solve the simultaneous equation:
y=x^2+3
y-2x=18

Answers

Answer 1

Answer:

(- 3, 12 ) and (5, 28 )

Step-by-step explanation:

Given the 2 equations

y = x² + 3 → (1)

y - 2x = 18 → (2)

Substitute y = x² + 3 into (2)

x² + 3 - 2x = 18 ( subtract 18 from both sides )

x² - 2x - 15 = 0 ← in standard form

(x + 3)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 5 = 0 ⇒ x = 5

Substitute these values into (1) for corresponding values of y

x = - 3 : y = (- 3)² + 3 = 9 + 3 = 12 ⇒ (- 3, 12 )

x = 5 : y = 5² + 3 = 25 + 3 = 28 ⇒ (5, 28 )


Related Questions

If a = 6 and b = 2, then what does ab equal?

Answers

Answer:

12

Step-by-step explanation:

ab

Let a = 6 and b = 2

6*2

12

The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?

Answers

Answer: 2 degrees + 3 degrees = 5 degrees

Step-by-step explanation: Though the times might be confusing, the problem itself is simple addition- if the temperature rises, or goes up, by a certain number, in this case three, you're just going to add that number to the initial number, two.

help I will give brainly!!!!!!!!

Answers

the rise is 4 and the run is 5

Can someone Help me please

Answers

Step-by-step explanation:

what do you need to do ? draw the line ? or find some intercepts on the x- or y-axis ? or ?

in any case it is important to bring this into the typical line equation form :

y = ax + b

so,

-4x = -1 + y

we leave y alone on one side

y = -4x + 1

to draw the line you need 2 points.

so, let's find some.

one typical choice is x = 0.

then y = -4×0 + 1 = 1

so, P1 = (0, 1)

and then e.g. let's pick x = 1

then y = -4×1 + 1 = -4 + 1 = -3

so, P2 = (1, -3)

there you have it

mark the two points on the coordinate graph, then take a ruler and draw the line all the way from top left to bottom right so that it goes through the two points.

Slope=-7​, through ​(-3​,2​)

Answers

Answer:

Final equation: y = -7x -19

Step-by-step explanation:

You are looking for slope intercept correct?

Formula: y = mx + B

Y = y-value of point ( coordinates )

M = slope

X = x - value of point ( coordinates )

B = Y - intercept

Equation:

2 = -7(-3) + B

2 = 21 + B

-21 = -21 = B

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

-19 = B

Final equation: y = -7x -19

Unless if it asks you to plug back the numbers for anything else then you do that but this is how you get slope intercept.

Does a rhombus have perpendicular line segments

Answers

Answer:

A rhombus is a geometric figure that lies in a plane. It is defined as a quadrilateral all of whose sides are congruent. It is a special type of parallelogram, and its properties (aside from those properties of parallelograms) include:

Its diagonals divide the figure into 4 congruent triangles.

Its diagonals are perpendicular bisectors of eachother.

If all of a rhombus' angles are right angles, then the rhombus is a square.

Answer:yes it does have perpendicular lines

Step-by-step explanation:

Two kids at a summer camp, Amelia and Jennifer, are competing in a potato sack race. Amelia is younger, so she is given a head start of 3 yards. When the race starts, Amelia hops at a rate of 3 yards per second, and Jennifer hops 4 yards per second. Eventually, Jennifer will overtake Amelia. How far will Jennifer have to hop? How long will that take?

Answers

It will take 12 yards

A right triangle has leg lengths of 6 cm and 9 cm,
find length of the missing side.

help please :)

Answers

Answer:

3*sqrt13

Step-by-step explanation:

You search for hypotenuse

Squared hypotenusw is equal to 6^2+9^2= 36+81=117

Hypotenuse is equal to sqrt117= sqrt9*sqrt13= 3*sqrt13

1. Which of the following is a true statement?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number whose
square root is an even number.
SHOW PROOF

Answers

Answer:

C

Step-by-step explanation:

Squaring is multiplying a number by itself

Examples:

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

etc.

Is the graph a linear function, nonlinear function, or relation?

Answers

Answer:

Non-linear

Step-by-step explanation:

just did it

Answer:

Nonlinear function

Step-by-step explanation:

Because it's along the x-axis but isn't a straight line if it was a straight line it would be considered a "Linear Function".

Please no links because they dont work :).

Answers

Answer:

C. x + 9

Step-by-step explanation:

[tex]x-\frac{5}{5}+10\\\\x-1+10\\\\x+9[/tex]

PLEASE HELPP MEEE I NEED THE ANDWER QUICKKK
20.00$ - a=8.45$

Answers

the answer to the equation is $11.55

Answer:

a= 11.55

Step-by-step explanation:

If the answer is 8.45, then the variable equals the difference of 20 minus the answer, 8.45

Hope this helps!

help!!! hurry......-_-

Answers

Replace x and y’all with the point and solve the equations

1. 2(0.5)+ 4(-6.75) = 1 + -27 = -26

This is true so is an answer.

2. Y = 0.5-7.5 = -7, -7 is not -6.75 so this is not true.

3. 2(-6.75) = 0.5 + 13

13.5 = 13.5

This is true so is also an answer.

4. -6.75 = 0.5(0.5) -7

-6.75 = 0.25-7

This is true so also an answer.

Answers are 1, 3 and 4

Answer:

Equation 1 and 4

Step-by-step explanation:

Point = (x,y) = (0.5,-6.75)

Hence,

x = 0.5 , y = -6.75

Equation 1:

2(0.5) + 4(-6.75) = -26

1 - 27 = -26

-26 = -26

This equation is true for the given point.

Equation 2:

-6.75 = 0.5 - 7.5

-6.75 ≠ -7

The equation is not true for the given point.

Equation 3:

2 (-6.75) = 0.5 + 13

-13.5 ≠ 13.5

The equation is not true for the given point.

Equation 4:

-6.75 = 0.5(0.5) - 7

-6.75 = 0.25 - 7

-6.75 = -6.75

This equation is true for the given point.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!

HELPPPPPPPPPPPPPPPPPPPPPPP
































(jus take the points dont really need help)

Answers

Answer:

Alright- if you want any help just reply to this

What is the value of the expression 5¼(-10.2)? Record your answer and be sure to use the correct place value.

Answers

The value of the given expression is - 53.55

[tex]5 \frac{1}{4}( - 10.2) \\ [/tex]

The bracket implies multiplication :

Hence,

[tex]5 \frac{1}{4}( - 10.2) \\ [/tex] = [tex]5 \frac{1}{4}\times - 10.2

Converting the fraction to improper :

[tex] \frac{21}{4} \times - 10.2[/tex]

Then, to decimal :

[tex]5.25 \times - 10.2 = - 53.55[/tex]

Hence, the value of the expression is - 53.55

Learn more : https://brainly.com/question/5992872

Write the rules for determining the sign of the product when multiplying integers. Then, write (4 points)
the rules for determining the sign of the quotient when dividing integers. Use your own words
and use complete sentences. Make sure you answer both questions presented in this problem.
I

Answers

Answer:

hahaaaaaaaaaaaaaaaaa

Step-by-step explanation:

Answer:

IF the signs ARE same the result is a POSITIVE, if the signs are NOT the same the result is NEGATIVE

Step-by-step explanation:

Find the possible subsets of A = {a,b}​

Answers

Answer:

Step-by-step explanation:

Subset of A = { {} , {a} , {b}, {a.b} }

Evaluate 2/11 + 1/17 + 2/3

Answers

Answer:

509/561

Alternate form is 0.9073

Step-by-step explanation:

The L.C.M is 561.

561/11 × 2 is 102.

561/17 × 1 is 33

561/3 ×2 is 374

102/561 + 33/561 + 374 /561

= 509/561

Alternate form is 0.9073

(3x+2)(x^2-4x-2) simplify the expression to a polynomial in standard form

Answers

(3x+2)(x²-4x-2)

(3x) (x²-4x-2) + (2) (x²-4x-2)

= 3x³ – 10x² – 14x – 4

I hope I helped you^_^

i dont know if im right or not

Answers

Answer:

You are right

Step-by-step explanation:

80% of a number is always going to be less than 100% of a number. Assuming the numbers positive, which it said

Answer: its >

Step-by-step explanation: beacuse80% x .01 =0.008 and 0.008= 0.8%

hey please help i’ll give brain

Answers

Answer:

The answer is 2. It is the commutative property of addition. This states that the order of numbers does not matter in addition or multiplication. As long as all the numbers are there, it will give the same answer :)

Step-by-step explanation:

d/3 =13 what is d and explain why its d.

Answers

Answer: d = 39

Solve:

Given

d / 3 = 13

In order to get the value of d, we need to isolate d, which means we should multiply 3 on both sides to delete the 3 on the left-hand side

d / 3 × 3 = 13 × 3

d = 39

Check:

Left-hand side = d / 3 = 39 / 3 = 13

Right-hand side = 13

13 = 13

Hope this helps!! :)

Please let me know if you have any questions

Answer:

39

Step-by-step explanation

so d ÷ 3 = 13

first we want to change these numbers into a fraction so

d ÷ 3 = [tex]\frac{d}3}[/tex]

13 is whole but we can still display it as 13÷1 =[tex]\frac{13}{1}[/tex]

line these up like this

[tex]\frac{d}{3} \frac{13}{1}[/tex]

now cross multiply the numbers that always line up diagonally so 13 and 3

13x3=39

next divide that answer by the number diagonal to the unknwon so 39÷1 = 39

that means d = 39

Josh sees that the ratio of boys to girls is 1/2, so he says that half of the students are boys?

Answers

Answer:

no.

Step-by-step explanation:

The ratio is 1/2. That means that if there is one boy, there are 2 girls. Altogether, there are 3 people.

The answer is no. Boys would be one-third and girls are two-thirds.

If this helped, please mark me as brainliest. Thank you! ;)

Can anyone explain how to do this pleaseee

-2+y/10=-6

Answers

Answer:

y = -58

Step-by-step explanation:

You have to isolate the y:

-2+y/10 = -6

First step, multiply both sides by 10:

-2+y = -60

Second step, add 2 on both sides:

y = -58

It's done!

Answer:

-2=-40/10=-6

Step-by-step explanation:

-2/10 alone is -0.2.

Using PEMDAS your problem should look more like, (-2)+((y)÷10)=

Using this new formula let's start plugging in numbers.

(-2)+((0)÷10)= -2

(-2)+((-1)÷10)= -2.1

(-2)+((-2)÷10)= -2.2

Now there is a pattern, you can calculate or just keep moving up the latter until you reach the desired sum.

After finding the plug-in use PEMDAS to solve.

(-2)+((-40)÷10)=

((-40)÷10)= -4

-4+-2=-6.

So (-2)+((-40)÷10)= -6

I have to write these equations in scientific notation:
870.4
32.508
0.8006

Answers

Answer:The solutions are in the attached file below

Step-by-step explanation:

A 3m ribbon is cut into two pieces.The shorter length measures 0.75m.Write the ratio of the shorter length to the longer length in the simplest form a:b,where a and b are both integers.

Answers

Answer:

1:3

Step-by-step explanation:

3 m - .75 m = 2.25 m Find the length of the longer piece.

.75:2.25 Ratio in un-simplified form

[tex]\frac{.75}{2.25}[/tex] Write it as a fraction.

[tex]\frac{75}{225}[/tex] Multiply the numerator and denominator by 100 to remove the decimal.

[tex]\frac{3}{9}[/tex] Divide the numerator and denominator by 25.

[tex]\frac{1}{3}[/tex] Simplify further by dividing the numerator and denominator by 3.

1:3 Convert back to ratio form.

Points A, B, and C are collinear. Point B is between A and C. Find the length indicated.​

Answers

Answer:

AB=1

Step-by-step explanation:

Colinear means all points are on the same line. We need to find the measure of AB.

Using the segment addition postulate,

ab+bc=ac

Subsitue this for our known values

[tex]2x + 15 + 9 = x + 17[/tex]

Solve for x

[tex]2x + 24 = x + 17[/tex]

[tex]x + 24 = 17[/tex]

[tex]x = - 7[/tex]

Plug this in for AB

[tex]2( - 7) + 15 = 1[/tex]

solve for A. W = a/3
PLEASEEEE

Answers

Answer:

3w

Step-by-step explanation:

[tex]w=\frac{a}{3} \\3w=a\\[/tex]

i got 3w! hope it help :)

HELP PLEAASSEE ?? ANYONE ???
The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of a rectangle, as shown in the diagram.
The radius of each circle is 2 mm.
Work out the exact area of the rectangle. Give your answer in the form
[tex]a \sqrt{3} + b[/tex]
where a and b are integers.​

Answers

Answer:

as the diagram is not provided by you

Step-by-step explanation:

proper an answer cannot be written if the three circles touch Each Other as well as the the sides of the rectangle it means that rectangles length and breadth are made by attaching to circles together which means that length and breadth of the rectangle are equal therefore length is equal to diameter of one circle into two that is 8 therefore length and breadth of the rectangle are 8 each other for exact area of rectangle is 8 x 8 = 64

Answer:

apparently 4root3 + 8

Step-by-step explanation:

PQR and SQR form a linear pair. Find the sum of their measures.

Answers

180 is your awnser too this one
Other Questions
Read the excerpt from The Mother of America:George Washington is frequently considered the "Father of America." Likewise, his wife, Martha Washington, could also be considered the "Mother of America," as demonstrated by her roles as the general's wife and the first lady.During the American Revolution, Martha Washington earned the title of "Mother of America" for her caring nature as the general's wife. She was also very brave. Despite the danger of kidnapping, Martha refused to abandon her home, Mount Vernon, in Virginia. When Martha did leave the plantation for periods of time, she traveled to the military camps where Washington was staying. First, Martha had to be vaccinated so that she would not suffer from smallpox. Once she was inoculated, Martha made the risky trip to camp. British and American soldiers roamed the countryside, and capture was a real possibility. Nevertheless, Martha arrived at each winter camp. She acted as confidant and secretary to George Washington, who believed that her presence was crucial. She encouraged the soldiers, helped their wives, and comforted those who were wounded. One of her key roles was also to entertain important visitors to the camp. Occasionally, Martha Washington even represented George at events he could not attend. Martha used her position to contribute to fundraising efforts for military supplies in 1780 and knit socks for the soldiers herself. Overall, her care and attention to others' needs made her the "Mother of America" during the American Revolution.What reason does the author provide to support the point that Martha Washington should be considered the "Mother of America"?A. Her bravery when being inoculated from smallpoxB.Her care and attention to others' needs as the General's wifeC. Her fear of being kidnapped by British soldiersD. Her willingness to knit socks for soldiers at the military camp -. JC=BFF cough medicine is marketing its' new medicine called "Devil Red". Theywant to know why religious customers seem to avoid their product. Can someone give me some examples on why hunter gather is better then todays society can any one solve this please....I kinda need this what is the opposite of A) 7 & B) -3A -7 , -3B -7 -3C -7 , 3D 7 , 3 how many axes of symmetry does a square have 4. What is the main hydrocarbon component of natural gas? A. ethaneB. ethene C. methane7.The fact that alpha particles cannot travel very far trough body tissues is the main reason that radioactive tracers use to detect diseases in internal organs emit beta particles or gamma rays.A. true B. false8.A wax is an ester of a long-chain fatty acid and a long-chain alcohol. A. trueB. false if this trapezoid is moved through the translation (x+3,y-2) what will the coordinates of B` be can anyone help me please on this function. A wedding planner uses 72 ivy stems for 18 centerpieces. When sh arrives at the venue , she realizes she will only need 16 centerpieces. How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same ? plz help me I need help if a=3x and b = 3x-4i, find the value of a3b In fully simplified form (7x2 - 2x - 5)(3x2 + 2x - 3) Who is the Step-Father to the Constitution? WHY? Pls help me in this my math exam is Tom and I wanna know how to solve theese Underline the adverbs in the following paragraphs. 1. Our new neighbour greeted us politely.2. "How long have you lived here?' she asked.3. "We arrived only yesterday," we replied.4. Well, I hope you'll be really happy."5. After that we met her quite frequently. However, we learned very little about her. 6. Strangely, she never talked about herself. She talked only about the weather and us.7. Personally, I found that annoying. Have you ever met anyone like that? Melany wants to hang a canvas, which is 8 feet wide, on his wall. Where on thecanvas should Melany mark the location of the hangers if the canvas requires ahanger every 1/5 of its length, excluding the edges? Justify your answer. what message does the cartoon portray about globalisation C^-24 times c^9 times c^-87 answer using positive exponents Evaluate the expression below