x+3y=0 9y=-3x how many solutions does this system have

Answers

Answer 1

Final answer:

The system of equations x + 3y = 0 and 9y = -3x is actually the same line, therefore there are an infinite number of solutions since the equations represent the same line with a slope of -3 and y-intercept of 0.

Explanation:

The student has given the linear equations x + 3y = 0 and 9y = -3x. To determine how many solutions this system has, we need to normalize the second equation. If we divide the second equation by 9, we get y = -\frac{1}{3}x, which, when reorganized, becomes x + 3y = 0. These two equations are actually the same line. In other words, every solution of the first equation is also a solution of the second equation, and vice versa.

Therefore, the system of equations has an infinite number of solutions because the lines represented by these equations overlap; they are the same line. This is an example of a dependent system where both equations represent the same relationship between x and y. In graph terms, the slope (m) of both lines is -3, and their y-intercept (b) is 0. This is evident from both the algebraic expression of the equations and from their graphical representation.

Answer 2

Final answer:

The system of equations has one solution.

Explanation:

The given system of equations is:

x + 3y = 0

9y = -3x

To solve this system, we can use the second equation to express y in terms of x.

Dividing both sides of the second equation by 9, we get:

y = (-3/9)x

Simplifying, we have:

y = (-1/3)x

We can observe that the equations of the lines represented by both equations in the system have the same slope, which is -1/3.

Since the lines have the same slope but different y-intercepts (0 for the first equation and 0 for the second equation), they will intersect at exactly one point, resulting in one solution for the system of equations.

Related Questions

help please thanks

Which trinomials are perfect square trinomials?

Select each correct answer.

a2+15a+75

a2+26a+169

a2+14a+49

a2+4a+16

Which expressions are differences of squares?

Select each correct answer.

t2−4

h2−20

x2−169

a2+1

Answers

Answer: Perfect squares are the middle two. Difference of squares are t^2 -4 and x^2 - 169

First, to be a perfect square the last term must be a perfect square number. Only 169, 49 and 16 are perfect squares. Second, the middle term must be twice the square root of the last term.

You can check this by using foil on the following expression:
(x + 13)(x + 13) You will get x^2 + 26x + 169 which is one of the perfect square trinomials.

For the difference of squares, you must be using subtraction and have two perfect squares.

t^2 - 4 and x^2 - 169 are the right answers, just took the test.

How did convenience store there is a 25% chance as customer enters the store within one minute of closing time describe the complementary and find this probability

Answers

The complementary is not entering the store one minute before closing.

The probability of not entering the store one minute before closing is 75%

The answer to your question is 75%

Need this answered today also explain the answers please

Julia measured the high temperature in her town for one week. Using the chart below, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth. Be sure to show your work for finding:

the mean of the set of data
the distance of each number from the mean
the mean absolute deviation

Answers

It's not much but to find the mean you add up all of the numbers in the set, and then divide by how many numbers there are. so like, if you have : 2, 2, and 3. You'd add them and get 7, then divide by 3 because there are three separate numbers.

16x-10y=10
-8x-6y=6

can someone help me understand this question?

Answers

This is a system of equations, and I am assuming that you are being asked to solve it.

This is finding the point where these two lines intersect.

The key to solving these algebraically is finding one part in terms of another part and substituting.

We can solve this system by Gaussian elimination, first by multiplying the second equation in its entirety by 2, so that the x-terms will cancel.

We have
[tex]16x-10y=10[/tex]
and
[tex]2(-8x-6y=6)[/tex].

The last equation is rewritten as [tex]-16x-12y=12[/tex].

Now, we cancel the x-terms.

[tex]16x-10y=10[/tex]
[tex]-16x-12y=12[/tex]

[tex]-22y=22 \\ y = -1[/tex]

We have our value for y, so we just plug this back into any of the original equations to get x.

[tex]16x-10(-1)=10\\16x=0\\x=0[/tex]

Thus, the solution to the system of equations is the point [tex](0,-1)[/tex].

what is 9.03×10^2 in standard form

Answers

9.03 * 10² =
9.03 * 100 =
903

The value of the exponent number in standard from is A = 903

What is Exponential Form?

The exponential form is an easier way of writing repeated multiplication involving base and exponents. It has a base and a power

The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.

It is often used in mathematics and science to represent large or small numbers more efficiently. It can also be used to simplify certain mathematical operations, such as multiplication and division, by using the properties of exponents.

Given data ,

Let the exponential form of the number be A

Now , the value of A = 9.03×10²

To convert 9.03×10² to standard form, we need to multiply the number by the appropriate power of 10 so that it is expressed as a number between 1 and 10.

Starting with 9.03×10² , we can move the decimal point two places to the right to get:

9.03×10^2 = 903

So the standard form of 9.03×10² is simply 903

Hence , the standard form is A = 903

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MATH HELP PLEASE WILL GIVE BRAINLIEST!!
What is the trigonometric ratio for cosN ?

Enter your answer, as a simplified fraction, in the boxes.

Answers

cos n=A/H=36/39
=12/13

THERFORE, COS N=12/13

Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.

Given are the sides LM = 15, MN = 36, and LN = 39.

It says to find cos(N) = ?

So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.

We know about the "Soh-Cah-Toa" rule in which cosine ratio is given by :-

[tex] cos(N) = \frac{Adjacent}{Hypotenuse} \\\\
cos(N) = \frac{MN}{LN} \\\\
cos(N) = \frac{36}{39} \\\\
cos(N) = \frac{12}{13} [/tex]

Hence, final answer is [tex] cos(N) = \frac{12}{13} [/tex].

There are 20 children at a library. Six of the children have an average age of 5 years. The remaining children have an average age of 8 years. What is the average age of the children at the library? Enter your answer in the box. WILL GIVE BARINLIYEST

Answers

Answer: The average age is 7.1 years.

This problem is an example of when we need to take a weighted average. We simply can't just find the average of 5 and 8, because there are different children of each each.

To start, lets multiply the total number of children by their individual ages.

6 x 5 = 30 years
14 x 8 = 112 years

There are 142 years among the 20 years, so divide 142 by 20. This gives us an average age of 7.1 years.

the triangle in the diagram are similar. how long will the footbridge be

Answers

You'll have to set up a proportion.

[tex] \frac{80}{24} = \frac{d}{30} [/tex]
24d = 2400
d = 100

The footbridge will be 100m long.

Are these correct please help

Answers

the triangle has no obtuse angles and a right triangle only has 1 right angle

A triangle only has one right angle also the triangle has no obtuse angle.

i need really need help please

Answers

2*(1.1) +3.75 = 5.95 miles
or 5 19/20 miles, if you want a mixed number.

A spherical balloon is inflated until its diameter is 24 in. Air is then released from the balloon until its diameter is 18 in. Approximately many cubic inches of air were released from the balloon?

formula: V =4π(r^3)/3 **make sure you use the radius and not the diameter**

Answers

Answer:
amount of air released = 4184.6 in³

Explanation:
We can get the volume of released air by calculating the difference between the volume of the balloon before and after the air was released. This difference will represent the amount of released air.

Initial volume of balloon:
V = [tex] \frac{4}{3} [/tex]πr³
We have diameter = 24 in
Therefore:
radius = 24/2 = 12 in
volume = [tex] \frac{4}{3} [/tex]π(12)³
initial volume = 2304π in³

Final volume of balloon:
V = [tex] \frac{4}{3} [/tex]πr³
We have diameter = 18 in
Therefore:
radius = 18/2 = 9 in
volume = [tex] \frac{4}{3} [/tex]π(9)³
final volume = 972π in³

Amount of air released:
amount of air released = initial volume - final volume
amount of air released = 2304π - 972π
amount of air released = 1332π = 4184.6 in³

Hope this helps :)

Answer:

4182 is ur answer

Step-by-step explanation:

rectangle abcd is similar to rectangle pqrs. given ab=14 cm, BC=8cm and pq=21cm, calculate the length of QR

Answers

QR =12 because you set up a proportion 21/14=x/8 then cross multiply and get 14x=168 then you divide and get 12

The length of QR in rectangle PQRS is 12 cm, found by setting up the proportional relationship 14/21 = 8/QR, where 14 cm and 8 cm are the lengths of sides AB and BC of rectangle ABCD, respectively, and 21 cm is the length of side PQ of rectangle PQRS.

Since rectangle ABCD is similar to rectangle PQRS, their corresponding sides are proportional. To find the length of QR, we will set up a proportion using the given lengths:

AB/PQ = BC/QR

Substituting the given lengths:

14/21 = 8/QR

Now, solve for QR:

QR = (21 * 8) / 14

QR = 168 / 14

QR = 12 cm

So, the length of QR in rectangle PQRS is 12 cm.

PLZ HELP, GRAPH IT THEN FOR BRAINLIEST

graph the quadratic function f(x)=x^2−12x+27.

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

see attached picture for solution and graph

f(x)=x^2−12x+27
find Vertex (h, k)
x = h= -b/2a = -(-12)/2(1) = 6
k = f(h) = 36 - 12(6) + 27
k = -9

so vertex (6,-9)

y = a(x - h)^2 + k

so
y = (x - 6)^2 - 9
x intercept when y = 0
x^2−12x+27 = 0
(x - 9)(x - 3) = 0
x - 9 = 0; x = 9
x - 3 = 0; x = 3
so x-intercept (9,0); (3,0)

y intercept when x = 0 so y = 27 (0, 27)

OK now you can use these to graph the function
(6, -9) (9,0) and (3,0)

If c=3k+4 and d=7+9k^2, what is d in terms of c?

Answers

Answer:

d = (c -4)² +7 = c² -8c +23

Step-by-step explanation:

Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.

Eliminating k

We recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.

c = 3k +4

c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k

Substituting into the equation for 'd', we have ...

d =7 +9k²

d = 7 +(3k)² . . . . . writing 9k² in terms of 3k

d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.

This can be simplified to ...

d = c² -8c +23 . . . . another form of d in terms of c.

Final answer:

To express 'd' in terms of 'c', solve the first equation for 'k' and substitute this value into the second equation. This yields: d=7+((c-4)^2)/3.

Explanation:

To express d in terms of c, we first need to make k the subject of c=3k+4. We do this by subtracting 4 from both sides, getting c-4=3k, and then dividing both sides by 3, which gives us k=(c-4)/3. Next, we substitute this value of k into the second equation: d=7+9k^2. Substituting, we get d=7+9*((c-4)/3)^2, which, when simplified, gives the result d=7+((c-4)^2)/3. This is the expression for d in terms of c.

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How do u solve g/12=-10

Answers

multiply -10 by 12

g=-120

The answer is -120 because you have to multiply both sides of the equation by 12

Suppose two fractions are both less than 1. Can their sum be greater than 1? greater than 2?

Answers

Their sum can be greater than 1 but it would be less than 2.

The biggest fraction which is less than 1 is 0.99

Sum of 0.99 + 0.99 = 1.98, which is greater than 1 but less than 2.

The sum can be greater than 1, but not two. For example say the fractions are, 3/4 and 5/6, the total is , 1 7/12. Which is greater than 1 but not two. It cannot be greater than 2 because fractions are a part of 1.UNLESS, it is a mixed number fractions, than they can be infinitely great. Such as 123 3/4 + 45 2/4 is definitely greater than 2.

A box of candy contains 6 lemon, 3 orange, and 4 cherry pieces. If you select a piece of candy at random, what is the probability that you select an orange OR a cherry piece?

Answers

7/13 would be the answer

It would be 7 maybe im not so sure

Find the AREA of this triangle

Answers

Answer: " 20 square units " ; or, write as: " 20 units² " .
________________________________________________________

Note:
________________________________________________________
The formula for the area, "A" of a triangle:

" A = (1/2) * b * h " ;

in which: "A = area" (for which we are to solve);

"b = base length" = 8 (given) ;

"h = perpendicular height = 5 (given) ;

A = (1/2) * b * h = (1/2) * 8 * 5 = 4 * 5 = 20 .
_________________________________________________________
Answer: The area of the triangle given is: " 20 units² " ;
or, write as: " 20 square units" .
_________________________________________________________
Edit: Another way to write the formula for the area, "A", of a triangle is:

" A = (b * h) / 2 " ;

and we can solve: " A = (b * h) / 2 = (8 * 5) / 2 = 40 / 2 = 20 .
_________________________________________________________
The answer is: " 20 square units " ; or, write as: " 20 units² " .
_________________________________________________________

help help help!!!ill return

Answers

Hello! For this question, all you have to do is the distributive property. Multiply -15 with each number inside the parenthesis. -15 * -10 is 150. -15 * -5x is 75x.Nothing else needs to be combined, so we are finished. There. The expression simplified is 150 + 75x.

-15 (-10 - 5x)
Since you never asked, I'll assume you need it simplified xP

Distribute Parenthesis
(−15)(−10) -15(-5x)

Apply + and - rules
(-15) (-10) + (-15) (-5x)

Finish
150 + 75x

A high-speed elevator can rise 480 feet in 30 seconds. Which expression represents the rate, in feet per minute, of the elevator?
a- 480 × 30
b- 480 ÷ 30
c- 480 × 0.2
d- 480 ÷ 1/2

Answers

Hi there!

The answer is d.

1 min ÷ 2 = 30 sec
so
30 sec × 2 = 1 min

So, the answer is D.

Hope this helps!

I NEED HELP ASAP!

A metal rod is
7/8
meters long. It will be cut into pieces that are each
1/56
meters long. How many pieces will be made from the rod?

Write your answer in simplest form.

Answers

There will be 49 pieces, each 1/56 meters long.

WE HAVE TO DO:
(7/8)/(1/56)= 7/8 * 56/1=49 pieces

I need the answer for B! whoever answers first will get a brainliest, a thanks, and 50 points! also plz tell me how you got the answer

Answers

Here's your graph. The clubs both have a balance of $80 after 6 weeks.

_____
A graphing calculator is helpful.

2x+3(x-4)=8
Solve the equation

Answers

2x + 3x - 12 = 8
5x = 20
x = 4

2x + 3(x - 4) = 8

2x + 3x - 12 = 8

5x = 20

x = 4

EMERGENCY PLEASE HELP REALLY HARD!

The first and fourth terms of a geometric sequence are shown.

−2,___ , ___, 128

What are the second and third terms of this geometric sequence?

Answers

geometric sequence nth term:
tₙ = t₁ · (r)ⁿ⁻¹

t₁ = -2
t₄ = 128 (4th term)

formula for 4th term:

t₄ = -2 · (r)⁴⁻¹ = -2· (r)³

since t₄ = 128

128 = -2(r)³
(r)³ = -64
r = ∛-64
r = -4

so second term is
t₂ = -2· (-4)²⁻¹ = 8

third term is
t₃ = -2 · (-4)³⁻¹ = -32

I WILL GIVE BRAINLIEST!!!!
Question 16 Unsaved
Which of the following statements is true?

Question 16 options:

-4.5 < -5.8

-3.4 > -4.2

0 < -8.5

3.9 < 1.3

Answers

- 3.4 > - 4.2 is the only correct statement

> means larger than
< means smaller than

A negative number which closer to 0 than an other negative number, is larger. Therefore - 3.4 is larger than - 4.2, and therefore - 3.4 > - 4.2

mario earns money mowing his neighbors lawns the revenue for mowing x lawns is r(x)=25x marios cost for gas and the mower rental is c(x)=6x+15 his profit from mowing x lawns is p(x)=(r-c)(x) what is p(x)

Answers

Well we know that
r IS 25x
c IS 6x+15.
So we can do r - c
(25x) - (6x + 15)

Now I gave you part of the answer. Can you simplify?

Answer:

p(x) = 19+15

Step-by-step explanation:

A student solved this problem by working backward. Janice went shopping with her mom and at the end of the day she had $59.50 left over. She spent $13.65 on a T-shirt, $22.99 on some new sandals, and $40.75 on a new skirt. How much money did Janice have at the beginning? Student's solution - Janice had $59.50 left. Add up all the amounts she spent ($13.65 + $22.99 + $40.75) and add to the amount she has left over ($77.39 + $59.50). So Janice had $136.89 to begin with. Solve this problem. Dale was fixing his fence. At the end of the day, he had 12.5 feet of wood left over. During the day he had used one 3.5 foot long piece of wood, two 5.9 foot long pieces of wood, and one 10 foot long piece of wood. How many feet of wood did Dale have at the beginning of the day? feet

Answers

Hello there! Your answer is (136.89) hope it helps and have a wonderful day!

(Btw nice car love it)

7y+4x=3; (-4,-7) write the equation in slope intercept form

Answers

y= -4/7x + 3/7

hope this helps

find the diameter of a circle with an area of 226.98

Answers

Remember the formula of the area of a circle is:
[tex]V = \pi * r^{2} [/tex]
SO given that
V = 226.98
and [tex] \pi = 3.14[/tex]
Plug in a chug
226.98 = 3.14 * [tex] r^{2} [/tex]
[tex] r^{2}= 72.287[/tex]
r = 8.50

Remember that d = 2 * r
d = 2 * 8.5 = 17

Last one give me the best answer

Answers

V = PI x r^2 x H

471 = 3.14 x 5 x H
471 = 15.7 x h

h = 471 / 15.7 = 30 cm

314/ 15.7 = 20 cm

30-20 = 10 cm difference

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