Solve the simultaneous equations
y = 3 – 2x
x2 + y2 = 18
Show clear algebraic working.

Answers

Answer 1

(

x

,

y

)

=

(

3

5

,

4

1

5

)

or

(

x

,

y

)

=

(

3

,

3

)

Explanation:

Given

[1]

XXX

y

2

x

=

3

[2]

XXX

x

2

+

y

2

=

18

Re-writing [1]

[3]

XXX

y

=

2

x

+

3

Substituting

(

2

x

+

3

)

from [3] for

y

in [2]

[4]

XXX

x

2

+

(

2

x

+

3

)

2

=

18

Simplifying

[5]

XXX

x

2

+

4

x

2

+

12

x

+

9

=

18

[6]

XXX

5

x

2

+

12

x

9

=

0

Factoring

[7]

XXX

(

5

x

3

)

(

x

+

3

)

=

0

x

=

3

5

or

x

=

3

case 1:

x

=

3

5

Substituting

3

5

for

x

in [3]

XXX

y

=

2

(

3

5

)

+

3

=

4

1

5

case 2:

x

=

3

Substituting

(

3

)

for

x

in [3]

XXX

y

=

2

(

3

)

+

3

=

3


Related Questions

PLEASE HELPPP!!!!!!!!

Answers

Answer:

C. y=-3x+5

Step-by-step explanation:

Looking at the line, you see that it goes down 3 places for every unit step to the right, so the slope is -3 and we expect a -3x in the answer.

Looking at the intersection with the y-axis, it is at (0,5), so we expect -3x + 5.

We have to be at the left of this line, i.e. y < -3x + 5.

That's answer B.

Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function h(t)= -16t^2+96t gives the height, in feet, of the soccer ball after t seconds. The function is shown in the graph below. What are the intercepts of the function and what do they mean?

Answers

Answer:

(d)

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 96t[/tex]

Required

The intercepts

The x intercepts are where the graph crosses x axis.

From the attached plot, they are:

[tex]x = (0,0)[/tex] and [tex]x = (6,0)[/tex]

These represent the start and end of the ball that is launched.

Hence, (d) is true

PLEASE HELP ME PLEASE what is the answer besides 3

Answers

I thinks it’s B I’m not 100% sure tho

Toby collected data about the population of a town for five years. Toby's data was linear. Which table could be Toby's data?
the answer choices are A) A B) B C) C D) D

Answers

Answer:

ok, so the answer is table A

Step-by-step explanation:

USA PREP TESTTTTTT

good luck :)

2 Find the area of the shape. Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal. units

Answers

Answer:

The problem is not provided so I cannot solve anything.

Step-by-step explanation:

Move each inequality to the table to match the appropriate situation describing x. HELPP FAST

Answers

Answer:

1. x < 10

2. x ≥ 10

3. x ≤ 10

4. x > 10

Step-by-step explanation:

1. Tiana read a book in less than 10 days.

Let

x = number of days Tiana read her book

x < 10

2. Charlie plans to run at least 10 miles this week

Let

x = number of miles Charlie plans to run

x ≥ 10

Jessica can spend at most 10 dollars on lunch

Let

x = amount of money Jessica can spend on lunch

x ≤ 10

Andre needs to buy more than 10 balloons for the party

Let

x = number of balloons Andre needs to buy

x > 10


7.4.PS-6
Question Help
Find the area of the polygon.
20 cm
14 cm
4 cm
3 cm
5 C

Answers

Answer:

The area of the given polygon is:

232 cm^2

Step-by-step explanation:

To find the area of the polygon in the picture, you can divide the polygon in three rectangles: a 3 cm by 14 cm, a 5 cm by 14 cm rectangle, and the last rectangle must have a base of 12 cm (20 cm - 3 cm - 5 cm), and a height of 10 cm (14 cm - 4 cm). We can calculate the area of the rectangles with the formula below:

Area of a rectangle = Base * height

Now, we're gonna replace the measurements in the formula.

First rectangle:

Area of a rectangle = 3 cm * 14 cmArea of a rectangle = 42 cm^2

Second rectangle:

Area of a rectangle = 5 cm * 14 cmArea of a rectangle = 70 cm^2

Third rectangle:

Area of a rectangle = 12 cm * 10 cmArea of a rectangle = 120 cm^2

By last, we must add the area of the rectangles:

Area of the polygon = 42 cm^2 + 70 cm^2 + 120 cm^2Area of the polygon = 232 cm^2

As you can see, the area of the polygon in the picture is 232 cm^2.

1. Translate the figure: Right 5 and Up 4

Answers

Step-by-step explanation:

Right 5 and 4 =9 that is the answer

Sketch a graph of a quadratic function that has a maximum value of (0, 2) and x-intercepts when x = +2.​

Answers

The graph of a quadratic function that has a maximum value of (0, 2) and x-intercepts when x = ± 2 is plotted and attached.

What is local maxima and minima?

Local Maxima

If f'(x) changes sign from positive to negative as x increases via point c, then f(c) represents the maximum value of the function in that range.

Local Minima

If f'(x) changes sign from negative to positive as x increases via point c, then f(c) gives the minimum value of the function within that range.

Given is to sketch a graph of a quadratic function that has a maximum value of (0, 2) and x-intercepts when x = + 2.​

Refer to the graph of the function attached.

It shows a parabola indicating a quadratic function that has a maximum value of (0, 2) and x - intercepts at x = ± 2.​

Therefore, the graph of a quadratic function that has a maximum value of (0, 2) and x-intercepts when x = ± 2 is plotted and attached.

To solve more questions on graph plotting, visit the link -

brainly.com/question/30098550

#SPJ1

Write an equivalent expression to show the relationship of multiplication and addition.


10+10+10




4+4+4+4+4+4+4




8×2




3×9




6m




d+d+d+d+d




Answers

4+4+4 is the equivalent to 10+10+10

5. A cabin rental costs $100 deposit plus $75 per day. Find the cost of renting a cabin for the
month of June.

Answers

Answer:

the answer to this question is $2,350

Step-by-step explanation:

june has 30 days so $75 × 30 + $100 = $2,350

Approximately 0.5% of computers in a shipment arrive broken. In a shipment of 20,000 computers, about how many will NOT be broken?

Answers

Rewrite 0.5% as a decimal by moving the decimal point 2 places to the left:

0.5% = 0.005

Multiply quantity by the decimal:

20,000 x 0.005 = 100 would be broken

20,000-100 = 19,900 would not be broken

2 3/7 - 5 6/7 Question I-Ready

Answers

Answer: I think so the answer is -3 3/7

HOPE THIS HELPS

HELP ME PLEASEEEEEEEEEEEE

Answers

First you would do base times night with is 224. Then you would divide 224 by 2, so your answer would be 112

Answer:

The area is 112.

Step-by-step explanation:

14 x 16 = 224

224/2 = 112

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the endpoints of the t-distribution with 5% beyond them in each tail if the samples have sizes ni = 8 %3D and 11 n2 Enter the exact number for the degrees of freedom and round your answer for the endpoints to two decimal places. degrees of freedom = endpoints

Answers

Answer:

i think it 36 sorry if it wrong tho have a nice day

Step-by-step explanation:

ABC = DEF What corresponds with B?

Answers

Answer:

answer is C

Step-by-step explanation:

<E corresponds with B

Hope it helps you

If LK is a midsegment of hij, find x

Answers

Answer:

you forgot to post the pic

Step-by-step explanation:

Help pls… 50points
Referring to the figure, find m∠1.
5. Answer:
Referring to the Fig. in Question #4, find m∠2.
6 Answer:
Referring to the Fig. in Question #4, find m∠3.
7 Answer:
Referring to the Fig. in Question #4, find m∠4.
8 Answer:
Referring to the Fig. in Question #4, find m∠5.
9 Answer:
Referring to the Fig. in Question #4, find m∠6.
10 Answer:
Referring to the Fig. in Question #4, find m∠7

Answers

Answer:

Step-by-step explanation:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Answer:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Step-by-step explanation:

Enter an integer to represent the situation.


an elevator ride down 35 stories

Answers

Answer:

-35

Step-by-step explanation:

this is a simple but confusing question

however,

since they said down the elevator, and the negative integers reduces, therefore we have our answer as

-35

find the height of a triangle with an area of 156 square kilometers and a base that measures 24 kilometers

Answers

Answer = 13 kilometers
hb = 2 a/b= 2 x 156/24 = 13

PLEASE PLEASE PLEASE PLEASE HELP ME! Image below I Am Crying :((

Answers

Answer:

Its X-1

Step-by-step explanation:

Answer:

x= 5

Step-by-step explanation:

the | | around a number is called an absolute. It simply means that the number is always going to be positive. If you have |-4| it's the same as saying 4.

What is the slope of the following equation?

y = 2x -3

Answers

Answer:

Step-by-step explanation:

2 is the slo[pe:)

50 points!!
Solve for x and y given the 2 triangles are SIMILAR​

Answers

Answer:

x/3=4.5/1.5

1.5x=3*4.5

x=13.5/1.5

x=9

Step-by-step explanation:

3.8.22
City planners want to construct a bike path
perpendicular to Bruckner Boulevard at point P. An equation for the Bruckner
Boulevard line is y=-x. Find an equation for the line for the bike path.
4
The equation of the line for the bike path is I.
(Simplify your answer. Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in th

Answers

Answer:

9

Step-by-step explanation:

Plz help me well mark brainliest if correct!!...

Answers

Answer:

The answer will be D

Have a great day :)

Answer: it would be D two of the fourth graders own two pets

Step-by-step explanation: if you look at the graph it is showing how many people own how many pets then look for the one with for and however many stars are there which is two people who own four pets

Hope this helps :)

What is the first step in evaluating the expression below?
12 + 6 - 4 X (12-5)
Add 12 + 6
O Multiply 4 x 12
Subtract 5 from 12
O Multiply 4x7

Answers

PEMDAS so parentheses first meaning you subtract 5 from 12

A pyramid has a volume of 1,944 inches cubed and a rectangular base with the dimensions 18 inches by 9 inches. What is the height of the pyramid?
4 in.
12 in.
24 in.
36 in.

Answers

Answer:

36

Step-by-step explanation:

I used a triangle height calculator on G0ogle

If the base area is 162 square inches, then the height of the pyramid will be 36 inches. Then the correct option is D.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A pyramid has a volume of 1,944 inches cubed and a rectangular base with the dimensions of 18 inches by 9 inches.

Then the height of the pyramid will be

The volume of the pyramid will be

Volume = (Base area x height) / 3

Then the base area will be

Base area = 18 x 9

Base area = 162 square inches

Then the height of the pyramid will be

1944 = (162 h) / 3

5832 = 162 h

      h = 36

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ2

In this composite function, (f◦g)(x) where f(x)=(X-3) and g(x)=X^2 what is (f◦g)(x) when x=1?

Answers

Answer:

When x = 1, (f◦g)(x) is -2.

Step-by-step explanation:

Composite function:

The composite function of f and g is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this question:

[tex]f(x) = x - 3, g(x) = x^2[/tex]

Composite function:

The composite function is:

[tex]f(g(x)) = f(x^2) = x^2 - 3[/tex]

At x = 1

[tex](f \circ g)(1) = 1^2 - 3 = 1 - 3 = -2[/tex]

So

When x = 1, (f◦g)(x) is -2.

Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the
coins, 12% are pennies and 34% are dimes. There are 7 more nickels than pennies. How much
money does the bag contain?

Answers

Answer:pennies: (0.12)(50) = 6

dimes: (0.34)(50) = 17

nickels: 6 + 2 = 8

Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.Use the edit icon to pin, add or delete clips.Welcome to Gboard clipboard, any text you copy will be saved here.​

Answers

Okay thank youu I needed this
Other Questions
What requirements are necessary in order for you to share a file?Check all that apply.You own it.You commented on it.You can edit.You know about the topic of the document. 14 and 15 please thank you What is the meaning of the word orderly as it is used in this paragraph?It started off nicely enough. There was a garden directly beneath Brunos window. Quite a large one too, and full of flowers which grew in neat orderly sections in soil that looked as it if was tended very carefully by someone who knew that growing flowers in a place like this was something good that they could do, like putting a tiny candle of light in the corner of a huge castle on a misty moor on a dark winters night. SOMEONE TELL ME THE ANSWER PLEASE AND I WILL GET YOU SOME COOKIES!!!!!! A skateboarder goes off of a ramp at a speed of 52 ft./s. The ramp is 5 ft. above the ground with a 30angle of elevation. Which set of parametric equations represents the skater's jump? The acceleration dueto gravity is 32 ft/s^2. Ich habe einen Freund in Deutschland. Er heitMartin. Er wohnt in Berlin. Martin sagt, Berlin istsehr interessant. Er mchte mir die Stadt malzeigen. Wir knnen dort ins Technik-Museumgehen. Wir knnen auch mal in den Kletterparkgehen. Ich mchte Berlin wirklich gern sehen.Das Flugticket kostet 250 . Ich kann leider nichtfahren. So ein Pech! if f(x) = 1/x^14, what is f'(x)? YasmeenHussainduz answer plas and one more random person 7 (3 + 5) = __ + __ is what? I want a possible solution please answer both ASAP (middle school) (probability) can sum1 help me pls ii'll give brainliest how we feel about summer and what we do If a triangle has an area of 24 square cm what is its base if the height is 3 cm PLZ HELP WILL MARK BRAINLIEST!!! Which of the following is different from others?(a) 100000 ones (b) 10 thousand (c) 1000 tens (d) 10 hundred on a scale of 1-10, how challenging do you find online learning? Whats going well? What are some of the challenges? What resources would make a difference? A thematic map of the U S and Canada. A key notes climate regions. Canada has Arctic, Subarctic, Northwest coast, Plateau, Great Plains, and Northeast regions. The U S has Plateau, Great Plains, Northeast, California, Great Basin, Southeast, and Southwest regions.Image by NikaterAnalyze the map above. Identify the regions where the following tribes lived prior to European contact:1. the Inuit2. the Pueblo3. the Iroquois4. the Cherokee5. the Cheyenne6. the Makah Ismael made a scaled copy of the following quadrilateral. He used a scale factor less than 1.What could be the length of the side that corresponds AD on the scaled copy of the quadrilateral?Choose 3 answersA: 4 unitsB: 6.5 unitsC: 12 unitsD: 32 unitsE: 64 units How Is This $20 Bill Related To The Indian Removal Act Of 1830?