What is an equation of the line that passes through the points (2,1) and (6,-5)?

Answers

Answer 1

Answer: I would go with number 3.

Answer 2

Answer:

Final answer:

The equation of the line that passes through the points (2,1) and (6,-5) is y = -3/2x + 4. This is calculated using the formula for a line y - y1 = m(x - x1) and the formula for slope.

Explanation:

In order to find the equation of the line passing through the points (2,1) and (6,-5), we can use the formula for a line y - y1 = m(x - x1). Here, m is the slope of the line. We can calculate the slope using the formula (y2 - y1) / (x2 - x1). Thus, for the points (2,1) and (6,-5), the slope m is (-5 - 1) / (6 - 2) = -6/4 = -3/2. We can substitute one pair of points and the slope into the line equation. Let's use (2,1). The equation of this line is then y - 1 = -3/2 * (x - 2). Simplifying, we get the equation of the line to be y = -3/2x + 4.

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In triangle DEF m D=43 , m E=62, m EF=22. What is DE to the nearest tenth

Answers

The measure of DE of the triangle is given by law of sines and DE = 31.3

What is the law of sines?

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔDEF

Now , the measure of sides of the triangle are

The measure of EF = 22

The measure of angle ∠D = 43°

The measure of ∠E = 62°

And , the measure of ∠F = 180° - 43° - 62° = 75°

From the laws of sines , we get

a / sin A = b / sin B

On simplifying , we get

EF / sin 43° = ED / sin 62°

So , the measure of DE = ( 22 / 0.7 ) ( sin 75° )

And , the measure of DE = 31.3 units

Hence , the measure of DE of triangle is 31.3 units

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DE = 31.3
Detailed solution is attached

Expand and simplify
4a^2(b^2-c)+2ab(ab-c)-ac(a+2b)

Answers

$4a^2(b^2-c)+2ab(ab-c)-ac(a+2b)\n-----------------------\nuse\ distributive\ property:a(b-c)=ab+ac\n-----------------------\n=4a^2b^2-4a^2c+2a^2b^2-2abc-a^2c-2abc\n=(4a^2b^2+2a^2b^2)+(-4a^2c-a^2c)+(-2abc-2abc)\n\n=\boxed{6a^2b^2-5a^2c-4abc}$

4a²(b² - c) + 2ab(ab - c) - ac(a + 2b)
4a²(b²) - 4a²(c) + 2ab(ab) - 2ab(c) - ac(a) - ac(2b)
4a²b² - 4a²c + 2a²b² - 2abc - a²c - 2abc
4a²b² + 2a²b² - 4a²c - a²c - 2abc - 2abc
6a²b² - 5a²c - 4abc

Numbers between 61 and 107 that is a multiple of 4,6, and 8

Answers

72 and 96. 72 is the answer once you multiply 18 by 4, 12 by 6, and 9 by 8. As for 96, you need to multiply 24 by 4, 16 by 6 and 12 by 8. If you divide 72 and 96 by 4, 6, and 8, you won't get any remainder for the answer - effectively making it a multiple of the three numbers.

Which ratio forms a proportion with 16/20

Answers

Answer:

4/5 forms a proportion with 16/20.

Step-by-step explanation:

We are given an rational number as 16/20.

we have to find another rational number which is equivalent to it.

as both 16 and 20 are multiple of 4 we could also represent the ratio 16/20 as:

$(16)/(20)=(4 * 4)/(4*5)$

we cancel 4 on both the numerator and denominator to get $(4)/(5)$ .

Hence, the ratio $(4)/(5)$ is proportion with $(16)/(20)$ .

4/5 is equivalent to the fraction 16/20

A triangle formed by the sides 3.8cm ,3.7 cm, and 5cm is

Answers

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides.

The triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.

How to find the type of triangle?

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides. Thus,

For a triangle to be right angle triangle,

$c^2=a^2+b^2$

By this law it is observed that,

For a triangle to be acute angle triangle,

$c^2<(a^2+b^2)$

For a triangle to be obtuse angle triangle,

$c^2>(a^2+b^2)$

The sides of the given triangle are 3.8 cm ,3.7 cm, and 5 cm.

Here the longest side is 5 cm. Thus check the type of triangle using above formula. Longest side,

$c^2=5^2\nc^2=25$

Other two sides,

$a^2+b^2=3.8^2+3.7^2\na^2+b^2=14.44+13.69\na^2+b^2=28.13$

Therefore,

$25<28.13\n$

Hence the triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is acute angle triangle.

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It is a scalene triangle because none of the sides are the same!

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