The conjecture for the relationship between the volume of the two spheres is "the volume of a sphere with radius 2y is 8 times greater than the volume of a sphere with radius y."
A conjecture is an educated guess or a hypothesis about a mathematical statement that has not yet been proven. It can be based on patterns or observations and can lead to further exploration and eventually a proof or disproof.
The formula for the volume of a sphere is given by (4/3)πr³, where r is the radius of the sphere. To compare the volumes of two spheres with different radii, we can substitute their respective radii into the formula.
If we let the radius of one sphere be y, then the volume of that sphere can be represented as (4/3)πy³. If we let the radius of the other sphere be 2y, then the volume of that sphere can be represented as (4/3)π(2y)³. Dividing the latter by the former, we get (4/3)π(2y)³ / (4/3)πy³ = (2y)³ / y³ = 8.
Thus, the volume of a sphere with a radius equal to 2y is 8 times greater than the volume of a sphere with a radius equal to y.
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Can some please help I need to get this answer?
The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the two shorter sides, according to the Pythagorean theorem.
Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated numerous times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.
The Pythagorean relation holds true when Euclidean space is represented by a Cartesian coordinate system in analytical geometry: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points.
[tex]c=\sqrt{ a2+b2}= \sqrt{ 3.92+82}=8.9[/tex]
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a pet store gives away 3 dog treats with every food bowl sold. write an expression to represent this situation please help asap tysm
Which of the following are solutions to the inequality below? Select all that apply.
d>5
>
d=7
d=9
d=4
d = 1
Solutions of given inequality expression are d = 7 and d = 9
What are Inequatility expressions:Mathematical expressions with inequalities are those in which the two sides are not equal to each other but less or greater than the other.
In other words, it is defined as a non-equal comparison between two expressions. Just like equations, these expressions are also made up of variable and constant terms.
The signs that we used in Inequatility expressions are
≠ for not equal
< for less than
> for greater than
Here we have
d > 5 is an Inequality, which means d is greater than 5
Then the given expression will be satisfied for all the values which are greater than 5
Therefore,
Solutions of given inequality expression are d = 7 and d = 9
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A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form. Select all the true statements about this relation. Number of squares, x 1 2 3 4 perimeter, y 8 12 16 20.
Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.
What is perimeter ?
Perimeter is the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of a shape. It is commonly used to measure the size of a closed shape such as a square, rectangle, or circle. The formula for perimeter depends on the shape in question.
The statements that are true about the relation between the number of squares and the perimeter of the rectangles they form are:
As the number of squares increases, the perimeter of the rectangle also increases.
The perimeter of the rectangle is 4 times the number of squares.
The perimeter increases by 4 for every increase in 1 square.
The perimeter is calculated by multiplying the number of squares by 4.
The perimeter is directly proportional to the number of squares.
Perimeter is directly proportional to number of squares, x and is 4x where x is the number of squares.
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What will be the area of an isosceles triangle with an equal side of 8 cm and each equal side of 5 cm?.
Answer::
Solution:
Altitude =
5
2
−4
2
=3
Area =
2
1
(base)(height)
=
2
1
×8×3=12cm
2
.
solutio
The average temperature during the winter in the Arctic tundra i -34C. You can convernt Celete C to degree farenhite F uing the formula F=9\5C 32
The average temperature during the winter in the Arctic tundra i -34C which is also 93.2 degrees Fahrenheit
The difference between the freezing point of water and its boiling point at normal atmospheric pressure is divided into exactly 100 equal parts to determine the temperature in degrees Celsius (degrees). Water has a freezing point set at 0° and a boiling point set at 100°.
Therefore, a 100°C difference is precisely equivalent to a 180°F difference. As a result, each degree in Celsius is equivalent to 1.8 degrees Fahrenheit.
The 34 Celsius to Fahrenheit formula is a linear function:
[°F] = ([34] x 9 ⁄ 5) + 32.
Therefore, we get:
34 C to F = 93.2 °F
34 °C in °F = 93.2 Fahrenheit
34 C in F = 93.2 degrees Fahrenheit
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A manufacturer of new smart phones purchases screens from two different suppliers. The company receives 55% of its screens from Corning Inc. And remaining screens from Philips. The quality of the screens varies between the suppliers: Corning Inc. Supplies 1% unsatisfactory screens while 4% of the screens from Philips are unsatisfactory. Given that a randomly chosen screen is unsatisfactory, what is the probability it came from Philips
The probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Let's call the probability that a screen came from Philips "P".
know that 55% of the screens came from Corning Inc. and the rest came from Philips, so:
P = 1 - 0.55 = 0.45
We also know that the probability of getting an unsatisfactory screen from Corning Inc. is 1%, while the probability of getting an unsatisfactory screen from Philips is 4%:
P(unsatisfactory | Corning Inc.) = 0.01
P(unsatisfactory | Philips) = 0.04
Using Bayes' theorem, the probability that a randomly chosen unsatisfactory screen came from Philips can be calculated as:
P(Philips | unsatisfactory) = P(unsatisfactory | Philips) * P(Philips) / [P(unsatisfactory | Philips) * P(Philips) + P(unsatisfactory | Corning Inc.) * P(Corning Inc.)]
Substituting the values we have:
P(Philips | unsatisfactory) = 0.04 * 0.45 / [0.04 * 0.45 + 0.01 * 0.55] = 0.444444... or approximately 0.4444
Therefore, the probability that a randomly chosen unsatisfactory screen came from Philips is approximately 0.4444.
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The probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.
Let's call P(Philips) the probability that a randomly chosen screen came from Philips, and P(Unsatisfactory | Philips) the probability that a screen is unsatisfactory given that it came from Philips. Then we can use Bayes' theorem to find P(Philips | Unsatisfactory), the probability that a screen came from Philips given that it is unsatisfactory.
Bayes' theorem states:
P(A | B) = P(B | A) * P(A) / P(B)
where A and B are events, P(A | B) is the conditional probability of A given B, P(B | A) is the conditional probability of B given A, P(A) is the probability of A, and P(B) is the probability of B.
In this case,
A = "the screen came from Philips"
B = "the screen is unsatisfactory"
So:
P(Philips | Unsatisfactory) = P(Unsatisfactory | Philips) * P(Philips) / P(Unsatisfactory)
We are given:
P(Unsatisfactory | Philips) = 4% = 0.04
P(Philips) = 45% = 0.45 (since 55% came from Corning Inc.)
P(Unsatisfactory) = P(Unsatisfactory | Corning Inc.) * P(Corning Inc.) + P(Unsatisfactory | Philips) * P(Philips)
= 1% * 55% + 4% * 45% = 0.55% + 1.8% = 2.35%
So:
P(Philips | Unsatisfactory) = 0.04 * 0.45 / 0.0235 = 46.48%
So the probability that a randomly chosen unsatisfactory screen came from Philips is 46.48%.
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how to find the zeros and multiplicity of a polynomial
The zeros of a polynomial are the values of x that make the polynomial equal to 0.
To find the zeros, you need to set the equation equal to 0 and solve for x. The multiplicity of a zero is the number of times that the factor (x – zero) is a factor of the polynomial. To find the multiplicity of a zero, you need to find the highest power that x appears in the equation. For example, if the equation is (x-2)2•(x+1)3, then the zero is 2, and the multiplicity is 2.
The zeros of a polynomial are the values of x that make the equation equal to zero. The multiplicity of a zero is the number of times the factor (x - zero) occurs in the equation. To find the zeros and multiplicity of a polynomial, the polynomial needs to be factored into linear factors. The zeros are the x-intercepts of the equation (where the graph crosses the x-axis). The multiplicity is the power of the factor (x - zero). For example, if the equation is (x-2)^2(x-5), the zeros are x=2 and x=5 and the multiplicity of the zeros is 2 for x=2 and 1 for x=5.
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Use the Distributive Property to simplify the expression.
9(2n+1) =
PLs help me fast .
Factorisation by remarkable identities
Factorization by remarkable identities use the following identities, a² + 2ab + b² , a² - 2ab + b² , a² - b² , and x² + x (a + b) + ab.
What is factorization?An algebraic expression is factorized when it is written as the product of its factors. These variables, factors, or algebraic expressions might be present.
Use of Identities in Factorization utilizing identities is substantially simpler when employing some of the identities that exist.
Several expressions that need to be factored have the following forms or may be transformed into them: a² + 2ab + b², a² - 2ab + b² , a² - b² , and x² + x (a + b) + ab. Using Identities, I, II, III, and IV, it is simple to factorize these expressions.
Using each identity individually, we will study factorization in this part.
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² – b² = (a + b) (a – b)
(x + a) (x + b) = x² + x (a + b) x + ab
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Complete question:
How to do factorisation by remarkable identities?
Use 4 of the 5 numbers shown to make the equations true.
Each number can be used only once.
The answers to the two blank portions are, √64 = 8 and ∛1000 = 10.
What are surds and indices?We are aware that there are two different sorts of radicals. Surds are created when a number is raised to a power that makes it greater than zero but less than one. Indices are created when a number is raised to a power that makes it bigger than one.
We know 10×10 = 100.
10¹×10¹ = 100.
10² = 100.
√100 = 10.
Similarly ∛1000 = 10.
As ∛1000 = ∛(10×10×10) = ∛10³ = 10.
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What is the inverse of a inverse?.
The inverse of an inverse function is the original function.
For example, if a function f(x) has an inverse function g(x) such that f(g(x)) = x and g(f(x)) = x for all x in their respective domains, then the inverse of g(x) is f(x).
This is because when you apply the inverse function twice, it cancels out the effect of the inverse, and leaves you with the original function.
In mathematical notation, if f^-1(x) is the inverse of f(x), then (f^-1)^-1(x) = f(x)
So the inverse of an inverse is the original function, which means that (f^-1)^-1 = f
It's also worth noting that any function and its inverse are always one-to-one function, meaning that each element of the domain of the function corresponds to exactly one element of the range and vice-versa, which makes it possible to define an inverse function.
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The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245. How much would it cost to have 320 bricks delivered
The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245 and the cost to have 320 bricks will delivered $217.6 .
How much would it cost to have 320 bricks delivered?The cost of 250 bricks, delivered to a worksite, is $170.
So , we can calculate the single brick cost need to divide 170/250=0.68
Single brick cost is 0.68
The cost of 400 bricks delivered is $245. In this case a single brick cost is 0.6125
The answers is different from the first answer we can calculate 320 brick cost 320×0.68=217.6
The following equation is used to calculate the Cost Per Brick. To calculate the cost per brick, divide the total cost of the bricks by the number of bricks. Bricks in 1 cubic Feet (cft) = Volume of brickwork/ Volume of one brick with mortar. Thus, thumb rule formula: No. of bricks in wall per Cubic Feet= (Area in Cft × 14).
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How do i solve this?
Answer:
x = 45/2 or 22.5
Step-by-step explanation:
Since we are given CDE ~ KLM, we know that C is similar to K, D is similar to L, and E is similar to M. The problem asks to find DE, so by comparison, it is known that DE is similar to LM.
From the two triangles, KM is similar to CE, and we can see that the ratio between the two is 8:15. We are given LM, which is 12, so we can find x using this equation to compare the smaller triangle to the bigger one:
KM/CE = LM/DE
Plug in your given values:
8/15 = 12/x
Find x:
x = 45/2 or 22.5
The ratio of peanuts to raisins is 2:8. What percent of the peanuts and the raisins are peanuts? I need this ASAP.
Answer:
20%
Step-by-step explanation:
2+8=10
10*10=100
2*10=2
Please can you give me brainliest?
Pls help me with this question (#4) !
I’m learning abt similar figures in math and I don’t know what this one is
Tysm!
Answer:
x = 17, y = 8
Step-by-step explanation:
Answer:
y-8
X-17
Step-by-step explanation:
Look at the ratio. If BC is 2x of ZY, then multiply the sides of XZ and YX by 2
The side length of a square can be expressed by the formula a = Radical s where s is the area of the square. If the area of a square is 343m?, what is length of the side?
The side length of the square is 18.5 m
How to determine the side length of the squareFrom the question, we have the following parameters that can be used in our computation:
a = Radical s
where s is the area of the square.
Rewrite the above equation
So, we have the following representation
a √s
Given that the area of a square is 343m
We have
a =√343
Evaluate the root
a =18.5
Hence, the side length is 18.5 meters
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A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. Answer parts (a) through (c) below.
After six months, the subjects' symptoms are studied and compared. Answer parts are given below.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
A pharmaceutical company wants to test the effectiveness of a new allergy drug.
The company identifies 250 females 30–35 years old who suffer from severe allergies.
The subjects are randomly assigned into two groups.
One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.
After six months, the subjects' symptoms are studied and compared.
Here, 30-35 year-old girls are used to test the new allergy medication's effects.
(a)
Females between the ages of 30 and 35 who are the test subjects are the experimental units.
The new allergy medication, whose results are being studied, is the remedy.
It's best to choose C.
(b)
A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.
In this case, choice B is preferable.
(c)
If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.
In this case, choice A is preferable.
Therefore, all the correct choices are given above.
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The complete question is given in the image.
A candy box i haped like a rectangular prim. The box i 8 inche long, three inche wide, and 2 inche high. How much paper i ued to wrap the box?
92 inches² paper would be needed to wrap the prism completely.
What is the Surface Area of a Rectangular Prism?
The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.
Given here, The dimensions of the rectangular prism are 8,3,2 in inches.
Total surface area of a rectangular prism
= 2(lb + bh + lh)
Thus TSA
= 2(24+16+6)
= 92 inches²
Hence, 92 inches² paper would be needed to wrap the prism completely.
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Select the correct answer
Nia wants to check whether the finance charge applied in her credit card statement is correct. To do this, she needs to calculate the average daily
balance in her account for the previous billing cycle. She made a table to do the calculation. The billing cycle is 31 days
What was Nia's average daily balance in this billing cycle?
Balance
Days
7
10
$745. 00
$585. 15
$245 20
$90. 75
A. $13,420. 00
B. $13,418. 00
c. $800. 00
D. $432. 84
E. $430. 48
The Nia's average daily balance in this billing cycle was equals to the $432.85. So, correct choice is option(D).
Nia wants to check whether the finance charge applied in her credit card statement is correct or not. For this she made a table to do this calculation. The billing cycle is 31 days is present in above figure. We have to calculate the Nia's average daily balance in billing. Average daily balance of Nid is represented by:
Average mean = (Days x Balance)/Total Number of days
So, Days × balance = (745.0 x 7) + (1555. 15 × 10) + (245.20 × 7) + (90.75 × 7)
= 5215 + 5851.5 +1716.4 + 635.25
= $13418.15
Total number of days = 7+ 10 + 7 + 7 = 31 days
Hence, the Average = 13418.15/31
= $432.84
Hence, required average daily balance is $432.84.
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Simplify 2/3+1/6 in the simplest form
Answer: answer is 5/6, check my photo to understand
Answer: 5/6
Step-by-step explanation:
A plane rises from take-off and flies at an angle of 14 with the horizontal runway. When it has gained 950 feet, find the distance, to the nearest foot, the plane has flown.
The distance, to the nearest foot, the plane has flown is 3926.887 feet.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Angles are usually measured in degrees or radians
The horizontal runway, the distance plane flied and the height gained forms a right angled triangle.
Let x be the distance plane flied.
Height gained = 950 feet
Angle that plane makes with the horizontal runway = 14°
Sin 14 = Opposite side / Hypotenuse
Sin 14 = 950 / x
x = 950 / sin 14
x = 3926.887 feet
Hence the distance plane flied is 3926.887 feet.
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What are the 5 steps in solving equations by substitution?.
The 5 steps in solving equations by substitution are
Solve one equation for either x or y.Substitute the expression from step one into the 2nd equation.Solve the second equation for the given variable.Plug you solution back into the first equation.Write your solution as a point.If we take an example ,
Equation 1: 3x + 2y = 11Equation 2: -x + y = 3Substituting y = 3+x in equation 1 we get,
3x + 2(3 + x) = 11
3x + 6 + 2x = 11
5x = 5
x = 1
Put the value of x = 1 in the equation -x + y = 3
we get -1 + y = 3
so y = 4
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How do you solve systems by elimination with multiplication?.
To solve the given system of equations using elimination method following steps need to follow:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
As given in the question,
Steps required to solve the given system of equations by elimination method with multiplication:
To eliminate x-term equate the coefficient of x in opposite sign.
4x + 3y = 1 __(1)
3x + 4y = 1 __(2)
1. Multiply 3 to (1) and -4 to (2) to eliminate the x-term.
12x + 9y = 3 __(3)
-12x - 16y = -4 __(4)
2. Now add (4) from (3) and eliminate x-term.
12x + 9y = 3
-12x - 16y = -4
0x -7y = -1
⇒ y = 1 / 7.
Therefore, solution of the system of equation using elimination method with multiplication is:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
The above question is incomplete , the complete question is :
How do you solve systems of equations by elimination method with multiplication?.
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18. The table shows the amount of time you work and your total wages. Write an equation in
slope intercept form that gives your wage at any time. What do the slope and y-intercept
represent?
Time worked, x Wages earned,
. y($)
1. 9.25
3. 27.75
7. 64.75
The slope and y-intercept represent, time worked, x Wages earned,
y($) is 9.25.
Give a brief account in slope?In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.
From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.
The point-slope form of a linear equation is y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
We can use the data from the table to find the slope of the line.
m = (y2 - y1) / (x2 - x1)
We can use the first two data points (x1 = 1, y1 = 9.25) and (x2 = 3, y2 = 27.75) to find the slope:
m = (27.75 - 9.25) / (3 - 1) = 18.5/2 = 9.25
Now we have the slope, we can use the point (x1 = 1, y1 = 9.25) to find the y-intercept, b
9.25 = 9.25 * 1 + b
we can find b is 0
So, the equation of the line in slope-intercept form is y = 9.25x + 0
The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.
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The slope and y-intercept represent, time worked, x Wages earned, y($) is 9.25.
Give a brief account of slope.In mathematics, the slope of a line is a measure of its steepness and direction. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on a line. The slope is often represented by the letter "m" and can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
The slope of a line can also be thought of as the coefficient of the x-term in the equation of the line in the form of "y = mx + b" where m is the slope.
From the table, we can see that the wages earned are directly proportional to the time worked. This is a linear relationship and we can find the equation of the line using the point-slope form.
The point-slope form of a linear equation is y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is a point on the line.
We can use the data from the table to find the slope of the line.
m = (y₂ - y₁) / (x₂ - x₁)
We can use the first two data points (x₁ = 1, y₁ = 9.25) and (x₂ = 3, y₂ = 27.75) to find the slope:
m = (27.75 - 9.25) / (3 - 1)
= 18.5/2
= 9.25
Now we have the slope, we can use the point (x₁ = 1, y₁ = 9.25) to find the y-intercept, b
9.25 = 9.25 * 1 + b
We can find b is 0
So, the equation of the line in slope-intercept form is y = 9.25x + 0
The slope of the line, m = 9.25, represents the rate of change of the wages earned with respect to the time worked. It means that for every one-hour increase in time worked, the wages earned increase by $9.25. The y-intercept, 0, represents the wage earned when no time has been worked, which is 0$.
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________ analysis is a statistical method for analyzing the intercorrelations among various measures or test scores. It can be used to identify clusters of correlated items that are assumed to measure the same underlying trait, ability, or aptitude
The Factor analysis is a statistical method for analyzing the intercorrelations among various measures or test scores.
Factor analysis is a technique used to reduce a large number of variables to a smaller number of factors. This technique extracts the maximum common variance from all variables and puts them into the common score. This score can be used for further analysis as an index for all variables. A "factor" is a set of observed variables with similar response patterns. These are associated with hidden variables that are not directly measured (called noise variables). Factors are listed by their factor loadings, or the amount of variation in the data they can explain. There are two types: exploratory and confirmatory.
Exploratory factor analysis is used when we do not know the structure of our data or the number of dimensions in a set of variables.Confirmatory factor analysis is used for validation as long as we have a clear idea of the structure of our data or the number of dimensions in a set of variables.To learn more about factor analysis, refer:
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PLEASE HELP I WILL GIVE YOU BRAINLY ! !!!!
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on blue is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true. Hence, statement 1 is true.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.
From the given spinner we can observe that:
P (Purple) = 2 / 8
P (Yellow) = 2/8
P (Blue) = 3/8
P (Orange) = 1/8
Using the probability, we see that the statement, the probability of landing on blue is greater than the probability of landing on purple is true.
Hence, statement 1 is true.
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What is the solution to y 6 =- 3y 26?.
The solution to y+6 =- 3y-26 is 8.
The solution to the equation y+6 =- 3y-26 is to solve for y. This can be done by rearranging the equation and combining like terms. The equation can be rearranged to -3y-y+6 = -26.
Combining the like terms yields -4y+6 = -26.
To solve for y, subtract 6 from both sides.
These yields -4y = -32.
Finally, divide both sides by -4 to obtain y = 8.
Therefore, the solution to the equation y+6 =- 3y-26 is y = 8.
Understanding the solution to an equation is a critical part of algebra and can be used to solve a variety of problems. There are many methods for solving equations, and it is important to understand each type and how to employ them appropriately. Solving equations like y+6 =- 3y-26 requires rearranging the equation and combining like terms to obtain the solution. Once the equation is in a simpler form, the solution can be found by applying basic math operations.
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What are the 4 ways to solve an equation?.
Four ways of solving an equation are Graphical, Elimination, Substitution, and Cross multiplication.
Graphical method: To solve linear equations graphically, first draw the graph for both equations in the same coordinate graph and locate the intersection point on the graph.
Elimination method: In this method, any of the coefficients is first eliminated by equating. After eliminating the coefficient, the equations are resolved to get the other equation. For example:
3x + 2y = 9 ———–(i)
x – y = 6 ———–(ii)
Here, if equation (ii) is multiplied by 3, the coefficient of “x” will become equal and can be eliminated.
So, multiply equation (ii) × 3 and then subtract equation (i)
3x + 2y - 9 - 3x-3y-18 = 0
y = -9/5
Now, put the value of y = 1.8 in equation (ii).
So, x – 1.8 = 6
x = 4.2
Substitution method: To solve a linear equation using this method, first, take the value of one variable separately from any of the equations. Then, substitute the value of this variable in the second equation and solve it.
Cross multiplication method: Linear equations can be easily solved using this method. This technique is used to simplify the solution. The following formula is used for solving 2 variable equation:
x /(b₁ c₂ − b₂ c₁) = y / (c₁ a₂ − c₁ a₁) = 1 /(b₂ a₁− b₁a₂)
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Subtract 33 1/3% of 36 from 50% of 88.
Add explanation.
The value of the expression is 32.
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,
50% of 88 - 33(1/3)% of 36
This can be written as,
= 50/100 x 88 - (100/3)/100 x 36
= 44 - 12
= 32
Thus,
The value is 32.
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