The expression for r in terms of R is: r = (1-R²) / R²
What is square root?In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by itself gives 9:
3 x 3 = 9
The square root symbol is √, and the number under the symbol is called the radicand. So, √9 is read as "the square root of 9."
According to question:Starting with the given equation:
R = √(r-1) / √(r+1)
Let's first clear the square roots by squaring both sides:
R² = (r-1) / (r+1)
Now, let's multiply both sides by (r+1) to eliminate the denominator on the right-hand side:
R²(r+1) = r-1
Expanding the left-hand side:
R²r + R² = r-1
Subtracting R²r from both sides:
R² - R²r = -1
Factoring out R² on the left-hand side:
R²(1-r) = -1
Dividing both sides by (1-r):
R² = -1 / (1-r)
Finally, we can take the square root of both sides and multiply by -1 to isolate r:
r = -1 / R² + 1
Therefore, the expression for r in terms of R is:
r = (1-R²) / R²
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Make r the subject of the following:
R= √(r-1) / √(r+1)
Any number that can be written as a decimal, write as a decimal to the tenths place.
Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio.
The point that partitions segment AB in a 1:4 ratio is (
).
The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:
[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]
and
[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]
Using the distance formula, we can find the lengths of AP, PB, and AB:
[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]
Substituting these into the section formula, we have:
[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]
Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].
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the population of toledo, ohio, in the year 2000 was approximately 540,000. assume the population is increasing at a rate of 4.7 % per year. a. write the exponential function that relates the total population, , as a function of , the number of years since 2000.
The exponential function that relates the total population, is [tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex] and the rate at which the population is increasing in the year 2019 is 69114.53.
The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
we know that ,
the population of any city can be modeled in the form of exponential function as follows:
[tex]P(t)=P(0)(1+R)^t[/tex]
where, P(t)=population of the town at any given time t
P(0)=population of the town initially (in the year 2000 for this problem)=540,000
R=rate of increase (=5.1% in the given problem)
substituting the values in eqn(1), we get
[tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex]
as we know that
[tex]\because \frac{d}{dx}(a^x )=a^xln(a)[/tex]
so differentiating w.r.t. we get,
[tex]P'(t)=540,000\left [ 1+(5.1/100) \right ]^t*ln(1+(5.1/100) )\\\\P'(t)=540,000\left [ (105.1/100) \right ]^t*ln(105.1/100)\\\\P'(t)=540,000\left [ (1.051) \right ]^t*ln(1.051)[/tex]
so, the rate at which population is increasing in the year 2019 =
[tex]P'(19)=540,000(1.051)^{19}*ln(1.051)[/tex]
P'(19)= 69114.53.
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Complete question:
The population of Toledo, Ohio, in the year 2000 was approximately 540,000. Assume the population is increasing at a rate of 5.1 % per year.
a. Write the exponential function that relates the total population, P(t), as a function of t, the number of years since 2000. P(t) = =
b. Use part a. to determine the rate at which the population is increasing in t years. Use exact expressions. P'(t) people per year
c. Use part b. to determine the rate at which the population is increasing in the year 2019. Round to the nearest person per year. P'(19) = people per year
If you have 4 purple marbles and 8 yellow marbles in a bag, what is
the probability of getting a purple marble ?
Answer: 1/3
Step-by-step explanation:
4 + 8 = 12 so there's 12 marble in the bag and only 4 purple ones. so the probability is 4/12 which we can simplify to 1/3
17 identical tasks are assigned to 7 different people. each task is assigned to exactly one person and there are no restrictions on the number of tasks that can be given to any one person. how many ways are there to assign the tasks?
There are 100,947 ways to assign the tasks to the 7 people.
This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.
Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,
The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is
(17 + 6) choose 6 = 23 choose 6 = 100947
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please help me and I will give brainlist!
Answer:
16/5
Step-by-step explanation:
We can see that the new triangle is larger than the original triangle so we know the scale factor is greater than 1.
The scale factor can be found by calculating the ratio of the length of any two corresponding sides. The length of the bottom side of the original triangle is 5. The length of the bottom side of the new triangle is 16. We can calculate the ratio which is 16:5 or 16/5.
A tetrahedron is a triangular pyramid with 4 congruent faces. If the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m, what is the volume of the figure in cubic meters?
Answer:
The volume of a tetrahedron can be found using the formula:
V = (1/3) * A * h
where A is the area of one of the faces of the tetrahedron, h is the height of the tetrahedron, and V is the volume of the tetrahedron.
In this case, we are given that the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m. Substituting these values into the formula, we get:
V = (1/3) * 21 m² * 6 m
V = 42 m³
Therefore, the volume of the tetrahedron is 42 cubic meters.
Kendrick bought a calculator priced at $71. Shipping and handling cost an additional 25% of the price. What was the total cost of the calculator, including shipping and handling?
Answer:
The answer to our problem is, $17.75
Step-by-step explanation:
First we need to find out what is 25% of 71
25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75
How I got it:
25 percent * 71
= (25:100)* 71
= (25* 71):100
= 1775:100
= 17.75
Percentage solution with steps:
Step 1: Our output value is 71.Step 2: We represent the unknown value with x.Step 3: From step 1 above, 71 = 100%.Step 4: Similarly, x = 25%.Step 5: This results in a pair of simple equations:71 = 100% (1)
X = 25% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have
[tex]\frac{71}{x} = \frac{25}{100}[/tex]
X = 17.75
Thus the answer to your problem is, $17.75
graph y=5x and y=4x–1
The line for y=5x passes through the origin (0,0) and has a steep slope of 5, meaning it rises 5 units for every 1 unit to the right. The line for y=4x-1 intersects the y-axis at -1 and has a slope of 4, meaning it rises 4 units for every 1 unit to the right.
What is the graph?To graph the equations [tex]y=5x[/tex] and [tex]y=4x–1[/tex] , we can plot their corresponding points on a coordinate plane and connect them to form a line.
For [tex]y=5x[/tex]
|
6 | .
| .
5 | .
| .
4 | *
| .
3 | .
| .
2 | .
| .
1 | .
| .
0 |________________________________________
0 1 2 3 4 5 6 7 8 9
Choose any x value, let's say x=0, and find the corresponding y value by substituting it into the equation: y=5(0) = 0. This gives us the point (0,0).
Choose another x value, let's say x=1, and find the corresponding y value: y=5(1) = 5. This gives us the point (1,5).
Therefore, A steep slope of 5 means that the line for y=5x climbs 5 units for every 1 unit to the right and passes through the origin (0,0). The line for [tex]y=4x-1[/tex] has a slope of 4, which means it rises 4 units for every 1 unit to the right, and it meets the y-axis at -1.
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sam wants to color the three sides of an equilateral triangle. he has five different colors to choose from. in how many different ways can sam color the sides of the triangle? (two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring.)
The number of different colors that Sam can use for the triangle is given as follows:
60 different colors.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem (also known as the multiplication rule) is a fundamental principle in combinatorics that describes how to count the number of possible outcomes in a sequence of events.
The theorem states that if there are m ways that one event can occur and n ways that a second event can occur, then there are m x n ways that both events can occur.
The parameters for this problem are given as follows:
5 colors for the first side.4 colors for the second side.3 colors for the third side.Hence the number of options is obtained as follows:
5 x 4 x 3 = 60 options.
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Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO
I don't know but i can help a little
Step-by-step explanation:
But If the slops are the same and the y-intercepts are different, the lines are parallel...
A juice can is in the shape of a cylinder with a diameter of 4 inches. It has a volume of 125 cubic inches. What is the height of the can? leave answers in terms of π.
The height οf the juice can is apprοximately 9.98 inches.
What is cylinder?A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο cοngruent and parallel circular bases, and a curved lateral surface that cοnnects the twο bases. The twο bases are usually circular, but they can be any οther shape as well. The lateral surface οf a cylinder is curved, and it has the same crοss-sectiοn alοng its entire length.
The volume of a cylinder is given by the formula [tex]\rm V = \pi r^{2}h[/tex], where V is the volume, r is the radius, and h is the height.
Since the diameter of the juice can is 4 inches, the radius is half of that, or 2 inches.
We are given that the volume of the can is 125 cubic inches, so we can set up the equation:
[tex]\rm 125 = \pi (2)^{2}h[/tex]
Simplifying this equation, we get:
125 = 4πh
Dividing both sides by 4π, we get:
h = 125 / (4π)
So the height of the juice can is approximately 9.98 inches when rounded to two decimal places.
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How much plastic wrap will be needed to completly cover an ice cream cone that has the slant height of 4,25 inches and a diameter of 2 inches
13.4 square inches of plastic wrap will be needed to completely cover an ice cream cone that has a slant height of 4.25 inches and a diameter of 2 inches.
To completely cover an ice cream cone that has the slant height of 4.25 inches and a diameter of 2 inches, a plastic wrap of about 13.4 square inches will be needed.
How to calculate the amount of plastic wrap required to cover the ice cream cone?
To calculate the amount of plastic wrap required to cover the ice cream cone, we need to find the lateral area of the cone. This can be calculated using the following formula:
Lateral area of cone = πrℓ
where r is the radius of the base of the cone, ℓ is the slant height, and π is the constant pi, which is approximately equal to 3.14.
In this problem, the diameter of the cone is given as 2 inches, which means the radius of the cone will be half of that, i.e., 1 inch. And the slant height is given as 4.25 inches. Therefore, we can calculate the lateral area of the cone as follows: Lateral area of cone = πrℓ = π × 1 × 4.25= 13.4 square inches.
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the gnollish language consists of $3$ words, ``splargh,'' ``glumph,'' and ``amr.'' in a sentence, ``splargh'' cannot come directly before ``glumph''; all other sentences are grammatically correct (including sentences with repeated words). how many valid $3$-word sentences are there in gnollish?
There are $22$ valid $3$-word sentences in gnollish.
We can count the number of valid sentences by counting the number of all possible 3-word sentences and subtracting the number of invalid sentences where "splargh'' comes directly before "glumph.''
The total number of possible 3-word sentences is 3³ = 27, as there are 3 choices for each word.
To count the number of invalid sentences where splargh'' comes before glumph,'' we can fix splargh'' in the first position and then there are only 2 choices for the second position and 2 choices for the third position (since we cannot use splargh'' or glumph'' again). Thus, there are 2 * 2 = 4 invalid sentences where splargh'' comes before ``glumph.''
Therefore, the number of valid sentences is 27 - 4 = 23. However, we must also exclude the sentence where all three words are the same (i.e., ``splargh splargh splargh''), since this sentence is not valid according to the given condition. Thus, the final answer is 23 - 1 = 22.
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suppose the canadian football league (cfl) drops the requirement of having 21 canadian players on each team's roster, what will happen the salaries of canadian players in the cfl?
If the Canadian Football League (CFL) drops the requirement of having 21 Canadian players on each team's roster, it is likely that the salaries of Canadian players in the CFL will (option C) decrease.
Currently, the Canadian player ratio is a key factor in determining the salary cap and roster construction for teams in the CFL. If the Canadian player ratio is eliminated, teams may choose to replace Canadian players with cheaper international players, potentially leading to a decrease in demand and salaries for Canadian players.
However, it is also possible that the market for Canadian players could remain strong due to factors such as fan interest and national pride. Therefore, while it is likely that the salaries of Canadian players would decrease without the Canadian player ratio requirement, it is not certain and other factors could come into play.
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Full question:
Suppose the Canadian Football League (CFL) drops the requirement of having 21 Canadian players on each team's roster, what will happen the salaries of Canadian players in the CFL?
A) Stay the same
B) Increase
C) Decrease
D) Uncertain
I need help pls pls pls
Based on the given circle with center Y, each of the measure include the following:
mBC = 71 degrees.mAB = 142 degrees.AD = 30 units.BD = 30 units.YD = 16 units.DC = 18 units.What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners.
Based on the given circle with center Y and line AD is perpendicular to line DB, we can reasonably infer and logically deduce that arc AC is equal to arc BC;
mAC = mBC = 71 degrees.
mAB = mAC + mBC
mAB = 71 + 71
mAB = 142 degrees.
Since line DC is the perpendicular bisector of line AB, the measure of line AB and line BD can calculated as follows;
AD = BD = AB/2
AD = BD = 60/2
AD = BD = 30 units.
Note: YB is the radius of this circle and the hypotenuse of right-angle triangle YDB, which is equal to 34 units.
In order to determine the length of YD, we would have to apply Pythagorean's theorem as follows;
x² + y² = z²
BD² + YD² = YB²
30² + YD² = 34²
YD² = 1156 - 900
YD = √256
YD = 16 units.
DC = YB - YD
DC = 34 - 16
DC = 18 units.
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Which of the following relations represent functions? Select all that
apply.
A. y=4x-19
D. (-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
The only option that represetns a function is the linear equation:
y = 4x - 19
Which of the given relations represent functions?A function is a relation that maps elements from one set, the domain, into elements of another set, the range.
Such that a relation is only a function if each element of the domain is mapped into a single value from the range.
For example, if you look at the second option, here we have the relation:
(-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
You can see that the input x = -15 is mapped into two different values, y = 10 and y = 5, so this is not a function.
In the other hand, the first option:
y = 4x - 19
Is a function, this is a linear equation, and each value of x gives a different value of y.
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baby mary recognizes the table as in the same shape, even though the table appears in different shapes depending on the angle from which it is observed. this is an example of
Even though the table appears to have varied shapes depending on the angle from which it is seen, Baby Mary recognizes the table as having the same shape. Shape constancy can be seen in this situation.
What is Shape Constancy?Shape constancy is the ability of an object to retain its shape, size, and orientation even when viewed from different perspectives or angles. In essence, when the shape of an object is known, this allows an individual to recognize the object as a whole.
It's an important part of perception, and it's what allows us to recognize objects even when they're partially obscured or viewed from a different angle. A child can recognize objects as having the same shape, regardless of the angle from which they are viewed. As the object is observed from a variety of angles, its proportions and the shapes of its edges and sides change. Even so, the child perceives the object as having a consistent shape, size, and orientation.
This can be attributed to the ability of a child's brain to maintain a mental image of the object's actual shape, even when presented with an altered image.
As a result, a child may perceive an object as having a consistent shape, even if it appears to be different from one angle to another.
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Classify the expression: 5x3 + 2x − 3
Answer:
12+2x
Step-by-step explanation:
5×3= 15
15+ 2x - 3
collect like terms
15-3+2x
12+2x
therefore 5×3+ 2x - 3 = 12 +2x
Given triangle XYZ with ZX = 30°, ZY= 20° and ZZ = 2aº, what is the value of a?
A. 130
B. 65
C. 40
D. 20
According to the question, we are given a triangle XYZ
where,
∠X = 30° ∠Y = 20° ∠Z = 2a°Angle sum property states that sum of all the angles of triangle is 180°. So by adding all the three angles we will get the required value of a.
∠X + ∠Y + ∠Z = 180°
30° + 20° + 2a° = 180°
50° + 2a° = 180°
2a° = 180° - 50°
2a° = 130°
a° = 130/2
a° = 65°
Therefore, required value of a is 65°
Answer:
B
Step-by-step explanation:
remember : the sum of all angles in a triangle is always 180°.
are you sure the third angle is called ZZ ?
I am rather sure it would be called XY !
so,
180 = ZX + ZY + XY = 30 + 20 + 2a
130 = 2a
a = 130/2 = 65°
the marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. what is the probability that a class of 36 has an average midterm mark that is more than 77.83?
The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.
Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)
P(x > 77.83) = 1 - P(x < 77.83)
P(x > 77.83) = 1 - 0.9234
P(x > 77.83) = 0.0766
The path of a firework is described by the function:
h(t) = -4.9(t-5)² + 124 where h(t) is the height of the firework, in meters, and t is the time in
seconds, since the launch.
What is the vertex of the function, and what does it mean in context?
A. (5, 4.9); At 5 seconds, the firework is 4.9 meters above the ground.
B. (124, 5); At 124 seconds, the firework is 5 meters above the ground.
C. (4.9, 124); At 4.9 seconds, the firework is 124 meters above the ground.
D. (5, 124); At 5 seconds, the firework is 124 meters above the ground.
Answer:
D
Step-by-step explanation:
Because this binary function opens down, and it has an extreme point, at t=5, and you plug it in and you get 124 as the maximum.
(-3m+3d):3 пожалуйста срочноооооо!!!!!!!!!
Answer:
-m + d
Step-by-step explanation:
(-3m + 3d) : 3 =
(-3m + 3d) x 1/3 =
-m + d
x(z ÷ 3)^2 where x = 4 and z = 9 calculate
Answer: 36
Step-by-step explanation:
4(9/3)(2) = 36
Answer:
x(z ÷ 3)² = 36
Step-by-step explanation:
Given expression,
→ x(z ÷ 3)²
Now we have to use,
→ x = 4
→ z = 9
Let's simplify the expression,
→ x(z ÷ 3)²
→ 4(9 ÷ 3)²
→ 4 × (3)²
→ 4 × 9
→ 36 => {answer}
Therefore, the answer is 36.
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. if each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? approximate using pi equals 22 over 7.
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the cylinder (which is half of the diameter) and h is the height of the cylinder.
For the mini muffins in question, the diameter is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches, or 5/4 inches.
So the surface area of one mini muffin is:
Surface Area = 2π(1)^2 + 2π(1)(5/4)
Surface Area = 2π + 5π/2
Surface Area = 9π/2
To wrap 6 mini muffins, we need to multiply this surface area by 6:
Total Surface Area = 6 x (9π/2)
Total Surface Area = 27π
Approximating π as 22/7, we get:
Total Surface Area ≈ 27 x (22/7)
Total Surface Area ≈ 84.857 inches^2
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Answer:
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
Step-by-step explanation:
The price of a television is dropped by 20% during a sale.After the sale the price is increased by 20%. what is the price of the television after the sale if the original price was 1200
The price of the television after the drop in its sales price would be = 1200
How to calculate the price of the television after deduction of sales discount?The percentage of money that was removed from the cost price for the television = 20%
The original price of the television = 1200
The percentage equivalent of 1200 that is 20 = 20/100×1200/1
= 24000/100
= 240
After the sales 240(20%) is added back to the sale price which show that it remains the same after sales.
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Solve 5^x=1÷5 solve it as fast as you can
if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The above table represents the contents ( colored marble) of a bag. The probability that selected marble had a color other than white or blue is equals to the 0.766234 ( nearest to milinoth).
We have a bag that contains five different types of marbles. See the above table
number of red marbles in a bag = 16
number of green marbles in a bag = 23
number of blue marbles in a bag = 13
number of pink marbles in a bag = 20
number of white marbles in a bag = 5
So, total number of marbles in a bag= 16 + 23 + 5 + 13 + 20 = 77
Now, a single marble is selected and out of the bag. We have to determine probability that it is a color other than white or blue. Let X , Y and Z be three events defined as the following
X = selected marble is white
Y = selected marble is blue
Z = selected marble is other than blue or white
Probability of seclecting white marble, P(X) = 5/77
Probability of seclecting blue marble, P(Y)
= 13/77
Probability of seclecting blue or white marble, P(Y UX) = P(X) + P(Y) = 5/77 + 13/77 = 18/77
So, probability that selected marble has a color other than white or blue, P(Z) = 1 - P( X UY) = 1 - 18/77
= 59/77 = 0.76623376623
Hence, required probability is 0.766234.
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Complete question :
The above table discribes the contents of a bag that contains red,green, blue,pink and white marbles if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
a 90% confidence interval for the average number of children per household based on a simple random sample is found to be (.7, 2.1). can we conclude that 90% of households have between .7 and 2.1 children?
No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.
Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.
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For the system of equations below, is the graphing method or the
substitution method the better method for solving? Why?
y=2x+6
y=−9x−1
The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.
what is equations ?It has one or more variables, and based on the values of the variables, it can either be true or false. Equations are frequently employed in a wide range of mathematical applications, from straightforward algebraic equations to more intricate differential equations used in calculus and physics. Equations are used to depict relationships between various mathematical objects or values. An essential part of addressing algebraic problems is to solve equations to determine the values of the variables that make the equation true.
given
We can solve one equation for one variable and then insert the expression into the second equation to apply the substitution method. For instance, we can resolve the first equation for y as follows:
y = 2x + 6
After that, we may enter the following expression in place of y in the second equation:
2x + 6 = -9x - 1
Then, we may find x:
11x = -7
x = -7/11
We may use one of the original equations to obtain the value of y once we have determined the value of x:
y = 2(-7/11) + 6 = 23/11
The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.
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Kathy had 20 dollars to spend on 3 gifts. She spent 10 7/10
dollars on gift A and 6 2/5 dollars on gift B. How much money did she have left for gift C?
If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.
How is the balance determined?The balance can be determined using subtraction operation.
Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.
Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.
The total spending budget that Kathy has = $20
The number of gifts to buy = 3
The amount spent on Gift A = $10.07 ($10⁷/₁₀)
The amount spent on Gift B = $6.04 ($6²/₅)
The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).
Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.
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