, y = -3
Strategy used is to eliminate the x terms by simply adding the equations since the coefficients of x are the same but of opposite signs. Solve for y and use this value to solve for x by substituting in any one equation
3. x = -5, y = 6
Strategy used was to set the RHS of the equations equal to each other since both equations are equations with y on the LHS. Solve for x then use this value to find y value
4. x = 0, y = 1
Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation
Step-by-step explanation:
Here is how I would answer this question. Remember there are multiple ways of solving a linear equation of two variables but looking at the equations and from experience, I have chosen the most efficient way (my opinion)
Q1.
y = x - 1 [1]
3x - 4y = 8 [2]
Since we are given y = x - 1 in Eq [1], an obvious strategy is to substitute for y in eqn [2]
=> 3x - 4y
=> 3x - 4(x-1)
=> 3x - 4x - 4(-1) =
=> 3x -4x + 4
=> -1x + 4
=> -x + 4
And we know that eqn [2] has 8 on the RHS
∴ -x + 4 = 8
Subtract 4 from both sides
-x + 4 - 4= 8 -4
-x = 4
Multiply by -1 both sides
x = -4
Substitute for x in equation [1] y = x - 1 to get
y = -4 - 1 = -5
Solution: x = -4, y = -5
Q2
3x + 2y = -12 [1}
-3x + 2y = 0 [2]
Here we can see the coefficients of x are the same but with opposite signs
Adding the two equations will eliminate the x terms and allow us to solve for y which can be used then to solve for x
Adding [1] and [2] gives
3x + 2y + (-3x + 2y) = -12 + 0
4y = -12
y = -3
Substitute for y in equation [1]
=> 3x + 2(-3) = -12
=> 3x - 6 = -12
=> 3x = -12 + 6 (adding 6 on both sides
=> 3x = -6
x = -2
Solution x = -2, y = -3
Strategy used: Adding both equations to eliminate x terms since x coefficients are same but of different signs
Q3
y = 3x + 21 [1]
y = 2x + 16 ][2]
Since we have two expressions for y in terms of x, set the RHS of equations [1] and [2] to be equal and solve for x
=> 3x + 21 = 2x + 16
Subtract 2x from both sides
=> 3x - 2x + 21 = 16
=> x + 21 = 16
Subtract 21 from both sides
x = 16 - 21 = -5
Substitute for x in equation [2]
y = 2x + 16
=> y = 2(-5) + 16
y = -10 + 16
y = 6
Solution: x = -5, y = 6
Q4
2x - 7y = -7 [1]
x + y = 1 [2]
We can make the coefficients of one of the variable in both equations the same and either add/subtract as necessary to eliminate one of the variable terms and solve for the other
Multiply [2] by 7 to get
7x + 7 y = 7 [3]
[1] and [3] have y coefficients same but of opposite signs so add [1] and [3] together
2x - 7y + (7x + 7y ) = - 7 + 7
2x + 7x - 7y + 7y = 0
9x = 0
x = 0
Sub for x in [2] x + y = 0 to get
0 + y = 1
or y = 1
Solution: x = 0, y = 1
Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation