MATHEMATICS HIGH SCHOOL

Solve the following system of equations by using the substitution method.x – y = 3
2x + 2y = 2

(3, 4)

(-4, 5)

(2, -1)

Answers

Answer 1
Answer:

Solution :

Given equations, x-y=3\n2x+2y=2

Applying Substitution method to solve the equation.

Solve the first equation x-y=3 for x,

x-y=3\:\Rightarrow x=3+y

Substitute the value of x in second equation,

2x+2y=2\n\n\Rightarrow 2(3+y)+2y=2\n\n\Rightarrow 6+2y+2y=2\n\n\Rightarrow6+4y=2\n\n\Rightarrow4y=2-6\n\n\Rightarrow4y=-4\n\n\Rightarrow y=(-4)/(4) =-1\n\n\Rigtharrow y=-1

To calculate the value of  x  substitute the value of y in first equation

x-y=3\n\n\Rightarrow x-(-1)=3\n\n\Rightarrow x=3-1=2\n\n\Rightarrow x=2

Hence, the solution of the equations x-y=3\n2x+2y=2 is (2,-1).
Answer 2
Answer: 3,4 would be the answer

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Ashton works as a marketing manager for a consumer products firm. His total earnings, A, in x months is given by the function A(x) = 2,400x + 40x2. His total savings, S, in x months is given by the function S(x) = 250x + 500.The function E(x) = 40x^2 + 2,150x - 500 40x^2 + 2,650x + 500 40x^2 + 2,150x + 500 40x^2 + 2,650x - 500 represents Ashton’s total expenses in x months.

Ashton’s expenses for 3 years total $ 6,310 8,810 128,740 147,740 .

Answers

E(x) = A(x) - S(x) = 2400x + 40x^2 - (250x + 500) = 2400x + 40x^2 - 250x - 500 = 40x^2 + 2150x - 500

Ashton's expenses for 3 years E(3) = 40(3)^2 + 2150(3) - 500 = 40(9) + 6450 - 500 = 360 + 5950 = $6,310

Final answer:

The functions for Ashton's earnings and savings are given, and his expenses should theoretically be his earnings minus savings. However, the question appears to contain errors, making this computation impossible. Therefore, the given scenario cannot be accurately analyzed.

Explanation:

From the question, we know Ashton's income is A(x) = 2,400x + 40x2, and his savings are S(x) = 250x + 500. His total expenses are represented by E(x) = 40x2 + 2,650x - 500, but it seems there was a mistake in the question with the repetition of the function E(x) and the incorrect total expenses over 3 years.

In principle, to get the equation for Ashton's expenses, we would subtract his savings from his earnings (A(x) - S(x) = E(x)), assuming the given functions are correct. This means, his expenses should equal to his earnings minus savings. However, this cannot be successfully applied because of inconsistencies in the given information.

Learn more about Functions here:

brainly.com/question/21145944

#SPJ12

Find three arithmetic means between -2 and 12.

Answers

a_1=-2;\ a_2;\ a_3;\ a_4;\ a_5=12\n\na_5-a_1=4d\n\n4d=12-(-2)\n4d=14\ \ \ /:4\nd=3.5\n\na_2=a_1+d\to a_2=-2+3.5=1.5\n\na_3=a_2+d\to a_3=1.5+3.5=5\n\na_4=a_3+d\to a_4=5+3.5=8.5\n\nSolutions:1.5;\ 5\ and\ 8.5

Given ∠ABE = 45° and ∠EAB = 63° in ΔABE and∠MNP= 72° and ∠NMP = 63° in ΔMNP. Are the two triangles, ΔABE and ΔMNP similar? If so, by what criterion?A) yes, by AA criterion
B) yes, by SAS criterion
C) yes, by SSA criterion
D) no, not possible to tell.

Answers

A.) Yes, by AA criterion.

Triangle ABE have these angles: 
∠ABE = 45° ; ∠EAB = 63° ; missing ∠ is 72°

Triangle MNP have these angles:
∠MNP = 72° ; ∠NMP = 63°; missing ∠ is 45°

AA criterion is "angle,angle" criterion. It means that the two triangles have at least two of their angles equal. Since a triangle have a total of 180°, when two of their angles are equal, the 3rd angle is also equal.

As you can see, both triangles have 45°, 63°, and 72° measurement of angles. Thus, they are similar.

The dataset below represents the population densities per square mile of land area in 15 states in the 2010 U.S. Census. What is the interquartile range?

Answers

Answer:

The Interquartile range is 188

Step-by-step explanation:

Missing Data:

1,19,35,43,49,55,63,94,105,110,175,231,239,351,738

Required

Determine the Interquartile range (IQR)

The given data is ordered already.

First, we need to determine the median

For odd number of data

Median = ½(n + 1)th

In this case, n = 15; so

Median = ½(15 + 1)th

Median = ½(16)th

Median = 8th

This implies that the median is at the 8th position.

So, we have:

1,19,35,43,49,55,63 ----> Lower

(94) ---- Median

105,110,175,231,239,351,738 ---- Upper

Next, we determine the median of the lower and upper sets.

These are called lower quartile (Q1) and upper quartile (Q3) respectively

Lower: 1,19,35,43,49,55,63

Number of data, n = 7

Q1 = ½(n + 1)th

Q1 = ½(7 + 1)th

Q1 = ½(8)th

Q1 = 4th position

From the list of data in the lower set,

Q1 = 43

Upper: 105,110,175,231,239,351,738

Number of data, n = 7

Q3 = ½(n + 1)th

Q3 = ½(7 + 1)th

Q3 = ½(8)th

Q3 = 4th position

From the list of data in the upper set,

Q3 = 231

IQR is then calculated as thus:

IQR = Q3 - Q1

IQR = 231 - 43

IQR = 188

Help please i don’t kneo

Answers

Answer:

x=4

Step-by-step explanation:

Which expression represents "the sum of 3 and n"a. n + 3
b. n3
c. 3n
d. n + n + n

Answers

  Answer:

Option (a) is correct.

n + 3 represents the given expression "the sum of 3 and n" correctly.

Step-by-step explanation:

Given : Expression "the sum of 3 and n"

We have to choose the correct option from the given options that represents the given expression "the sum of 3 and n" correctly.

Consider the given expression "the sum of 3 and n"

We know the mathematical symbol for sum is '+'

So, The sum of 3 and n is written mathematically as 3 + n

Thus,  n + 3 represents the given expression "the sum of 3 and n" correctly.
The answer would be A, yet if this was for homework or a test, you would write it out as "3 + n".
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