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lutik1710 [3]
3 years ago
12

Which statement describes the solution to the system of equations?

Mathematics
1 answer:
Lena [83]3 years ago
4 0

For this case:

D.-) The system has infinitely many solutions.

<h2>Explanation:</h2>

Remember that you have to write complete questions in order to find exact and good answers. In this exercise, the system is missing. However, I'll provide the following system:

\text{\ensuremath{\left.\begin{array}{c}(1)\\(2)\end{array}\right.\left\{ \begin{array}{c}3x+y=-6\\6x+2y=-12\end{array}\right.}}

So we have two equations and two variables. Our first equation is:

3x+y=-6

And the second equation is:

6x+2y=-12

When graphing these two lines, we can get the following possibilities:

  • They have a unique solution. This means the graphs intersect at a single point.
  • They have infinitely many solutions. This implies the lines are basically the same.
  • They have no solution. This implies they are parallel but with different y-intersect.

By dividing equation (2) by 2 we get:

\frac{6x+2y}{2}=\frac{-12}{2} \\ \\ 3x+y=-6

So we get the same equation as line (1), so <em>the conclusion is that they have infinitely many solutions.</em>

<h2>Learn more:</h2>

Infinitely many solutions: brainly.com/question/13771057

#LearnWithBrainly

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Estimate the answer to the<br> calculation below<br> 21 X 385<br> 52
Andrei [34K]

Answer:

809,592

Step-by-step explanation:

21 x 38552= 809592

3 0
3 years ago
0)
hichkok12 [17]

Answer:

The coordinates of C(22/3, 7)

Step-by-step explanation:

Partitioning between two points A and B in the ratio a:b.

The x-coordinate of the point of partition C is found at

XC = XA*(b/(a+b)+XB(a/(a+b) ..............(1)

Similarly, the x-coordinate of the point of partition is found at

YC = YA*(b/(a+b)+YB(a/(a+b)...............(2)

Given A(8,8), B(4,2), partition ratio of A:B = 1:5,

substitute in (1)

XC = 8*5/6+4*1/6 = 44/6 = 22/3

YC = 8*5/6 + 2*1/6 = 42/6 = 7

The coordinates of C(22/3, 7)

7 0
3 years ago
Quadrilateral ABCD is translated to get quadrilateral A′B′C′D′. Vertex A is at (-5, 2), and vertex A′ is at (2, -2).
fgiga [73]
Then vertex B’ is at (1,1)
proof: the translation from A to A’ is (7,-4) therefore applying the same conditions to B would give you the outcome of (1,1)
4 0
2 years ago
Louisa ran at an average speed of five miles per hour along an entire circular park path. Calvin ran along the same path in the
docker41 [41]

Answer:

15 miles

Step-by-step explanation:

Let x be the miles in the circular park path, t_{L} the time Louisa takes to finish and t_{C} the time Calvin takes to finish both in hours.

Then x, the longitude is equal to the velocity times the time used to finish. So

x=5t_{L}

x=6t_{C}

And the difference between Louisa's time and Calvin' time is 30 minutes, half an hour. So:

t_{C}=t_{L}-0.5

Three equations, three unknowns, the system can be solved.

Equalizing the equation with x :

5t_{L}=6t_{C}

In this last equation replace t_{C}  with the other equation and solve:

5t_{L}=6(t_{L}-0.5)\\ 5t_{L}=6t_{L}-3\\ 3=6t_{L}-5t_{L}\\ 3=t_{L}\\ t_{L}=3

With Louisa's time find x:

x=5t_{L}\\ x=5(3)\\ x=15

7 0
3 years ago
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

Learn more about factorizing a quadratic expression at

brainly.com/question/52959

#SPJ1

5 0
1 year ago
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