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3 years ago

Consider the system of equations

1 answer:

5 0

Make the equation the same or a multiple of the other to have an infinite number of solutions. See how the -8/2= -4 and 6/2=3 ? then -2/2 = c
Make c = -1 and they are the same linear equation. (same slope, same intercepts, same line) and therefore have infinite solutions.

In order to have no solutions, the lines cannot cross at all and so they must be parallel but not the same line. Parallel lines have the same slope with different intercepts. if you rearrange both equations in slope intercept form:
y = x/3 - 4/3
y = - cx/3 - 4/3

no matter what you make c the lines will always cross at the y-intercept (0, -4/3). this is a solution and therefore there's no value of c that would produce a system with no solution.

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Rectangle STUV is shown on a coordinate plane. Rectangle STUV with vertices S at negative 7 comma 6, T at negative 2 comma 6, U

rusak2 [61]

The coordinate of the point T after the given transformations is; T''(-2, -4)

<h3>How to carry out Translation Transformations?</h3>

We are given the coordinates of the rectangle STUV as;

S(-7, 6)

T(-2, 6)

U(-2, 1)

V(-7, 1)

Now, we are told that all these coordinates are translated using the transformation rule; (x, y) → (x − 2, y − 4)

Thus, the new coordinates using this transformation rule are;

S'(-9, 2)

T'(-4, 2)

U'(-4, -3)

V'(-9, -3)

Now, we are told that these new points are rotated 90° counterclockwise and as such the new coordinates formed will follow the pattern (x, y) → (-y, x).

Thus, our final coordinates are;

S''(-2, -9)

T''(-2, -4)

U''(3, -4)

V''(3, -9)

Thus, the coordinate of the point T after the given transformations is; T''(-2, -4)

Read more about Translation Transformation at; brainly.com/question/4289712

#SPJ1

4 0

2 years ago

Read 2 more answers

Please help its only A B C D which should equal 105degree to prove that f // g?

ELEN [110]

Answer:

Option (4)

Step-by-step explanation:

From the figure attached,

∠b = 75° [Vertical angles]

If the lines f and g are parallel then,

∠b = ∠c [Corresponding angles]

Therefore, ∠c = 75°

Since m∠c + m∠d = 180° [Supplementary angles]

75° + m∠d = 180°

m∠d = 180° - 75°

m∠d = 105°

Therefore, measure of angle d should be equal to 105° to prove f and g are parallel.

Option (4) will be the answer.

5 0

3 years ago

Find the exact length of the curve. x = 9 + 9t2, y = 6 + 6t3, 0 ≤ t ≤ 4

andrew11 [14]

ANSWER

$=102 \sqrt{ 17}$

EXPLANATION

The equation of the curve is:

$x = 9 + 9 {t}^{2}$

$y = 6 + 6 {t}^{3}$

We differentiate to obtain:

$\frac{dx}{dt} = 18t$

$\frac{dy}{dt} = 18t$

The length of the arc

$l = \int _0 ^{4} \sqrt{ {( \frac{dx}{dt} )}^{2} + {( \frac{dy}{dt} )}^{2} } dt$

This implies that:

$= \int _0 ^{4} \sqrt{ {( 18t )}^{2} + {( {18 {t}^{2} } )}^{2} } dt$

$= \int _0 ^{4} 18t \sqrt{ 1+ { {18 {t}^{2} } }} dt$

$=102 \sqrt{ 17}$

3 0

3 years ago

20x -10x to the second power + 5x to the third power . In descending order

mario62 [17]

It'd be best if you'd stick to symbols. My interpretation of what you've typed here is 20x - 20x^2 + 5x^3. In descending order by powers of x, that gives us

5x^3 - 20x^2 + 20x.

7 0

3 years ago

Simplify : (√x + √y ) (√x − √y) (x + y)(x2 + y2)

Ivan

$Solution, \mathrm{Expand}\::\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\left(x+y\right)\left(x^2+y^2\right):\quad :x^4-:y^4$

$Steps:$

$\mathrm{Expand}\:\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right):\quad x-y, =\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)$

$\mathrm{Expand}\:\left(x-y\right)\left(x+y\right):\quad x^2-y^2, =:\left(x^2-y^2\right)\left(x^2+y^2\right)$

$\mathrm{Expand}\:\left(x^2-y^2\right)\left(x^2+y^2\right):\quad x^4-y^4, =:\left(x^4-y^4\right)$

$\mathrm{Expand}\::\left(x^4-y^4\right):\quad :x^4-:y^4, =:x^4-:y^4$

The correct answer is <u><em> $x^4-y^4$ </em></u>

Hope this helps!!!

4 0

3 years ago