2x - 3y = 1, x + 2y = -3 equivalent equation and solution

Answers

Answer 1

Answer:

x = -1, y = -1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}2x-3y=1\\ x+2y=-3\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=\frac{1+3y}{2}[/tex]

[tex]\begin{bmatrix}\frac{1+3y}{2}+2y=-3\end{bmatrix}[/tex]

Simplify

[tex]\begin{bmatrix}\frac{1+7y}{2}=-3\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=\frac{1+3y}{2}[/tex]

[tex]\mathrm{Substitute\:}y=-1[/tex]

[tex]x=\frac{1+3\left(-1\right)}{2}[/tex]

[tex]x=-1[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=-1,\:y=-1[/tex]

Check Answer:

2(-1)-3(-1) = 1

True

-1+2(-1)= -3

True

~Lenvy~


Related Questions

Express 6 m as a percentage of 16 m.

Answers

Answer:

37.5%

Step-by-step explanation:

the percentage is calculated as a fraction of the quantities multiplied by 100% , that is

[tex]\frac{6}{16}[/tex] × 100% = 0.375 × 100% = 37.5%

Answer:

37.5%

Step-by-step explanation:

6/16×100

37.5%

brainiest please

Solve for x if 2(5x + 2)^2 = 48

Answers

Distribute=2(5x+2) and 2(5x(5x+2)+2(5x+2))

Distribute
2
(
2
5

2
+
1
0

+
2
(
5

+
2
)
)
2
(
25
x
2
+
10
x
+
2
(
5
x
+
2
)
)
2
(
2
5

2
+
1
0

+
1
0

+
4
)



Combine like terms
2
(
2
5

2
+
1
0

+
1
0

+
4
)
2
(
25
x
2
+
10
x
+
10
x
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2
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2
5

2
+
2
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4
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i think x= 3.2 but who knows i’m not that good at math

The following shape has 1 pair of parallel sides

Answers

what is the rest of the question?

Please help answer the attached question

Answers

Answer:

angle BCD = 108

Step-by-step explanation:

opposite angles in a cyclic quadrilateral add to 180

so angle BDC is 180 - 72 = 108

what are the angles 32 and 114 there for??

Help me due in 5 mins!

Answers

In order: 6, 6, 12
1st: l x w | 3 * 2
2nd: 1/2(l x w) | 1/2(12)
3rd: 1st + 2nd | 12

What is the measure of arc XZ if the angle equals 135 and the radius is 17 km

Answers

now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]

Elena drives for 3 hours at 44mph claire drives 144miles in 4 hours how far would elena travel if she drove for 3hours at the same speed as claire?

Answers

Answer:

108 miles

Step-by-step explanation:

144m/4h = 36m/1h or 36mph

36mph · 3 = 108m

Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.​

Answers

By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.

What is the half-life?

We define half-life as the time such that the initial amount is reduced to its half.

So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:

S(t) = A*e^{-t*ln(2)/T}

Where t is the variable in time units.

We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:

S(t) = 500mg*e^{-t*ln(2)/6h}

Then after 4 days (or 4*24h = 96h) the amount of medication is:

S(96h) =  500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.

If the initial dose was 750mg, after 4 days the person would have:

S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg

So the person would have:

0.0114 mg -  0.0076 mg = 0.038 mg more of medication.

If you want to learn more about the half-life, you can read:

https://brainly.com/question/11152793

A construction company transported 8 stones that weighed a total of 70.22 kilograms. How much did each stone weigh?

Answers

Answer:

8.7kilos

Step-by-step explanation:

70.22 divided by 8

hope this helps!

Helen is having a birthday
party. Her friends arrive at
her house at 8:15 p.m. They
leave three hours later. What
time do Helen's friends leave?

Answers

Answer: 11:15 p.m 5:15 p.m.

Step-by-step explanation:

100 BRAINLY POINTS!!!

The scatter plot below shows the association between two variables.


Which two variables are most likely to have the association displayed by the scatter plot?

A. An animal's height and the number of legs it has.

B. The day of the month on which a person was born and the person's height.

C. The number of hours a person works and the amount of tips the person earns.

D. The number of hours a person spends studying and the number of hours the person spends doing
other activities.

HURRY CUH PLS

EXPLAIN YOUR ANSWER
SHOW YOUR WORK

Answers

Answer:

C

Step-by-step explanation:

This is a very interesting question,

Let's start off by determining what kind of function this is,

by looking at the graph we can say this is an almost linear function. So the correlation between the 2 values must be that if one increases the other increases according to a certain ratio which is our slope.

We want to eliminate wrong answers.

A. Does it make sense that an animal acquires more legs the taller it is?

This doesn't make any sense so A is out.

B. This is like saying, if i'm born in august i must be a good manager. There absolutely no correlation with the month you're born in, to your height.

So B is out.

C. Thus might actually make sense, the more you work, the more tips you make.

D. So basically here i'm saying is, the more i study the more activities i can do? this would be logical if the function were to be a line with a negative slope or "a decreasing line" or a "line going down". But this is not the case.

D is out.

so C must be our answer

Rachel's starting salary was $45,000 per year.
Rachel received a 3.7% raise every year after her first
year. How much is Rachel making now, & years later?

Answers

Answer:

After 1 year $46,665

Vf = Vi ( 1 + r/m) ^ tm

Step-by-step explanation:

Vf = Final Value

Vi = Initial Value ($45,000)

r = Interest Rate (3.7%, put in decimal form so .037)

m = Compound Rate (amount of times it increases every year, for this it would be 1)

t = Amount of years you are forecasting

45000 * (1 + .037)²

45000 * (1.037)²

45000 * 1.075369

$48,391.605 in 2 years

Literacy
Fill in the missing letters to make Maths related words:
Venn
Set
Diagram
Universal
S_r_i_g
Event
Probability
Not

Answers

Answer:

Sorting

Step-by-step explanation:

steps for Is (–5, 5) a solution to the equation y=x?

Answers

Answer:

Step-by-step explanation:

To check , substitute x = -5 and y = 5 into the given equation:

y = x

5 = -5

which is not true so (-5, 5) is not a solution.

very easy math do you know whats the answer?

Answers

3 is less than w , 7 is greater than or equal to w

[tex]3 < w \\ 7 \geqslant w[/tex]

Answer:

3 < w = 7 ≥ w

Step-by-step explanation:

Less than= "<"

Greater than or equal to = ≥

A national survey is conducted to assess the association between hypertension and stroke in persons over 75 years of age with a family history of stroke. Development of stroke is monitored over a 5 year follow-up period. The data are summarized below and the numbers are in millions. Compute the RELATIVE RISK of stroke in hypertensive as compared to non-hypertensive persons.

Answers

The relative risk of stroke in hypertensive as compared to non-hypertensive persons will be 1.8367.

How to calculate relative risk?

From the complete information, those with hypertension that had strike is 12. Those with no hypertension but had stroke is 4.

Also, those with hypertension but don't have stroke is 37 while those with no hypertension but had stoke is 26.

Therefore, the relative risk will be:

= (12/12 + 37) / (4/4 + 26)

= 12/49 / 4/30

= 1.8367

In conclusion, the correct option is 1.8367.

Learn more about relative risk on:

https://brainly.com/question/25264302

Ayan has $48 andis saving $10 per week and Gemma has $300 and is spending $8 per week. When will they both have the same amount of money? ​

Answers

Answer:

14 weeks

Step-by-step explanation:

First, write as an equation with x the number of weeks Ayan and Gemma's money:

-> Ayan's money: 48+10x because every week he wins 10 more dollars

-> Gemma's money 300-8x

Finally just solve the equation for x where ayan's money = gemma's money so :

48+10x=300-8x

add 8x on both side: 48+18x=300

substract 48 on both side to isolate x : 18x =252

devide by 18 on both side : x=14

A circular counter top has a radius of 5 feet.
Enter the area, in square feet, of the counter top. Round your answer to the nearest tenth.

Answers

Answer:78.6[tex]ft^{2}[/tex]

Step-by-step explanation:

Area=π[tex]r^{2}[/tex]

Area=[tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex]

=[tex]\frac{22}{7}[/tex] x 25

=78.6[tex]ft^{2}[/tex]

A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5. 9 at a 95% level of confidence. If the mean of the sample is 18. 7, what is the 95% confidence interval for the population mean? 18. 7 ± 5. 9 18. 7 ± 9. 7 18. 7 ± 11. 6 18. 7 ± 15. 2.

Answers

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The population mean with a 95% confidence interval is 18.7±5.9.

What is the margin of error?

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

In order to find the population of the mean, we need to subtract the margin of error from the sample mean. Therefore, the population mean with a 95% confidence interval is 18.7±5.9.

Learn more about Margin of Error:

https://brainly.com/question/6979326

Solve this for 100 points

Answers

Answer:

you may check in your book this question is related with stastics

Answer:

(S)=0

Step-by-step explanation:

base radius of 7cm and height of 35cm what is the cylinder's volume

Answers

Answer:

5390 cm³

Step-by-step explanation:

It is given that the base radius of a cylinder is 7cm and the height is 35cm and we are asked to find the volume of the cylinder.

We must know this formula :

⇒ Volume(Cylinder) = πr²h

We will take the value of π as 22/7

Now substituting the values :

⇒ Volume(Cylinder) = 22/7 × (7)² × 35

⇒ Volume(Cylinder) = 22/7 × 49 × 35

⇒ Volume(Cylinder) = 22 × 7 × 35

⇒ Volume(Cylinder) = 22 × 245

Volume(Cylinder) = 5390

Therefore,

The volume of the cylinder is 5390 cm³

on thursday and friday last week miss kelly rode her snowmobile 249 miles. ON friday she rode 35 more miles than she did on thursday. Howmany milesdid she ride each day? Write a system of eqautions for this situation and solve.

Answers

Step-by-step explanation:

x = miles ridden on Thursday

y = miles ridden on Friday

x + y = 249

y = x + 35

we can use the identity of the second equation in the first equation and solve :

x + (x + 35) = 249

2x + 35 = 249

2x = 214

x = 107 miles

y = x + 35 = 107 + 35 = 142 miles

on Thursday she rode 107 miles.

on Friday 142 miles.

Tom knows that in his school 10 out of every 85 students are left-handed.
There are 391 students in Tom's school.
how many students in Tom's school are left handed?

Answers

Answer:

46 are left handed

Step-by-step explanation:

divide 10 by 85 and you get 0.11764705882352941176470588235294 then multiply that by 391 and you get 46

Find the missing value to the nearest hundredth.

Answers

Answer:

24.62°

Step-by-step explanation:

sin^-1 (5/12)

=24.62

Answer:

24.62°

Step-by-step explanation:

sin^-1(5÷12) = 24.62°

(if you are allowed to use calculator)

Possible or impossible?

The difference is 3.
The difference is also
-3.

Answers

The difference is minus
So
x -(3) = x - 3
But
x -(-3) = x + 3
They are not equal
Impossible

Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b.

Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going the same direction.
If a third plane could be drawn which contains both lines a and b, then

lines a and b must be parallel.
lines a and b cannot be parallel.
lines a and b must be skew.
lines a and b must be perpendicular.

Answers

Answer:

lines a and b must be parallel

Step-by-step explanation:

if lines a and b are parallel in plane r and q, then the lines must always be parallel.

Answer:

A

Step-by-step explanation:

on e2020

An electrician has an income of $41,500. The income tax the electrician has to pay is 12%. What is the amount of income tax that the electrician has to pay? A) $3,840 B) $4,164 C) $4,980 D) $5,210.

Answers

Answer:

he has to pay 4980$ in tax So its C) 4,980

The amount of income tax that the electrician has to pay is $4980. Then the correct option is C.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

An electrician has an income of $41,500.

The income tax the electrician has to pay is 12%.

Then the amount of income tax that the electrician has to pay will be

Amount of income tax = 0.12 × $41500

Amount of income tax = $ 4980

Thus, the amount of income tax that the electrician has to pay is $4980.

More about the percentage link is given below.

https://brainly.com/question/8011401

help me quickly
102% of 120=

Answers

102 is what percent of 120? = 85.

Answer:

122.4

Step-by-step explanation:

this is easy, all we need to do is multiply 120 by 1.02, since it is 2%, and it is increasing not decreasing. when we do that, we get 122.4. to check, you can also do .02x120, to get 2.4. please mark as brainlest.

A large company produces an equal number of brand-mame lightbulbs and generic lightbulbs. The director of quality control sets guidelines that lightbulbs that are defect lightbulbs that are defective is not equal to the director wants to estimate the average of the two proportions. Production will be stopped if there is evidence that the proportion of all ve is greater than 0. 10. The director also believes that the proportion of brand-name proportion of generic lightbulbs that are defective. Therefore, the o estmate the proportion of brand-name lightbulbs that are defective, a simple random sample of 400 brand-name lightbulbs brand-name lightbulbs that are defective in a sample of 400, and let px represent the proportion of all brand-name lightbulbs that are defective. It is reasonable to assume that X is a binomial random variable.

(a) One condition for obtaining an interval estimate for px is that the distribution of px is approximately number of is taken and 44 are found to be defective. Let X represent the normal Is it reasonable to assume that the condition is met? Justify your answer.

(b) The suandard error of hr is approumately O 0156 Show how the value of the standard error is calculated

Answers

Using the Central Limit Theorem, we have that:

a) Since there are at least 10 successes and 10 failures, the condition is met.

b) Using the formula [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], with n = 400 and p = 0.11, the standard error is of 0.0156.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

Item a:

44 are found to be defective, hence:

np = 44.n(1 - p) = 356.

Which means that the conditions are met.

Item b:

We have that the parameters are:

[tex]n = 400, p = \frac{44}{400} = 0.11[/tex]

Hence, the standard error is given by:

[tex]s = \sqrt{\frac{0.11(0.89)}{400}} = 0.0156[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Pleaseeeee helpppp neeed doneee asappp

Answers

Answer: 107 meters

Step-by-step explanation:

There are 2 ways to solve this:

1. The formula for arc length is: arc length = angle (in radians) * radius.

Thus, convert 123 degrees to radians by multiplying it by (pi/180), and then multiply this number by 50 (half of the diameter is the radius) in order to get 107.

2. Find the circumference of the track using C = pi*diameter and get 314.16. Then, set up a proportion: 314.16 meters / 360 degrees = x meters / 123 degrees and solve to get 107 :)

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