If 3x – y = 5 and 2x + y = 15 then evaluation of x^2 + 2y is equal to 72.
What is evaluation ?
Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.
3x-y=5 and 2x+y= 15
Add the two equations together to eliminate y
3x-y=5
2x+y= 15
---------------------
5x = 20
Divide by 5
5x/5 = 20/5
x = 4
Now we can find y
2x+y = 15
2(4) +y = 15
8+y =15
Subtract 8 from each side
8+y-8 = 15-8
y =7
We want to find
x^2+2xy
(4)^2 +2(4)(7)
16+56
72
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Solve the system using the substitution method. If the system does not have one unique solution, also state the number of solutions and whether the system is
inconsistent or the equations are dependent. Express numbers as integers or simplified fractions.
10x-y-1
5x-4y=-3
The system has one solution.
The solution set is
{0}.
O The system has no solution ().
The system is inconsistent.
The equations are dependent.
O The system has infinitely many solutions.
The solution set is
The system is inconsistent.
The equations are dependent.
X
0-0
The system has one solution. Option A
How to solve the system of equationsThe substitution method of solving simultaneous equations involving substituting the value of one variable I to a given equation.
Given the equation;
10x - y = 1 (1)
5x -4y = -3 (2)
Make 'y' the subject from equation (1)
-y = 1 - 10x
y = -1 + 10x
Substitute the value into equation(2)
5x - 4(-1 + 10x) = -3
expand the bracket
5x + 4 - 40x = -3
collect like terms
-35x = -7
x = 1/5
Now, substitute the value of x as 1/5
y = -1 + 10(1/5)
y = -1 + 2
y = 1
Hence, the values are 1/5 and 1
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Which are samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center? Select all that apply.
The samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center are:
100 residents who live near the proposed site for the youth center.50 children at each of the city’s four elementary schools.100 parents of children at each of the city’s four elementary schools.What is sample?Sample can be defined as the way of randomly collecting data or information from a group of population so as to draw or reach a conclusion.
Most researcher tend to collect sample when carrying out a survey in which they will then examine, analyze and evaluate the sample they collected before reaching a conclusion.
When a researcher want to carryout survey so as to know how the resident of a city feel about building a new youth center. The researcher has to collect the survey sample from :
100 residents who live near the proposed site for the youth center.50 children at each of the city’s four elementary schools.100 parents of children at each of the city’s four elementary schools.Therefore the correct option is B,D,E.
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The complete question is:
Which are samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center? Select all that apply.
10 names selected from the city phone book.
100 residents who live near the proposed site for the youth center.
100 tourists at the city park last Friday.
50 children at each of the city’s four elementary schools.
100 parents of children at each of the city’s four elementary schools.
100 POINTS URGENT!
Simplify the expression.
fraction with negative 7 times the quantity 2 minus the cube root of 64 times 3 end quantity as the numerator and 5 as the denominator
Group of answer choices
−14
negative twelve sevenths
twelve sevenths
14
Answer:
the simplified expression is negative twelve sevenths
Step-by-step explanation:
To simplify the expression, we can start by applying the rules for combining like terms:
(-7) * 2 - (3 * sqrt(64)) = (-14) - (3 * sqrt(64))
Next, we can use the fact that the square root of 64 is 8 to simplify the expression further:
(-14) - (3 * sqrt(64)) = (-14) - (3 * 8) = (-14) - 24 = -38
Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor:
-38 / 5 = (-38 / 2) / (5 / 2) = -19 / 2 = negative twelve sevenths
Therefore, the simplified expression is negative twelve sevenths.
Answer:
the simplified expression is negative twelve sevenths
Step-by-step explanation:
MODELING WITH MATHEMATICS The table shows the total numbers y of people who reported an earthquake x minutes after it ended.
a. Use a graphing calculator to find the equation of the line of best fit. Round all values to the nearest integer.
The equation of the line of best fit, rounded to the nearest integer, is y = 381x - 566.
What does "Line of Best Fit" mean?
The trend line sometimes referred to as the line of best fit in statistics, uses a straight line on the scatter plot to best depicts the given data points. All of the points, part of the points, or none may be traversed by a straight line. In the statistical approach, it is regarded as one of the significant results of regression analysis.
Given values of x and y, we will use the graphing calculator to find the line of Best Fit, we will get an equation in linear form as:
or, y = 381x - 566
Hence, the equation of the line is y = 381x - 566.
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Exhibit 17-5 State Division of Motor Vehicles (DMV) statistics show the rate of new driver's license applications to be as shown below. Month April Week1 1 Application 238 199 Nm 215 212 207 211 May nm 196 206 Refer to Exhibit 17-5. Using a five-week moving average, what is the forecast for the first week in April? a. 198.45 Ob. 202.83 C. 206.40 d. 200.20
Previous question
The forecast for the first week of June is 206.40.
The forecast for for the first week of June will be based on the five-week moving average.
Five-week moving average: (applications of (week 1 + week 2 + week 3 + week 4 +week 5)) / 5
For first 5 week: (238 + 199 +215 +212 +207)/5 = 214.20
For second 5 week: (199 + 215+ 212+ 207+ 211)/5 = 208.80
For third 5 week : (215 + 212 + 207 + 211 + 196)/5 = 208.20
For the fourth 5 week or the first week of June:
(212 + 207 + 211+ 196 + 206)/5 = 206.40
The question is incomplete, the complete question is:
Exhibit 17-5 State Division of Motor Vehicles (DMV) statistics show the rate of new driver's license applications to be as shown below.
Month Week Application
April
1 238
2 199
3 215
4 212
May 1 207
2 211
3 196
4 206
Refer to Exhibit 17-5. Using a five-week moving average, what is the forecast for the first week in June?
a. 198.45
b. 202.83
C. 206.40
d. 200.20
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