One can solve basic algebraic expressions by following these steps.
In grade 6, students typically learn to solve basic algebraic expressions by following these steps:
Identify the variable and the coefficient (number in front of the variable) in the expression.
Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.
Use the distributive property to combine like terms.
Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).
Substitute in a value for the variable to find the numerical value of the expression.
It's good to practice with a lot of examples and check the solutions and ask for help if needed.
Example:
Solve for x: 3x + 2 = 12
variable is x, coefficient is 3
nothing to simplify
nothing to combine
subtract 2 from both sides: 3x = 10
divide both sides by 3: x = 10/3 or 3.3333
x = 3.3333
It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.
Thus, One can solve basic algebraic expressions by following these steps.
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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?
X/4 + 11 = 25
Solve for x
Answer: x=56 you can just look it up on
Answer:
[tex]x=56[/tex]
Step-by-step explanation:
[tex]\frac{x}{4}+11=25\\\\[/tex]
Mutiply by 4 every each number you see.
[tex]x+44=100[/tex]
Subtract -44 in both sides.
[tex]x+44-44=100-44[/tex]
So,
[tex]x=56[/tex]
Hope this helps :D
Is 64 a cube number?.
Yes, 64 a cube number.
64 is the cube of 4.
As, 4 x 4 x 4 = 64
The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.
Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.
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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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Please help quick!!!
Answer: x = 13, and the angle measures are 131, 49, 131, 49.
Step-by-step explanation:
7x + 40 = 10x + 1
40 = 3x + 1
39 = 3x
x = 13
The obtuse angle is 131, and the acute one is 49.
A Foucault pendulum can be used to demonstrate that the Earth rotates . The time , t , in seconds , that it 2n 67 takes for one swing or period of the pendulum can be modeled by the equation where L is the length of the pendulum in meters and g is a constant of 9.81 m / . The first Foucault pendulum was constructed in 1851 and has a pendulum length of 67 m . Determine , to the nearest tenth of a second , the time it takes this pendulum to complete one swing . Another Foucault pendulum at the United Nations building takes 9.6 seconds to complete one swing . Determine , to the nearest tenth of a meter , the length of this pendulum
The time to complete one swing or period is 16.4 seconds and the length is 3.3 meters
The time to complete one swingFrom the question, we have the following parameters that can be used in our computation:
L = 67 meters and g = 9.81 m/s²
The time, t, in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation:
t = 2π(√(L/g))
Substitute the known values in the above equation, so, we have the following representation
t = 2π(√(67/9.81))
Evaluate
t = 16.4 seconds (approx)
The length of the pendulumHere, we use the same equation and solve for L
In this case, t = 9.6
t = 2π(√(L/g))
substitute the known values in the above equation, so, we have the following representation
9.6 = 2π(√(L/9.81))
So, we have
L = (9.6/(2π))² * 9.81
Evaluate
L = 3.3 meters (approx)
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Can you help please?
To be a function, each x-value (or input) can only be used once. Each x-value (or input) can only be paired with a single y-value (or output).
If any x-value (or input) is paired with more than one y-value (or output), it's not a function.
Top Left:
Not a function
"rock" and "leaf" are paired with two outputs.
Top Right:
Not a function
The one input goes to three outputs.
Bottom Left:
Function
Each x-value/input is used only once.
Bottom Right:
Not a function
The x-value of 4 is used twice and paired with two different y-values.
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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At a local print shop, 20 copies can be made for $8. At this rate, how much would it cost to make 75 copies?
Fill out the table of equivalent ratios until you have found the value of x.
At a local print shop, 20 copies can be made for $8. At this rate, it would cost $30 to make 75 copies.
What is the equivalent ratio?
Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.
To solve this problem, we can set up a ratio between the number of copies and the cost:
20 copies / $8 = 75 copies / x
We can cross-multiply to find the value of x:
20 copies * x = 75 copies * $8
20x = 600
x = 30
Therefore, it would cost $30 to make 75 copies.
Here's the completed table of equivalent ratios:
Number of copies Cost
20 $8
75 x
We know that these ratios are equivalent, so we can set up a proportion:
20/8 = 75/x
Then we cross-multiply:
20x = 75 * 8
20x = 600
And solve for x:
x = 600/20
x = 30
Therefore, it would cost $30 to make 75 copies.
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which choice is equivalant to the quotient shown here for acceptable values of x? sqrt 9x^2 divided by sqrt 5x
a. x sqrt 9x/5
b. sqrt 9x^3/5
c. sqrt 45x^3
d. sqrt 9x/5
The equivalent expression of the given value is sqrt 9x/5. Option D
What is the equivalent?We have to note that when we are dealing with this expression, we have to bear in mind one of the rules of surd that states that; √P/√Q = √P/Q. This is the rule of surd that would guide our operation here.
We have that;
√9x^2/√5x
This would be the same as;
√9x^2/5x
According to the rule above, we now have;
√9x/5
Thus, by the use of the laws of surd we would have the expression √9x/5 as shown in the solution above.
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15 scouts can sell all of their troop's cookies in 24 days. How many days will it take for 18 scouts to sell cookies if the rate stayed the exact same? (Please give step-by-step solution too)
Answer:
28.8 days
Step-by-step explanation:
If. 15 scout = 24 days
than. 18 scout = ?
= 18/15 × 24 days
= 432/15
= 28.8 days.
If 15 scout can sell all their troops cookie's in 24 days than 18 scout too will sell cookies in 28.8 days.
what is the equation of the parabola with vertex (-1,-3) and the origin as zero
The equation of the parabola with vertex (-1,-3) and the origin as zero point is given by y = (x + 1)2 - 3.
What is Equation?An equation is a mathematical statement that expresses two expressions as being equal. It consists of two expressions, one on either side of an "equals" sign, and indicates that the expressions have the same value. For example, the equation "2 + 2 = 4" states that the value of the expression "2 + 2" is equal to the value of the expression "4".
This equation can be derived by transforming the standard form of a parabola, which is y = ax2 + bx + c, into a form where the vertex of the parabola lies at the origin of the coordinate system. The standard form of the equation can be written as y = (x - (-1))2 -3. When the terms inside the parentheses are multiplied out, the equation becomes y = (x + 1)2 – 3.
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How to multiply 4 x 0.27
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 17)(0,17) and (2, 153)(2,153).
The locations (0, 17) and are traversed by an exponential function of the type y = abx, where a and b are constants (2, 153). We can utilise these points to solve for the values of a and b in order to determine the equation of the exponential function.
Since we now know that y = abx when x = 0, we can change the first point to read as follows:
17 = a(b^0)
We can simplify this to: since anything raised to the power of 0 is 1,
17 = a
We can now determine b using the second point (2, 153):
153 = ab^2
By applying the formula:
153/a = b^2
taking square root
b = sqrt(153/a)
Substitute a = 17
b = sqrt(153/17)
The equation will now look like this when we add the value of a back in:
y = a * b^x
y = 17 * sqrt(153/17)^x
y = 17 * sqrt(9)^x
Consequently ,y = 17 * 3^x, is the exponential function that passes between the positions (0, 17) and (2, 153).
Therefore , the exponential function is y = 17 * 3^x .
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Hello need this due in 5 minutes
Answer:
C) 12%
Step-by-step explanation:
Answer: The answer is B.
Step-by-step explanation:
Add all of the students who chose English together and u get 24 and 12 is 50% of 24
Please help me with this math problem!! Will give brainliest!! :)
Answer:
42 feet
Step-by-step explanation:
Since they are similar, that means the rectangles are reduced copies of each other. So, to find the length, you have to do 60/(40/28), to get the length of the pool. 40/28 is the ratio. 60/(40/28) = 42, so the answer is 42 feet.
Answer: 42 feet
Step-by-step explanation:
Width of pool to patio = 28 : 40
28 : 40 = 7 : 10
Multiply both sides by 6:
42 : 60, so the length of the pool is 42 feet
line graph shows number of pairs of shoes owned by some children
The modal number of the pairs of shoes owned by the children is 3 pairs of shoes.
What is the modal number ?In mathematics, the modal number or mode, is the number that appears on the data set the most times out of all the numbers that appear on a set of numbers or data.
In the case of this line graph on the number of pairs of shoes that children own, the modal number would be 3 pairs of shoes as this is the highest number according to the fact that 5 students own 3 pairs of shows.
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The question is:
What is the modal number of pairs of shoes owned by the children?
How do you find the roots of a quadratic equation in factored form?.
By setting one side of a quadratic equation to zero, factoring the resulting polynomial, and then using the Zero Product Property, you can obtain the solutions, or roots, of these equations.
According to the Principle of Zero Products, if ab = 0, then either an or b, or both a and b, are 0, or both are 0. The roots of a function (f (x) can be any function) are the answers to y = f (x) when y = 0. These are the locations where an equation's graph crosses the x-axis.
To use factoring to solve a quadratic equation:
1. Convert the equation to standard form with a zero on one side.
2. Factor the non-zero side.
3. Reset each component to zero.
4. Solve each of the ensuing equations.
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Think of a number, double the number and add 6. The answer is 3 times the number. Find the number.
Answer:
The number is 6
Step-by-step explanation:
"Think of a number," [I'm thinking of x]
"double the number" [OK, that would be 2x]
"and add 6 " [If you insist: 2x + 6] ["The Answer"]
"The answer is 3 times the number" [Answer = 3x]
We take the answer, 2x+6 and set it equal to 3x
2x+6 = 3x
x = 6Solve the following quadratic equation, giving your answer accurate to 2 decimal places:
3x^2-16x+6=0
The solutions to the equation are x = 2.61 and x = -0.61
To solve the quadratic equation 3x² - 16x + 6 = 0, we'll use the quadratic formula:
x = (-b ± √(b²-4ac)) / 2a
Where a = 3, b = -16 and c = 6.
x = (-(-16) ± √((-16)²-4(3)(6)))/2(3)
x = 16 ± √(256-72) / 6
x = 16 ± √(184) / 6
x = 16 ± √184 / 6
x = (16 ± 4√23) / 6
So the solutions are:
x = (16 + 4√23) / 6 ≈ 2. 61 or x = (16 - 4√23) / 6 ≈ -0.61
Therefore, the solutions to the equation are x = 2.61 and x = -0.61.
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When Lavaughn moved into a new house, he planted two trees in his backyard. At the
time of planting, Tree A was 30 inches tall and Tree B was 15 inches tall. Each year
thereafter, Tree A grew by 2 inches per year and Tree B grew by 5 inches per year. Let
A represent the height of Tree At years after being planted and let B represent the
height of Tree B t years after being planted. Write an equation for each situation, in
terms of t, and determine which tree is taller after 6 years.
PLSSS HELPPPP
The height of Tree A t years after being planted can be represented by the equation:
A = 30 + 2t
This equation states that the initial height of the tree (30 inches) plus the annual growth of the tree (2 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.
The height of Tree B t years after being planted can be represented by the equation:
B = 15 + 5t
This equation states that the initial height of the tree (15 inches) plus the annual growth of the tree (5 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.
To determine which tree is taller after 6 years, we can substitute t = 6 into each equation and compare the results:
A = 30 + 2(6) = 30 + 12 = 42 inches
B = 15 + 5(6) = 15 + 30 = 45 inches
Tree B is taller than Tree A after 6 years because 45 inches is greater than 42 inches.
What is the value of x in the triangle?
Answer: 33
Step-by-step explanation:
66 - 33
Answer:
x is 33...........................
Step-by-step explanation:
33 +x =66
66-33=x
The sum of frequencies for all classes will always equal
a. 1
b. the number of items in a data set
c. the number of classes
d. a value between 0 and 1
The sum of frequencies for all classes will always equal to the number of element in a data set. Between 0-100 there will be 100 numbers.
So that it's 100 and correct option is b
What is frequencies ?
A frequency is a measurement of how frequently a certain value, occurrence, or feature takes place. It is employed in a wide range of disciplines, including science, engineering, mathematics, and statistics. Frequency is often expressed as a number, percentage, or ratio. For example, a frequency chart might show the number of times a particular product was purchased over a certain time period. Frequency can also refer to the number of times a particular wave pattern occurs in a given time period. In physics and engineering, frequency is used to measure the number of cycles per second of a wave or periodic phenomenon. For example, a wave with a frequency of 440 hertz (Hz) has 440 complete cycles per second.
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show york work for brainliest
what is the value for f?
Answer:
f = 21
Step-by-step explanation:
since the rectangles are scaled copies then the ratios of corresponding sides are in proportion, scaled copy to original, so
[tex]\frac{f}{28}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
12f = 28 × 9 = 252 ( divide both sides by 12 )
f = 21
Find the distance from point B to point C.
Enter as a decimal rounded to the nearest tenth.
58°
6 mi
B
BC = [?]
The distance between points B and C is 10.3 miles.
How to find distance using trigonometric functions?Trigonometry is the study of angles and the angular relationships of planar and three-dimensional figures. Trigonometry is made up of trigonometric functions (also known as circular functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.
If we have a triangle with a right angle,
Then, tan = Opposite/Adjacent side
To find the distance,
In the ABC right angle triangle,
5.7 miles on the adjacent side = AB
θ = 61°
We must locate the BC.
tan = Opposite/Adjacent side
tan61°= BC/5.7
BC = 5.7×tan61°
BC = 10.283 = 10.3 (to the nearest tenth).
The figure is attached below.
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For what value of k do the system of equations 2x 3y 4 and 6x 27y 12 has infinite solutions?.
The system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions when the coefficients of x and y are the same ratio on both equations,
2x + 3y = 4
6x + 27y = 12
For the system of equations to have infinite solutions, the ratio of the coefficients of x and y must be the same. In this case, the ratio of the coefficients of x is 2/6 = 1/3 and the ratio of the coefficients of y is 3/27 = 1/9. Since the ratio of the coefficients is not the same, the system of equations does not have infinite solutions.
Hence, the value of k for which the system of equations 2x + 3y = 4 and 6x + 27y = 12 has infinite solutions is not exist.
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A rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the other. How long is the diagonal path? a. B. C. 50 yd. D.
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Since we have a right-angled triangle, we can use the Pythagorean Theorem to find our answer. The Pythagorean Theorem states the following:
[tex]a^{2} +b^{2} =c^{2}[/tex]
In this formula a and b represent the legs of the triangle and c represents the length of the hypotenuse.
Let's substitute our data from the question.
[tex]42^{2} +20^{2} =c^{2}[/tex]
Square.
1764 + 400 = [tex]c^{2}[/tex]
And finally take the root of both sides. We only need to use the positive solution, since the length of the hypotenuse can't be negative.
[tex]c = \sqrt{2164}[/tex]
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .
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Answer: 53
Step-by-step explanation:
The length and width of the garden represent the legs of a right triangle, and the diagonal path represents the hypotenuse.
The Pythagorean Theorem states that a squared plus b squared equals c squared, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.
Let p equal the length of the diagonal path in yards.
Applying the Pythagorean Theorem gives us p squared equals forty-five squared plus twenty-eight squared.
Now square forty-five and twenty-eight to get p squared equals two thousand twenty-five plus seven hundred eighty-four.
Next, find the sum of two thousand twenty-five and seven hundred eighty-four, which is two thousand eight hundred nine.
Finally, calculate the square root of two thousand eight hundred nine to find that p equals fifty-three.
So the length of the diagonal path is fifty-three yards.
Need help with this
Gross profit is the profit that a business makes after the manufacturing and selling costs are subtracted from the total sales.
What is Gross profit?Gross profit is the profit a company makes after deducting the costs associated with making and selling its products, or the costs associated with providing its services. Gross profit will appear on a company's income statement and can be calculated by subtracting the cost of goods sold (COGS) from revenue (sales). These figures can be found on a company's income statement. Gross profit may also be referred to as sales profit or gross income.Gross profit=Net sales−CoGS.Gross margin is the difference between revenue and cost of goods sold, divided by revenue. Gross margin is expressed as a percentage. Generally, it is calculated as the selling price of an item, less the cost of goods sold, then divided by the same selling price.To learn more about Gross profit refer to:
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What is a commutative property in math?.
A commutative property in math is
with respect to Addtion : x + y = y + x With respect to Multiplication : xy = yx.Commutativity says that the numbers we are dealing with can be shifted or swapped without affecting the answer. This property applies to addition and multiplication, but not to subtraction and division.
Commutative law of addition:a + b = b + a; where a and b are
integers. Example: 3 + 4 = 4 + 3 = 7.
Commutative law for multiplication:a × b = b × a; where a and b are
non-zero integers. Example :
2×3 = 3×2 = 6
So this rule simply states that you can change the order of numbers in a question by adding or multiplying them without affecting the answer.
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what is the value of x? WILL MARK BRAINLIEST FOR CORRECT ANSWER!!!
Answer:
x = 49Step-by-step explanation:
are two similar triangles, we can solve with a proportion between the corresponding sides
42 : x = 12 : 14
x = 42 x 14 : 12
x = 49
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