Solve the problem using a system of equations: The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.
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Answers

Answer 1

The numbers which hold true for the situation modelled in the task content are; (-√15, 0) and (+√15, 0).

Which numbers hold true for the situation?

The system of equations which model the situation is;

x²- y² = 15

2x² - y² = 30.

Hence, by subtracting equation 1 from 2; we have;

x² = 15

x = ±√15.

and hence by substitution; the value of y is;

(√15)² + y = 15

y = 0.

Hence, the required values of the numbers are;

(-√15, 0) and (+√15, 0).

Read more on system of equations;

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Related Questions

PLEASE HELP WITH THIS QUESTION

Answers

Answer:

which question can I help you

Segments KN and LM are transversals. What is true about the measure of angle N?

Answers

Answer:

It is congruent to M

Step-by-step explanation:

We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)

Evaluate the information given by the pilot.
Show calculations to support your answer.

Answers

Answer:

Step-by-step explanation:

500 mph with a flight time of 10 hours and 20 minutes  [(20 min)*(1 h/60 min) = 0.333 hr]

Distance = Speed * Time

Time = 10.333 hours

Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles

The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles.  That is a 4.3% reduction from the pilot's numbers.  Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.

My preference would be to trust the pilot's data.  I don't know where Mark got his math education.

Three business partners, Ren, Jaffary and Abel put money into a business in the ratio 2:3:4. From the profits they shared, Abel got 3400 dollars. How much did ren and Jaffary receive?

HELP GUYS PLS I HAVE 3 MIN TO GO

Answers

Answer:

Ren has 755.4

Jaffray has 1,133.1

Abel has 1,510.8

A school has 320 girls and 250 boys
The probability that a girl is left handed is 0.2
The probability that a boy is left handed is 0.1
Estimate the umber of left handed students in the school.

Answers

320/100 • 20 = 64
250/100 • 10 = 25
64+25= 89 <33

pls help its an image scroll down

Answers

Answer:

D. y = 3x + 9

Step-by-step explanation:

Use the point-slope formula to find the equation in slope-intercept form.

[tex]y-y_1=m(x-x_1)\\\\y-33=3(x-8)\\\\y-33=3x-24\\\\y=3x+9[/tex]

Determine the slope and y-intercept of a line that passes through the points (2, 4) and (–4, 1).
m = [ A. –2.5 , B. –1.5 , C. 0.5 ]
b = [ A. 3, B. 7, C. 9 ]

Answers

Answer:

m = [C. 0.5]b = [A. 3]

Step-by-step explanation:

Slope- intercept form:

y = mx + b, where m is the slope, b is the y-intercept

Given points:

(2, 4) and (-4, 1)

The slope is:

m = (1 - 4)/(- 4 - 2) = - 3/ - 6 = 1/2 = 0.5

Use point (2, 4) to find the value of the y-intercept:

y = mx + b4 = 0.5*2 + bb = 4 - 1b = 3

Jim swam 8 laps on Tuesday, 19 laps on Wednesday, 30 laps on Thursday, and 41 laps on Friday. What kind of sequence is this? both neither arithmetic geometric​

Answers

It may be the Harmonic Sequence but I am not sure.

The table gives the temperature (in °F) in five citiesſat 6 a.m. on the same day. Use the table to answer the questions.
City
Temperature
(°F)
Toronto
-16
Fairbanks
:-24
Dayton

43
San Antonio
74
Buffalo
-3
5
?
(a) By noon, the temperature in Buffalo had risen by 10 °F.
What was the temperature there
at noon
How much higher was the 6 am temperature in Toronto than in Fairbanks

Answers

Answer:

a) buffalo will be at 7

b) it will be -8

Step-by-step explanation:

a) because if u add - 3 + 10 it will equal 7

b) reason why is because if u substract -24 from - 16 it will be - 8

I took a test on the same thing thats why i kno it

Find the complementary Angle of 24 / 1/5

Answers

The answer is 24
Ok done. Thank to me:>

The temperature of a substance in an experiment changes by −8.7°F from 10 a.m. to 1 p.m. At 5 p.m., the temperature is 33.5°F. It is 2/3 of what the temperature was at 1 p.m. What was the temperature at 10 a.m. of the substance? Enter your answer as a decimal in the box.


PLS HELP

Answers

The temperature of the substance at 10am  =  63.95°F

Let the temperature at 10 am be x

The temperature changes by −8.7°F from 10 a.m. to 1 p.m

The temperature at 1 pm = x  -  8.7

At 5 p.m., the temperature is 33.5°F

The temperature at 5 pm = 33.5°F

The temperature at 5 pm is 2/3 of what the temperature was at 1 p.m

[tex]33.5 = \frac{2}{3} ( x-8.7 )[/tex]

Solve for x

3(33.5)  =  2(x  -  8.7)

110.5  =  2x  -  17.4

2x  =  110.5 +  17.4

2x   =  127.9

x   =  127.9/2

x   =  63.95°F

The temperature of the substance at 10am =  63.95°F

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Quiz

2² =
4² =

use the method, no calculation ​

Answers

Step-by-step explanation:

= 2 × 2

= 4

▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎

= 4 × 4

= 16

▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎

I Hope This Help

A driver travels 120 miles, stops, and then travels ¼ of the distance she has already driven. After stopping again, the driver travels ⅔ of the distance she has already traveled. Now, the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. How many miles does the driver still have to travel?

Answers

Answer:

75 miles

Step-by-step explanation:

We know that she has driven 120 miles before the first stop.

Then she drives for 1/4 of the the distance she has already driven (120 miles). One fourth of 120 is 30.

So now, she's driven for 120 + 30 miles, or 150 miles.

She drives for another 2/3 of the distance she's traveled (150 miles). Two thirds of 150 is 100.

So now, she's driven for 150 + 100 miles, or 250 miles.

What we need to find out now is how much of the trip has she traveled.

We know that the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. So, in other words, the distance she has traveled minus 55 is equal to 1 2/3 of the trip.

To put this in an equation:

250 - 55 = 1 2/3t

t = the whole trip

Now, we solve for t.

250 - 55 = 195

1 2/3 = 5/3

so, 195 = 5/3t

t = 325

We subtract what she has already driven to the total to get the remaining distance.

325 - 250 = 75

select the reasons

options for #3
- definition of a quadrilateral
- if two lines are parallel and cut by a transversal, then the alternate interior angles are congruent

options for #5
- ASA congruence property
- SAS congruence property
- definition of a quadrilateral

Answers

Step-by-step explanation:

Givens:

ParallelogramQR || TSQT || RSQS ≅ SQ

With that information, we can figure out the rest.

∠RQS≅∠TSQ and ∠QSR≅∠SQT --- these are alternate interior angles, on opposite sides of the transversal QS while between parallel lines

Finally, ΔQST≅SQR because of ASA.

===============

sorry that took so long, I severely overcomplicated things before seeing the simple solution

Explain what a graph for Jed’s test scores {61%, 65%, 73%, and 79%} would look like if it was not misleading. Make sure it is different than Jed’s graph – that some may say is misleading.

Answers

Answer:

61

  ^

  ^

  ^                                                                 65                                 73

  ^                                      79                        ^                                  ^

  ^                                      ^                           ^                                  ^

                                                                 

-----------------------------------------------------------------------------------------------------------------

  Test 1                            Test 2                   Test 3                       Test 4

Answer: the test doesn't explain the order it was taken or dates. So it can be misleading

Step-by-step explanation:

HELP!! DUE IN 10 MINS!!!
Solve the following system using the elimination method.

x+y=12
x−y=12

Answers

Answer:

x = 12

y = 0

Step-by-step explanation:

Sum them:

2x = 24

so x = 12

12 - y = 12

so y = 0

Given that angle a = 15° and angle b = 5°, work out x

Answers

this cant be all the question

Please help! How to do this? Ill give brainly

Answers

Answer:

c=60

d=45

Step-by-step explanation:

3c=180

c=60

4d=180

d=45

Which relation has a domain of (2, 4) and a rang of (2, 8)
A (2, 4) (2,8)
B (2, 2) (2,8) (4,2)
C{(2,4)(8,2)(8,4)}
D{(2,2)(2,4)(4,2)(8,8)}

Answers

Domain: x values
Range: y values
The relation would need to have (2, y) and (4, y). And also (x, 2) and (x, 8)
See which ones match

Solution: B

39. The area of a triangle A varies jointly as b and h. If A = 225 in- when b = 18 in. and h = 25
in., find A when b = 35 in. and h = 40 in.
37

Answers

Answer: B

Step-by-step explanation:

Answer:

700 in^2

Step-by-step explanation:

If A = 225 in- when b = 18 in. and h = 25

225 = 18 * 25 / 2

a = 35 * 40 / 2

a = 700

How many Solutions does 6 + x/5 = x/5 - 5 - 3x/10 have?

Answers

9514 1404 393

Answer:

  1 solution (x = -36 2/3)

Step-by-step explanation:

  6 + x/5 = x/5 - 5 - 3x/10 . . . . . . . given

  60 +2x = 2x -50 -3x . . . . . . . . . multiply by 10

  3x = -110 . . . . . . . . . . . . . . . .  add x-60 to both sides

  x = -110/3 = -36 2/3 . . . . . .divide by the coefficient of x

There is one solution to the equation.

_____

Additional comment

The coefficient of x on the left side of the equation is not equal to the coefficient of x on the right side. When that is the case, the equation will have one solution.

When the coefficients are equal, there will be no solutions if the constants are different, and there will be infinite solutions if the constants are the same.

√12 - 1 √3=?
is correct the answer is 1/√3
THANK YOU

Answers

Answer:

[tex]\huge\boxed{\text{Is inorrect. Correct answer is:}}\\\boxed{\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt{12}-1}{\sqrt3}=\dfrac{\sqrt{12}}{\sqrt3}-\dfrac{1}{\sqrt3}=\sqrt{\dfrac{12}{3}}-\dfrac{1}{\sqrt3}=\sqrt4-\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=2-\dfrac{\sqrt3}{3}\\\\=\dfrac{6}{3}-\dfrac{\sqrt3}{3}=\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}\\\\\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}[/tex]

. Bobignment In what year was the LAWMA Established-​

Answers

1977. All that took was a 3 second search...

Pls Help! Worth 8 Points Will Give Brainlest ​

Answers

Answer:

D. x - 5

Step-by-step explanation:

The text said that Sienna's hight is LESS than her brothers hight and less = minus

Answer:D

Step-by-step explanation:hope i helped i love helping people like you. :)

Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?

Answers

Answer:

He is on the 5th floor

Step-by-step explanation:

9 - 2 = 7

7 + 4 = 11

11 - 6 = 5

Answer:

he goes 1 +9=10

10-2=8

8+4=12

12-6=6

so he is ont the sixth floor

share £650 in the ratio of 4:9

Answers

Answer:

200:450 that would be the answer i believe

change the following numbers to decimals and round to the nearest hundredth 3÷4 and ✔10​

Answers

Answer:

0.75 and 10.00

Step-by-step explanation:

NO LINKS!!!

Complete the following problems to the best of your knowledge. Show all your work. Part 1

Answers

Step-by-step explanation:

#1

a. -6, -9, 12

There is no sequence since the difference between the terms is not common and the ratio of the terms is not common

b. t(n) = 0.5 - 6

There is no sequence as all the terms are same regardless the value of n

c. 32, 16, 8

The sequence is geometric as common ratio is 1/2, each next term is half the previous one#2

a. 8, 16, 32, 64, ...

This is a geometric sequence as the common ratio is 2

b. 1, 1, 2, 3, 5, 8, ...

This is neither one since no common difference or ratio between the consecutive terms

c. 5, 5, 5, ...

This is neither one since common difference is zero or common ratio is 1

d. -101, -99, -97, -95, ...

This is a arithmetic sequence since the common ratio is 2#3

According to question the sequence is:

200000, 100000, 50000, ...

We see each number is half the previous one so this is a GP with common ratio of 1/2

identify the pair of similar triangles in each of the groups of triangle below​

Answers

Answer:

its triangle ABC and XYZ

Step-by-step explanation:

A and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?

Answers

Answer:

so no answer

Step-by-step explanation:

no answer

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