As per the elimination method, in order to solve a system of equations when multiplication is necessary to eliminate a variable.
The term equation is known as algebra is a statement of equality that contains one or more unknown quantities or variables.
Here we have given that When using the multiplication method, it is important to multiply all the terms on both sides of the equation, then here we do not just the one term you are trying to eliminate.
According to the rule of elimination method we all know while solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.
So in order to multiplying to solve linear systems is to find a number to multiply to one or both of the equations so that the x or y terms in one of the equations will have opposite coefficients from the x or y in the other equation.
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Solve using Cramer's rule.
6x + 5y = 25
7x − 9y = 44
x = 7, y = −1
x = 5, y = −1
x = 5, y = −2
x = 7, y = −2
The solution to the simultaneous equations using Cramer's rule is;
x = 5, y = −1
How to use Cramer's rule to solve simultaneous equations?The simultaneous equations are;
6x + 5y = 25
7x − 9y = 44
We will first find the determinant of the left hand side;
[tex]\left[\begin{array}{ccc}6&&5\\7&&-9\\\end{array}\right][/tex]
|A| = (6 * -9) - (7 * 5)
|A| = -89
Now, will replace the x part of the matrix with the right side values to get;
[tex]\left[\begin{array}{ccc}25&&5\\44&&-9\\\end{array}\right][/tex]
The determinant is;
|A_x| = (25 * -9) - (44 * 5)
|A_x| = -445
Now, will replace the y part of the matrix with the right side values to get;
[tex]\left[\begin{array}{ccc}6&&25\\7&&44\\\end{array}\right][/tex]
The determinant is;
|A_x| = (6 * 44) - (25 * 7)
|A_x| = 89
Thus;
x = |A_x|/|A|
x = -445/-89
x = 5
y = |A_y|/|A|
y = 89/-89
y = -1
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In circle G the length of arc HI = 2 pi and measures angle HGI = 60 degrees. Find the area shaded below
The area of the circular sector is equal to 6π square units.
How to find the area of a circular sector
In this question we must determine the area of the circular sector between points H, G and I from given information of the central angle (θ), in degrees, and arc (p). The perimeter and area of the circular sector are described by the following formulae:
Area
A = (θ / 360) · π · r²
Perimeter
p = (θ / 360) · 2π · r
Where r is the radius of the circle.
If we know that p = 2π and θ = 60°, then the area of the circular sector is:
r = (360 / θ) · (p / 2π)
r = (360 / 60) · (2π / 2π)
r = 6
A = (60 / 360) · π · 6²
A = 6π
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There are 5
green apples and 7
red apples in a basket.
(a) What is the ratio of all
apples in the basket to green apples?
0
(b) What is the ratio of all apples in the basket to red apples?
0
a.
5+7=13
total amount of apples = 13
green apples = 5
5:13
b.
total amount of apples = 13
red apples = 7
7:13
Determine how (if possible) the triangles can be proved similar.
Select one:
A. SAS~
B. SSS~
C. Not Similar
D. AA~
The triangles are proved similar by; D. AA similarity.
What are similar angles of triangles?When on comparing the sides and measures of internal angles of two or more triangles, if there is a common properties among them, then the triangles are similar. Note that being similar does not imply that they are congruent.
So that on comparing the properties of the two triangles given, it can be inferred that:
the two traingles are similar by Angle-Angle theorem which states that; when two angles of two triangles are the same, then the triangles are similar.
Therefore, the statement to prove that the triangles are similar is giben in option D. AA similarity.
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the directions are : The table shows a proportional relationship between x and y. What is the unit rate of y per x.
Since the table shows a proportional relationship between x and y, the unit rate of y per x is equal to 4.
What is a proportional relationship?In order to have a proportional relationship and equivalent ratios, the variable (x) and the variable (y) must have the same constant of proportionality.
Next, we would calculate the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 12/3 = 20/5 = 24/6 = 32/8
Constant of proportionality (k) = 4.
In this context, we can reasonably infer and logically deduce that the unit rate for this proportional relationship is equal to 4.
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Complete Question:
The table shows a proportional relationship between x and y what is the unit rate of y per x (3, 5, 6, 8) (12, 20, 24, 32)?
Sally has a leaking faucet in her bathroom. When she first noticed the leak, there was a puddle that was 2 inches in diameter. Each hour, the diameter will triple in size. If Sally doesn’t do anything to stop the leak, how large will the puddle be after 10 hours?
The required size of the hole after 10 hours will be 118098 inches.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Sally has a leaking faucet in her bathroom. When she first noticed the leak, there was a puddle that was 2 inches in diameter.
According to the given condition
let Y be the size of the hole after 10 hours
Y=2×3¹⁰
Y=118098
Thus, the required size of the hole after 10 hours will be 118098 inches.
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What is the value of x in this proportion?
56=−4x+2
Responses
x=−2 4/5
x equals negative 2 and 4 over 5
x=−4 2/5
x equals negative 4 and 2 over 5
x=−5 1/5
x equals negative 5 and 1 over 5
x=−6 4/5
x equals negative 6 and 4 over 5
The value of x or the expression 56 = -4x + 2 is -27/2.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
56 = -4x + 2
Solve for x.
56 = -4x + 2
Subtract 2 on both sides.
56 - 2 = -4x
54 = -4x
Divide -4 into both sides.
-54/4 = x
x = -54/4
x = -27/2
x = -13(1/2)
Thus,
The value of x is -27/2.
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Which icon points out the Essential Question that you should be able to answer by the end of the lesson?
A.
A question mark icon is shown.
B.
An icon of a computer mouse is shown.
C.
A hand icon is shown.
D.
A book icon is shown.
The icon that points out the Essential Question that you should be able to answer by the end of the lesson is this:
C. A hand icon is shown.
What is the function of a hand icon in a text?A hand icon is used for the purpose of identifying the important questions that should be answered at the end of the lesson. It shows that the reader should pay careful attention to the indicated question as they may have to provide an answer to it by the end of the lesson.
Icons in reading have different meanings and understanding their purposes will lead to a more immersive reading.
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at a certain bakery, the price of each doughnut is $1.50. let the random variable d represent the number of doughnuts a typical customer purchases each day. the expected value and variance of the probability distribution of d are 2.6 doughnuts and 3.6 (doughnuts)2, respectively. let the random variable p represent the price of the doughnuts that a typical customer purchases each day. which of the following is the standard deviation, in dollars, of the probability distribution of p?
The standard deviation, in dollars, of the probability distribution of p is √(1.50 × 3.6) dollars.
We are given the following parameters -
Expected value = 2.6
Variance = 3.6
Price per doughnut = $1.50
Now we can write the price for the variance of the distribution as -
Price per doughnut × Variance
Variance = $1.50 × 3.6
The formula for the standard deviation of the distribution D in relation to the variance is given by -
Standard deviation = √variance
Standard deviation = √(1.50 × 3.6)
Therefore, the standard deviation of P in dollars will be √(1.50 × 3.6).
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Select all the equations that are NOT equivalent to p-7=22
The equivalent expressions are B. p-7-p = 22 -, C. p - 7 + 22 = 22 - 7, D. p - 7 + 7 = 22 - 22
What are algebraic expressions?Algebraic expressions are simply defined as expressions that comprised of terms. coefficients, factors, constants and variables.
They are also made up of some operations which are arithmetic. They include;
AdditionMultiplicationBracketFloor divisionParenthesesSubtractionDivisionFrom the information given, we have the equation as;
p- 7 = 22
To solve the equation, collect like terms
p = 22 + 7
Add the like terms
p = 29
Hence, the value is 29
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The complete question:
Which equation is NOT equivalent to p- 7 = 22? Select all that apply.
A. p-p-7 = 22-p
B. p-7-p = 22 -
C. p - 7 + 22 = 22 - 7
O
D. p - 7 + 7 = 22 - 22
Ep-7 + 7 = 22 +7
In the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.
The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday. (Select all that apply.)
A. Students who are skipping class cannot be sampled.
B. Home-schooled students cannot be sampled.
C. Students who are not taking statistics cannot be sampled.
D. Dropouts cannot be sampled.
E. Students who are on a school trip cannot be sampled.
F. Students who are out sick cannot be sampled.
Answer:
c
Step-by-step explanation:
according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.) A. P( z>(0.27-0.22)/root((0.22)(0.73))/300 B. P( z>(0.27-0.22)/root((0.27)(0.73))/300 C. P( z>(0.22-0.27)/root((0.22)(0.78))/300 D. P( z>(0.22-0.27)/root((0.27)(0.73))/300
The probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex] Hence, the correct answer is option D.
This probability can be calculated using the normal approximation to the binomial distribution, with the sample proportion (p-hat) being 0.27, the population proportion (p) being 0.22, and the sample size (n) being 300.
The formula for the standard error of a sample proportion is -
[tex]\sqrt{p(1-p)/n}[/tex]
substituting the values, we get,
[tex]\sqrt{(0.27)(0.73)/300}.[/tex]
Then, we use the formula for a standard normal probability -
P(z > (p-hat - p)/standard error),
substituting the values, we get,
[tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]
Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]P(z > (0.22-0.27)/ \sqrt{(0.27)(0.73)/300}.[/tex]
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Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?
The number of questions that were answered per minute 20 questions
How to determine the number of questions?the question reads: Jamie answered 16 questions in 4/5 minutes. How many questions were answered per minute?
You should number that a minute is made up of 60 seconds
This implies that 4/5 of a minute is given as 4/5 * 60
This is equal to 48 seconds
So every 48 seconds, Jamie answers 16 questions
This implies that (16*60)/48 = 20
Therefore in one minute Jamie would answer 20 questions
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An experiment was conducted to investigate the relationship between the dose of a puin medication and the number of hours of pain relief; Twenty individuals with chronic pain wcre randomly assigned t0 one of five doses 0.0,0.5,1.0,1.5.2.0 in milligrams (mg) of medication. The results are shown in the scatterplot below. The data were used to fit least-squares regression line to predict the number of hours of- pain relief for given dose. Which of the following would be revealed plot of the residuals of the regression versus the dose" (A)The SUm of the residuals is less than 0, (B) The sum of the residuals is greater than 0_ (C) There are outliers associated with the lower doses (D) The variation in the hours of pain relief is not the same across the doses. (E) There is positive linear relationship between the residuals and the dose _
The least-squares regression line can be used to predict the number of hours of pain relief given a certain dose.
This is done by taking the sum of the squares of the residuals and finding the minimum value. The residuals are the differences between the observed values and the predicted values. The plot of the residuals versus the dose would reveal the variation in the hours of pain relief across the doses.
For example, the formula for finding the least-squares regression line is
Y = b0 + b1X
where Y is the predicted value, b0 is the intercept, b1 is the slope, and X is the dose.
To calculate the residuals, we take the difference between the observed values and the predicted values for each dose.
residual = Y (observed) - Y (predicted)
The plot of the residuals versus the dose would reveal if the variation in the hours of pain relief is not the same across the doses. This is because if the variation is not the same, then the residuals would not be evenly distributed. If the residuals were evenly distributed, then the sum of the residuals would be equal to zero.
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