The cost of the bag of cat food is $6.22
What is cost prize ?
The prize at which the good and services have been bought is known as cost prize.
here, the given information is :
Cost of a container of cat liter = $13.75
Cost of a bag of cat food = X dollars
Total amount of money required to purchase the items = $20.80
Percentage of sales tax that had to be given = 4%
Then,
Amount of sales tax given = (4/100) * 20.8 dollars
= 20.8/25 dollars
= 0.83 dollars
Then the total purchase price for the two items = 20.80 - 0.83 dollars
= 19.97 dollars
Now we can easily find the cost of the cat food by subtracting the cost of the liter from the total purchase amount :
Cost of the cat food = 19.97 - 13.75 dollars
= 6.22 dollars
Therefore, the cost of the bag of cat food is $6.22
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Andre bought a new bag of cat food. The next day, he opened it to feed his cat. The graph shows how many ounces were left in the bag on the days after it was bought.
Using the graph, where the vertical axis represents ounces of food and horizontal axis represents the days bag was bought,
a. It took 24 days for the cat food to be 16 ounces
b. The weight of the bag before it was opened is 56 ounces,.
How to solve graphs?The graph represents the number of ounces of cat food that were left in the bag and the days it was bought.
The vertical axis represents the ounces of cat food bought while the horizontal axis represents the days since the bag was bought.
Therefore, according to the graph, the days the bag takes to contain 16ounces of cat food can be calculated as follows:
According to the y-axis, the ounces of cat food reduces as the days goes by.
If you trace 16 ounces of cat food to the horizontal side, it shows it took 24 days for the cat food to be 16 ounces.
The amount the bag weigh before it was open should be on zero's days.
Therefore, the amount of bag is 56 ounces before it was opened.
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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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Is it possible to perform two reflections of an object so that the final image is identical to the original image? If so, give an example. If not , explain your reasoning
Answer:
Yes, it is possible
Step-by-step explanation:
Take a function y= f(x). When it is reflected across the x-axis the x-coordinates do not change but the y coordinates become the negative of the pre-image
In other words reflection f'(x) of f(x) over the x-axis is y = -f(x)
If we reflect f'(x) over the x-axis then the resultant reflection is
f''(x) = -f'(x) = -(-f(x)) = f(x)
So we get the original image after two consecutive reflections along the x-axis
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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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?
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 teacher makes Hawaiian popcorn
for the 26 students in her class by adding 1 batch of
Hawaiian popcorn seasoning to 13 cups of popcorn.
Each student gets 2 cups of popcorn. How many
batches of seasoning does the teacher use?
The number of seasoning batches required by the teacher is 4.
Given, there are 26 students in a class.
The teacher is adding 1 batch of hawaiian popcorn seasoning to 13 cups of popcorn.
Each student gets 2 cups of popcorn.
If 26 students are getting 2 cups of popcorn, then the total cups required by the students will be :
26×2
= 52 cups.
Now, one batch of seasoning is consumed by 13 cups.
how many batches of seasoning will be required for 52 cups = ?
⇒ 13 cups + 13 cups + 13 cups + 13 cups = 52 cups
Hence 4 batches of seasoning is required for 26 students to get two cups each popcorn with seasoning.
Therefore 4 batches of seasoning the teacher used.
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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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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:
¿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
2. Given the perimeter of the figure is 35 km,
Find the missing side length.
X
9 km
4 km
3 km
12 km
Answer:
x = 7 km
Step-by-step explanation:
Perimeter of a polygon is P = sum of the sides of a polygon
In this figure we are given all the sides except one designated as x and the perimeter
We can add up all the sides and solve for x
Sum of sides = 4 + 3 + 12 + 9 + x
Perimeter = 35
=> 4 + 3 + 12 + 9 + x = 35
=> 28 + x = 35
=> x = 35 - 38 = 7
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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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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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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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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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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in a sale a tv has been reduced by 20%. it now costs £280. how much was it before the sale?
Answer:
How do I take 20 % off a price?
Take the original price.
Divide the original price by 5.
Alternatively, divide the original price by 100 and multiply it by 20.
Subtract this new number from the original one.
The number you calculated is the discounted value.
Enjoy your savings!
Step-by-step explanation:
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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A candy store sells lollipops and the money they collect is shown in the graph. x=number of lollipops y=cost Select the true statement. 2 Select one: O Each lollipop costs $1.50 O Each lollipop costs $0.75 2 4 O Each lollipop costs $0.25 Each lollipop costs $1.00
X is the number of lillipops
y is the cost
the first point on the graph is 1 unit away from origin through x axis and 0.75 unit unit away from origin through y axis
so, x = 1 , y =0.75
The second coordinate is 2 unit away from origin through x axis and 1.5 unit away from origin through y axis
Answer: 0.75
Step-by-step explanation:
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:
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.
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
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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Consider the first five terms of the following sequence
-5, -10, -20, -40, -80, ...
If the sequence defines a function, what is a reasonable domain and range of the function?
PLS HELP!!
A reasonable domain and range of the function is as follows:
Domain = {1, 2, 3, 4, 5, ....}Range = {-5, -10, -20, -40, -80, ....}What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
By critically observing the given sequence, we can reasonably and logically deduce that it follows the following function rule:
f(x) = -5(2)^{x - 1}
When x = 1, we have:
f(x) = -5(2)^{1 - 1}
f(x) = -5(2)^{0}
f(x) = -5
When x = 2, we have:
f(x) = -5(2)^{2 - 1}
f(x) = -5(2)^{1}
f(x) = -10
When x = 3, we have:
f(x) = -5(2)^{3 - 1}
f(x) = -5(2)^{2}
f(x) = -5(4)
f(x) = -20
When x = 4, we have:
f(x) = -5(2)^{4 - 1}
f(x) = -5(2)^{3}
f(x) = -5(8)
f(x) = -40
When x = 5, we have:
f(x) = -5(2)^{5 - 1}
f(x) = -5(2)^{4}
f(x) = -5(16)
f(x) = -80
Therefore, a reasonable domain and range of the function is given by:
Domain is equal to {1, 2, 3, 4, 5, ....}
Range is equal to {-5, -10, -20, -40, -80, ....}
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Another music store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better? Should Maria change her rental plan? Part A: Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for $495. Should she buy or rent the trombone? Explain. How much does she pay? dont have to answer part a but u can if u want i only put it there so u can see it all, thank you friend: )
Answer:
Yearly fee of $48 is better
Step-by-step explanation:
It is obvious. We know that a year have 12 months so if we compare between the $30 per months deal (which is $360 a year when we multiple it with 12) and the $48 a year deal, the difference is $312 which is a lott.
If Maria only want to use it for a month then its fine but if she want to use it more than 1 month, she definitely should choose the no 2 deal because if she even only rent it for 2 months using the no 1 deal ($30+$30=$60), the no 2 deal ($48) is far more better with a $12 difference.
Part A: Just like the top we know that its costs $34 per month and we need to know how much it would costs for 12 months/a year. So we just have to multiple it with 12=$408. Now which is better $495 or $408? Of course its $408 right? Maria could save $87 with renting the trombone than buying the trombone.
What is NOT another name for line qA) line RLB) line LQC) line LGD) line RG
In the given figure, RL, LG and RG are line segments, which are portions of a line q connecting two endpoints.
Therefore, RL, LG and RG a are another name of line q.
LQ is not another name of line q.
So, option B is correct.
What kind of transformation converts the graph of f(x)=3x+9 into the graph of g(x)=3x–10?
The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up
How to determine the transformation?The equations of the functions are given as
f(x) = 3x + 9
g(x) = 3x - 10
Let the translations from f(x) to g(x) be h and k
So, we have
g(x) = f(x + h) + k
This gives
f(x + h) = 3(x + h) + 9 + k
Open the brackets
f(x + h) = 3x + 3h + 9 + k
Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k
g(x) = 3x + 3h + 9 + k
This means that
3x + 3h + 9 + k = 3x - 10
Evaluate the like terms
3h + 9 + k = - 10
This gives
3h + k = - 19
Express -19 as -21 + 2
3h + k = -21 + 2
Express 21 as 3 * 7
3h + k = -3 * 7 + 2
By comparison, we have
h = -7 and k = 2
This means that the transformation is 7 units right and 2 units up
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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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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