Answer: To keep both sides of the equation balanced
Step-by-step explanation:
The Golden Rule states that what you do to one side of an equation, that side being what is on one side of the equal sign, you must do to the other side. This is very important.
How do you solve 3 variable equations with 3 variables?
The linear combination method will be used to resolve a system of three equations in three variables.
What is equation ?Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." The slope-intercept form, standard form, and point-slope form are the three primary formats for linear equations. A mathematical expression known as an equation has an equals sign. Many equations contain algebra. When you don't know the exact number to compute in math, algebra is used.
given
The linear combination method will be used to resolve a system of three equations in three variables.
This time, we will consider two equations at a time, eliminate one variable using the resulting equations in two variables, then solve for the third variable. with respect to this instance.
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Tim's book has 50 pages.
Lisa's book has 2 1 2 times as many pages.
Which shows how many pages (y) Lisa's book has?
Lisa's book has 10,600 pages.
What is multiplication?Multiplication is an operation that represents repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication is the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Tim's book has 50 pages, if Lisa's book has 212 times as many pages, therefore;
Lisa's book has 212 x 50 pages
Lisa's book has 10,600 pages.
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Marshall divides his money into four categories. He saves of his money. He gives of his money to a charity. He uses of his money to buy snacks at school, and he spends of his money on fun. What fraction of his money does he save and spend on fun?
Answer:
Marshall saves 1/4 of his money and spends 1/4 of his money on fun. Therefore, he saves and spends 1/4 + 1/4 = 1/2 or 50% of his money on those two categories.
Step-by-step explanation:
Sydney is playing a game. She draws a fraction card labeled, Then she rolls a number cube labeled 1 through 6. sydney mutuplles the fraction b. the number rolled. If her score is greater than 1. she gets another turn. If her score is less than or equal to 1. her turn is over. What is the lowest number that Sydney can roll to get another turn? Enter the answer in the box.
Answer: To get another turn, Sydney's score must be greater than 1. Therefore, to find the lowest number that Sydney can roll to get another turn, we need to find the smallest number that, when multiplied by the fraction on the card, will give a result greater than 1.
It's not mentioned which fraction card Sydney drew, so we can assume any fraction.
Let's assume the fraction card is labeled 1/4.
To get another turn, Sydney's score must be greater than 1. Therefore, we need to find the smallest number that, when multiplied by 1/4, will give a result greater than 1.
1/4 * x >1
x > 4
so the smallest number that Sydney can roll to get another turn is 5.
It should be noted that this is assuming that the fraction card is labeled 1/4 , if the fraction card is labeled with any other fraction the answer would be different.
Step-by-step explanation:
NEED ANSWER PLS!
WORTH 60 POINTS!
Select the correct answer.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(0) = 2
B.
g(-13) = 20
C.
g(7) = -1
D.
g(-4) = -11
Answer:
7
Step-by-step explanation:
7
Solve for x= 2 11/12x-5/6(x-2/5)
The value of the equation on x = 2 is 0.5
Given Quadratic equation,
[tex]= \frac{11}{12} x - \frac{5}{6}( x - \frac{2}{5})[/tex]
Put the value of x = 2 in the above equation and we get
[tex]= \frac{11}{12} *2 - \frac{5}{6}( 2 - \frac{2}{5})[/tex]
[tex]= \frac{11}{6} - \frac{5}{6} * \frac{8}{5}[/tex]
[tex]= \frac{11}{6} - \frac{4}{3}[/tex]
[tex]= \frac{1}{2}[/tex]
= 0.5
Therefore, the value of the equation on x = 2 is 0.5
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If m = −72 is slope, y - intercept is 12 and the point ( x, 5 ) lies on the line. What is the value of x ?
A line can be represented in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Given that m = −72 and the y-intercept is 12, we can represent the line as y = −72x + 12
We are also given that the point (x, 5) lies on the line. So we can substitute the x and y values of the point into the equation of the line to find the value of x.
y = −72x + 12
5 = −72x + 12
-7 = -72x
x = 7/72
So the value of x is 7/72.
We can also get this by solving the equation of the line for x.
y = -72x + 12
y - 12 = -72x
(y - 12)/-72 = x
x = (y - 12)/-72
So for any point (x, y) on the line, the value of x can be obtained by substituting y and the slope-intercept form equation.
What are 4 ways to find a midpoint?
The four ways to find the midpoint of a line segment are using the Midpoint Formula, using the Distance Formula, using a Graph, and using a Ruler.
Using the Midpoint Formula:
This method involves using the midpoint formula, which is (x1 + x2)/2, (y1 + y2)/2. This formula gives the coordinates of the midpoint when the coordinates of the two endpoints of the line segment are known.
Using the Distance Formula:
This method involves using the distance formula to find the distance between the two endpoints of the line segment and then dividing the distance by 2. The midpoint will be located at the point that is half the distance from each endpoint.
Using a Graph:
This method involves plotting the two endpoints of the line segment on a graph and then drawing a line segment connecting the two points. The midpoint of the line segment will be located at the point where the line segment is bisected.
Using a Ruler:
This method involves measuring the distance between the two endpoints of the line segment with a ruler or measuring tape, and then marking the point that is halfway between the two endpoints. The midpoint of the line segment will be located at the point that is marked.
All of these methods can be used to find the midpoint of a line segment, it depends on what information is given and what tools are available.
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my square orchid garden abuts my house so that the house itself forms the northern boundary. the fencing for the southern boundary costs $5 per foot, and the fencing for the east and west sides costs $3 per foot. find the total cost of the fencing as a function of the length (in feet) of a side x.
The total cost of the fencing as a function of the length of the x side is 11x
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
southern = 5$east = 3$west = 3$side = xTotal cost = ?Calculating the total cost:
Total cost = (southern + east + west) * side
Total cost = (5 + 3 + 3)*x
Total cost = 11x
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Heidi has made a sequence of patterns using tiles. use the rule to find out how many tiles there are in the 7th pattern.
Answer:
29 is the correct answer
Can you guys help me with this?
I just need to know what to do when it’s negative cause I’ve been doing positive the whole time..
The positive exponent for the given expression is 1/5.
What is a positive exponent?A positive exponent tells us how many times to multiply a base number, and a negate
ve exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
The given exponent is [tex]25^{-\frac{1}{2}[/tex].
Now, [tex]25^{-\frac{1}{2} }=(5^2)^{-\frac{1}{2}[/tex]
= 5⁻¹
= 1/5
Therefore, the positive exponent for the given expression is 1/5.
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(PLEASE HELP QUICKLY) At a particular restaurant, each pizza roll has 55 calories and each mini hot dog has 70 calories. A combination meal with pizza rolls and mini hot dogs is shown to have 910 total calories and 12 more pizza rolls than mini hot dogs. Determine the number of pizza rolls in the combination meal and the number of mini hot dogs in the combination meal.
There are____ pizza rolls and ___ mini hot dogs in the combination meal.
Answer:
There are 14 pizza rolls and 2 mini hot dogs in the combination meal.
Step-by-step explanation:
From the question, we have the following parameters
Pizza roll = 55 calories each
Mini hotdog = 70 calories each
Combination meal = 910 calories in total
Let the pizza roll be x and the mini hotdog be y
So, we have
55x + 70y = 910
x = 12 + y
Make x the subject in x = 12 + y
x = 12 + y
Substitute x = 12 + y in 55x + 70y = 910
55(12 + y) + 70y = 910
Evaluate
660 + 55y + 70y = 910
So, we have
125y = 250
This gives
y = 2
Recall that
x = 12 + y
So, we have
x = 12 + 2
x = 14
Hence, there are 14 pizza rolls and 2 mini hot dogs
What is a polygon with 4 called?
A 4 polygon is a two-dimensional shape with four sides and four angles.
What is polygon?Polygon is a closed figure in a plane made up of straight lines or curved lines that intersect in pairs. A polygon has at least three sides and angles. The sides can be of any length and the angles can be of any measure. Polygons are classified according to the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), etc. Polygons are used in many fields, from mathematics to engineering.
It is a type of quadrilateral, which is a polygon with four sides. Examples of 4 polygons include squares, rectangles, rhombuses, and trapezoids. All 4 polygons have four sides of equal length, and all their interior angles add up to 360 degrees.
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What is an equation of the line that passes through the points (3, 3) and (-1, 7)?
Answer:
the equation of the line = y + x -3 -3 = 0
Step-by-step explanation:
Equation of the line is give n by the formula
y - y¹ = m
x - x¹
note: m is the gradient.
Point = (3, 3) and (-1, 7).
Gradient =m= y2 - y1 = 7 - 3 = 4 = -1
x2 - x1 -1 -3 -4
the equation of the line
y - y1 = m
x - x1
y - 3 = -1
x - 3
note: Perform cross multiplication also remember every whole number is over one.
=y - 3 = -1 (x - 3)
=y - 3 = - x + 3
y + x - 3 - 3 = 0.
State whether a dashed line or solid line would represent the graph of each inequality.
Part A: y > 2x − 9
b- y − 6 ≤ x
In part A; The graph of inequality y > 2x - 9 shows the dashed line.
And, In part B; The graph of inequality y - 6 ≤ x shown the solid line.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality are,
Part A: y > 2x − 9
Part b; y − 6 ≤ x
Now,
In part A; The inequality '<' used which represent the dashed line
And, In part B; The inequality ≤ used which represent the solid line.
Hence, The graph of inequality y > 2x - 9 shows the dashed line.
And, The graph of inequality y - 6 ≤ x shown the solid line.
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Using standard British coins, list the number of different ways to pay 10p.
[Note: A: (2p, 1p, 1p, 2p, 1p, 2p, 1p) is not considered to be different
from B: {1p, 2p, 1p, 1p, 2p, 1p, 2p), both are just (3x2p, 4x1p}.]
The number of different combinations to pay 10p with British coins is given as follows:
6.
How to obtain the number of different combinations to pay 10 pounds with British coins?The British coins are defined as follows:
1p: one pound coin.2p: two pound coins.Hence the different combinations to pay 10p with British coins are given as follows:
10 one pound coins.1 two pound coins and 8 one pound coins.2 two pound coins and 6 one pound coins.3 two pound coins and 4 one pound coins.4 two pound coins and 2 one pound coins.5 two pound coins and 0 one pound coins.Which means that the number of combinations is of six, and the six combinations are the ones listed by the bullet points, above.
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NEEDS HELP ASAP Figure B is a scaled copy of Figure A.
What is the scale factor from Figure to Figure B
Answer: 3
If you look at the left-most side on figure A, youll notice that it is 2 units long. On figure B, it is 6 units long. 2*x=6 where X is the scale factor. You'll find that X=3. YW BRO
Somebody help please I don’t understand!!
The unit rate of the 76th player is [tex]1\frac{1}{3}[/tex] miles per hour.
The unit rate of the 91st player is [tex]1\frac{1}{9}[/tex] miles per hour.
The unit rate of the 44th player is [tex]1\frac{1}{2}[/tex] miles per hour.
What is an improper fraction?
An improper fraction is one in which the denominator is greater than or equal to the numerator. 5/2 and 8/5, for example, are incorrect fractions. Every fraction is made up of two parts: the numerator and the denominator. Proper fractions and improper fractions are the two main types of fractions in mathematics based on the numerator and denominator values.
For 76 number of players:
In 1/4 hour he can run 1/3 mile
In 1 hour he can run (1/3)/(1/4)mile
=4/3 miles
Convert it into a mixed number:
= [tex]1\frac{1}{3}[/tex] miles per hour
For 91 number of players:
In 3/4 hour he can run 5/6 mile
In 1 hour he can run (5/6)/(3/4)mile
=10/9 miles
Convert it into a mixed number:
= [tex]1\frac{1}{9}[/tex] miles per hour
For 44 number of players:
In 1/2 hour he can run 3/4 mile
In 1 hour he can run (3/4)/(1/2)mile
=6/4 miles
=3/2 miles
Convert it into a mixed number:
= [tex]1\frac{1}{2}[/tex] miles per hour
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In the of 76th player's unit rate is 1 1/3 miles per hour , 91st player's unit rate is 1 1/9miles per hour and the 44th player's unit rate is 1 1/2miles per hour.
What is meant by an unit rate?When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.
For a total of 76 players:
He can run 1/3 mile in 1/4 hour.
He can run (1/3)/(1/4) mile in 1 hour.
= 4/3 miles
Change it to a mixed number:
= 1 1/3 miles per second.
For a total of 91 players:
He can run 5/6 mile in 3/4 hour.
He can run (5/6)/(3/4) mile in an hour.
= 10/9 miles
Change it to a mixed number:
= 1 1/9 miles per hour.
For a total of 44 players:
He can run 3/4 mile in half an hour.
He can run (3/4)/(1/2) mile in 1 hour.
=6/4 miles
=3/2 miles
Change it to a mixed number:
= 1 1/2 miles per hour.
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Two groups are hiking on a glacier. Group B starts ahead of Group A and walks . To catch up to Group B, Group A walks . : since the start of the hike Group A from the start of the trail Which equation shows Group A's distance from the start? Group B Start J
Speed = 7.7miles/2.2hours = 3.5miles/hour
Which equation shows Group A's distance from the start?In physics, the average speed is defined as the ratio of distance traveled during a certain time period.
Distance/Time = Speed
If the problem stated that the two groups’ average speeds are equal,
Mark’s Group Speed Equals Sally’s Group Speed
The problem now suggests that the time is likewise equal. That means Sally’s group took t = 4.7 – 2.5 = 2.2 hours to travel the remaining 7.7 miles.
That implies that the speed is,
7.7 miles/2.2 hours = 3.5 miles/hour.
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PLease help me find the distance between AB BC and CA please help
The distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
The coordinates of A are (-18, -18)
coordinates of B are (20, 0)
coordinates of C are (-12, 16)
The formula for distance is Distance=√(x₂-x₁)²+(y₂-y₁)²
Distance AB=√(20-(-18))²+(0-18)²
=√(20+18))²+(0-18)²=√38²+18²
AB=√1444+324=√1768=42.04 units
Distance BC=√(-12-20)²+(16)²
=√(-32)²+(16)²=√1024+256
=√1280
=35.77
Distance CA=√(-12-(-18))²+(16+18)²
=√(6)²+(34)²
=√36+1156=34.5
Hence, the distance of AB is 42.04 units, BC is 35.77 units and CA is 34.5 units.
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Which is a correct solution for the following system of Inequalities
HELPP DUE IN 30MIN
Answer:
I think the answer is A
1,2
Would the following compound inequality be classified as an “and” inequality or an “or” inequality? Inequality: 6 > x + 1 > 3
dont guess please
The compound inequality says that x+1 is greater than 3 and less than 6.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than the relation between variables and the numbers.
Given that the compound inequality is 6 > x + 1 > 3. The compound inequallity says that the value of x +1 is greater than 3 and is less than 6.
The inequality can be written as,
6 > x + 1 > 3
x + 1 > 3
x +1 < 6
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Who is the father of geometry?
Euclid is the father of geometry
Euclid and René Descartes was often called the father of modern mathematics because he created analytic geometry and the Cartesian coordinate system.
What is modern mathematics?
Different methodologies have been used in contemporary mathematics. It focuses mostly on entities, whereby interconnections follow themes and patterns.
René Descartes was a person who was very famous for his philosophy of science and mathematics. He was considered a person who evaluate and made various new development in the field of math as well as time in separate fields like geometry and algebra with new properties that is developed by him.
He had the main idea of having finite and infinite particles or numbers in geometry. And also used various scientific methods to prove that.
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19/2-1/3-9/6=?????????
Answer:
[tex] \frac{23}{3} ....in \: fraction \: or \\ 7.666666...in \: decimal[/tex]
Step-by-step explanation:
Greetings!!!
look at the image attached
Hope it helps!!!
Why is the exponent 0 1?
The exponent 0 refers to the number being raised to the power of 0.
When any number, except 0, is raised to the power of 0, the result is always 1. This is known as the "zero power property" and it is true for any non-zero number a. The mathematical statement can be represented as:
a^0 = 1
For example, 2^0 = 1, 5^0 = 1 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.
The exponent 1 refers to the number being raised to the power of 1. When any number is raised to the power of 1, the result is always the same as the number itself. This is known as the "identity property" and it is true for any non-zero number a. The mathematical statement can be represented as:
a^1 = a
For example, 2^1 = 2, 5^1 = 5 and so on. This property holds true for any base a, including real numbers, complex numbers, and even matrices.
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Pleaseeee help me thx
When the length of JK is 9.5 feet and the angle L is 61 degrees trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.
what is trigonometry ?The relationship between triangle side lengths and angles is investigated in the branch of mathematics known as trigonometry. The application of geometry in astronomical study gave rise to the area's first appearance during the Hellenistic era, roughly in the third century BC. Exact methods mathematics focuses on certain trigonometric functions and how they might be applied to calculations. In trigonometry, there are six widely used trigonometric functions. Their respective names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, especially of right triangles. The features of all geometric shapes are studied in geometry, though.
given
△JKL
JK=9.5ft
∠L=61∘
Find:KL
We may determine the outcome using the tangent's trigonometric ratio.
Tan = JK/KL = 61
When we separate KL, we get KL=9.5ft/tan61.
When the length of JK is 9.5 feet and the angle L is 61 degrees trigonometric ratio of the tangent, solving yields: KL=9.5ft/1.804 KL=5.27 ft.
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The correct question is :-
Given triangle JKL, find the length of KL. The length of JK is 9.5 ft and the angle L is 61 degrees.
What is the scale factor of 10 cm 5m?
You want to build a structure with a length of 5 m, where the proportions of other dimensions are conserved. Estimate the scale factor, 10 cm / 5 m = 0.02 .
How do you figure out the scale factor?The scale factor is a number that represents the ratio of the measurements of two similar figures, such as geometric shapes or maps. To find the scale factor, you can compare corresponding side lengths or angles of the two figures. The scale factor is the ratio of the length of a side in one figure to the corresponding side in the other figure. You can also find the scale factor by taking the square root of the ratio of the areas or the ratio of the volumes of the two similar figures.
Once you have the scale factor, you can use it to find the missing measurements of a similar figure by multiplying any measurement of one figure by the scale factor. In summary, the scale factor is a numerical value that allows to relate the measurements of two similar figures.
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Can someone help me and show the work
ans is 90 and 30
Step-by-step explanation:
LN=90° (right angle)
MN=30°(DO THE MATH)
given that 2x + 3y divideby 3x+4y ,find the ratio y : x
Although part of your question is missing, you might be referring to the question :
Given that 2x+3y / 3x+4y = 5, find the ratio of y:x
Given : 2x+3y / 3x+4y =5
To find : y : x
Solution :
(2x+3y) / (3x+4y) = 5, or
2x + 3y = 15x + 20y, or
-15x + 2x = 20y - 3y, or
-13x = 17y
Therefore, x/y = -17/13
Hence, y/x = -13/17
y : x = -13 : 17.
The answer is -13 : 17.
Identify the perimeter and area of an equilateral triangle with height 11 cm. Give your answer in simplest radical form.
The perimeter of an equilateral triangle is equal to three times the length of the side. Perimeter = 33 cm and Area = 30.58 cm^2 (√30.58 cm^2)
Perimeter of an equilateral triangle = 3 x side
=> 3 x 11 cm = 33 cm
Area of an equilateral triangle = (√3/4) x (side^2)
=> (√3/4) x (11 cm^2)
=> (√3/4) x (121 cm^2)
=> 30.58 cm^2
=> √30.58 cm^2
The perimeter of an equilateral triangle is equal to three times the length of the side. Therefore, an equilateral triangle with a height of 11 cm will have a perimeter of 33 cm (3 x 11 cm). The area of an equilateral triangle can be calculated using the equation (√3/4) x (side^2). In this case, the area of the triangle is 30.58 cm^2 ((√3/4) x (11 cm^2)). This can be simplified to √30.58 cm^2 in its simplest radical form.
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