Answer:
Total students = 1240
Step-by-step explanation:
Given that,
Number of boys: number of girls=11:9
[tex]\dfrac{x}{y}=\dfrac{11}{9}\\\\9x=11y[/tex] ......(1)
There are 124 more boys than girls i.e.
x = 124+y .....(2)
Put the value of x from equation (2) in equation (1). So,
9(124+y) = 11y
1116 +9y = 11y
1116 = 2y
y = 558
Put the value of y in equation (2).
x = 124+558
x = 682
Total students = x+y
= 682+558
= 1240
So, there are 1240 students at the school.
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.
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 certain math test has a mean of 50 and a standard deviation of 12. the teacher wants to convert the scores to a new scale using the transformation x*=65+0.6x. what are the new mean and standard deviation?
a) mean=50, standard deviation=7.2
b) mean=95, standard deviation=7.2
c) mean=95, standard deviation=12
d) mean=95, standard deviation=72.2
e) mean=77, standard deviation=12
Answer:
(b) mean=95, standard deviation=7.2.
Step-by-step explanation:
To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.
The new mean is given by: x*=65+0.6x
Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95
The new standard deviation is given by: s*=0.6s
Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2
Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.
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 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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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.
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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I need help with this
The value of the function (f o g )(11) is -1
How to find the value of the given function?Applying composite function formula,
(f o g )(x) = f [g (x)]
Here ,f(x) = [tex]\sqrt{x} - 3[/tex]
g (x ) = x - 7
(f o g )(x) =f [x - 7 ]
=[tex]\sqrt{x-7} -3[/tex] --(1)
Substitute x = 11 in the given function in (1)
[tex](f o g )(11) =\sqrt{11-7} -3\\(f o g )(11) =\sqrt{4} - 3\\(f o g )(11) = 2 -3 = -1[/tex]
The value of the function (f o g )(11) is -1
What is a composite function?A composite function is a function whose values are obtained by applying one function to an independent variable.Then using the result to apply the second function, and the domain of which is made up of the independent variable values for which the output of the first function falls within the domain of the second. The composition of functions is a particular instance of the composition of relations, and it is sometimes also indicated by °.Therefore, all characteristics of composition of relations, including associativity, are also characteristics of composition of functions. However, composition of functions differs from multiplication of functions ,if it is defined at all and has a number of distinct characteristics, most notably that it is non-commutative.So, option 2 is correct .To learn more about composite function, refer:
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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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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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Which numbers for the numerator
and denominator make the equation.
true? Complete the equation. Fill in
the bubble before the number that is
correct.
Answer:
Step-by-step explanation
So in the fraction 3/8 the numerator is 3. In the fraction 1/9 the numerator is 1.
Is algebra a hard math?
Linear algebra is too hard because it is not very intuitive, it places a powerful emphasis on rigorous proofs, and its concepts are very different and difficult to visualize.
Linear algebra is difficult because it is naturally different from most high school and college courses you have taken until now.
Linear algebra is a branch of mathematics that deals with mathematical structures closed under the operations of addition and scalar multiplication and that comprises the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
Linear algebra is hard to study. Linear algebra is one of the most difficult courses that most STEM majors will study in university.
Linear algebra is not a simple class because it is a very abstract course, and it requires strong analytical and logical skills.
Linear algebra is considered a demanding course by STEM majors since it gets exponentially complex and perplexing as the term progresses.
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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
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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The dot plots show rainfall totals for several spring storms in highland areas and lowland areas.
The dot plots show that the lowland areas experienced significantly more rainfall than the highland area during spring storms, with a larger range and maximum rainfall.
The dot plots show the rainfall totals for several spring storms in both highland and lowland areas. The dots representing the lowland areas are more spread out and have a larger range compared to the dots representing the highland areas. This indicates that the lowland areas experienced more rainfall than the highland areas during these storms. Additionally, the maximum rainfall for the lowland areas is greater than the maximum rainfall for the highland areas, further emphasizing the difference in rainfall between the two areas. This could be due to a number of factors, such as the higher elevation of the highland areas resulting in less moisture being able to accumulate, or the lower temperature of the highland areas resulting in less evaporation and thus less rainfall. Additionally, the lower elevation of the lowland areas could result in more moisture being able to accumulate, and the higher temperature of the lowland areas could result in more evaporation, leading to increased rainfall. Regardless of the cause, the data from the dot plots clearly show that the lowland areas experienced more rainfall than the highland areas during these spring storms.
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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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Your couing ay 5,953 round to 5,053 when rounded to the nearet hundred. If your couin correct ? Explain
No , cousin is not correct because when 5,953 is rounded to the nearet hundred the value should be 6000 .
Given :
What is rounding to the nearest hundred ?
Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number .
if the hundred value number is less than 5 then we must round to the lowest value .if the hundred value number is greater than 5 then we must round to the highest near value .so here given number = 5,953
so here the number 53 is greater than 50 .
We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
so the number after rounded = 6000
so his cousin is incorrect .
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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.
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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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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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 }-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
Mavis is interested in whether military dependency is related to gender in american samoa. Here is data she collected about the population of american samoa in 201020102010:.
Mavis is interested in whether military dependency is related to gender in american samoa. then Male = 0.4193 and Female = 0.5087
What does distribution mean in work?
Distribution is the activity of both selling and delivering products and services from manufacturer to customer. This can also be called product distribution. As businesses become more global it becomes important to improve distribution to ensure that customers and all members of the distribution channel are happy.
To obtain the marginal distribution of gender :
Total number of civilians (male + female)
(26393 + 27330) = 53,723
Male :
P(male) = number of male / total
P(male) = 26393 / 53,723 = 0.4912793
P(Female) = number of Female / total
P(Female) = 27330 / 53,723 = 0.5087206
Complete question :
Mavis is interested in whether military dependency is related to gender in American Samoa. Here is data she collected about the population of American Samoa in 2010.
Millitary status _________ female ____ Male
In armed forces _________ 28 _______ 59
Millitary dependent ______ 928 ______ 781
Civilian _______________ 26393 ___27330
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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.
question 6 do these data provide convincing evidence that age and body fat percentage are significantly positively associated? why or why not? use quantitative information based on the model output to support your answer, and make sure to note the p-value you use to make this decision. 0 / 1 point yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.000. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039 / 2
The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.
In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.
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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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[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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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 greatest common of 45?
Answer:
Step-by-step explanation:
If it is the greatest common factor then it would be 5 I think.