log 30+ log 6 is not equivalent to log 36
What is equivalent expressions?Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).
The original phrase is as follows
Log 36
Following that, we write the alternatives (a) log 2+ log 18
Apply the logarithmic rule log 2+ log 18 log (218)
Log 2 plus log 18 log (36)
Remove the bracket
Log 2 plus log 18 log36
(a) Log 2+ Log 18 is the same as log 36.
(b) Log 30 plus log 6
Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)
Log 30 plus log 6 Equals log (180)
Remove the bracket
Log 30-plus log 6-log180
Hence,
(c) Log 30+log 6 does not equal log 36.
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Is angle 1 vertically opposite to angle 4?
Yes, angle 1 is vertically opposite to angle 4 because they are formed due to the intersection of straight lines.
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.
For example, if two lines intersect and make an angle, say X=55°, then its opposite angle is also equal to 55°. And the adjacent angle to angle X will be equal to 180 – 55 = 125°
In the given figure, ∠AOC and ∠BOD form a pair of vertically opposite angles and similarly ∠AOD and ∠BOC form such a pair. Therefore,
∠AOC = ∠BOD
∠AOD = ∠BOC
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Write an equation in slope-intercept form for each line at the right. Line one goes from (-6,7) to (1,-7) and line two goes from about (1.25,7) to (3.25,-7)
y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find equation in slope-intercept form of line passing through of (-6,7) to (1,-7) and one more line passing through (1.25,7) to (3.25,-7)
Slope of line with (-6,7) to (1,-7) is m=-7-7/1+6=-14/7
=-2
y intercept we have to find
7=-2(-6)+b
7=12+b
-5=b
So slope intercept form of line passing through (-6,7) to (1,-7) is y=-2x-5
Now Slope of line with (1.25,7) to (3.25,-7) is
m=-7-7/3.25-1.25
m=-14/2=-7
y intercept we have to find
7=-7(1.25)+b
7=-8.75+b
b=15.75
So slope intercept form of line passing through (1.25,7) to (3.25,-7) is y=-7x+15.75
Hence, y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
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Regan has Rs.10,000 in total. He lent a part of it to Sandip and the remaining to Saline. If Saline paid Rs.2160 more interest than Regan at the end of 3 years and at the rate of 18% simple interest rate. Find how much money did Regan give to Sandip and Saline. (Assume 365 days in a year)
The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.
What is an equation?An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.
The amount Regan has = Rs. 10,000
Let x represent the amount Regan lent to Sandip, we get;
The amount Regan lent to Saline = 10,000 - x
The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest
The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan
The simple interest formula is; I = P·R·T/100
Where;
P = The principal amount loaned
R = The interest rate = 18%
T = The time or duration of the loan = 3 years
Therefore;
(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3
5400 - 0.54·x = 2160 + 0.54·x
5400 - 2160 = 0.54·x + 0.54·x = 1.08·x
3240 = 1.08·x
x = 3240 ÷ 1.08 = 3000
The amount Regan lent to Sandip, x = Rs. 3000
The amount Regan lent to Saline = 10,000 - x
x = 3000
10,000 - x = 10,000 - 3000 = 7,000 (substitution property)
The amount Regan lent to Saline = Rs. 7,000
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What is the best approximation for the area of this figure?
21+14. 5π units²
21+7. 25π units²
10. 5+7. 25π units²
10. 5+14. 5π units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 5 comma negative 2 to negative 5 comma 1. Another segment extends from negative 5 comma 1 to 2 comma 1. A semicircle extends from 2 comma 1 to negative 5 comma negative 2. What is the area of this polygon?
28. 5 units²
34. 5 units²
37. 5 units²
40. 5 units²
6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)
1) The best approximation for the area of this figure is 21+14. 5π units².
2) The total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) This is a hexagon with vertices at the specified coordinates on a coordinate plane.
FIGURE AND POLYGON1) The best approximation for the area of this figure is 21 + 14.5π units². The area of a semicircle with a radius of 7 is 14.5π units², and the two segments form a rectangle with an area of 21 units². Adding these two values together gives 21 + 14.5π units².
2) This closed figure can be divided into two parts: a triangle and a quarter of a circle. The area of the triangle can be found using the formula for the area of a triangle (base times height divided by 2). The base of the triangle is the length of the segment from negative 5 comma negative 2 to negative 5 comma 1, which is 3 units. The height of the triangle is the length of the segment from negative 5 comma negative 2 to 2 comma 1, which is 7 units. So the area of the triangle is (3*7)/2 = 10.5 square units.
The area of the quarter of a circle can be found using the formula for the area of a circle (pi times the radius squared). The radius of the semicircle is the length of the segment from 2 comma 1 to negative 5 comma negative 2, which is 5 units. So the area of the quarter of the circle is (pi*5²)/4 = 19.63 square units.
So the total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) A hexagon is a polygon with six sides and six angles. In this case, the hexagon is placed on a coordinate plane, with each of its vertices (or corners) located at specific x and y coordinates.
The coordinates provided are: (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2). These coordinates correspond to six points on the plane, and the hexagon is formed by connecting these points in the specified order.
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Can someone show me step by step what to do next please I’m confused?!!! Please anyone
Answer:
You need to combine like terms
Miguel has three times as many dimes as he has quarters. He has as many nickels.as he has dimes and quarters.combined. The total amount of money he has is $3.00. How many of each coin does Miguel have?
Answer:
Step-by-step explanation:
fter solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.
What is algebra?
One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x
$3.00 when converted to cents is 300 cents.
The value of nickels is 5 x 4x=20x.
The value of dimes is 10 x 3x=30x.
The value of quarters is 25x.
As the total value of money Miguel has is 300 cents, then the algebraic equation will be -
20x + 30x + 25x = 300
Solve to get the value of x -
75x = 300
x = 4
Therefore, the amount of quarters is x = 4 quarters.
The amount of dimes is x = 3x = 3 x 4 = 12 dimes.
The amount of nickels is 4x = 4 x 4 = 16 nickels.
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please help: solve for x
Step-by-step explanation:
since the height from M (line MB) to the baseline is splitting the baseline into 2 identical halves, the triangle must be an isoceles triangle (both legs are identical long).
and therefore,
5x - 5 = 3x + 1
2x - 5 = 1
2x = 6
x = 6/2 = 3
Jared’s monthly income is 4500 Jared spend 11%of his income on grocies
Answer:
Jared's groceries = 495
Step-by-step explanation:
We calculate 11% from Jared monthly income:
11% x 4500 = 495
Jared's groceries = 495
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A six-foot long ladder is leaning against a wall. The bottom of the ladder is 3 feet away from the wall. How high up the wall is the ladder
The six-foot long ladder is 3√5 feet high up the wall having 3 feet distance from bottom of the ladder.
How to find height ?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder is the hypotenuse, and the wall and the ground make up the other two sides.
The ladder is 6 feet long, and the bottom of the ladder is 3 feet away from the wall, so the triangle is a 3-4-5 right triangle, which means the wall is 3 feet high.
So, if we square the length of the ladder (6^2 = 36)
The length of the base (3^2 = 9),
and add them together, then take the square root of that, we get the height of the wall.
sqrt(36+9) = sqrt(45) = 3*sqrt(5)
so the ladder is 3√5 feet high up the wall.
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The perimeter of a rectangle is 84cm and it's length is 6cm longer than it's breadth. Find the length and breadth of the rectangle
Answer:
Step-by-step explanation:
The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:
2l + 2b = 84
Where l is the length of the rectangle and b is the breadth.
We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:
l = b + 6
Substituting the second equation into the first equation, we get:
2(b + 6) + 2b = 84
Expanding the left side of the equation gives:
2b + 12 + 2b = 84
Combining as terms gives:
4b + 12 = 84
Subtracting 12 from both sides gives:
4b = 72
Dividing both sides by 4 gives:
b = 18
Substituting this value back into the equation l = b + 6 gives us:
l = 18 + 6
l = 24
Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.
Condos in Georgetown go up in value by 10% each year. If the Sutton family's condo is now worth $120,000, what will it be worth in 8 years? If necessary, round your answer to the nearest cent.
The Sutton family's condo's worth in 8 years will be $216000.
What is exponential function?An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.
Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.
We can write the function to calculate the worth after {T} years as follows.
A{T, R} = A{i} {1 + RT}
A{T, R} = {120000} {1 + (10/100) x 8}
A{T, R} = {120000} {1 + 0.1 x 8}
A{T, R} = {120000} {1 + 0.8}
A{T, R} = {120000 x 1.8}
A{T, R} = 216000
Therefore, the Sutton family's condo's worth in 8 years will be $216000.
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What kind of triangle has 65 65 50?
Isosceles Triangle has 50°, 65°, 65°
An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.
Properties of Isosceles Triangle:
The two equal sides of an isosceles triangle are known as ‘legs’, and the angle between them is called the vertex angle or apex angle.In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. The side opposite the vertex angle is called the base and the base angles are equal, and perpendicular to the apex angle bisecting the base and the apex angle.To know more about Isosceles Triangle:
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if x+3=9 whats the answer:)
enjoy
Answer:
x=6
Step-by-step explanation:
then x=6 because replacing x 6+3=9
What does log () do in mathematics?
Log () helps to determine the single number to be multiplied.
Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.
Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.
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The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
what is volume?The area occupied within an object's three-dimensional bounds is referred to as its volume. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.
given
Calculate the box's volume and provide your answer in units.
Due to the fact that x = 4.28, the remaining sides are 2x + 5 = 2(4.28) + 5 = 13.56
and x - 2 = 4.28 -2 = 2.28.
We are aware that volume is calculated as follows: 13.56 (4.28) ( 2.28 )
=[tex]135.25cm^{3}[/tex]
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
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The perimeter of triangle ABC is 26 units. The altitudes of triangle ABC are in the ratio 2: 3: 4. Compute the area of triangle ABC.
please help me w step by step explanation and work tysm !
Answer:
59
Step-by-step explanation:
What is step 3 in problem solving?
Step 3 is Define the problem Goals.
there are 8 steps, which are as follows,
1- Define the Problem
2- Clarification of the Problem
3- Define the problem Goals
4- Identify main Cause of the Problem
5- Develop a Action Plan
6- Execute that Action Plan
7- Analyze the Results
8- Continuous Improvements
Problem solving
Problem solving is the method of determining the problem and then clarify the doubts and prepare a action plan and then execute the action plan and find out the desired results and if the results are not appropriate then improve the action plan and your way of doing until you get the desired results.
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What is the difference between a difference of two squares and a perfect square trinomial?
Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
what is perfect square ?When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.
Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
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The waitress had a table with a bill of $75.29 and received $12.80. What was the percent tip she received?
Answer:
17%
Step-by-step explanation:
Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%
Figure ABCD is a parallelogram if point C lies on the line y=-1 what is the x vale of point C
The value of x of point C is 4. The coordinate of C is (4,-1).
What is the coordinate of a point?
The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.
The distance between points A and B is 4 units.
The opposite sides of a parallelogram are equal and parallel.
To make parallelogram, the point C lies on the left side of point D.
The distance between point C and D must be 4 unit.
The coordinates of C is (4,-1).
The x value of point C is 4.
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A new social media site is increasing its user base by approximately 5% per month. If the site currently has 27,870 users, what will be the approximate user base be 6 months from now?
Answer:
37,349
Step-by-step explanation:
month 1
27870 x .05 = 1394
27870 + 1394 = 29264
month 2
29264 x .05 = 1463
29264 + 1463 = 30727
month 3
30727 × .05 = 1536
30727 + 1536 = 32263
month 4
32263 x .05 = 1613
32263 + 1613 = 33876
month 5
33876 x .05 = 1694
33876 + 1694 = 35570
month 6
35570 x .05 = 1779
35570 + 1779 = 37349
Answer:
35,570
Step-by-step explanation:
solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.
1. 27870*1.05= 29,263.5
2. 29263.5*1.05=30726.675
3.repeat
4.repeat
5.repeat
6.repeat
if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)
1. 27870÷10= 2,787
2. 2787÷2= 1393.5
3. 27870+1393.5 = 29263.5
solution 2 -Fast but probably needs a calculator
1. 27870*1.05^(5)= 35570
1.05 = monthly increase
power of 5 = ^(5) = 6 months - 1 = 5
An achievement exam was given to a population of 1,000 students. However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table. TEST SCORE 42 57 67 72 77 87 97 z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25 percentile rank 10 25 30 45 50 75 95 Using the table information, the test score representing the 3rd decile is: a. 67 b. 77 c. 57 d. 72 e. 97
The test score representing the 3rd decile is 67. So the option a is correct.
In the given question, an achievement exam was given to a population of 1,000 students.
However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.
TEST SCORE 42 57 67 72 77 87 97
z score -1.50 -0.75 -0.25 0 0.25 0.75 1.25
percentile rank 10 25 30 45 50 75 95
Using the table information, we have to find the test score representing the 3rd decile.
As we know that the 3rd decile is equal to the 30th percentile.
So that the 3rd decile have the percentile rank = 30
The test score equivalent to percentile rank 30 is 67.
So, the test score representing the 3rd decile is 67. So the option a is correct.
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Find the lengths of the diagonals of rectangle WXYZ.
WY= 16x + 2-
XZ=36x-6
The length of each diagonal is
units.
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6 8 = 20x x = 8/20, simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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a. Kiran tried to double this recipe. He used 2 cups of
yogurt, 6 tablespoons of peanut butter, 5 teaspoons of
chocolate syrup, and 4 cups of crushed ice. He didn't
think it tasted right. Describe how the flavor of Kiran's
recipe compares to Clare's recipe.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
Define unitary method.A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.
1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
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What is the solution to this system of linear equations 2x 3y equals 3?
The solution to this system of linear equations is x = 3, y = 2.
2x - 3y = 3
2x = 3 + 3y
2x = 3y + 3
x = (3y + 3) / 2
x = 3/2 + 3/2y
x = 3, y = 2
This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.
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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.
1. Rewrite the equation in standard form is
2x + 3y = 3
2. Subtract 2x from both sides of the equation:
3y = 3 - 2x
3. Divide both sides by 3:
y = (3 - 2x)/3
4. Solve for x by substituting y in the original equation:
2x + 3(3 - 2x)/3 = 3
5. Simplify and solve for x:
2x + 3 - 2x = 3
x = 1
6. Substitute x into the equation y = (3 - 2x)/3
y = (3 - 2(1))/3
y = -1/3
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How do you simplify 3 Way ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 225: 125: 25
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
225/5: 125/5: 25/5
45: 25: 5
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 9: 5: 5.
45/5: 25/5: 5/5
9: 5: 1
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Question 2 (Essay Worth 2 points)
(05.06 HC)
Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning.
In accordance with comparative comparative, the x-intercept of function g(x) = ㏒ (x + 4) is equal to x = - 4.
How to determine the x-intercept of a logarithmic functionAccording to function theory, a function f(x) has an x-intercept when f(x) exists for x = 0. Besides, logarithms of 1 for any base is equal to zero, that is:
Logarithm of 1 at any base.
㏒ₐ 1 = 0
If ㏒ x = 0, then x = 1. And if ㏒ (x + 4) = 0, then x + 4 = 0, that is, x = - 4.
Then, by direct comparison between the two logarithmic expression, the logarithmic function g(x) = ㏒ (x + 4) has x = - 4 as its x-intercept.
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Find the volume of the cylinder. Round your answer to the nearest tenth if necessary. Use 3. 14 for pi.
A can of juice has a radius of 5 inches and a height of 6 inches. What is the volume of the can?
The volume of the can based on mentioned radius and height of can is 471 inches³.
Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.
Use the below mentioned formula to calculate the volume -
V = πr²h, where V is volume, r is radius and h is height.
Keep the values in formula to find the value of volume of cylinder
V = 3.14×5²×6
Next step is to perform multiplication on Right Hand Side of the equation
V = 471 inches³
The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.
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write an explicit rule for -2, 5, 12, 19
The explicit rule for the sequence -2, 5, 12, 19 is
-2 + (n - 1) 7.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-2, 5, 12, 19
This is an arithmetic sequence.
The first term.
a = -2.
The common difference.
d = 5 - (-2) = 7
= 12 - 5 = 7
= 19 - 12 = 7
Now,
The nth term of an arithmetic sequence.
= a + (n -1)d
= -2 + (n - 1)7
Thus,
The explicit rule is -2 + (n -1) 7.
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