What is the greatest common of 45?
Answer:
Step-by-step explanation:
If it is the greatest common factor then it would be 5 I think.
[tex]14-4 \sqrt{ 6 \phantom{\tiny{!}}} = { \left( \sqrt{ x \phantom{\tiny{!}}} -2 \sqrt{ y \phantom{\tiny{!}}} \right) }^{ 2 }[/tex]
Answer:
(x=2, y=3) and (x=12, y=1/2)
Step-by-step explanation:
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])^2
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])
14 - 4[tex]\sqrt{6}[/tex] = [tex]\sqrt{x}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) - 2[tex]\sqrt{y}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) ==> distribute ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) to [tex]\sqrt{x}[/tex] and
2[tex]\sqrt{y}[/tex]
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] * [tex]\sqrt{x}[/tex]) - ([tex]\sqrt{x}[/tex] * 2[tex]\sqrt{y}[/tex]) - (2[tex]\sqrt{y}[/tex] * [tex]\sqrt{x}[/tex]) - (2[tex]\sqrt{y}[/tex] * (-2[tex]\sqrt{y}[/tex])) ==> use
distribution property
14 - 4[tex]\sqrt{6}[/tex] = (x) - (2[tex]\sqrt{xy}[/tex]) - (2[tex]\sqrt{xy}[/tex]) - (-4[tex]\sqrt{y}[/tex] *[tex]\sqrt{y}[/tex]) ==> simplify
14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) - (-4y)
14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) + 4y ==> subtracting by a negative number is
equivalent to adding by a positive number
14 - 4[tex]\sqrt{6}[/tex] = x + 4y - 4[tex]\sqrt{xy}[/tex] ==> notice any similarities?
x + 4y = 14
[tex]\sqrt{xy}[/tex] = [tex]\sqrt{6}[/tex]
xy=6 ==> solve for x
x = 6/y ==> isolate x by dividing by y on both sides
6/y + 4y = 14 ==> plugin 6/y for x in x + 4y = 14
(6/y + 4y = 14) * y ==> multiply the equation by y to remove fractions
6 + 4y^2 = 14y
4y^2 - 14y + 6 = 14y-14y
4y^2 - 14y + 6 = 0
2y^2 - 7y + 3 = 0 ==> divide both sides by 2 to simplify the equation
2y^2 - 1y - 6y + 3 = 0 ==> -1y - 6y = -7y
y(2y - 1) - 3(2y - 1) = 0 ==> factor the equation
(y - 3)(2y - 1) = 0
y - 3 = 0 ==> y=3
2y - 1 = 0 ==> 2y = 1 ==> y = 1/2
y=3: 3x = 6 ==> plugin 3 for y in xy = 6
x = 2 ==> divide both sides by 3
y=1/2: x/2 = 6 ==> plugin 1/2 for y in xy = 6
x = 12 ==> multiply both sides by 2
When y=3, x=2. When y=1/2, x=12
Hence, the answers are (2, 3) and (12, 1/2).
The expression will be simplified as x + 4y + 4√x√y -14 + 4√6 = 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 14 - 4√6 = ( √x - 2√y)². The given expression will be simplified as below,
14 - 4√6 = ( √x - 2√y)²
14 - 4√6 = (√x )² + (4√x√y) + 4(√y)²
14 - 4√6 = x + 4√x√y + 4y
x + 4√x√y + 4y -14 + 4√6 = 0
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LT 1.5 I can determine if a number is a factor of another number.
Directions: Is 6 a factor of 35? Explain how you know that it is or is not a factor. Yes or No,
then EXPLAIN!
No. The GCF of 6 and 35 is 1.
To determine the biggest factor that perfectly divides both 6 and 35, i.e. 1, we must factor each number separately (factors of 6 are 1, 2, 3, 6; while factors of 35 are 1, 5, 7, 35).
What is Factors of 35?
Factors of 35 are the list of integers that we can split evenly into 35. It has a total of 4 factors of which 35 is the biggest factor and the positive factors of 35 are 1, 5, 7 and 35. The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).
Factors of 35: 1, 5, 7 and 35
Negative Factors of 35: -1, -5, -7 and -35
Prime Factors of 35: 5, 7
Prime Factorization of 35: 5 × 7 = 5 × 7
Sum of Factors of 35: 48
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What is the vertical asymptote of the graph of f X?
The vertical asymptotes of the graph of f(x) = (2x² + 7x - 4)/(x² + 5x + 4) is x = -1
How to determine the vertical asymptote?The equation of the function is given as
f(x) = 2x² + 7x - 4/x² + 5x + 4
Introduce bracket, to differentiate the numerator and the denominator
So, we have
f(x) = (2x² + 7x - 4)/(x² + 5x + 4)
Next, we plot the graph of the function
The asymptotes are the points on the graph is a line that acts as the limit of another line or curve
From the graph, we have the asymptotes to be
x = -1 and y = 2
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Complete question
What is the vertical asymptote of the graph of f X?
f(x) = 2x² + 7x - 4/x² + 5x + 4
Select the correct answer.
What is the zero of the function represented by this graph?
The graph shows the cube root function with no start or end point. Some major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
A.
B.
C.
D.
The zero of the graph is x = -4
How to determine the zero of the graph?From the question, we have the following parameters that can be used in our computation:
Major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
Express the points, properly
So, we have the following representation
Major points on the graph are (-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
Write out the points
(-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
The zeros of the graph are the point where y = 0
In this case, the points are
(-4, 0)
So, we have
x = -4
Hence, the zero is x = -4
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Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
= 12, b = 12, C =
Answer:
17.0
Step-by-step explanation:
pythag theorem is a^2 + b^2 = c^2
12^2 + 12^2 = c^2
144+144=288=c^2
[tex]\sqrt{288}[/tex]= 16.97056275
round to nearest tenth, 17.0
A local plumber makes house calls. She charges $30 to come out to the house and $40 per hour for
her services. For example, a 4-hour service call costs $30 + $40(4) = $190.
A. Statistic Hours of Service Call Cost of Service Call
Mean 4.5 30+40(4.5) = 210
Median 3.5 30+40(3.5) = 170
SD 1.2 40(1.2) = 48
IQR 2.0 40(2.0) = 80
Minimum 0.5 30+40(0.5) = 50
Do these summary statistics indicate that a Normal model is appropriate here? Explain.
The mean and the median of the given data are 210 and 170.
What are Mean and Median?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
The four-hour service call costs
$30 + $40(4) = $90
(a) The given table summary details and finds the cost of the service cells
Statics Hour of service call cost of service call
Mean 4.5 30 + 40(4.5) = 210
Median 3.5 30 + 40 (3.5 = 170
SD 1.2 30 + 40 (1.2) = 78
TQR 2.0 30 + 40 (2.0) = 110
Minimum 0.5 30 + 40 (0.5) = 50
(b) The service call corresponding score is 1.50
z score = 138-4.5/1.2 = 113.75
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Jessica drinks 5/6 cup of milk for breakfast every day.
How many cups of milk has Jessica drink after 8 days?
Answer:
20/3 cups of milk
Step-by-step explanation:
Take 5/6 time 8 = 40/6 = 20/3
So, Jessica drinks 20/3 cups of milk after 8 days
What are the roots of the quadratic equation x² 5x 6 0?
The two solutions to the equation x² + 5x + 6 = 0 are x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.
To find the roots of a quadratic equation, we need to set the equation equal to 0 and then solve for x. In this case, we have the equation x² + 5x + 6 = 0. we can use the quadratic formula. The quadratic formula states that the two solutions for x are given by x = (-b ± √(b² - 4ac))/2a. For our equation, this gives us x = (-5 ± √(5² - 4(1)(6)))/2(1). Once we simplify this, we get x = (-5 ± √(-19))/2. Since the square root of a negative number is not real, we can discard this solution. This leaves us with x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.
x = (-5 ± √(5² - 4(1)(6)))/2(1)
= (-5 ± √(-19))/2
= (-5 ± i√19)/2
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What is the slope intercept form of the inequality 2x 3y 12?
The level of a line's slope indicates its steepness, y = (2/3)x - 4 is the slope intercept form of the inequality 2x - 3y = 12.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.
Now, it is given that,
2x - 3y = 12
or, - 3y = 12 - 2x
or, 3y = 2x - 12
or y = (2/3)x - 4
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The complete question is as follows:
What is the slope intercept form of the inequality 2x - 3y = 12.
Solve and graph by using systems of inequalities.
A 24 hour radio station plays only classical music, jazz music, talk programs, and news. It plays at most 12 hours of music per day, of which at least 4 hours is classical. Jazz music gets 25% as much time as classical. Write and graph a system of inequalities.
PLEASE HELP!!!
The inequality that represents the most no. of music played is,
C ≤ 4, J ≤ 1 and 4C + 0.25C ≤ 12
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 relation between variables and the numbers.
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, the radio station plays at most 12 hours of music per day. Let C denotes classical music, J denotes jazz music, and 25% of 4 hours be 1 hour.
The inequality representing this situation is
C ≤ 4 and J ≤ 1.
4C + 0.25C ≤ 12. (less than or equal to is at most)
4.25C ≤ 12.
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f(x) = x^8e^x f'(x) = f"(x) = Find an equation of the tangent line to y= e^x/x, (1, e).
As per the given function, the equation of tangent line is y - e = e(x -1)
The term tangent line in math referred as a function y=f(x) can be calculate the slope by taking derivative m=f′(x) then at a given point (x1,y1) equation of tangent line is given by the formula y−y1=m(x−x1)
Here we have given the expression y = eˣ/x
Now, we have to calculate the tangent line for the given function,
Let us consider, Slope of the tangent line is written as,
=> m = dy/dx
Now, we have written it as,
=> dy/dx = eˣ/x
then the equation is equate with the slope, then we get,
=> m = eˣ/x
When we put the value of x as 1, then we get
=> m = e
Here we know that the point value is (1, e)
Therefore, the equation of the tangent line is written as,
=> y - e = e(x -1)
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The points scored per game by a professional basketball player are represented by the box plot below. A number line plots points per game by the basketball player. The plots are 16 through 21 and 21 through 24. If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected? A. The median points per game increases. B. The effect on the median points per game cannot be determined. C. The median points per game decreases. D. The median points per game is not affected.
The median of the data set would be affected as the median points per game decreases. That is option C.
What is a median of a data set?The median of a data set is defined as the value of a data set the is found in the middle of a data after it has been arranged in an ascending order.
The first number line plots points per game;
= 16, 17 ,18 ,19 ,20 ,21 = 18+19 = 37/2 = 18.5
The second number line plots points per game;
= 21, 22, 23, 24 = 22 + 23 = 45/2 = 22.5
The third number line plots points per game:
= 9 points through 35 points
= 22 as the median.
Therefore, the scores of the next two games led to a decrease in the median determined per game point.
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How much can evan make and how many bagels will be leftover please help
Answer:
okay he can make 62 packages with 1 bagel left over
Step-by-step explanation:
Answer:
Step-by-step explanation:
381/6 = number of packages = 63 packages
63 * 6 = 378; 381-378 = 3 bagels left over
GIVING 70 POINTS AND I WILL MARK BRAINLIEST PLEASE HELP! :D sorry for the all caps im just rlly energetic right now
A square garden is expanded to a rectangle in which the width is 1.5 times the original side length and the length is 3.5 times the original side length. The area of the expanded garden can be modeled by the expression (1.5s)(3.5s).
Simplify the expression (1.5s)(3.5s).
(A)5s
(B)5s2
(C)5.25s2
(D)5.25s
Answer:
C) 5.25s^2
Step-by-step explanation:
1. Multiply 1.5s x 3.5s = 5.25.
2) Because 1.5 has one s, and 3.5 has another s, these 2 s combine (s+s)=s^2. Meaning there is 2 s in the equation. s^2 happens when you multiply two numbers that each have an s. Multiplication in this problem is brought by the use of parenthesizes surrounding these 2 numbers.
How many terms are in the expression 3x2y xy2 2x 5?
The expression 3x²y + xy² + 2x + 5 has in its entirety 4 term.
First let's define what algebraic expressions are.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:
x + y has two termsAs we can see the expression has addition operations so it has more than 1 term:
1 = 3x²y2 = xy²3 = 2x4 = 5this expression has 4 terms.
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What are the three methods of mean?
They are the three methods of mean - Direct Method. Assumed Mean Method. Step-deviation Method.
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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Who introduced judicial activism?
Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".
What is judicial activism?
Judicial activism is a judicial philosophy that is sometimes referred to as "legislating from the bench". It is an exercise of judicial review and generally refers to the willingness of a judge to strike down legislative or executive actions regarding constitutional issues. Judicial restraint is generally thought of as the opposite of judicial activism.[1]
Earlier in the january of 1947 ,Arthur Schlesinger Jr. introduced the term "judicial activism" .An article by Keenan Kmiec says that in its early usage, it was sometimes used with a positive connotation akin to the term "civil rights activist".
Thus , Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".
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What is an example of a linear line?
An equation that depicts a straight line on a graph is said to be linear line.
What is linear line?
Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.
A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them.
2x - 3 = 0 and 2y = 8 are few examples of linear lines.
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Match each value of r to its scatterplot: Data 100 09 09 GRAPHA OP 8 3 40 8 0 100 Det 001 OH 0 GRAPH B OP 30 100 Duta 00 GRAPH C 爱 arch Data 100 80 60 OOO GRAPHD 20 0 0 20 40 80 100 Data 100 80 09 OOOOOOOOOOOOOOOO GRAPHE ON OZ 0 0 20 40 50 09 100 A [Choose B [ Choose -1 0.373 -0.908 0.881 -0.732 [ Choose C > D [ Choose E [Choose ]
Graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1What is Scatter plot?
A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -
U-shapedlinear exponential.There are the three most important correlations as -
positive correlationnegative correlationno correlationGiven are the scatter plots and the associated correlation coefficient.
Correlation coefficient : it is a measure of linear correlation between two sets of data. Mathematically, we can write -[tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
r = correlation coefficient
[tex]$x_{i}[/tex] = values of the x-variable in a sample
[tex]$\bar x[/tex] = mean of the values of the x-variable
[tex]$y_{i}[/tex] = values of the y-variable in a sample
[tex]\bar y[/tex] = mean of the values of the y-variable
The graph and their corresponding values of [r] are mentioned below -
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1Therefore, graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1To solve more questions on scatter plots, visit the link below-
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how do you solve this ?
Step-by-step explanation:
first of all, remember for life :
the sum of all angles in a triangle is always 180°.
so, in this right-angled triangle we have therefore
180 = b + 90 + 71
b = 180 - 90 - 71 = 19°
and then regarding a and b :
the sum of all angles around a single point on one side of a line is also always 180°.
why ? because the line can be seen as the extended diameter of a circle, with that point being the center of the circle. and one side of the line is representing half of that circle. and a half-circle is 180°.
so,
a + b = 180
a + 19 = 180
a = 180 - 19 = 161°
FYI, the reason for the first principle (all angles in a triangle are together 180°) is also based on a half-circle concept : any right-angled triangle can be seen as inscribed into a half-circle, with the Hypotenuse (the baseline opposite of the 90° angle) being the diameter of the circle, and the center of the circle being the midpoint of the Hypotenuse.
What shape has 4 sides and 1 set of parallel?
The trapezoid has 4 sides and 1 set of parallel
What is trapezoid?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. The top and bottom bases are parallel to one another. An isosceles trapezoid has opposite sides that are the same length. Angles next to one another add up to 180 degrees. Both bases are parallel to the median. Equal sides and parallel opposing sides make up a rhombus. In general, a trapezoid has uneven sides with two parallel sides. Only the trapezoid's legs can have equal lengths.To learn more about trapezoid refer to:
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Simplify.
-7+8i / 10i
A) 2i+4 / 5
B) - i / 5
C) 7i+8 / 10
D) 4i+4 / 5
The outcome of the complex number given is 7i+8/10 in its most basic form. Option C
Simplifying complex expressionsComplex numbers are referred to as the square root of negative numbers. For instance √-1 = i.
In this expression 'i" is a complex number.
Given the expression below;
-7+8i / 10i
Rationalise
-7+8i / 10i * 10i/10i
= 10i(-7+8i)/10(i²)
= -70i+18(-1)/10(-1)
= -70i - 18/-10
= 7i+1.8
Hence the result of the given complex number in its simplest form is 7i+8/10
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*URGENT NEED TO PASS FOR GRADUATION*
built for the 1976 olympic games in montreal canada, the tower is 156 meters tall, measured vertically from the ground to the top. the tower makes a 45 degree angle with the ground. if you were to climb to the top and then accidentally drop your keys, where would you start looking for them?
Answer:
156 meters from the bottom of the tower--------------------------------
The height of the tower is the leg of the isosceles right triangle, since one of angles is 45 degrees.
The horizontal distance from the to the point where you dropped your keys is same as the vertical distance, 156 meters, because it is the other leg of the triangle.
What is the quotient?
1065 ÷ 33
Enter your answer as a mixed number in simplest form in the box.
The quotient of 1065 ÷ 33 is [tex]32\ \frac{3}{11}[/tex] .
What is quotient in fraction?Fractions. A fraction's quotient is the whole number that results from simplifying the fraction. The quotient is the fraction's decimal form if the simplified fraction yields a non-whole number. Dividend / divisor = quotient can also be used as the answer to a division issue involving two fractions.1065 ÷ 33 = 32.2727272727
Dividend = 1065
divisor = 33
quotient = 32
balance = 9
answer as a mixed number [tex]32\ \frac{9}{33} = 32\ \frac{3}{11}[/tex]
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Please help me with this question
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The average rate of change (m) for the given line segment can be found with
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the graph, the following values can be recorded:
[tex](x_1,y_1)=(-1,-5)\\(x_2,y_2)=(1,-4)[/tex]
So,
[tex]m=\frac{(-4)-(-5)}{(1)-(-1)}\\m=\frac{-4+5}{1+1}\\m=\frac{1}{2}[/tex]
This answer makes sense in both sign and scale with the given image.
Judy and Cassie each opened a savings account on the same day. Judy started by putting $300 in her account, and she will deposit an additional $12 each week. Cassie made an initial deposit of $100, and she will add $20 more each week. Eventually, Judy and Cassie will each have the same amount saved. How many weeks will that take?
Write a system of equations, graph them, and type the solution.
Answer: 25 weeks
Step-by-step explanation:
Let W represent the number of weeks
Judy equation is
12W + 300
Cassie equation is
20W + 100
Now let's solve it! Our system of equation is
12W + 300 = 20W + 100
Subtract 300 from both sides
12W = 20W -200
Subtract 20W from both sides
-8W = -200
W = 25 weeks
So, it takes 25 weeks for Judy and Cassie to have the same amount saved.
Answer:
let judy = 300 + 12W
cassie = 100 + 20W
300 + 12W = 100 + 20W
300 - 100 = 20W - 12W
200 = 8W
W = 25
CHECKING:
300 + 12(25) = 100 + 20(25)
300 + 300 = 100 + 500
600 = 600
Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.
THE GRAPH IS IN THE PICTURE,line graph
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-How do you work out 2x 3y 12?
The resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.
What is an equation?The concept of an equation in algebra is a mathematical statement that shows the equality of two mathematical equations.
For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are divided by the 'equal' sign.
So, we have the equation:
2x - 3y = 12
Now, solve the equation by taking x as the subject as follows:
2x - 3y = 12
2x = 12 + 3y
x = (12 + 3y)/2
Therefore, the resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.
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Correct question:
How do you work out 2x - 3y = 12?
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4, and each adult ticket sells for $8. There was a total of $640 in revenue from the sale of 100 total tickets. Graphically solve a system of equations in order to determine the number of student tickets sold, x, and the number of adult tickets sold, y.
The number of student tickets sold is 40 and the number of adult tickets sold is 60.
Define System of equations
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Each student ticket sells for = $4
Each adult ticket sells for = $8
Total tickets sale = 100
Revenue from the sale of 100 tickets = $640
Let, x = number of student tickets sold
and, y = number of adult tickets sold
so, let's form a equation
x + y = 100 ------(i)
4x + 8y = 640 -------(ii)
Rewrite eq(i),
x = 100 - y
Now, substitute x value in eq(ii)
4(100- y) + 8y = 640
400 - 4y + 8y = 640
4y = 640 - 400
y = 240 / 4
y = 60
Now, put y value in eq(i)
x + 60 = 100
x = 40
Hence, the number of student tickets sold is 40 and the number of adult tickets sold is 60.
Now, to solve graphically
Let's rewrite the eq(i) and eq(ii)
y = 100 - x
y = 80 - (1/2) x
Plot these lines on graph as mentioned below.
And, the solution is the point of intersection(40,60)
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18 The three solids A, B and C are similar such that
and
the surface area of A: the surface area of B=4:9
the volume of B: the volume of C = 125:343
Work out the ratio
the height of A: the height of C
Give your ratio in its simplest form.
Answer:
1:1
Step-by-step explanation:
Since the surface area of A is 4 times the surface area of B, and the volume of B is 125 times the volume of C, we can write the following proportion:
(surface area of A) / (surface area of B) = (volume of B) / (volume of C)
(height of A)^2 / (height of B)^2 = (height of B)^3 / (height of C)^3
We can then cross-multiply and simplify to find the ratio of the heights:
(height of A)^2 / (height of C)^2 = (height of B)^3 / (height of B)^3
(height of A)^2 = (height of C)^2
Therefore, the ratio of the height of A to the height of C is 1:1, or simply 1.