Answer:
Solving a system of equations by substitution involves isolating a variable in one equation, then substituting that expression into the other equation. This allows you to solve for the remaining variable in one equation and then substitute it back into the first equation to find the solution for the other variable.
Here is the general process for solving a system of equations by substitution:
Isolate a variable in one of the equations. This is typically done by adding or subtracting one of the variables from both sides of the equation.
Substitute the isolated expression into the other equation by replacing the corresponding variable with the expression you found in step 1.
Solve the new equation for the remaining variable.
Substitute the value you found for the remaining variable back into the first equation and solve for the other variable.
Check your solution by substituting the values you found for the variables back into both equations to make sure they are true statements.
Write your solution in the form of an ordered pair (x, y)
An example of solving a system of equation by substitution :
2x + 3y = 8
4x - 3y = 2
Isolate a variable in one of the equations, for example:
3y = 8 - 2x
Substitute this expression into the other equation:
4x - 3(8 - 2x) = 2
Solve the new equation for the remaining variable:
4x - 24 + 6x = 2
10x = 26
x = 2.6
Substitute the value you found for x back into the first equation and solve for y:
2(2.6) + 3y = 8
5.2 + 3y = 8
3y = 2.8
y = 0.93
Check your solution by substituting the values you found for the variables back into both
The sum of the first four terms of an arithmetic progression is 14. If the sum of the first eight terms is 108, find the sixth term of this progression.
The sixth term of the arithmetic progression is 94.
An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.
Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:
an = a + (n-1)d
We know that the sum of the first four terms is 14, so we can set up the following equation:
a + (a+d) + (a+2d) + (a+3d) = 14
We also know that the sum of the first eight terms is 108, so we can set up another equation:
a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
Now we can use the first equation to substitute for the first four terms of the second equation:
14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108
This gives us:
a + 4d = 94
So the sixth term can be found by substituting n = 6 into the first formula:
a + (6-1)d = a + 5d = 94
Therefore, the sixth term of the arithmetic progression is 94.
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Write it using this format (example): △ABC = △DEC due to AAS
Angle A = Angle D Given
Angle C1 = Angle C2 Vertically Opposite
AB=DE
Shapes that are identical to each other are considered congruent. There are no differences in the matching sides or angles.
What is a congruent shape?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Here is the format you requested:
△ABC = △DEC due to AAS
Angle A = Angle D Given
Angle B = Angle E Alternate Interior
Angle C1 = Angle C2 Vertically Opposite
AB = DE Congruent Sides
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I need help i cant figure out what im doing wrong, im confused (just number 15)
the length of the sections will be 24 and 18 respectively.
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given, Some pair of lines in that three lines are parallel and two of them are intersecting them.
Since, these are the the section made by two parallel lines. Thus, these given section will be Proportional to each other.
Thus,
20/15 = ( 7x - 11)/(4x - 2)
4/3 = ( 7x - 11)/(4x - 2)
16x - 8 = 21x - 33
5x = 25
x = 5
therefore, the length of the sections will be 24 and 18 respectively.
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2. If 60 adults ages 18 - 29 made resolutions, how many people were surveyed?
picture is the percentages of people that age
ex: 10% of adults are ages 18-29
If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.
How to calculate percentages?
Percentages are a way to express a number as a fraction of 100. To calculate a percentage, you can use the following formula:
(Part/Whole) x 100 = Percentage
The question states that 60 adults ages 18-29 made resolutions, but does not provide information about the total number of people surveyed. In order to determine the total number of people surveyed, we would need additional information about the percentage of adults that fall within the age range of 18-29.
If the percentage of adults ages 18-29 is 10%, and 60 adults in that age range made resolutions, we can use that information to determine the total number of people surveyed.
We can use the following formula:
(Total number of people surveyed) = (Number of adults ages 18-29 who made resolutions) / (Percentage of adults ages 18-29)
(Total number of people surveyed) = (60) / (0.10) = 600
Hence. If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.
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What are the solutions of the quadratic equation 3x² 14x 5 0?.
The solutions of the quadratic equation 3x^2 + 14x + 5 = 0 can be found by factoring the equation into the product of two binomials, which are equal to zero.
3x^2 + 14x + 5 = (3x+1)(x+5) = 0
To find the solutions, we set each factor equal to zero and solve for x:
3x+1 = 0 or x+5 = 0
x = -1/3 or x = -5
Therefore, the solutions of the quadratic equation 3x^2 + 14x + 5 = 0 are x = -1/3, x = -5.
Alternatively, you can use the Quadratic formula to find the solutions.
The Quadratic formula is: x = (-b ± √(b^2-4ac))/(2a)
Where a,b and c are the coefficients of the equation.
x = (-14 ± √(14^2-435))/(2*3) = (-14 ± √(196-60))/6 = (-14 ± √(136))/6
It's worth noting that both solutions x = -1/3 and x = -5 are correct.
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Where is the vertex of the graph of the quadratic function f/x )= x² located?.
The vertex of the graph of the quadratic function f(x )= x² located at the origin of the graph.
The function f(x)=x² looks like a quadratic equation.
The most basic quadratic function is f(x) = x², Its shape should look familiar from Intermediate Algebra – it is called a parabola. The point (0,0) is called the vertex of the parabola.
To find the vertex of a quadratic function on a graph:
Get the equation in the form y = ax²+bx+c.
Calculate -b/2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b/2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
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Sam ha 3. 50 le than junhao and 2. 30 le than Nora. Junhao ha 4. 25. How much money doe Nora have
Nora will have $ 4.05 money.
Given that, Sam has 3. 50 less than Junho and 2. 30 less than Nora. Junhao has 4. 25.
By using the unitary method
The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.
The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.
Junhao has $4.25
so, Sam has =$4.25-3.50
= $1.75
::NORA HAS = $ 1.75 +2.30
= $ 4.05
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Write the equation of the line passing through the points (-2,9) and (-9,2)
Answer:
Step-by-step explanation:
A vertical line has undefined slope, but will always have an x-intercept. In this case, since the line goes through the point (-2,-9) we know that x will always equal -2. So therefore the equation of this vertical line will be x=-2.
The Rose department store chain was closing one of its stores so they had to sell most of the inventory in the store. In the final markdown, they
marked all items 1/3
off the ticketed price. How much would a shirt that was ticketed at $24.99 cost?
The cost of the shirt given the ticketed price is $16.66.
What is the cost of the shirt?When the price of an item is marked down, it means that the price of the item is reduced. The item would become cheaper after the mark down. The shirt would become cheaper after it is marked down.
Price of the shirt after the mark down = (1 - fraction of mark down in price) x ticketed price
= (1 - 1/3) x $24.99
= 2/3 x $24.99
= $16.66
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whats x-8< -2?x−8<−2?
you get 15 points for solving
The solution to the inequality is x < 6
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
x - 8 < -2
Add 8 to both sides of the inequality
So, we have the following representation
x - 8 + 8 < -2 + 8
Evaluate the sum in the expression
x < -2 + 8
Evaluate the other sum
x < 6
Hence, the solution is x < 6
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How do you change a improper fraction to a mixed fraction class 7?.
Divide the numerator by denominator. Carry the quotient as a whole number and the remainder as the numerator of the proper fraction, maintaining the denominator the same.
A mixed fraction is a type of fraction described as having a fraction and a whole number.
Let's take an example to understand the process completely.
For example, 3(1/7), where 3 is a whole number and 1/7 is a fraction.
Step 1: Divide the Fraction’s numerator by the denominator, i.e. 22/7.
Step 2: The integer portion of the answer will be the integer portion for a mixed fraction, i.e. 3 is an integer.
Step 3: The Denominator will be the same as the original fraction, i.e. 7.
Step 4: So, the improper fraction 22/7 is changed to a Mixed fraction as 3 (1/7).
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How do you know if a function has an inverse that is also a function?.
If and only if a function is a bijective function, it has an inverse that is also a function.
Only in the condition, if a function is bijective, meaning it is both onto (surjective) and one-to-one (injective), it has an inverse that is itself a function. If there are no two random input values resulting in a similar output value, then the function is said to be injective. As a result, there is only one x-value that can yield a given y-value.
A unique inverse function cannot be determined for a function if it is not injective. Whereas, a function is surjective if at least one input value is required to produce each output value. As a result, there is at least a single x-value in the domain of the function that yields each y-value in the function's range. A function's inverse would not be defined for values in the range if it were not surjective.
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5 = –6x2 + 24x
5 = –6(x2 – 4x)
inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot
Answer:I apologize, but I am not able to understand your question as it is written in a mix of mathematical notation and text that is not clear. Could you please rephrase your question or provide more context? I'll be happy to help you with your question.
Step-by-step explanation:
Please help me again, part 3
Answer:
c
Step-by-step explanation:
c
Complete the ratio table.
145 52
290 104
435 156
580
725
Step-by-step explanation:
since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.
the basic ratio is here
145/52 (or written 145:52 - it has the same meaning)
290/104 is just (145×2)/(52×2)
435/156 is just (145×3)/(52×3)
to complete the table we simply have to keep following that structure :
580 = 145×4
so, 52×4 = 208
and the ratio is
580/208
725 = 145×5
52×5 = 260
and the ratio is
725/260
7th grade math questoion will give bring list thingy pls answer asap
Answer: Expression - 10.2x
The weight carried by each hiker is 10.2 pounds.
Step-by-step explanation:
Hello! To find the answer, you have to add all of the weight together. Do 3.4 + 4.6 + 2.2 = 10.2. You know the total combined weight that all hikers will have to carry is 10.2 pounds. The expression will be 10.2x. You can check this by putting a random number in for x to represent the number of hikers. 10.2 (2) = 20.4. 20.4 would be the total weight that two hikers would have to carry, so the expression is correct. You already know the weight each hiker will have to carry, 10.2 pounds, so you can put that in for the second question.
What i the range of the variable x
X 2 4 6 8 10 12
p (x) 0. 10 0. 20 0. 15 0. 10 0. 12 0. 25
A. 2
B. 10
C. 8
D. 12
Answer:
B.10
Step-by-step explanation:
Because it increases by 10
Factorize x⁴-2x³-x²+2x
Answer:
x⁴-2x³-x²+2x = (x²-2x+2)(x²+2x+1)
Answer:
x(x-2)(x+1)(x-1)
Step-by-step explanation:
just add and subtract the second term to the expression and factor by grouping
ez
brainliest pls have good day
Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The most likely happened in Sandy's experiment is that,
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Option D is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Tossing a coin:
The probability of getting a head = 1/2
The probability of getting a tail = 1/2
This is the theoretical probability.
Now,
Experiment probability:
Virtual coins too have the same probability of getting a head and a tail as compared to the theoretical probability.
Thus,
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
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Answer:Not Sure but it is not D at all so please don't use that!
Step-by-step explanation:
a girl lifts her cat up to her face to give him a kiss The mass of the cat is 2.5 kg. she lifts him up a distance of 1.2m. Use the formula Fg= mg to find the weight of the cat in newtons (N)
The weight of the cat is equal to 24.5 Newton.
What is weight?In Science, weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Mathematically, the weight force on a physical body can be calculated by using this formula:
Fg = mg
Where:
Fg represents the weight.m represents the mass.g represents the acceleration due to gravity.Note: Acceleration due to gravity is equal to 9.8 m/s².
Substituting the given parameters into the weight formula, we have;
Weight, Fg = 2.5 × 9.8
Weight, Fg = 24.5 Newton.
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Find An Equation Of The Plane Consisting Of All Points That Are Equidistant From (1, 4, 4) And (-4, 1, 2). Note: You Have To Enter The Full Equation.This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.See AnswerFind an equation of the plane consisting of all points that are equidistant from (1, 4, 4) and (-4, 1, 2).Note: you have to enter the full equation.
An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0
Given, the points are (1, 4, 4) and (-4, 1, 2).
We have to find an equation for the plane consisting of all points that are equidistant from the given points.
Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.
Using the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]
Distance between the points (x, y, z) and (1, 4, 4)
=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]
Distance between the points (x, y, z) and (-4, 1, 2)
=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
By using algebraic identity,
(a-b)² = a²-2ab+b²
(a+b)² = a²+2ab+b²
(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)
x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4
By grouping,
-2x-8x-8y+2y-8z+4z+33-21
-10x-6y-4z+12=0
Dividing by -2 into both sides,
5x+3y+2z-6=0
Therefore, the equation of the plane is 5x+3y+2z-6=0
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What is inverse of a number?.
In common inverse meaning is “something that is contrary or reverses”. When we define inverse meaning we will talk mostly from the mathematics point of view where we find the inverse of different operations and functions
The inverse of a given number is equal to number that is obtained by solving the operation 1/x where x is the initial number.
The inverse operation of subtraction is addition, the inverse operation of division is multiplication.
The inverse of a number should not be muddled with its opposite. While the inverse is 1/x, the opposite is equal to -x. That is, the inverse of 3 is equal to 1/3 while its opposite will be equal to -3.
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Choose Efficient Methods Determine whether b = 6 is a solution or is not a solution of each equation. please help!!
Here, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54 ÷ b = 9 but not a solution for 4 = b + 11 - 3b.
What is the solution of equation?Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and typically consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.
One or more variables are designated as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.
To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. The term "equation's root" is frequently used to refer to an equation's solution, especially but not exclusively for polynomial equations.
Given to prove b = 6
a. 8b = 48
b = 48/8
b = 6
b = 6 is a solution
b. 4 = b + 11 - 3b
3b - b = 11 - 4
2b = 7
b = 7/2
b = 3.5
b = 6 is a not solution
c. b + 3 = 9
b = 9 - 3
b = 6
b = 6 is a solution
d. 54 ÷ b = 9
9b = 54
b = 54/9
b = 6
b = 6 is a solution
Thus, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54 ÷ b = 9 but not a solution for 4 = b + 11 - 3b.
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What will be the additive inverse of âž– 7 by 5?.
The additive inverse of 7/5 will be -7/5.
The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.
That is, Number + Additive inverse = 0
OR
The negative of a number.
Now we are given the number
7/5
So, the additive inverse of 7/5:
⇒7/5 + Additive inverse = 0
⇒Additive inverse = -7/5
Thus the additive inverse of is 7/5 is -7/5.
--The given question is incorrect; the correct question is
"What will be the additive inverse of 7/5?"--
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Which of the following describes a median of a triangle?
a segment drawn from a vertex to
the midpoint of the opposite side
a segment drawn from the vertex perpendicular to
the line containing the opposite side
a segment drawn through the midpoint of a side and at a right angle to the side.
a segment drawn from the center of an angle to the side opposite.
A segment drawn from a vertex to the midpoint of the opposite side is the correct option.
What does a perpendicular line look like?Lines that cross each other at a correct angle are considered to be perpendicular. Examples are the ends of a horizontal ladder and the opposing sides of a rectangle. the symbol that denotes two parallel lines In geometry, a pair of lines that meet or intersect with right angles (90°) are said to be perpendicular.
How is a perpendicular line drawn?Drawing the dotted line for the specified measurement is the first step in the line segment construction process. Then, make a mark at that location on the line and set the compass at that location. Now, draw an arc across each side of the indicated line. Draw another arc without adjusting the compass.
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The quotient of a number x and 19 is 10.
yes no
The value of the number x such that the quotient of the number,x and 19 is 10 is; 190.
What is the value of x from the word problem?As evident in the task content, the value of x is to be determined such that the quotient of a number, x and 19 is 10.
Since the statement given above can be written algebraically as;
x / 19 = 10
By multiplying both sides of the equation by 19; we have that;
x = 10 × 19
x = 190.
Ultimately, the value of x is; 190.
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x(-2.54y+6y-3.77)+x
pls help asap it’s already 2 days late
Answer: To find the answer to the expression x(-2.54y+6y-3.77)+x, I followed these steps:
Distribute the x coefficient:
x(-2.54y+6y-3.77) = -2.54xy + 6xy - 3.77x
Combine like terms:
-2.54xy + 6xy - 3.77x + x = -2.54xy + 6xy - 2.77x
Simplify the expression:
-2.54xy + 6xy - 2.77x
The result is a polynomial with x and y as variables, and the coefficients -2.54, 6, -2.77.
It is a good practice to check the work by substituting the variables with some numbers to see if the output is correct.
Step-by-step explanation:
Answer:
he given expression can be simplified as:
X(-2.54y+6y-3.77)+x
= X(-2.54y + 6y) + X(-3.77) + x
= X(3.46y) - 3.77X + x
= 3.46xy - 3.77X + x
So, the simplified form of the given expression is 3.46xy - 3.77X + x.
Derek bought a pack of 8 baseball cards for $16. He bought I football card for $11.
How much more did Derek spend on I football card than on I baseball card? Enter the answer in the box.
Answer:
9
Step-by-step explanation:
16 divided by 8 equals 2
11-2=9
An angle measures 93.8° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of each angle is 136.9 and 43.1.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
An angle measures 93.8° more than the measure of its supplementary angle.
This means,
There are two angles whose sum is 180.
x + y = 180 ____(1)
x = y + 93.8 _____(2)
Now,
From (1) and (2) we get,
y + 93.8 + y = 180
2y = 180 - 93.8
2y = 86.2
y = 43.1
Now,
x = 43.1 + 93.8
x = 136.9
Thus,
The angles are 136.9 and 43.1.
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Megan purchaed a weater that cot $34. 0. She ued a 20% off coupon and had to pay 7% ale tax how much did her purchae cot un total
Megan has to pay 29.10 dollars for the sweater after 20 % decrease in cost and a tax of 7 %.
After the discount and the tax is applied, Megan will pay 29.10 dollars for the sweater.
Here we have to determine that how much did Megan pay in total
We know that originally, the sweater costs $ 34.00, and there is a 20 % decrease in that cost and a tax of 7 %.
The decrease of 20 % is written as a factor:
[tex]$1- \frac{20}{100}[/tex] = (1 - 0.2)
The decrease of 20 % is (1 - 0.2).
And an increase of 7 % is written as a factor:
[tex]$1+\frac{7}{100}[/tex] = (1 + 0.07)
The increase of 7 % is (1 + 0.07).
Then the amount that Megan pays for the sweater is:
P = 34.00 × (1 - 0.2) × (1+0.07)
P = 34.00 × (0.8) × (1.07)
P = 29.10
She pays 29.10 dollars for the sweater.
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Megan purchased a sweater that costs $34.00. She used a 20% off coupon and had to pay 7% sales tax how much did her purchase cost on total
