What is 45x62 Please help.

Answers

Answer 1

Answer:

45

62x

______

  90

2700+

_________

2790

Step-by-step explanation:


Related Questions

What is the error in this problem?

Answers

Answer:

wrong position of tan 64

Please help solve for the median !!

Answers

Answer:

Median = 14

Step-by-step explanation:

2, 5, 14, 15, 21, 18, 15, 9, 2

First, order the numbers:

2, 2, 5, 9, 14, 15, 15, 18, 21

Then, cancel out the numbers, starting the first and last number, going outwards in. If there is 1 number left, it is your median. If there are 2 left, add the 2 numbers together and divide them by two:

2, 2, 5, 9, 14, 15, 15, 18, 21

2, 5, 9, 14, 15, 15, 18

5, 9, 14, 15, 15

9, 14, 15

14

The median is 14.

Please tell me if I was wrong! I hope this helps you!

Answer: The median is 14

Step-by-step explanation: The median is the number that is halfway into the data set. To find the median, the data should be arranged in order from least to greatest. For this example.  2,2,5,9,14,15,15,18,21. Find the number that is halfway. which is 14

Which of the following classifications of polygons could be a valid description? an equilateral scalene triangle an obtuse scalene triangle a square trapezoid a rectangular kite

Answers

Answer:

B. An obtuse scalene triangle

Step-by-step explanation:

Polygons are plane figures bounded by three or more straight sides. Examples are: trigon, quadragon, hexagon, nonagon etc.  They are  named with respect to their number of sides.

An obtuse triangle has one of its angles greater than [tex]90^{0}[/tex] but less than [tex]180^{0}[/tex]. While a scalene triangles has non of its sides to be equal in length.

The valid description of the classes of polygons is: an obtuse scalene triangle. Which implies that the triangle has one of its angles to be obtuse, and non of its sides equal.

Sienna is solving the quadratic equation by completing the square. 3x2 + 9x – 4 = 0 3x2 + 9x = 4 A(x2 + 3x) = 4 What is the value of A? –4 –3 3 4

Answers

Answer:

I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.

Answer:

its c

Step-by-step explanation:

Pentagon ABCDE and pentagon A”B”C”D”E” are shown on the coordinate plane below. Which two transformations are applied to pentagon ABCDE to create A”B”C”D”E”?

Answers

Answer:

Translated according to the rule (x, y)⇒ (x+7, y+1)  , reflected across the  x-axis

Step-by-step explanation:

Transformation involves changing the orientation, or even size of a given figure or object to produce its image. The methods of transformation include; translation, rotation, reflection, and dilation.

Comparing the pentagon ABCDE and A”B”C”D”E”, the two transformations applied are reflection across the x-axis first, then translation.

what is the radius for a circle whose equation is x2 + y2 = 64

Answers

Answer:

radius of 8

Step-by-step explanation:

step one :

Given that the equation of the circle is described as

[tex]x^2 + y^2 = 64[/tex]

To correctly identify the center of the circle we have to place the equation in the standard form.

the standard equation for a circle is

[tex](x-h)^2+(x-k)^2= r^2[/tex]

step two :

let us re-write the given equation so that we can compare it with the general equation of circle

[tex](x-0)^2+(x-0)^2= 8^2[/tex]

step three:

From this above equation in step two we can see that the circle has a radius of 8

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t.
A = $8000.00, r = 10.5%, t = 9 months
$
(Round up to the nearest cent as needed.)

Answers

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

The diameter of a large lawn ornament in the shape of a sphere is 16 inches. What is the approximate volume of the ornament? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch. Recall the formula V = four-thirds pi r cubed.

Answers

Answer:

Sphere Volume = 4/3 * PI * radius^3

Sphere Volume = 4/3 * PI * 8^3

Sphere Volume = 4/3 * PI * 512

Sphere Volume = 2,144.7 cubic inches

Step-by-step explanation:

A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?

Answers

Answer:

The answer is 660.4 millimeters

Step-by-step explanation:

Diameter = 26 inches

From the question

1 inch = 25.4 mm

To find it's equivalent in millimeters multiply 26 inches by 25.4 millimeters and divide by 1 inch

so we have 26 inches as

[tex] \frac{26 \: inches \times 25.4mm}{1 \: inch} [/tex]

Simplify

We have

26 × 25.4 mm

We have the final answer as

660.4 millimeters

Hope this helps you

Answer: B.) 26 inches  (25.4 millimeters/ 1 inch)

Step-by-step explanation: i hope this helps :)

For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.

Answers

Answer:

The z-score is [tex]z = 0.6[/tex]

The percentile is  [tex]p(Z < 0.6) = 72.57\%[/tex]

Step-by-step explanation:

From the question we are told that

   The  data value is  0.6 standard deviations above the mean i.e  [tex]x = \mu + 0.6 \sigma[/tex]

Where  [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation

Generally the z-score is mathematically represented as

        [tex]z = \frac{x - \mu }{\sigma }[/tex]

=>     [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]

=>    [tex]z = 0.6[/tex]

The percentile is obtained from the z-table and the value is

     [tex]p(Z < 0.6) = 0.7257[/tex]

=>   [tex]p(Z < 0.6) = 72.57\%[/tex]

Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!

Answers

Answer:

see below

Step-by-step explanation:

4,7,12,19

We are adding 3,5,7,9..... each time

The sequence is not arithmetic because we are not adding a constant.  It is not geometric since we are not multiplying by a constant term each time

There is no common difference  or common ratio.

The explicit formula is

an =n^2 +3

 

The recursive formula is

(n+1)^2 +3 - (n^2 +3)

    n^2 +2n+1+3 - ( n^2+3)

      2n+1

a sub(n+1) = a sub( n) + 2n+1

The 10th term

an      = n^2 +3

Let n=10

an = 10^2+3

    = 100+3

    = 103

summation

see image

since the numbers are increasing and greater than 1 the sum does not exist

renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake

Answers

Answer:

1.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]

Cross multiply:

40x = 60

x = 1.5

= 1.5 hours

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.

Explain in context the conclusion of the test if H0 is rejected.

Answers

Answer:

For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value

Step-by-step explanation:

Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.

Mathematically, the null hypothesis is as expressed as below;

H0: μ = 1,200

The alternative hypothesis H1 would be;

H1: μ > 1,200

Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics

For us to reject the null hypothesis, one of two things, or two things must have occurred.

The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.

If this happens, then we can make a rejection of the null hypothesis

Jamar rolls a 6-sided number cube with the numbers 1 through 6 on it. What is the
probability that he does not roll a prime number?​

Answers

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

In a 6 sided die, the numbers that are possible to be rolled are

1, 2, 3, 4, 5, and 6.

We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.

3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.

So the fraction is [tex]\frac{3}{6}[/tex]

This simplifies to [tex]\frac{1}{2}[/tex].

Hope this helped!

Answer:

1/2

Step-by-step explanation:

the prime numbers between 1 and 6 inclusive are:  2, 3, 5  (i.e 3 possible outcomes)

the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)

for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)

P(does not roll a prime number) = P (rolls 1, 4 or 6)

= number of possible non-prime outcomes / total number of outcomes

= 3/6

= 1/2

What is the solution to X+9 = 24?
A. x = 33
B. x= 15
C. x= 18
D. x= 9​

Answers

Answer:

X+9=24

Or,x=24-9

:.x=15

Step-by-step explanation:

Answer:

B. x=15

Step-by-step explanation:

To find the solution to the equation, we must get x by itself on one side of the equation.

[tex]x+9=24[/tex]

9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.

[tex]x+9-9=24-9[/tex]

[tex]x=24-9[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]x+9=24 (x=15)[/tex]

[tex]15+9=24[/tex]

[tex]24=24[/tex]

This checks out, so we know our solution is correct. The answer is B. x=15

I need some help with this please :)

Answers

Answer:18 ft

Step-by-step explanation: Perimeter=2(L+B)

Perimeter=2(7 + 2)

2×9=18

Answer:

18feet.

Step-by-step explanation:

To find the perimemter of a rectangle, you just add all the sides.

A rectangle has 4 sides in total, where 2 are equal, and the other 2 are als equal.

So, you just add 7+2+7+2, which gives 18.

This is why, the perimeter of this rectangle is 18feet.

Hope this helped, have a nice day!

The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) – 5.
Which statement describes how the graph of his different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted right 5 units.
B.
The graph of h is the graph of g vertically shifted up 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
OD.
The graph of h is the graph of ghorizontally shifted left 5 units.

Answers

Answer:

Option C

The graph of g is vertically shifted 5 units down

Does coordinate x or coordinate y represent a greater number?

Answers

Answer:

Y

Step-by-step explanation:

You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

Y represents the greater number.

We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

What is an example of a coordinate?

A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.

Learn more about coordinate here: https://brainly.com/question/11337174

#SPJ2

PLEASE HELP !! (1/5) - 50 POINTS - no wrong answers please. A) y = 6x - [tex]\frac{11}{8}[/tex] B) y = -6x - 2 C) y = [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{8}[/tex] D) y = -3x + 9

Answers

Answer:

C) 3/2x-1/8

Step-by-step explanation:

We can see that it has a generally positive slope, which rules out B and D.

Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10).  This rules out A.

While it doesn’t fit perfectly, C is by far the closest.

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.

Answers

Answer:

The answer is "Choice B, C, and F is correct".

Step-by-step explanation:

The following are choices, which is missing in the question, that can be defined as follows:

A) {x| x ≥ 3} is the domain.  

B) The set shall be {y| y ≥ –1}.  

C) over the interval  (–∞, 3), is the function, that decreases.  

D) it's over the duration the function increases its value, that is (–1, ∞).  

E) The symmetry axis will be x = – 1.  

F) vertex is (3, – 1).

In choice A, It is incorrect even though f is the domain, which is all true numbers because it has a quadrant function.  In choice B, it is correct.  In choice C, It is valid because it was a parable open with vertex so if we exploded view f (3, -1). Because as value opens up, its value with x from-∞ to 3 drops while it goes up from increasing from 3 to ∞.    In choice D, It is wrong since we have just said f decreases from-∞ to 3. Therefore, f decreases from -1 to 3, too. Therefore, f doesn't grow from -1 to ∞.  In choice E, It is incorrect because the symmetry axis is x = 3.  In choice F, it is true.

Answer:

the answers are b, c, e

Step-by-step explanation:

i just took the test

Find a • b. a = 5i + 7j, b = -4i + 3j

Answers

Answer:

[tex]a \cdot b = 1[/tex]

Step-by-step explanation:

[tex] a = 5i + 7j [/tex]

[tex] b = -4i + 3j [/tex]

[tex] a = a_xi + a_yj [/tex]

[tex]b = b_xi + b_yj[/tex]

[tex] a \cdot b = a_xb_x + a_yb_y [/tex]

[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]

[tex] a \cdot b = -20 + 21 [/tex]

[tex]a \cdot b = 1[/tex]

Answer:

[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]

Step-by-step explanation:

[tex]\sf Plug \ in \ the \ values.[/tex]

[tex](5i+7j) \cdot (-4i+3j)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]

[tex]-20i^2 +15ij+-28ij +21j^2[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]-20i^2 -13ij+21j^2[/tex]

Eliminate the parameter for the following set of parametric equations: x= t^2 + 2 y= 4t^2

Answers

Answer:

Solution : y = 4x - 8

Step-by-step explanation:

The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )

x = t² + 2,

t² = x - 2

Now let's substitute this value of t² in the second equation --- ( 2 )

y = 4t²,

y = 4(x - 2),

y = 4x - 8 ~ And hence our solution is option c.


Find the value of the variable x in the equation x - 21 = 8.
A) -13
B) 29
C) -29
D) 13​

Answers

Answer: x=29

Step-by-step explanation:

[tex]x-21=8[/tex]

add 21 to both sides

[tex]x-21+21=8+21[/tex]

[tex]21+8=29\\[/tex]

[tex]x=29[/tex]

The correct answer is letter B.
29 - 21= 8

Hope this helps ya.

Find the length of AC¯¯¯¯¯¯¯¯ A. 211.63 B. 44.98 C. 9.35 D. 207

Answers

Answer:

Step-by-step explanation:

tanθ= opp / adj

tan(12) = AC/44

now

AC = tan(12)/44

AC = ...

use calculator to find the value

I just broke mine

According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard deviation of $1,200. The dean of graduate studies at a large state university in PA claims that his graduate students earn more than this. He surveys 100 randomly selected students and finds their average salary is $16,000. Use a significance level of 0.05 to test if there is evidence that the dean's claim is correct. What are the hypotheses

Answers

Answer:

Step-by-step explanation:

Given that :

population Mean = 15000

standard deviation= 1200

sample size n = 100

sample mean = 16000

The null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}[/tex]

Using the standard normal z statistics

[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}[/tex]

[tex]z = \dfrac{1000}{\dfrac{1200 }{10}}[/tex]

[tex]z = \dfrac{1000\times 10}{1200}[/tex]

z = 8.333

degree of freedom = n - 1 = 100 - 1 = 99

level of significance ∝ = 0.05

P - value from the z score = 0.00003

Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis

Conclusion: There is sufficient evidence  that the Dean claim for his graduate students earn more than average salary of $15,000

Dean's Claim of Average Salary = 16000, ie greater than 15000 : is correct

Null Hypothesis [ H0 ] : Average Salary = 15000

Alternate Hypothesis [ H1 ] : Average Salary > 15000

Hypothesis is tested using t statistic.

t = ( x - u ) / ( s / √ n ) ; where -

x = sample mean , u = population mean , s = standard deviation, n = sample size

t = ( 16000 - 15000 ) / ( 1200 / √100 )

= 1000 / 120

t  {Calculated} = 8.33,

Degrees of Freedom = n - 1 = 100 = 1 = 99

Tabulated t 0.05 (one tail) , at degrees of freedom 99 = 1.664

As Calculated t value 8.33 > Tabulated t value 1.664 , So we reject the Null Hypothesis in favour of Alternate Hypothesis.

So, conclusion : Average Salary > 15000

To learn more, https://brainly.com/question/17099835?referrer=searchResults

Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below.4,3

Answers

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

5

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g

Answers

Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

Help Me With This
show work​

Answers

Answer:

1. Make a list of activities and the number of students:

Watching TV: 32

Talking on the phone: 41

Video games: 24

Reading: 15

2. Then combine the data in a bar graph as shown in the picture

Sammy the Sailor swears entirely too much. The following probability distribution shows the number of times Sammy swears per day and the corresponding probabilities:
# of swear words: 2 5 9 14 20
Probability: 0.01 0.09 0.30 0.40 0.20
In an effort to reduce his amount of swearing, Sammy places $1.00 in a jar every time he swears. Further, if at the end of the day he swears more than 10 times, he places an extra $2.00 in the jar per swear word over 10. If Sammy swears less than 5 times, he takes out $0.50 for each of his swear words.
A B C D E F G
1 # of swear word Probability
2 Cost per swear word $1.00 2 0.01
3 Extra cost per swear
word over 10 $2.00 5 0.09
4 Refund per swear word
less than 5 $0.50 9 0.3
5 14 0.4
6 20 0.2
7
8
9 # Regular Extra cost Refund Total
swear swear if over 10 if under money
words word swear 5 swear in the jar
cost words words for the
day
10
Based off the partial simulation spreadsheet above, answer the following questions:
A) What formula should go into cell C10 to calculate the Regular Swear word cost?
B3*B4 SUMPRODUCT(B2:B4, B10) B4*B10 SUM(B2:B4) B2*B10 B3*B2 B3*B10
B) What formula should go into cell D10 to calculate the Extra Swear word cost?
=IF(B10>10,(B10-10)*B3,0) =IF(B10>10,(10-B10)*B3,0) =(B10-10)*B3 =IF(B10>10,0,(B10-10)*B3) SUMPRODUCT(B10,B3) B10*B3
C) What formula should go into cell E10 to calculate the Refund amount?
B10*B4 =IF(B10>5,(B10-5)*B4,0) =IF(B10<5,0,B10*B4) =IF(B10<5,B10*B4,0) SUMPRODUCT(B10:B4) =IF(B10<5,(B10-5)*B4,0)
D) What formula should go into cell F10 to calculate the total money in the jar?

Answers

Full question attached:

Answer and explanation:

A) B2*B10: cell B2 and B10 have the values regular swear costs and number of swears respectively and we need to multiply these two values to get our answer

B) =IF(B10>10,(B10-10)*B3,0): Sam is supposed to pay an extra $2 for swear words over 10 and so we check if his swear words are above 10 and if they are we find out how many they are by subtracting 10 from them and then we multiply the value gotten by the cost for extra swear words($2)

C) =IF(B10<5,B10*B4,0): here we check if swear words are less than 5 and if they are we multiply number of swears words less than by 5 by the cost ($0.50)

D) F10=C10+D10+E10: to calculate total money in jar(F10), we simply add up regular cost(C10), extra cost(D10) and refund(E10)

A system of equations consists of the two equations shown.
{4x+5y=18
6x−5y=20
Which procedure will produce a single equation in one variable? Select all the procedures that apply.
A. Subtract the first equation from the second equation.
B. Subtract the second equation from the first equation.
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order.

Answers

Answer:

C, D, E and F

Step-by-step explanation:

Given

4x+5y=18

6x−5y=20

Required

Determine which procedure will result in a single equation in one variable

To do this; we'll test each of the options

A. Subtract the first equation from the second equation.

[tex](6x - 5y=20) - (4x+5y=18)[/tex]

[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]

[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result

B.  Subtract the second equation from the first equation.

[tex](4x+5y=18) - (6x - 5y=20)[/tex]

[tex]4x - 6x + 5y + 5y =18 - 20[/tex]

[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result

C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.

First Equation

[tex]18 * (4x+5y=18)[/tex]

[tex]72x + 90y = 324[/tex]

Second Equation

[tex]18 * (6x - 5y=20)[/tex]

[tex]108x - 90y = 360[/tex]

Add Resulting Equations

[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]

[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]

[tex]72x + 108x = 324 + 360[/tex]

[tex]180x = 684[/tex] --- This procedure is valid

D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.

First Equation

[tex]-6 * (4x+5y=18)[/tex]

[tex]-24x - 30y = -108[/tex]

Second Equation

[tex]4 * (6x - 5y=20)[/tex]

[tex]24x - 20y = 80[/tex]

Add Resulting Equations

[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]

[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]

[tex]-50y = -28[/tex]

[tex]50y = 28[/tex]  --- This procedure is valid

E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]-2 * (6x - 5y=20)[/tex]

[tex]-12x + 10y = -40[/tex]

Add Resulting Equations

[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]

[tex]12x - 12x + 15y - 10y =54 - 40[/tex]

[tex]5y = 14[/tex]  --- This procedure is valid

F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]2 * (6x - 5y=20)[/tex]

[tex]12x - 10y = 40[/tex]

Subtract equation 1 from 2 or 2 from 1 will eliminate x;

Hence, the procedure is also valid;

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