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3 years ago

What is the slope of a line that contains the two points (4, 6) and (2,-5)?

Mathematics

2 answers:

timama [110]3 years ago

8 0

The slope of the line that contains these two points is m = 11/2

Ber [7]3 years ago

4 0

Use the formula:
m = (y2 -- y1) / (x2 -- x1).

First, do -5 - 6, which equals -11.
Next, do 2 - 4, which equals -2.
Finally, divide -11 / -2 to find the slope.

You should get 5.5 as your answer.

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Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it

Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

$\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}$

Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

$\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}$

$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

$\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta$

$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{2}{2\cdot \sqrt{2} }$ or $\sin \beta=\frac{-4}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{1}{\sqrt{2} }$ or $\sin \beta=-\frac{2}{\sqrt{2} }$

$\sin \beta=\frac{\sqrt{2}}{2}$ or $\sin \beta=-\sqrt{2}$

When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

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3 years ago

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kodGreya [7K]

Answer:

B. 16 feet

Step-by-step explanation:

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2 years ago

Can someone please help

Andru [333]

A) Growth: f(x) because it is getting larger exponentially due to an integer greater than 1 being raised to an exponent.

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kolezko [41]

Answer:

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Which equation can be used to find two numbers such that twice the first equals three times the second and three times their dif

Musya8 [376]

Let the numbers be a and b and b>a

2a=3b and 3(b-a)=2(b-a)+13

Solving the first for a:

2a=3b

a=3b/2, now using this value of a in the second equation gives you:

3(b-3b/2)=2(b-3b/2)+13 upon performing indicated operations.

3b-9b/2=2b-6b/2+13 making all terms have a common denominator of 2

(6b-9b)/2=(4b-6b+26)/2 multiplying the whole equation by 2

6b-9b=4b-6b+26 combining like terms

-3b=-2b+26 adding 2b to both sides

-b=26 dividing both sides by -1

b=-26, since a=3b/2

a=3(-26)/2

a=-39

So the numbers are -39 and -26

check...

2a=3b becomes:

2(-39)=3(-26)

-78=-78

3(b-a)=2(b-a)+13 becomes:

3(-26--39)=2(-26--39)+13

3(13)=2(13)+13

39=26+13

39=39

correct :P

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3 years ago