Answer:
61
Step-by-step explanation:
Let's see what to do buddy...
_________________________________
KJI = KJR + RJI
So :
172° = ( 6x -5 )° + ( 12x -3 )°
172° = 18x - 8°
Subtract the sides of the equation plus 8°
180° = 18x
Divided the sides of the equation by 18
x = 180/18
x = 10°
_________________________________
So we have :
KJR = 6x -5 = 6(10) - 5 = 60 - 5 = 55°
KJR = 55°
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Which equation has no solution A.) 4(x+3)+2x=6(x+2) B.) 5+2(3+2x)=x+3(x+1) C.) 5(x+3)+x=4(x+3)+3 D.) 4+6(2+x)=2(3x+8)
Answer:
B. 5+2(3+2x)=x+3(x+1)
Step-by-step explanation:
Expand the brackets.
5 + 6 + 4x = x + 3x + 3
11 + 4x = 4x + 3
Add -4x and -11 on both sides.
4x - 4x = 3 - 11
0 = -8
There are no solutions.
Answer:
B
Step-by-step explanation:
I could explain this to you by using process of elimination but I think it would be easier to explain to you straight forward why answer choice B has no possible answers. First I did the equation out on a piece of paper:
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 +4x = x + 3x +3
11 + 4x = 4x +3
Now we have 4x + 3 = 4x + 11. It is impossible for 4x to be added to two entirely different numbers and still produce the same outcome, so that is why B is the correct answer choice.
Find and classify the critical points of f(x,y)=8r³+ y² + 6xy
The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point
To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.
Taking the partial derivative with respect to x, we have:
∂f/∂x = 24x^2 + 6y = 0.
Taking the partial derivative with respect to y, we have:
∂f/∂y = 2y + 6x = 0.
Solving these two equations simultaneously, we get:
24x^2 + 6y = 0,
2y + 6x = 0.
From the second equation, we can solve for y in terms of x:
Y = -3x.
Substituting this into the first equation:
24x^2 + 6(-3x) = 0,
24x^2 – 18x = 0,
6x(4x – 3) = 0.
Therefore, we have two possibilities for x:
1. x = 0,
2. 4x – 3 = 0, which gives x = ¾.
Substituting these values back into y = -3x, we get the corresponding y-values:
1. x = 0 ⇒ y = 0,
2. x = ¾ ⇒ y = -9/4.
Hence, the critical points of the function are (0, 0) and (3/4, -9/4).
To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.
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Please help!! 20 points to anyone who gives the RIGHT answer!!
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
Answer:
Step-by-step explanation:
Kiran’s recipe is more chocolate because when doubled the recipe he should have added 4 teaspoons of chocolate syrup but instead he added 5 teaspoons
Michelle read 33 pages of her book on the weekend and read 19 pages per day jillian read 45 pages of her book on the weekend and then read 23 per day write an inequality to represent the number of days that Michelle must read in order to read more pages than jill
The inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.
What is inequality?
An inequality is a mathematical statement that compares two values, expressing that they are not equal.
Let "x" be the number of days that Michelle must read in order to read more pages than Jill.
The total number of pages Michelle reads can be represented as:
33 + 19x
The total number of pages Jill reads can be represented as:
45 + 23x
To write an inequality to represent the number of days that Michelle must read in order to read more pages than Jill, we need to compare the two expressions:
33 + 19x > 45 + 23x
Simplifying the inequality, we get:
-12 > 4x
Dividing both sides by 4 (and flipping the inequality because we're dividing by a negative number), we get:
x < -3
However, this solution doesn't make sense in the context of the problem because we can't have negative days of reading.
Hence, there is no solution to the inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.
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Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
Answer:
x-intercept (and intersection of both lines)- (-3,0)
Step-by-step explanation:
A passenger on a boat notices that there is a dolphin 3.4 yards below the boat. There is also a fish 1.2 yards below the boat. They also see a bird that is 1.2 yards above the boat. Part A: Explain how you would create a number line for these points. (1 point) Part B: What does zero represent on your number line? (1 point) Part C: Determine which two points are opposites, using absolute value. Be sure to show your work.
Part A: To create a number line for these points, we can choose a reference point on the number line, which we can consider as the boat itself. We can then represent distances below the boat as negative numbers and distances above the boat as positive numbers.
Let's choose the reference point on the number line as the boat. We can represent distances below the boat as negative numbers and distances above the boat as positive numbers. Based on the given information, we have:
-3.4 yards (dolphin) - below the boat
-1.2 yards (fish) - below the boat
+1.2 yards (bird) - above the boat
So, our number line representation would look like this:
-3.4 -1.2 0 +1.2
|--------|--------|--------|
Part B: On the number line, zero represents the reference point, which is the boat. It is the point of reference from which we measure the distances below and above the boat.
Part C: To determine which two points are opposites, we can look for the pair of points that have the same absolute value but differ in sign.
In this case, the two points that are opposites are the dolphin (-3.4 yards below the boat) and the bird (+1.2 yards above the boat). Both of these points have an absolute value of 3.4 but differ in sign.
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Order the number from least to greatest -12, 3/25, -0.41
Answer:
-12, -0.41, 3/25
Step-by-step explanation:
Answer:
the answer is -12, -0.41, 3/25.
5
A Petri dish is filled with 250 bacterial cultures. The number of bacteria in the dish triples
every hour.
Select the recursive and explicit formulas that model the scenario.
The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹
Calculating the recursive and explicit formulas that model the scenario.From the question, we have the following parameters that can be used in our computation:
Initial = 250 bacterial cultures.Rate = triples every hour.This means that
Initial, a = 250 bacterial cultures.
Rate = 3
So, the recursive formulas is
f(n) = 3f(n - 1), where f(1) = 250
For the explicit formula, we have
f(n) = 250(3)ⁿ‐¹
Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹
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Desperate
please Hurry
Question Down Below
Hi!
Lets walk through this together.
Lets start with the top.
4-8 is -4.
what that line is- its pretty much telling you to divide.
-4 divided by 3 is -1.3~ (infinant 3's)
-1.3~ Is your answer. Hope this helps!
decrease 9 3/8 by 4.37
Declining is the process of getting gradually smaller (in size, amount, number, or intensity): it refers to a drop in productivity. 2. a reduction in size Violent crime decreased by 20% with a reduction of 20,000.
The answer is to reduce 9 3/8 by 4.37, or 1001/200.
How do I figure out a decrease?To find the difference between the old and new value, use the formula a - b. By multiplying the difference by the starting amount: (a - b) / a . To convert the value to percentages, multiply it by 100. I'm done now! As you can see, figuring the percent drop is really not that difficult.The percent decrease formula is created by taking the difference between the old and new values, dividing it by the old value, and multiplying it by 100. Percent Decrease = [(Old Value - New Value) / Old Value] 100 is the formula for percent decrease. Percent decrease refers to the percentage change in a value when it is reduced over time. Percentage decrease expresses the percentage decrease in the given value with respect to its initial value.To learn more about percent decrease, refer to:
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according to the census data, which racial group has seen a steady decline as a percentage of the total population since 1900?
According to census data, the racial group that has seen a steady decline as a percentage of the total population since 1900 is the non-Hispanic White population in the United States.
This decline can be attributed to various factors, including lower birth rates among non-Hispanic Whites compared to other racial and ethnic groups, as well as increased immigration and higher birth rates among other racial and ethnic groups.
Over the years, these demographic shifts have led to a gradual decrease in the proportion of non-Hispanic Whites in the overall population, highlighting the increasing diversity within the United States. This trend underscores the ongoing demographic changes and the importance of understanding and addressing issues related to race and ethnicity in the country.
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I need Help plzz!!! ASAP!
Answer:
3/2
Step-by-step explanation:
Slope= rise over run
rise=3
run=2
So 3/2
Answer:
the slope is -2
Step-by-step explanation:
hope it helps
have a nice day ^_^
Select 3 solutions to inequality graphed below.
Equations and inequalities are both mathematical constructions made by joining two expressions.
What is meant by inequality?A connection in mathematics that compares two numbers variables or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. Less than or equal to, larger than, less than, and more than or equal to are the four fundamental inequalities.
Here,
Given :
-1 to 2 in the graph ,
To find the solution for the inequality ,
We get option -1 as the inequality
=> -1 ,0 ,1,2
=> -1 is the solution for this
These symbols for inequality are not equal (≠), less than (<), greater than (>), less than or equal (≤), and more than or equal (≥). Comparing numbers and identifying the range or ranges of values that satisfy the requirements of a given variable are both done using inequalities.
Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >, <, ≤ or ≥ indicate that the two expressions in an inequality are not always equal.
Therefore, the correct answer is option b.
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in a simple linear regression model, which of the coefficients in the estimated sample regression equation indicates the change in the predicted value of y when x increases by one unit?
In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.
In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.
The linear regression equation is given as:
y = b0 + b1 * x
Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable
In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.
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Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.
Gauge Readings ( pounds per square inch )
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Pressure readings ( pounds per inch) answers:
The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.
Given readings:
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Expressed as rational numbers with a common denominator:
25 psi = 25/1
13 psi = 13/1
6.3 psi = 63/10
7.8 psi = 78/10
1.9 psi = 19/10
2 psi = 2/1
7.8 psi = 78/10
Now, let's order these rational numbers from least to greatest:
1.9 psi = 19/10
6.3 psi = 63/10
7.8 psi = 78/10
7.8 psi = 78/10
13 psi = 13/1
25 psi = 25/1
2 psi = 2/1
Ordered from least to greatest:
19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1
Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
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What are the coordinates of point S?
(Negative three-fourths, one-half)
(Negative one-half, negative three-fourths)
(One-half, Negative three-fourths)
(Three-fourths, one-half)
Answer:
-3/4, 1/2
Step-by-step explanation:
Because the axis are split into 4ths, we can assume that each line is worth 1/4 in coordinates. S is located 3/4ths in the negative x direction and 2/4, or 1/2 in the positive y direction.
PLEASEEE I NEED HELP WILL GIVE BRAINLIEST AND 100 POINTS
Functions f(x), g(x), and h(x) are defined below.
Part A
Which function has the greatest y-intercept? Explain your answer.
Part B
When the input is 2, which function has the greatest output? Explain your answer.
Part A:
For the function f(x) = 1 - (4)^x -> y -intercept = 0
For the given table we are given the point (0, 2) -> y-intercept = 2
For the graph we can see that the graph intersects the y-axis at point "(0, 1)"
-> the y-intercept = 1
The table has the greatest y-intercept
Part B:
Function: f(x) = 1 - (4)^2 = 1 - 16 = - 15,
Table: Given g(x) (output) = 6
Graph: Output = -7
The table again has the greatest output
-91=6p + 9 - 4p solve for p
Answer:
p= - 50
Step-by-step explanation:
Move the p variables to one side and the constant numbers (intergers) to the other
-91=6p + 9 - 4p
-91 - 9 = 6p- 4p
-100 = 2p
\(\frac{-100}{2}\) = \(\frac{2p}{2}\)
-50 = p
p= -50
ANSWER: p=50
-91=6p + 9 - 4p solve for p
1. 6p - 4p = 2p
2. -91= 2p + 9
-91-9= 100
3. 100 = 2p
p= 100/2
p= 50
(Likelihood MC)
Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3). Optin C.
The likelihoods of the three players hitting the ball can be compared by examining their batting averages, which are given as probabilities.
Player 1 has a batting average of seven elevenths, which can be written as 7/11. This means that out of 11 times at bat, Player 1 is expected to hit the ball successfully 7 times.
Player 2 has a batting average of six ninths, which can be simplified to 6/9 and further reduced to 2/3. This means that out of 9 times at bat, Player 2 is expected to hit the ball successfully 6 times.
Player 3 has a batting average of five sevenths, which can be written as 5/7. This means that out of 7 times at bat, Player 3 is expected to hit the ball successfully 5 times.
To compare the probabilities and interpret the likelihood, we can examine the fractions directly.
Comparing Player 1 and Player 2, we have 7/11 for Player 1 and 2/3 for Player 2. In this case, P(Player 1) = 7/11 is greater than P(Player 2) = 2/3. Therefore, Player 1 is more likely to hit the ball than Player 2.
Comparing Player 2 and Player 3, we have 2/3 for Player 2 and 5/7 for Player 3. In this case, P(Player 2) = 2/3 is greater than P(Player 3) = 5/7. Therefore, Player 2 is more likely to hit the ball than Player 3.
Comparing Player 1 and Player 3, we have 7/11 for Player 1 and 5/7 for Player 3. In this case, P(Player 1) = 7/11 is greater than P(Player 3) = 5/7. Therefore, Player 1 is more likely to hit the ball than Player 3.
Based on these comparisons, the correct statement is: Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3). So Option C is correct.
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I need help with how to write the expressions in its simplest form which is 15 and I also need help with 16
Recall that like terms are terms that have the same variables and powers. The coefficients of the terms do not have to match.
a.- Notice that 4z and -3z are like terms since they have the same variables with the same exponents, therefore:
\(4z-3z=(4-3)z=1z=z\text{.}\)b.- Notice that 3n and -3n are like terms, but 6 is a constant, therefore:
\(6-3n+3n=6+(-3+3)n=6+0n=6.\)c.- In the given expression, the similar terms are 2g and -8g, and -3 and 11, therefore:
\(2g-3+11-8g=(2-8)g+(-3+11)=-6g+8.\)d.- In the last expression, first, we have to apply the distributive property:
\(3(4x-5)+4(2x+6)=12x-15+8x+24.\)Now, adding like terms we get:
\(12x-15+8x+24=20x+9.\)Answer:
a.-
\(z\text{.}\)b.-
\(6.\)c.-
\(-6g+8.\)d.-
\(20x+9.\)let c and d be nonempty disjoint subsets of rn. consider the set of (a,b) 2 rn 1 for which a'x less than or equal to b for all x belonging to c, and a'x greater than or equal to b for all x belonging to d.show that it is a convex cone
The set of (a, b) ∈ ℝⁿ¹ for which a'x ≤ b for all x ∈ C, and a'x ≥ b for all x ∈ D, where C and D are nonempty disjoint subsets of ℝⁿ, forms a convex cone.
To show that this set is a convex cone, we need to demonstrate that it satisfies two properties: convexity and non-negativity.
Convexity: Let (a₁, b₁) and (a₂, b₂) be two points in the set. We need to show that the line segment between these two points, denoted as t(a₁, b₁) + (1-t)(a₂, b₂), also belongs to the set for any t in [0,1].
Consider any x ∈ C. Since (a₁, b₁) and (a₂, b₂) belong to the set, we have a₁'x ≤ b₁ and a₂'x ≤ b₂. Now, let's examine the inequality for the line segment:
(t(a₁) + (1-t)(a₂))'x = t(a₁'x) + (1-t)(a₂'x) ≤ tb₁ + (1-t)b₂,
Since a₁'x ≤ b₁ and a₂'x ≤ b₂, the above inequality holds. Similarly, for any x ∈ D, we can show that (t(a₁) + (1-t)(a₂))'x ≥ tb₁ + (1-t)b₂. Thus, the line segment between (a₁, b₁) and (a₂, b₂) satisfies the inequalities for both C and D, and therefore, it belongs to the set. Hence, the set is convex.
Non-negativity: To show that the set is a cone, we need to prove that for any point (a, b) in the set and any non-negative scalar k, the point (ka, kb) also belongs to the set.
Consider any x ∈ C. Since (a, b) belongs to the set, we have a'x ≤ b. Now, let's examine the inequality for the point (ka, kb):
(ka)'x = k(a'x) ≤ kb,
Since a'x ≤ b, the above inequality holds. Similarly, for any x ∈ D, we can show that (ka)'x ≥ kb. Therefore, (ka, kb) satisfies the inequalities for both C and D, and thus, it belongs to the set. This demonstrates the non-negativity property of the set.
In conclusion, we have shown that the set of (a, b) ∈ ℝⁿ¹ for which a'x ≤ b for all x ∈ C, and a'x ≥ b for all x ∈ D, where C and D are nonempty disjoint subsets of ℝⁿ, forms a convex cone. It satisfies the properties of convexity and non-negativity, which define a convex cone.
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Three yams are chosen at random from 15 tubers of which 5 are spoilt Find the probability that, of the three chosen tubers (A) none is spoilt. (B) all are spoilt. (C) exactly one is spoilt. (D) at least one is spoilt
Step-by-step explanation:
.....................
the absolute value of the difference between the point estimate and the population parameter it estimates is ? precision. the sampling error. the error of confidence. the standard error.
The absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.
What is absolute value?The number's absolute value, which ignores orientation, indicates how far it is from zero on the number line. A number can never be negative in absolute terms.
Concepts which are used in the given problems:
Standard error - It is a gauge of how closely a sample statistically approximates the entire population. Standard deviation in sampling distribution refers to standard error.Sampling error - Instead of studying the entire population, a sample is used to determine the sampling error. The distinction between sample statistics and population parameter estimation is what causes this.Precision - It is described as how closely two estimates from several samples agree with one another.Error of confidence - A statistic that indicates the degree of sampling error in a specific research is known as the error of confidence. Additionally, the margin of error indicates the percent by which the actual findings would deviate from the stated population figure.Point estimates - Point estimates refer to population parameters that are calculated using sampling statistics.The incorrect options can be found below:
Because the precision is the estimate that is near from the various samples, the absolute magnitude of the difference between the point estimate and the population parameter would not be a precision. Additionally, it is not a standard error since a standard error is an error that is far beyond the range of the sample mean. However, it is not a confidence error since a confidence error is a measure of how far the findings would deviate from the population under consideration.
By using the concept of precision, standard error and error of confidence, the incorrect choices are discovered.
The correct choice may be found below:
Sampling error is the measurement of the distance or difference between the population parameter and the sample's point estimate. The sampling mistake is an inaccuracy that results from drawing conclusions about the sample rather than the population being studied.
The idea of sampling error is used to calculate the absolute value of the distinction between both the point estimate and the population parameter is predicts.
Thus, the absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.
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What are the three unbiased estimators?
The three unbiased estimators are the sample mean, sample variance, and sample proportion. These estimators provide unbiased estimates of the population mean, population variance, and population proportion, respectively.
There are several unbiased estimators commonly used in statistics, but three notable examples are the sample mean, the sample variance, and the sample proportion.
1. Sample Mean: When estimating the population mean, the sample mean is an unbiased estimator. It is calculated by taking the average of all the observations in a sample. Under certain conditions, such as random sampling, the sample mean provides an unbiased estimate of the population mean.
2. Sample Variance: When estimating the population variance, the sample variance is an unbiased estimator. It measures the dispersion of the data points around the sample mean. By dividing the sum of squared differences by the sample size minus one, the sample variance provides an unbiased estimate of the population variance.
3. Sample Proportion: When estimating the population proportion, the sample proportion is an unbiased estimator. It represents the proportion of a specific characteristic or outcome within a sample. If the sample is obtained randomly and meets certain conditions, the sample proportion provides an unbiased estimate of the population proportion.
These three unbiased estimators play crucial roles in statistical inference, allowing researchers to make inferences about population parameters based on sample data.
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Which is not equivalent to
A
x
+
B
y
=
C
?
y
=
C
B
−
A
B
x
y = C B − A B x
y
=
C
−
A
x
B
y = C − A x B
y
=
C
B
−
A
x
B
y = C B − A x B
y
=
C
−
A
B
x
Expressions separated by an equal sign are known as an equation. From the given equation in the question, the value of y is expressed as \(\frac{C -Ax}{B}\)
Given the expression Ax + By = C, we are to make y the subject of the formula as shown:
Given Ax + By = C
Subtract Ax from both sides
Ax + By - Ax = C - Ax
By = C - Ax
Divide both sides by B
\(\frac{By}{B} = \frac{C -Ax}{B} \\y=\frac{C -Ax}{B}\)
Hence the value of y is expressed as \(\frac{C -Ax}{B}\)
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Problem 13 Second Ses 2015
There are some missing numbers in the following text:
- For buying pencils and 2 pens we pay ...LL. and for buying
pencils and 3 pens we pay 7800 L.L. >>
Setting up the complete givem of the text in equations give the following system:
(4x + 2y = 5600
2x + 3y = 7800
1 Copy again the complete text according to the given system.
2 Solve, showing all the steps of calculation, the preceding system and find the price of one pencil and the price of
pen
Answer:
1. For buying 4 pencils and 2 pens we pay 5600 L.L. and for buying 2 pencils and 3 pens we pay 7800 L.L.
2. The price of one pencil is 150 L.L. and the price of one pen is 2,500 L.L
Step-by-step explanation:
The given system of equation are;
4·x + 2·y = 5,600...(1)
2·x + 3·y = 7,800...(2)
Where x represent the price of one pencil and y represents the price of one pen
Therefore, we have;
1. For buying 4 pencils and 2 pens we pay 5600 L.L. and for buying 2 pencils and 3 pens we pay 7800 L.L.
2. By making y the subject of both equations we have;
For equation (1)
y = 5,600/2 - 4·x/2 = 2,800 - 2·x
y = 2,800 - 2·x
For equation (2)
y = 7,800/3 - 2·x/3 = 2,600 - 2·x/3
y = 2,600 - 2·x/3
Equating both values of y gives;
2,800 - 2·x = 2,600 - 2·x/3
2,800 - 2,600 = 2·x - 2·x/3
200 = 4·x/3
600 = 4·x
x = 600/4 = 150
∴ The price of one pencil = 150 L.L.
y = 2,800 - 2·x = 2,800 - 2 × 150 = 2,500
∴ The price of one pen = y = 2,500 L.L.
Select the correct answer.
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 7?
OA. It is the graph of y = x translated 7 units up.
B.
It is the graph of y = x translated 7 units to the right.
C.
It is the graph of y = x where the slope is increased by 7.
D. It is the graph of y = x translated 7 units down
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Answer:
A. It is the graph of y = x translated 7 units up.
Step-by-step explanation:
Imagine you have a friend named Y who always copies what you do. If you walk forward, Y walks forward. If you jump, Y jumps. If you eat a sandwich, Y eats a sandwich. You and Y are like twins, except Y is always one step behind you. Now imagine you have another friend named X who likes to give you money. Every time you see X, he gives you a dollar. You're happy, but Y is jealous. He wants money too. So he makes a deal with X: every time X gives you a dollar, he also gives Y a dollar plus seven more. That way, Y gets more money than you. How do you feel about that? Not so happy, right? Well, that's what happens when you add 7 to y = x. You're still doing the same thing as before, but Y is getting more than you by 7 units. He's moving up on the money scale, while you stay the same. The graph of y = x + 7 shows this relationship: Y is always above you by 7 units, no matter what X does. The other options don't make sense because they change how Y copies you or how X gives you money. Option B means that Y copies you but with a delay of 7 units. Option C means that Y copies you but exaggerates everything by 7 times. Option D means that Y copies you but gets less money than you by 7 units.
A theater is being designed to hold 700 people the first two rows are shown there are 20 seats per row in the main section and 4 seats per row in each wing. How many rows will they need to hold 700?
Answer:
25 rows of seats
Step-by-step explanation:
20 + 4 + 4=28 (the middle and both wings)
700/28=25 (divide the whole row by the total number of seats)
I think of a number and halve it. The answer is two hundred and sixty. What number did I start with?
Let the number be x
Now we have a equation,
X÷2=260
x=260×2
x=520
Hence, the number you started with was 520.