Mathematics High School

What are the solutions of the following system?
=
[x2 + y2 = 25
2x+y=-5
(0, -5) and (-5,5)
(0, -5) and (5, -15)
(0, -5) and (-4,3)
O (0,-5) and (4, -13)
What is it?

Answers

Answer 1

Answer:

Third option: (0,-5) and (-4,3)

Step-by-step explanation:

x^2 + y^2 = 25

2x + y = -5

y = -5 - 2x

x^2 + (-5-2x)^2 = 25

x^2 + 25 + 20x + 4x^2 = 25

5x^2 + 20x + 25 = 25

5x^2 + 20x = 0

5x(x+4) = 0

5x=0 --> x=0

x+4=0 --> x=-4

2(-4) + y = -5

-8 + y = -5

y = 3 --> (-4,3)

2(0) + y = -5

0 + y = -5

y = -5 --> (0,-5)

Therefore, the solutions to the system of equations are (0,-5) and (-4,3)

Related Questions

if p(q) = q^2 4q- 12 then what is p(-1)

Answers

the solution:

(1): "q2" was replaced by "q^2".

Step by step solution :

STEP
1
:
Trying to factor by splitting the middle term

1.1 Factoring q2-4q-12

The first term is, q2 its coefficient is 1 .
The middle term is, -4q its coefficient is -4 .
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -4 .

-12 + 1 = -11
-6 + 2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 2
q2 - 6q + 2q - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
q • (q-6)
Add up the last 2 terms, pulling out common factors :
2 • (q-6)
Step-5 : Add up the four terms of step 4 :
(q+2) • (q-6)
Which is the desired factorization

Equation at the end of step
1
:

(q + 2) • (q - 6) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : q+2 = 0

Subtract 2 from both sides of the equation :
q = -2

Solving a Single Variable Equation:

2.3 Solve : q-6 = 0

Add 6 to both sides of the equation :
q = 6

Supplement : Solving Quadratic Equation Directly

Solving q2-4q-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = q2-4q-12

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Aq2+Bq+C,the q -coordinate of the vertex is given by -B/(2A) . In our case the q coordinate is 2.0000

Plugging into the parabola formula 2.0000 for q we can calculate the y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 12.0
or y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = q2-4q-12
Axis of Symmetry (dashed) {q}={ 2.00}
Vertex at {q,y} = { 2.00,-16.00}
q -Intercepts (Roots) :
Root 1 at {q,y} = {-2.00, 0.00}
Root 2 at {q,y} = { 6.00, 0.00}

Which expression can be used to find the surface area of the following triangular prism?
5
5
2.
11
8.

Answers

Answer:

214.

Step-by-step explanation:

To get Surface area take

(cross section area) × 2 +(perimeter of crossection area × length)

the cross section area is a triangle

so area of a triangle =1/2 base times height

1/2×8×2=8

let's get perimeter of cross section

the cross section is still at triangle so let's find its perimeter.

5+5+8=18

18×length of which is 11

18×11=198

and 188 + 16=214. that's the answer

maybe you can get a expression from the work that I've just done cuz I can't see the answers clearly in the picture you have taken.if you don't mind just send the picture back then I'll get the answer.

Write the slope-intercept form of the equation of the line. ​

Answers

The slope- intercept of the line is y= x + 2. This is because for every time you go up or “rise” 1 unit you move to the right or “run” 1 unit. Therefore, 1/1 is just 1 so we can just leave this as x, however 1x would still work. Also, the line first touches the y-axis when x is 0 and y is 2. Therefore, the slope intercept is 2. So the slope intercept form of this line is still y = x + 2.

How many solutions does the system of equations below have?
4x + 10y = –7
–3x + 9y = –14
No solution
One solution
Infinitely solutions

Answers

Answer:

There is one solution to this system of equations

Step-by-step explanation:

When solving, there is a specific point of intersection which is (7/6,-7/6), making the answer one solution.

Plz need help

What is the value of (2/3)

Answers

Answer:

2/9

Step-by-step explanation:

2(2/3)^2-4(2/3)+2

2(4/9)-8/3+2

8/9-8/3+2

-16/9+2

2/9


Will mark brainliest

Answers

Answer:

Point  H is in the first Quadrant (5,4)

Step-by-step explanation:

Answer:

quadrant 1

Step-by-step explanation:

yw:)

Find the distance travelled by Rubina if she takes 4 rounds of rectangular park whose length and breadth is 45m and 30m

please give me a valid answer with a step by step explanation and i will mark you as brainliest

Answers

Length (l) = 45 mBreadth (b) = 30 mWe know, perimeter of a rectangle = 2(length + breadth)Therefore, perimeter of the rectangle = 2(I + b) = 2(45 + 30) m = 2 × 75 m = 150 mSo, the distance travelled by Rubina = 4 × 150 m= 600 m

Answer:

The distance travelled by Rubina is 600 m.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Helpppp me please omg

Answers

the first graph looks right

​George has $3 in his savings account. He then adds $4 per day to the account. Let y represent the total amount in the account after x days.

Which equation represents this situation in the form of y=mx+b ?

Question 9 options:

y = 4x + 3


y = 3x + 4


y = 3/4x - 3


y = 4/3x - 4

Answers

Answer:

The answer is the 1st option, y = 4x + 3

Step-by-step explanation:

x is the amount of days that the 4 dollars will be multiplied by

( 4 * x )

The + 3 is the money that George already had in his savings account, so that money will be added to the total amount in his savings account.

( 4x + 3 )

Lastly, the y stands for the total amount of money in his savings account so the answer is the 1st option.

y = 4x + 3

Hope this helps! :)

plz help with my math hw

Answers

Answer:

cant see

Step-by-step explanation:

ANYBODY HELP. EXPERTS HELP!!!!!!!!!!

Answers

Answer:

Question 1  Between 3 - 4 hrs

Question 2 Between 1 - 3 hrs

Question 3 Between 4 - 8 hrs

Question 4 Between 2 - 3 hrs

Question 5 Represents the starting position

Step-by-step explanation:

please help me quick

Answers

Answer:

D) The answer is AB and HG

Step-by-step explanation:

sides that are equal:

AD=EH

DC=EF

BC=FG

AB=HG

Choose the linear equations.

Answers

Answer:

y = [tex]\frac{3}{3}[/tex]x - 5

y = 2x + 5

Step-by-step explanation:

In linear equations, both variables x and y must have the exponent of 1 (i.e. they cannot have a small number at the top-right). And they cannot be in the exponents (i.e. cannot be the small number at the top-right).

Please help :)
M is the midpoint of segment AT.
Solve for X and AM

Answers

Because M is the midpoint of segment AT
So AM = TM
<=> 5x = 3x + 4 <=> 5x - 3x = 4
<=> 2x = 4 <=> x = 2

The answer: x = 2
Ok done. Thank to me :>


Please helpppppppppppp

Answers

Answer:

5/4

Step-by-step explanation:

35/4 ÷ 14 = 5/4

That means 14 was multiplied by 5/4 to get 35/2

What is the solution to this quadratic equation

Answers

The answer is: B, C, and E

(0,12)
(2,0)
(6,0)


Marcus is it mixing blue and yellow paint in the ratio of 2 to 3 to make green paint. He wants to make 45 L of green paint. Him being to make a table to help him think about the problem but is unsure of what to do next. Marks find Amandas also mixing paint she wants to make purple paint by mixing 2 cups of blue with a4 cups are red paint. Amanda makes her pain in his left with 48 cups of purple paint how many more cups of purple paint did she use than blue paint? If Amanda has 15 cups of blue paint how many cups repair does she need? Amanda wants her purple paint mixture from part bead to be a little lighter so she mixes in two more cups of white paint what is the ratio of blue paint to repaint the white paint that she used?

Answers

This question is based on the concept of ratio. Therefore, he needs to have 18 liters of blue paint and  27 liters of yellow paint to make 45 liters of green paint.

Given:

Mark was mixing blue and yellow paint ratio of 2:3.

He wants to make 45 liters of green paint.

According to the question,

Blue : Yellow =  Green

2 : 3 : 2+3 (Given)

2 : 3 : 5

Therefore, he wants to make 45 liters of green paint.

So, 5 parts = 45 liters

Now, calculating for each part.

We get,

Each part = 45÷ 5 = 9 liters

Now for 2 parts = 9 x 2 = 18 liters

And, for 3 parts = 9 x 3 = 27 liters

Therefore, he needs to have 18 liters of blue paint and  27 liters of yellow paint to make 45 liters of green paint.

I need is the answer of please
thank you

Answers

Answer:

39.2m

Step-by-step explanation:

The ratio would be 14/20 which is 0.7. So, you would take 56 and multipy it by 0.7 to get 39.2.

Answer:

39.2

Step-by-step explanation:

ok so you are given 2 triangles that are proportional

the 20 m side and the 56 m side go together

so this leaves 14 and L

so the ration is 2.8

multiply 14 by 2.8 and you get 39.2

If f(x) = 2x - 1 and g(x) = x^2 - 3x - 2, find (f + g)(x).​

Answers

Answer:

SEE attched pic

Step-by-step explanation:

Download symbolab

2+2=4 but you plus me = forever



i got smooth with it​

Answers

dam bro

thats pretty smooth

URGENT!!! THANK YOU!!!!!

Answers

Answer:

101,100

280

Here's your answer

lesson 5 practice problems

Answers

Answer:

Step-by-step explanation:

ok ill help but can soke one help me too

solve the following methods

Answers

don't know when you find out tell me


It takes 5 minutes to fill an empty aquarium to a depth of
5/8
meters. What is the unit rate in minutes per meter?

Answers

Answer:

1/8 meters per minute

Step-by-step explanation:

5/8 ÷ 5

I hope this helps!!

wich is greater 45%, 1/2, 0.55

Answers

Answer:

0.55

Step-by-step explanation:

45/100 = 0.45

1/2 = 0.50

Answer:

0.55 is the biggest

Step-by-step explanation:

45% can be converted to 0.45

1/2 is the same as 50%, so in decimal form, it is 0.50 (although no matter how many 0s you put at the end, it will still be the same, so this could effectively be 0.5.)

0.55 is already done for you, so there is nothing to do here.

Therefore, the biggest is 0.55

Plz HELP...(MATH)........

Answers

Answer:

36 times

Step-by-step explanation:

Because half the marbles are blue, you can predict that about half of the 72 times you will choose the blue marble, or 36 times.

I was so late when I got to this question I could of helped earlier:/

Which of the functions below could have created this graph? O A. F(x) = - x ^ 0 + x ^ 3 - x ^ 2 O B. F(x) = - x ^ 2 + 4x ^ 3 - 2x ^ 2 C. F(x) = x ^ 9 + 12x ^ 8 + x ^ 7 D. F(x) = x ^ 2 + 4x ^ 4 + 20x ^ 2

Answers

Answer:

B

Step-by-step explanation:

even roots bounce at (0,0)

negative leading coefficient: initial graph descending to right, curve up

4 local extremes means remaining 5 degree of the function

The function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph. which is the correct answer would be an option (B).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To create a graph of the function F(x) = - x⁷ + 4x³ - 2x², you can follow these steps:

Choose a range of x-values to use for the graph. For example, you might choose x = -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2.

Substitute each x-value into the function to find the corresponding y-value. For example, if x = -1, then y = F(-1) = - (-1)⁷ + 4(-1)³ - 2(-1)² = -1 + 4 + 2 = 5.

Plot the points (x, y) on a coordinate plane. For example, you would plot the point (-1, 5) on the coordinate plane.

Connect the points with a smooth curve to create the graph of the function.

Therefore, we can conclude that function F(x) = - x⁷ + 4x³ - 2x² could have created the given graph.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

Find ℎ(x) = f(x) − g(x)

Answers

I need to know what f(x) and g(x) is first

Answer:

h(x) = 7x - 3

Step-by-step explanation:

f(x) = 4x − 1 and g(x) = −3x + 2

h(x) = f(x) - g(x)

h(x) = 4x - 1 - (-3x + 2)

h(x) = 4x - 1 + 3x - 2

h(x) = 7x - 3

HELP ME WITH THIS PLEASEEE !

Answers

Answer:

34 i think i got it really wrong but...

Step-by-step explanation:

Will give brainliest

Answers

Slope equals rise over run

The distance of the points is 4 units down and 2 units right

-4/2 = -2

Slope = -2
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