Solve algebraically the simultaneous equations
x^2– y^2 = 24
x= 3 + 2y
Write your two pairs of answers in this form:
when x =... y =...
When x=... y=...

Solve Algebraically The Simultaneous Equations X^2 Y^2 = 24x= 3 + 2yWrite Your Two Pairs Of Answers In

Answers

Answer 1

Answer:

(5, 1) and (-5, -7)

Step-by-step explanation:

Given the simultaneous equations

x^2– y^2 = 24 .... 1

x= 3 + 2y .... 2

Substitute 2 into 1

(3-2y)^2-y^2 = 24

Expand

9 - 12y + 4y^2 - y^2 = 24

9 - 12y + 3y^2 = 24

3y^2 - 12y + 9-24 = 0

3y^2 -12y -15 = 0

y^2-4y-5 = 0

y^2+5y - y - 5 = 0

y(y+5) - 1 (y+5) = 0

y-1 = 0 and y+5 = 0

y = 1 and -5

Substitute the values of y into 2

Recall that x = 3+3y

when y = 1

x = 3 + 2(1)

x = 5

when x = -5

x = 3 + 2(-5)

x = 3 - 10

x = -7

Hence the solutions are (5, 1) and (-5, -7)


Related Questions

Please help me label the diagram beaded on the word bank given. (Geometry)

Answers

i think this should help a bit

Mhanifa, can you help me with this?

Answers

9514 1404 393

Answer:

shape: rectangle27.5 square inches1 1/8 inches by 1 2/3 inchessee attached

Step-by-step explanation:

The drawing scale is ...

  1/4" : 1 ft = 1/4" : 12" = 1 : 48

1) The bedroom shape has two pairs of parallel sides and right-angle corners. It is a rectangle.

__

2) The area of the drawing is 20(1/4 in) × (22(1/4 in)) = 440(1/16 in²)

  = 27.5 square inches . . . . area of the bedroom on the drawing

__

3) The drawing side of the bed is 1/48 of the bed's actual dimensions, so is ...

  54/48 in × 80/48 in = 1 1/8 in × 1 2/3 in . . . . size of the bed on the drawing

__

4) The drawing looks like it may have been made on a 1/4" grid, but there are only 17 grid squares along the side labeled 20 (feet). So, we actually have no good reference for size. Using the dimension marked as 3 feet for reference we estimated the bed size, trying for 4 1/2 by 6 2/3 feet.

When we print the figure to a piece of paper, we have to scale it to 88.1% to make the 20-foot dimension come out 5 inches. Doing that shows our bed outline is about 82 inches long, not 80 inches long. YMMV

help please ???!!?! :)asap

Answers

Answer:

the answer is c

Step-by-step explanation:

Makayla has $740 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $465.34.
She buys 4 bicycle reflectors for $13.25 each and a pair of bike gloves for $18.12.
She plans to spend some or all of the money she has left to buy new biking outfits for $25.69 each.

What is the greatest number of outfits Makayla can buy with the money that's left over?

Answers

Answer:7.922927...

or just 7

Step-by-step explanation:

The western starts at 6:35 pm and ends at 9:10 how long is the movie

Answers

2 hours 35 minutes or 2:35.
hope this helps

Answer: 2 hours and 35 minutes. Aka 2:35

Step-by-step explanation: to find when it starts and ends, subtract 6:35pm by 9:10pm

So 9-6 is 3 and there is a problem when you do 10-35. 35 is bigger which means you have to take away an hour so the 3 becomes a 2 and then you add 60 onto the 10 even though the limit is 60 minutes because it equals an hour. So you now have 2 hours and 70 minutes - 35. Well that is 35 because 35+35 = 70 meaning the movie is 2 hours, 35minutes

Help me please will give b if correct

Answers

Answer:

true

false

true

false

true

Step-by-step explanation:

Hello There!

We are going to convert each fraction to decimal form to make it easier to tell if the statement is true or false

[tex]\frac{2}{3} =.66\\\\\frac{2}{6}=.33[/tex]

.66 is greater than .33 therefore [tex]\frac{2}{3} >\frac{2}{6}[/tex] is a true statement

[tex]\frac{8}{10} =.8\\\\\frac{6}{5} =1.2[/tex]

1.2 does not equal 8 therefore [tex]\frac{8}{10} =\frac{6}{5}[/tex] is a false statement

[tex]\frac{1}{8} =.125\\\\\frac{1}{4}=.25[/tex]

.25 is greater than .125 therefore  [tex]\frac{1}{8} <\frac{1}{4}[/tex] is a true statement

[tex]\frac{2}{4} =.5\\\\\frac{1}{2} =.5[/tex]

.5 is equal to .5 therefore [tex]\frac{2}{4} >\frac{1}{2}[/tex] is a false statement

[tex]\frac{4}{10} =.4\\\\\frac{4}{6} =.66[/tex]

.66 is greater than .4 therefore [tex]\frac{4}{10} <\frac{4}{6}[/tex] is a true statement

Answer: true false true false true sorry and just give the other person brainly and thank u

Step-by-step explanation: have a nice day

PLEASE HELP im super confused

Answers

Answer:

7 Quarters and 3 dimes

Step-by-step explanation:

You have to find how many quarters (0.25) and dimes (0.10) are in $2.05. There are 7 quarters, which will add up to $1.75. You can't have 8 quarters because then you would have 2 dollars, and there wouldn't be enough for a dime, there would only by 5 cents left, or a nickle. Then, you find out how many nickels you need, which is 3.

.10x3=.30. 1.75+0.3=2.05.

I hope you understood:)

Answer:

x=quarters

x-4 =dimes

.25x+.10(x-4)=2.05

.25x + .10x-.40=2.05

.35x = 2.45

 

divide by 0.35, both sides

x=7

x-4=3

7 quarters ($1.75)

3 dimes ($0.30

Total=$2.05

so you need 7 quarters and 3 dimes

Step-by-step explanation:

A principal of $4500 is invested at 6.25% interest, compounded annually. How much will the investment be worth after 6 years? (round the answer)

first question! =^^=

Answers

Answer:

Problem:

If you deposit $4500 into an account paying 6.25% annual interest compounded yearly , how much money will be in the account after 6 years?

Step-by-step explanation:

Result:

The amount is $6474 and the interest is $1974

I rounded it for ya ==^-^==

Please help someone, give me correct answer to these 2 problems.

I will mark you brainliest for the correct answer.

Please help!!!!!

I need the answer to both pictures!!!!!!!

Answers

Answer:

60° 60° 60°

60°

Step-by-step explanation:

In any triangle, the sum of its interior angles is 180°, and 60+60+60=180.

As for the other question, we can see that angle5=angle1, and angle6=angle2, due to the parallelism of the lines.

Angle5+angle6=180°, therefore

Angle6=180-120=60°=angle2

Look at the photo for the question the possible answers are

A. 9
B. 81
C. 3
D. 24

Answers

The square root of 27 is 3 so the answer is C hope this help and to help me mark as brainlist

Find the slope between (1, 2) and (-3, 18).

Answers

Answer:6

Step-by-step explanation:

WILL GIVE BRAINLIEST IF ANSWERED CORRECTLY!!!!!!!!

Answers

Answer:

I can't make out whether you're asking for = or ≅. It's too blurry.

A) Triangle ΔEFG is equal

ΔEFG, RSY, and XYZ are congruent

Step-by-step explanation:

Ana has 20 stickers. After 1 year she has 150 stickers. What percent increase in stickers?

Answers

Answer:

650% increase

Step-by-step explanation:

150/20 = 7.5

7.5 - 1 = 6.5

6.5 × 100 = 650%

Let's make sure this is correct.

650/100 = 6.5

6.5 + 1 = 7.5  The extra 1 represents the increase!

20 × 7.5 = 150

I hope this helps!! ^-^

The base of a rectangular pyramid is 13 inches long and 12 inches wide.
The height of the pyramid is 8 inches. What is the volume of the
pyramid?

Answers

Answer:

Area = 1/2 (Base) (Height)

Area = 1/2 (12 in) (8 kn)

Area = 1/2 (96 in)

Area = 48 in^2

Volume = (Area) (Length)

Volume = (48 in^3) (13 in)

Volume = 624 in^3

Answer:

V=L•W•H

3=13·12·8

3=416

=416³

Step-by-step explanation:

Finding the Volume of a Rectangular Pyramid

Your overall formula for finding the volume of these multi-faceted shapes is V = (l x w x h) / 3. Basically, your first step is finding the area of the base by multiplying length by width. Once you determine the area of the base, multiply that by the height.

The general volume of a pyramid formula is given as: Volume of a pyramid = 1/3 x base area x height.

If the cube has a side length s, then each pyramid has an s by s base and height s/2, and its volume is 1/6 the volume of the cube, which is 1/3 base times height. ... They are congruent, so have volume 1/3*base*height as the base is a square the side of the cube and the height is the side of the cube as well.Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

#CarryOnLearning

Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to find the number of games, g, that Roberto can buy. Enter your answer in the box.

Roberto can buy up to _________ video games.

I need this answer right away, please!!!

Answers

Answer:

He can buy up to 7 games

Step-by-step explanation:

200 divided 25.50 is 7.84 so therefore he can only buy 7

Answer:

7

Step-by-step explanation:

since it costs 25.50 dollars for each game say that x is each game and 25.50 times x equals the amount of money he spent on his games.

since he only has 200 dollars the inequality has to be greater than or equal to 25.50x

200>=25.50x

7.843>=x

so he can only buy up to 7 games

what is compound interest?​

Answers

Answer:

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Step-by-step explanation:

can someone help me with the equation and the diagram and the answers for this question please and thank you

Answers

Answer:

i dont know about the diagram but the answer is 9

Step-by-step explanation:

A TEAMS TOP SPEED FOR EACH LEG OF THE RACE IS 56.81 SECONDS, 59.22 SECONDS ,57.39 AND 60.1 WHAT IS THE BEST TIME

Answers

Answer:

56.81 SECONDS

Step-by-step explanation:

The best time would be the shortest time it takes to complete the race. This is 56.81 SECONDS

5. This diagram of a baseball field is composed of a square, a semicircle, and a quarter
circle.
PLEASE HELP GIVING 25 points


Which measurement is the best estimate of the area of the field in square feet?
A:12717
B:8100
C:27176
D:19074

Answers

Answer:this one is hard

Step-by-step explanation:

What is the ratio of the calories Robyn burned on Thursday to the total number of calories she burned for the week?

Answers

Answer:

1:7

Step-by-step explanation:

One day out of the week (1/7)

If she burned the same number of calories every day, this should be the answer.

Answer:

5:18

Step-by-step explanation:


1. Determine if the polygons are similar.
2. If they are, write a similarity statement. If they aren't, put n/a in this blank.
3. If the polygons are similar, find the scale factor of EFGH to KLMN. If they aren't similary, put n/a in this blank.
help please

Answers

Yes they’re similar. The scale factor is 2:1

What Is The Measure Of X?

Answers

Answer:

Its a:70 degrees..........

Answer:

60 degrees

Step-by-step explanation:

This is because on the other side there is 30 degrees, and since a right angle= 90 degrees, simply do 90-30=60

Okay so i need to know the area of the rectangle on the inside its 5ft on the right side its 6ft and on the bottom its 5ft please and thank you :)

Answers

Answer:

30ft^2

Step-by-step explanation:

Area of a rectangle = Length * Width

Given

Length = 6ft

Width = 5ft

Substitute

Area of the rectangle = 6ft *5ft

Area of the rectangle = 30ft^2

Hence the area of the rectangle is 30ft^2

Which graph represents the table below?
х
-1
0
1
y
4
1
-2

Answers

Huh send a picture of it

On a coordinate plane, triangle A B C has points (negative 2, 7), (negative 2, 3), and (negative 6, 3) and triangle D E F has points (negative 2, negative 10), (negative 2, negative 2), and (6, negative 2). Given that StartFraction A B Over D E EndFraction = StartFraction B C Over E F EndFraction = one-half, complete the statements to show that △ABC ~ △DEF by the SAS similarity theorem. Horizontal and vertical lines are . So, angles are right angles by definition of perpendicular lines. All right angles are . Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Answers

Question:

On a coordinate plane, △ABC has points (-2, 7), (-2, 3), and (-6, 3) and △DEF has points (-2,-10), (-2, -2), and (6, -2).

Given that

[tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{1}{2}[/tex]

Complete the statements to show that △ABC ~ △DEF by the SAS similarity theorem.

Horizontal and vertical lines are __(1)__. So, angles are right angles by definition of perpendicular lines. All right angles are __(2)__

Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Answer:

(1) perpendicular

(2) congruent

Step-by-step explanation:

Required

Fill in the gaps

[tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{1}{2}[/tex] implies that:

[tex]AB : DE= BC : EF[/tex]

In other words:

AB ~ DE ---- Side (S)

and

BC ~ EF ---- Side (S)

Now to fill in the gap with:

(1) perpendicular

(2) congruent

Further explanation

(1) Vertical lines and horizontal lines meet at a right angle (i.e. 90 degrees). Any two lines that meet at a right angle are perpendicular

(2) Angles with equal measures are congruent. Because right angles have a congruent angles of 90 degrees, then they are congruent.

Answer:

Given that StartFraction A B Over D E EndFraction = StartFraction B C Over E F EndFraction = one-half, complete the statements to show that △ABC ~ △DEF by the SAS similarity theorem.

Horizontal and vertical lines are

✔ perpendicular

.

So, angles

✔ B and E

are right angles by definition of perpendicular lines.

All right angles are

✔ congruent

.

Therefore, △ABC ~ △DEF by the SAS similarity theorem.

Step-by-step explanation:

What is the value of x in the figure? Enter your answer in the box.

Answers

Answer:

x = 65°

Step-by-step explanation:

these are vertical angles, which are congruent

145 = 2x + 15

130 = 2x

65 = x

Trigonometry math, help needed!!!

Find Q, R, and S. I think R is 123. I have provided a picture. Please put the right answer I would appreciate it.

Answers

Answer:

Step-by-step explanation:

Here is the question 13. Higher Order Thinking In the equation 8x - the variable x represents the same value. Which value of x is the solution of the equation; x = 0, 1, 2, or 3? Explain. Can i have the answer please because right now for me i have been ding this since 3pm and its 9:19 right now

Answers

Answer:

[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ 8x & {0} & {8} & {16} & {24} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]8x[/tex]

Required:

Solve for [tex]x = 0,1,2,3[/tex]

For x = 0

[tex]8x = 8 * 0[/tex]

[tex]8x = 0[/tex]

For x = 1

[tex]8x = 8 *1[/tex]

[tex]8x = 8[/tex]

For x= 2

[tex]8x = 8 * 2[/tex]

[tex]8x = 16[/tex]

For x = 3

[tex]8x = 8 *3[/tex]

[tex]8x = 24[/tex]

Hence, the results are:

[tex]\begin{array}{ccccc}x & {0} & {1} & {2} & {3} \ \\ 8x & {0} & {8} & {16} & {24} \ \end{array}[/tex]

Help plz I have time and I need to show work

Answers

21 I think but I was just guessing

hii please help i’ll give brainliest!!

Answers

Answer:

2

Step-by-step explanation:

For every action, there is an equal and opposite reaction.

Answer:

For every action, there is an equal and opposite reaction.

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