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3 years ago

Which of the following systems of equations has no solution?

2 answers:

8 0

The system of equations that has no solution are the equations that has the same slope which means they are parallel and do not intersect with each other at any point. From the choices, the correct answer is option D.

 7y = 5x − 10
y = (5/7) - 10/7
slope = 5/7

10x − 14y = 8
-14y = -10x + 8
y = (5/7) - 4/7
slope = 5/7

Law Incorporation [45]3 years ago

7 0

For option d:
5x - 7y = 10 . . . . . (1)
10x - 14y = 8 . . . . (2)

(1) x 2 => 10x - 14y = 20 . . . . . (3)

(2) - (3) => 0 = -14 [not possible]

Therefore, the set of equations in option d, has no solutions.

You might be interested in

What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a sum of cubes.

Sum of cubes

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

8 0

3 years ago

Please show full solutions! WIll Mark Brainliest for the best answer. SERIOUS ANSWERS ONLY

Ierofanga [76]

Answer:

vertical scaling by a factor of 1/3 (compression)
reflection over the y-axis
horizontal scaling by a factor of 3 (expansion)
translation left 1 unit
translation up 3 units

Step-by-step explanation:

These are the transformations of interest:

g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k

g(x) = f(x) +k . . . . vertical translation by k units (upward)

g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis

g(x) = f(x-k) . . . . . horizontal translation to the right by k units

Here, we have ...

g(x) = 1/3f(-1/3(x+1)) +3

The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:

vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
reflection over the y-axis . . . 1/3f(-x)
horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
translation left 1 unit . . . 1/3f(-1/3(x+1))
translation up 3 units . . . 1/3f(-1/3(x+1)) +3

_____

Additional comment

The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.

The horizontal transformations could also be described as ...

translation right 1/3 unit . . . f(x -1/3)
reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)

The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.

8 0

2 years ago

Cause I lowkey suck at math How do I do this

dimaraw [331]

1. The slope is -2/5 not 3-/10

5 0

3 years ago

The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) →

Ket [755]

Answer:

x+2y=12-------(1)

x-2y=3---------(2)

Adding equations 1 and 2

we get

2x=18

x=9

Equation 1

9+2y=15

2y=15-9

2y=6

y=3

The solution of the given system is x=9, y=3

Step-by-step explanation

6 0

3 years ago

Keely scored 128 points, which was 4 times as many points as Grayson scored. Which equation can be used to find the number of po

Ludmilka [50]

Answer:

Step-by-step explanation:

take 128 divide by 4

4 0

3 years ago