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2 years ago

Write an equation in point-slope form of the line that passes through the point (9,0) and has a slope of m=-3 .

Mathematics

1 answer:

aksik [14]2 years ago

5 0

Answer:

$y = - 3x + 27$

Step-by-step explanation:

The standard form for the equation of the line is

$y = mx + c$

Recall that:

$y = 0 \: \: \: x = 9 \: \: \: m = - 3 \\ y = mx + c \\ 0 = - 3(9) + c \\ 0 = - 27+ c \\ 27 = c$

Therefore the equation of the line is:

$y = mx + c \\ y = - 3x + 27$

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Find the estimates of x^2-x-2=3

Julli [10]

Answer:

$x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79$

Step-by-step explanation:

Given

Quadratic equation is

$x^2-x-2=3\\x^2-x-5=0$

Roots of the quadratic equation $ax^2+bx+c=0$ are

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

So, for the given equation roots are

$x=\frac{1\pm\sqrt{(-1)^2-4(1)(-5)}}{2\cdot 1}\\x=\frac{1\pm\sqrt{21}}{2}\\so, x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79$

5 0

3 years ago

Simplify: <img src="https://tex.z-dn.net/?f=4%5Csqrt%7B320%7D%20-%203%5Csqrt%7B80%7D" id="TexFormula1" title="4\sqrt{320} - 3\sq

aleksandrvk [35]

Answer:

20 √ 5

Step-by-step explanation:

1. You'll need to simplify each term. You'll get 32 √ 5-12 √ 5.

2. After you subtract 12 √ 5 from 32 √ 5, you'll get 20 √ 5.

8 0

4 years ago

La parte superior de un edificio de 48m de altura es observada bajo un ángulo de elevación de 53°. ¿Cuál es la distancia entre e

mrs_skeptik [129]

Answer:

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Step-by-step explanation:

5 0

3 years ago

Find the tenth term of the geometric sequence, given the first term and common ratio.

Natalija [7]

Answer:

$a_{10}=\dfrac{1}{128}$

Step-by-step explanation:

In the geometric series:

$a_1=4\\ \\r=\dfrac{1}{2}$

The nth term of the geometric sequence can be calculated using formula

$a_n=a_1\cdot r^{n-1}$

In your case, n = 10, then

$a_{10}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^{10-1}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^9\\ \\=2^2\cdot \dfrac{1}{2^9}\\ \\=\dfrac{1}{2^{9-2}}\\ \\=\dfrac{1}{2^7}\\ \\=\dfrac{1}{128}$