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3 years ago

Which equation has infinitely many solutions?

Mathematics

2 answers:

Vlad1618 [11]3 years ago

8 0

Answer:

5x-5x = 0

the third one.....

allochka39001 [22]3 years ago

6 0

Answer:

the equation that has infinite solutions is

5x-5x=0.

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Prove that the points (a, -3a), (2a, a) and (0, -2a) form a scalene trqingle

Dmitry [639]

Answer:

See below.

Step-by-step explanation:

Remember that a scalene triangle has lengths of different values.

Therefore, we just need to find the length or distance from each point to the next. If the three distances we acquire are different, then we prove that the point do indeed form a scalene triangle.

Let's let A be (a, -3a), B be (2a, a), and C be (0, -2a).

So, let's find each of the side lengths using the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Side AB:

Let's let A:(a, -3a) be (x₁, y₁) and let's let B:(2a, a) be (x₂, y₂). Substitute this into our formula:

$d=\sqrt{(2a-a)^2+(a-(-3a))^2$

Subtract:

$d=\sqrt{(a)^2+(4a)^2$

Square:

$d=\sqrt{a^2+16a^2}$

Add:

$d=\sqrt{17a^2}$

Simplify:

$d=\sqrt{a^2}\cdot \sqrt{17}\\d=|a|\sqrt{17}$

So:

$\overline {AB}=|a|\sqrt{17}$

Note: We need the absolute value because anything squared will be positive, and if you take the square root of something positive, the result will be positive. The absolute value ensures that the a value will be positive no matter what a is to begin with.

Side BC:

Let's let C:(0, -2a) be (x₁, y₁) and let's let B:(2a, a) be (x₂, y₂).

$d=\sqrt{(2a-0)^2+(a-(-2a)^2}$

Subtract:

$d=\sqrt{(2a)^2+(3a)^2}$

Square:

$d=\sqrt{4a^2+9a^2}$

Add:

$d=\sqrt{13a^2}$

Simplify:

$d=\sqrt{a^2}\cdot \sqrt{13}\\d=|a|\sqrt{13}$

Therefore:

$\overline{BC}=|a|\sqrt{13}$

Side AC:

Let's let A:(a, -3a) be (x₁, y₁) and let's let C:(0, -2a) be (x₂, y₂).

$d=\sqrt{(0-a)^2+(-2a-(-3a))^2$

Subtract:

$d=\sqrt{(-a)^2+(a)^2}$

Square:

$d=\sqrt{a^2+a^2}$

Add:

$d=\sqrt{2a^2}$

Simplify:

$d=|a|\sqrt2$

Therefore:

$\overline{AC}=|a|\sqrt2$

So, our three side lengths are:

$\overline {AB}=|a|\sqrt{17}\text{, }\overline{BC}=|a|\sqrt{13}\text{, and } \overline{AC}=|a|\sqrt2$

We can see that the three side lengths are different since they do not equal to same thing.

Therefore, we can deduce that the triangle must be scalene.

And we're done!

4 0

3 years ago

Read 2 more answers

In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?In ΔFGH, the measure of ∠

mihalych1998 [28]

$tan \: j \: = \frac{opp}{adj}$

$tan \: j \: = \frac{11}{60}$

$sin \: f = \frac{opp}{hyp}$

$sin \: f = \frac{12}{37}$

8 0

3 years ago

I need help don’t know how to do

ivann1987 [24]

Let x be the unknown angle.
We know that x+50=120 because the value of an exterior angle of a triangle is equal to the sum of the other 2 interior angles.

x+50 = 120
Subtract both sides by 50
x = 70

The value of the unknown angle is 70 degrees.

Have an awesome day! :)

5 0

3 years ago

Read 2 more answers

A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?

Naya [18.7K]

First we will find the total measure of the second base.

Second base is extended more so that meas it will measure extended part plus the first base.

Second base = 7 + 5 = 12.

Now for the area.

A = 1/2(b1+b2)(h)
A = 1/2(7 + 12)(7)
A = 66.5

The area is 66.5 ft²

Hope this helps :)

4 0

3 years ago

Read 2 more answers

Simplify rational expression

zubka84 [21]

Answer:

The final answer is 35n/17r

Step-by-step explanation:

Let's simplify the expression, this way:

1. Start with the coefficients:

(10 * 42)/(6 * 34)

We cancel 6 in the denominator and change 42 by 7. Now we have:

(10 * 7)/34

We now divide by 2 both in the numerator and the denominator. Now we have:

(5 * 7)/17.

The remaining numbers are prime numbers and it's not possible to continue simplifying, so we got:

35/17

2. Variable r:

We have r⁴/r⁵ = r ⁴⁻⁵ = r⁻¹ = 1/r¹ = 1/r

3. Variable n:

We have n⁴/n³ = n ⁴⁻³ = n¹/1 = n

4. Adding the pieces:

We put coefficients and variables together: 35/17 * 1/r * n

The final answer is 35n/17r

7 0

4 years ago